diff --git "a/batch_s000008.csv" "b/batch_s000008.csv" new file mode 100644--- /dev/null +++ "b/batch_s000008.csv" @@ -0,0 +1,10345 @@ +source,target + AGN feedback results in a stellar-to-halo mass ratio is consistent with the preclicition of abundance matching (?).., AGN feedback results in a stellar-to-halo mass ratio is consistent with the predicition of abundance matching \citep{Moster:2010p5423}. + A comparison with the massive earlv-tvpe galaxies in the samples analysed by ο shows that the mass. the velocity dispersion and the effective radius are consistent with those of the most massive earlv-type galaxies observed in the SDSS ab zo0. and cluster galaxies at z1.," A comparison with the massive early-type galaxies in the samples analysed by \cite{2008ApJ...688...48V} shows that the mass, the velocity dispersion and the effective radius are consistent with those of the most massive early-type galaxies observed in the SDSS at $z\sim0$, and cluster galaxies at $z\sim 1$." + We note that a slight decrease in the cllicicney of ACN feedback. would. produce a slightly larger mass and a lower effective radius at z=1. bringing our simulated galaxy into an even closer agreement with the observations.," We note that a slight decrease in the efficiency of AGN feedback would produce a slightly larger mass and a lower effective radius at $z=1$, bringing our simulated galaxy into an even closer agreement with the observations." + The existence of the core in the stellar surface density distribution is in agreement with what is observed for the most luminous and massive galaxies in the Virgo cluster that show significant mass deficiencies in their central. regions (7?77).. ," The existence of the core in the stellar surface density distribution is in agreement with what is observed for the most luminous and massive galaxies in the Virgo cluster that show significant mass deficiencies in their central regions \citep{2004AJ....127.1917T, 2007ApJ...671.1456C, 2009ApJS..182..216K, 2011arXiv1108.0997G}." +Wo have discussed several mechanisms that could contribute to the shaping of the final properties of the BCC ancl. especially. to the formation of its core: (1) a series of dry mergers that lead to SMDIIS sinking to the halo center via dynamical frietion.," We have discussed several mechanisms that could contribute to the shaping of the final properties of the BCG and, especially, to the formation of its core: (I) a series of dry mergers that lead to SMBHs sinking to the halo center via dynamical friction." + Vhis process can eject a [arge fraction of stars and dark matter from the central regions of the BCC (2?) (11," This process can eject a large fraction of stars and dark matter from the central regions of the BCG \citep{2003ApJ...596..860M, 2010ApJ...725.1707G}. (" +) AGN feedback driven. gas outllows can moclily the gravitational potential in the regions close to SAIBLIs: these outllows are impulsive and the revirialisation! of the inner material can Lead to the formation of a core (?).. (,II) AGN feedback driven gas outflows can modify the gravitational potential in the regions close to SMBHs; these outflows are impulsive and the 'revirialisation' of the inner material can lead to the formation of a core \citep{1996MNRAS.283L..72N}. ( +LLL) The central hot gas. slowly cools racdiativelv. falling onto the SMIBIL in a convective Dow and is subsequently ejected impulsively.,"III) The central hot gas slowly cools radiatively, falling onto the SMBH in a convective flow and is subsequently ejected impulsively." + The slow loss of mass from the central region will result in the inner mass distribution expanding., The slow loss of mass from the central region will result in the inner mass distribution expanding. + The ellicieney of cach of these mechanisms will be explored using idealised numerical experiments in a subsequent study., The efficiency of each of these mechanisms will be explored using idealised numerical experiments in a subsequent study. + Observations show that low mass earlv-tvpe. galaxies typically have cusps in their surface brightness profiles. while high mass early-tvpe galaxies preferably have centrally cored profiles (777).. ," Observations show that low mass early-type galaxies typically have cusps in their surface brightness profiles, while high mass early-type galaxies preferably have centrally cored profiles \citep{2004AJ....127.1917T, 2007ApJ...671.1456C, 2009ApJS..182..216K}." +We find that neglecting the presence of SMDBlISs anc AGN feedback. produces a cusp. while inclucing these ellects produces a core.," We find that neglecting the presence of SMBHs and AGN feedback produces a cusp, while including these effects produces a core." + These considerations sugeests that there may be a close connection between the mass dichotomy in early-type galaxies and the presence of SALBLs., These considerations suggests that there may be a close connection between the mass dichotomy in early-type galaxies and the presence of SMBHs. + In high mass early-tvpe galaxies the cllicioney of the processes that lead to a core formation are expected to be higher than in lower mass early-type galaxies. thus lower mass galaxies may retain the cusps in the clistribution of their stars.," In high mass early-type galaxies the efficiency of the processes that lead to a core formation are expected to be higher than in lower mass early-type galaxies, thus lower mass galaxies may retain the cusps in the distribution of their stars." + We thank our anonymous referee for helpful suggestions that greatly improved the quality of the paper., We thank our anonymous referee for helpful suggestions that greatly improved the quality of the paper. + We also thank Lea Giordano for her suggestions about the topies discussed in this paper., We also thank Lea Giordano for her suggestions about the topics discussed in this paper. +" We thank Robert Feldmann for providing us the eroup simulation data and ""ThorstenNaab for providing us the Milky-Way-sized simulation data.", We thank Robert Feldmann for providing us the group simulation data and ThorstenNaab for providing us the Milky-Way-sized simulation data. + The XMIU simulations presented herewere performed on the Cray NT-5 cluster at CSCS. Manno. Switzerland.," The AMR simulations presented herewere performed on the Cray XT-5 cluster at CSCS, Manno, Switzerland." +"the Bondi Hoyle rate for turbulent gas, Mgy, the thermal sound speed of the gas has been replaced by an effective sound speed defined as the quadrature sum of the thermal sound speed and turbulent velocity.","the Bondi Hoyle rate for turbulent gas, $\dot{M}_{\textrm{BH}}$, the thermal sound speed of the gas has been replaced by an effective sound speed defined as the quadrature sum of the thermal sound speed and turbulent velocity." +" The vorticity-reduced rate, Mi», given by Equation 3 of 7, is computed cell by cell, producing a log-normal probability density function (PDF) of accretion rates within individual spherical shells centered on the black hole particle."," The vorticity-reduced rate, $\dot{M}_{\textrm{turb}}$, given by Equation 3 of \citet{Krumholzetal06}, is computed cell by cell, producing a log-normal probability density function (PDF) of accretion rates within individual spherical shells centered on the black hole particle." +" The geometric mean of the distribution, (Miurb), gives characteristic accretion rates under this prescription and is shown for several different radii in Figure 6.."," The geometric mean of the distribution, $\langle +\dot{M}_{\textrm{turb}}\rangle$, gives characteristic accretion rates under this prescription and is shown for several different radii in Figure \ref{fig:mbondi}. ." + The vorticity-reduced rates are 2—3 orders of magnitude smaller than the standard Bondi Hoyle rates., The vorticity-reduced rates are $2-3$ orders of magnitude smaller than the standard Bondi Hoyle rates. +" These results are qualitatively consistent with those of ?,, who find that accretion in their merger simulations is regulated by angular momentum transport processes in the host galaxy, keeping the accretion rate below the Bondi rate, except during peak activity (when the accretion rate approaches Mpaa, which is + Mgn)."," These results are qualitatively consistent with those of \citet{Debuhretal09}, who find that accretion in their merger simulations is regulated by angular momentum transport processes in the host galaxy, keeping the accretion rate below the Bondi rate, except during peak activity (when the accretion rate approaches $\dot{M}_{\textrm{Edd}}$ , which is $\approx \dot{M}_{\textrm{BH}}$ )." +" As revealed in Figure 6,, the Bondi prescription gives large estimates for the accretion rates (> 10Mmgaa) inside the central few hundred parsecs."," As revealed in Figure \ref{fig:mbondi}, the Bondi prescription gives large estimates for the accretion rates $\gg 10 +\dot{M}_{\textrm{Edd}}$ ) inside the central few hundred parsecs." +" The steep, power-law, density profile of the gas in the circumnuclear disk contributes to the large accretion rates shown in Figure 6 (which are proportional to density)."," The steep, power-law, density profile of the gas in the circumnuclear disk contributes to the large accretion rates shown in Figure \ref{fig:mbondi} (which are proportional to density)." + The inclusion of an approximation for optically thick cooling in the simulations does not significantly change the density profile or the velocity dispersion of the gas., The inclusion of an approximation for optically thick cooling in the simulations does not significantly change the density profile or the velocity dispersion of the gas. +" Therefore, the Bondi prescription produces similar results for runs ZAL20 and Z4L20.OT (dashed and solid curves in Figure "," Therefore, the Bondi prescription produces similar results for runs Z4L20 and Z4L20.OT (dashed and solid curves in Figure \ref{fig:mbondi}) )." +"Additional effects not included in our current simulations6)). may contribute to the depletion of gas in the circumnuclear disk, such as AGN feedback and stellar feedback (not included in the zoom-in portion of the simulation), thus lowering the estimated Bondi rate."," Additional effects not included in our current simulations may contribute to the depletion of gas in the circumnuclear disk, such as AGN feedback and stellar feedback (not included in the zoom-in portion of the simulation), thus lowering the estimated Bondi rate." +" However, if the disk remains self-gravitating and therefore susceptible to instabilities, the Bondi prescription will inaccurately describe the transport of gas through this region."," However, if the disk remains self-gravitating and therefore susceptible to instabilities, the Bondi prescription will inaccurately describe the transport of gas through this region." + The average accretion rate through the circumnuclear disk over cosmological times can be estimated by comparing the mean interior gas mass (the averages shown in Figure 1)) for the different redshift simulations., The average accretion rate through the circumnuclear disk over cosmological times can be estimated by comparing the mean interior gas mass (the averages shown in Figure \ref{fig:gmr}) ) for the different redshift simulations. +" Figure 7 shows the mean gas mass, interior to radius r as a function of the age of the universe, tage."," Figure \ref{fig:mz} shows the mean gas mass, interior to radius $r$ as a function of the age of the universe, $t_{\textrm{age}}$." + Once again we emphasize that the different redshift simulations do not necessarily describe different stages of growth of the same galaxy because they each contain the same mass SMBH (rather than a black hole that grows with redshift)., Once again we emphasize that the different redshift simulations do not necessarily describe different stages of growth of the same galaxy because they each contain the same mass SMBH (rather than a black hole that grows with redshift). +" However, the black hole particle does not currently play a large role in the evolution of the simulated galaxy (at least not below z=4, where the mass of the black hole is dominated by the gas mass all the way down to the resolution limit)."," However, the black hole particle does not currently play a large role in the evolution of the simulated galaxy (at least not below $z=4$, where the mass of the black hole is dominated by the gas mass all the way down to the resolution limit)." +" The dashed line in Figure 7 shows the mass of a black hole, initially 3x107Mo at z=6, if it grows continuously at the Eddington limit according to where tg is the Salpeter time (?) of 4.5x10’yr, for a radiative efficiency η=0.1."," The dashed line in Figure \ref{fig:mz} shows the mass of a black hole, initially $3\times10^7 \dim{M}_{\sun}$ at $z=6$, if it grows continuously at the Eddington limit according to where $t_{\textrm{S}}$ is the Salpeter time \citep{Salpeter64} of $4.5\times10^7 \dim{yr}$, for a radiative efficiency $\eta=0.1$." +" If the dynamics of the circumnuclear disk extend all the way down to scales beneath the resolution (which cannot be assumed) then the growth rate approximated by the simulation points, which appears to steepen at early times with decreasing scale, may continue to steepen down to smaller scales, approaching the Eddington limit."," If the dynamics of the circumnuclear disk extend all the way down to scales beneath the resolution (which cannot be assumed) then the growth rate approximated by the simulation points, which appears to steepen at early times with decreasing scale, may continue to steepen down to smaller scales, approaching the Eddington limit." +" Therefore, a black hole in our simulations will be able to grow according to Equation 5 at high-z, as long as efficient fueling from the circumnuclear disk can be sustained."," Therefore, a black hole in our simulations will be able to grow according to Equation \ref{eq:sal} at $z$, as long as efficient fueling from the circumnuclear disk can be sustained." +" This is perhaps consistent with the isolated disk galaxy simulations of ?,, where a sufficiently massive black hole will grow according to Equation 5,, in the absence of AGN feedback."," This is perhaps consistent with the isolated disk galaxy simulations of \citet{Springeletal05a}, where a sufficiently massive black hole will grow according to Equation \ref{eq:sal}, in the absence of AGN feedback." +" Once gas reaches sub-parsec scales, the actual accretion rate onto the black hole is governedby the physics of the accretion disk, not modeled by our simulations."," Once gas reaches sub-parsec scales, the actual accretion rate onto the black hole is governedby the physics of the accretion disk, not modeled by our simulations." +" Nonetheless, Figure7 shows that the increase in the mass of the circumnuclear gas disk over"," Nonetheless, Figure\ref{fig:mz} shows that the increase in the mass of the circumnuclear gas disk over" +cosmic shear see Retregier(2003): see also Moellier and Bartchuamn&Schneider(2001).,cosmic shear see \cite{refregier03}; see also \cite{mellier99} and \cite{bartelmanns01}. +". Cosmic shear ais to measure this correlation function * dneasumnue observed cllipticitics of distant ealaxics c"" and taking iuto account how intrinsic (pre-shear) cllipticities e are modified bv shear.", Cosmic shear aims to measure this correlation function by measuring observed ellipticities of distant galaxies $e^o$ and taking into account how intrinsic (pre-shear) ellipticities $e^i$ are modified by shear. +" For παπα] shears js reduces to e""=ο|: we define e=(ab/(e|b) throughout.", For small shears this reduces to $e^o = e^i + \gamma$; we define $e \equiv (a-b)/(a+b)$ throughout. + Au estimate of the shear two yoint correlation fiction is obtaiued frou the observed ellipticity correlation fiction $&.=(264) where (2 is the served ellipticity of a distant galaxy s and e$ is that of a wearer galaxy d., An estimate of the shear two point correlation function is obtained from the observed ellipticity correlation function $\xi_{e}=\langle e^o_{\rm s} e^{o*}_{\rm d}\rangle$ where $e^o_{\rm s}$ is the observed ellipticity of a distant galaxy ${\rm s}$ and $e^o_{\rm d}$ is that of a nearer galaxy ${\rm d}$. +" Therefore we can expand the correlation tuuctious to &ud &=€|€-,. where the shear-cllipticity correlation is given by €.,=(5.67; if we ignore iutriusie aliguiiecuts = 0) aud use (254?=0. Tevinan"," Therefore we can expand the correlation functions to find $\xi_{e} = \xi_{\gamma} + \xi_{\gamma e}$, where the shear-ellipticity correlation is given by $\xi_{\gamma e} =\langle \gamma_{\rm s} e^{i*}_{\rm d} \rangle$ if we ignore intrinsic alignments $\langle e^{i}_{\rm s} e^{i*}_{\rm d} \rangle=0$ ) and use $\langle e^{i}_{\rm s} \gamma_{\rm d} \rangle=0$." +s(cele)etal.(2006) calculated the shear-cllipticity correlation function uuncerically using u-bocy simulations., \cite{heymanswhvv06} calculated the shear-ellipticity correlation function numerically using n-body simulations. + The aim of that work was to quautify the intrinsic Higmmuent - shear correlation preseuted by Irata&Sel-jak(200 1)., The aim of that work was to quantify the intrinsic alignment - shear correlation presented by \cite{hiratas04}. +. Their results should iu fact contain a mixture of the intrinsic alieumient - shear correlation and the ealaxy-ealaxy lensing sigual we preseut here., Their results should in fact contain a mixture of the intrinsic alignment - shear correlation and the galaxy-galaxy lensing signal we present here. + However. they do not discuss the distinction between the two effects. or specifically state that the ealaxy-ealaxy lensing contribution might be significant.," However, they do not discuss the distinction between the two effects, or specifically state that the galaxy-galaxy lensing contribution might be significant." + Tere we preseut simple analytical and wmuerically integrated results to quantity oulv the galaxy-galaxy lensing contribution., Here we present simple analytical and numerically integrated results to quantify only the galaxy-galaxy lensing contribution. +" We assune oa concordance ACDAL cosinology throughout./ with parameters taken from Spereelctal. (2006): IIubble coustaut My=73 kin | |l Q4,0.2328. Opp—1.OL. Οι=0.017. σς=O1. dark energv equation of state w=1l except where otherwise stated."," We assume a concordance $\Lambda$ CDM cosmology throughout, with parameters taken from \cite{spergelea06}: Hubble constant $H_0=73$ km $^{-1}$ $^{-1}$, $\Omega_{\rm m}=0.238$, $\Omega_{\rm DE}=1-\Omega_{\rm m}$, $\Omega_{\rm b}=0.047$, $\sigma_8=0.74$, dark energy equation of state $w=-1$ except where otherwise stated." + We assume a flat universe with a scale iuvariaut primordial power spectrum., We assume a flat universe with a scale invariant primordial power spectrum. + Iu this Section we calculate the galaxyv-ealaxy lensing contribution to &. οἴνοι by ἕνα as discussed. above.," In this Section we calculate the galaxy-galaxy lensing contribution to $\xi_e$, given by $\xi_{\gamma e}$, as discussed above." +" To estimate this quantitv we first calculate the sigual for a single elliptical lens averaged over backeround galaxies at a fixed augular distance. aud then average over a population of lenses,"," To estimate this quantity we first calculate the signal for a single elliptical lens averaged over background galaxies at a fixed angular distance, and then average over a population of lenses." + We assume that the lens light has the same ellipticity aud oricutation as the leis mass., We assume that the lens light has the same ellipticity and orientation as the lens mass. + By default we consider an NEW. (Navarroetal.1997) lass profile. calculating the projected mass from the equations eiven in Wrielt&Brainerd(2000) ancl Bartclmann(1996).," By default we consider an NFW \citep{nfw} mass profile, calculating the projected mass from the equations given in \cite{wrightb00} + and \cite{bartelmann96}." +.. We use Afsyy. the mass enclosed within the radius at which the deusitv is 200 times the mean deusitv of the Universe. for consistenev— with simulations.," We use $M_{200}$ , the mass enclosed within the radius at which the density is 200 times the mean density of the Universe, for consistency with simulations." + We derive the concentration parameter. e. as a function of Afoyy using Eq.," We derive the concentration parameter, $c$, as a function of $M_{200}$ using Eq." + 12 of Seljak(2000) with >=0.15. as appropriate for an NEW inodel.," 12 of \cite{seljak00} + with $\beta=-0.15$, as appropriate for an NFW model." + We calculate the shear for an elliptical mass distribution using the equations in Ἱνουίοι(2001)| and Schranuu (1990).," We calculate the shear for an elliptical mass distribution using the equations in \cite{keeton01} + and \cite{schramm90}." +". Note that this is not the same as calculations using elliptical potentials. which eive dumbbell shaped mass distributions οιο,,Nassiola&Ixovnuer1993)."," Note that this is not the same as calculations using elliptical potentials, which give dumbbell shaped mass distributions \citep[e.g.,][]{kassiolak93}." +. The projected mass distribution is squashed aud stretched to have elliptical isodeusity contours a factor f smaller (lureer) along the iiuor GQuajor) axes. as compared to the corresponding spherical mass distribution.," The projected mass distribution is squashed and stretched to have elliptical isodensity contours a factor $f$ smaller (larger) along the minor (major) axes, as compared to the corresponding spherical mass distribution." + The shear map for an elliptical NEW leus of ellipticity ο=0.3 aligned along the .« axis is shown in Fie. 1.., The shear map for an elliptical NFW lens of ellipticity $e =0.3$ aligned along the $x$ axis is shown in Fig. \ref{fig:map}. + The shading and contours show the couverseuce lap (projected lass density iun units of the critical lens density)., The shading and contours show the convergence map (projected mass density in units of the critical lens density). + The overlaid shear sticks show two particularly interesting features: (4) the shear ou the major axis ofthe chs is larger than that ou the minor axis. for a given aneular separation from the leas ceuter: (i) the shear 15 degrees around frou the major axis is approximately aueenutial to the ceuter of the leus.," The overlaid shear sticks show two particularly interesting features: (i) the shear on the major axis of the lens is larger than that on the minor axis, for a given angular separation from the lens center; (ii) the shear 45 degrees around from the major axis is approximately tangential to the center of the lens." + These two features do depend on the details of the mass profile. but are eeucral orrelevant radii for an clliptical NEW. profile. aud also for a sineular isothermal ellipsoid (SIE) (forwhichtheshear L)..," These two features do depend on the details of the mass profile, but are general forrelevant radii for an elliptical NFW profile, and also for a singular isothermal ellipsoid (SIE) \citep[for which the shear is always exactly tangential and its + amplitude follows the mass, see][]{kassiolak93,kormannsb94}. ." + These two characteristics poiut towards our main result:, These two characteristics point towards our main result: +and therefore all self-gravitating condensations should be reasonably well resolved.,and therefore all self-gravitating condensations should be reasonably well resolved. +" We three simulations, all with the same initial conditions, performand differing only in their treatments of the luminosities of "," We perform three simulations, all with the same initial conditions, and differing only in their treatments of the luminosities of protostars." +"In all three simulations the initial collapse leads to protostars.the formation of a primary protostar (i.e. a first sink) at t~77kyr, and this quickly acquires an extended accretion disc."," In all three simulations the initial collapse leads to the formation of a primary protostar (i.e. a first sink) at $\,t\!\sim\!77\,{\rm kyr}$, and this quickly acquires an extended accretion disc." + The simulations only diverge after this juncture., The simulations only diverge after this juncture. +" In the first simulation there is no radiative feedback from the protostar, and the gas in the disc is only heated by compression and by viscous dissipation in shocks."," In the first simulation there is no radiative feedback from the protostar, and the gas in the disc is only heated by compression and by viscous dissipation in shocks." + It is therefore cool enough to experience strong GI (?)., It is therefore cool enough to experience strong GI \citep{Stamatellos09}. +" The resulting gravitational torques transport angular momentum outwards, allowing matter to spiral inwards and onto the at a rate 1075.to10-Mgyr-!, but primaryin the protostarouter parts of the at radii R=50AU, the GI also becomes highly disc,non-linear locally, resulting in the formation of seven protostars, with masses ranging from 0.008Mc to secondary0.24Mo."," The resulting gravitational torques transport angular momentum outwards, allowing matter to spiral inwards and onto the primary protostar at a rate $10^{-5}\;{\rm to}\;10^{-4}\,{\rm M}_\odot\,{\rm yr}^{-1}$, but in the outer parts of the disc, at radii $R\ga 50\,{\rm AU}$, the GI also becomes highly non-linear locally, resulting in the formation of seven secondary protostars, with masses ranging from $0.008\,{\rm M}_\odot$ to $0.24\,{\rm M}_\odot$." + This is illustrated in the sequence of frames on Fig., This is illustrated in the sequence of frames on Fig. + 1., 1. + The accretion rate onto the primary protostar and the growth of its mass are shown on Fig., The accretion rate onto the primary protostar and the growth of its mass are shown on Fig. + 4 (red lines)., 4 (red lines). +" In the second simulation, we assume that the matter entering a sink is immediately accreted onto the protostar at its centre."," In the second simulation, we assume that the matter entering a sink is immediately accreted onto the protostar at its centre." + This results in an accretion luminosity which is typically 10to100Lo.," This results in an accretion luminosity which is typically $10\;{\rm to}\;100\,{\rm L}_\odot$." +" It therefore heats the surrounding disc, and as a result GI saturates, generating low-amplitude spiral waves that transport angular momentum outwards and allow matter to spiral into the protostar, but entirely suppressing disc at all radii."," It therefore heats the surrounding disc, and as a result GI saturates, generating low-amplitude spiral waves that transport angular momentum outwards and allow matter to spiral into the protostar, but entirely suppressing disc fragmentation, at all radii." +" This is illustrated in the sequence of fragmentation,frames on Fig.", This is illustrated in the sequence of frames on Fig. + 2., 2. + At all times the spiral, At all times the spiral +the difference between two of the reference slars while the triangles represent the difference between PQ And and one of the reference stars.,the difference between two of the reference stars while the triangles represent the difference between PQ And and one of the reference stars. + The horizontal axis is the time since the start of observations Lor each night., The horizontal axis is the time since the start of observations for each night. + The light curves of both nights clearly show fluctuations of up to —0.1 magnitudes., The light curves of both nights clearly show fluctuations of up to $\sim$ 0.1 magnitudes. + All reference stars and PQ And were of similar magnitude therefore the seatter in the reference star data gives an estimate of the errors in the magnitude change lor PQ And., All reference stars and PQ And were of similar magnitude therefore the scatter in the reference star data gives an estimate of the errors in the magnitude change for PQ And. + From Figure { we see that (he magnitude errors are on order of 0.015., From Figure 1 we see that the magnitude errors are on order of 0.015. + To search for any periodiciües in the light curves the data were pul through a Fourier transform routine., To search for any periodicities in the light curves the data were put through a Fourier transform routine. + The resulting power spectra for each date are shown in Figure 2., The resulting power spectra for each date are shown in Figure 2. + Dased on the length of time PQ And was observed and the sampling rate of each night. we searched the lrequency space [rom 0.5 to 30 4.," Based on the length of time PQ And was observed and the sampling rate of each night, we searched the frequency space from 0.5 to 30 $^{-1}$." + To determine the level of signilicance lor peaks in the power spectrum we added a (racer signal to our data and ran it through the Fourier routine unti] we were unable to detect it., To determine the level of significance for peaks in the power spectrum we added a tracer signal to our data and ran it through the Fourier routine until we were unable to detect it. + From (his we found that peaks with a power less (han ~10? were nol significant., From this we found that peaks with a power less than $\sim10^{-5}$ were not significant. + Three strong peaks appear in the power spectra of both nights., Three strong peaks appear in the power spectra of both nights. + The strongest peak is found ab a frequency of 5.6 |. a period. of 10.5 minutes. in both spectra.," The strongest peak is found at a frequency of 5.6 $^{-1}$, a period of 10.5 minutes, in both spectra." + We also see what appear to be harmonics of this peak at frequencies of ~2.8 ! and 14 |., We also see what appear to be harmonics of this peak at frequencies of $\sim$ 2.8 $^{-1}$ and $\sim$ 1.4 $^{-1}$. + At higher frequencies the (vo power spectra differ slghtlv., At higher frequencies the two power spectra differ slightly. + In. the September dala we see no significant peaks bevond the three already mentioned while the October power spectrum shows a few small, In the September data we see no significant peaks beyond the three already mentioned while the October power spectrum shows a few small +"eiven bv where pois the ποσα mass per molecule aud we adopt a cohuun density «Aq> which is the average column density of fragments of mass Mig, Qvhlich by definition have peak column densities ereater than the threshold to be identified as fragments).",given by where $\mu$ is the mean mass per molecule and we adopt a column density $ $ which is the average column density of fragments of mass $M_{\rm lim}$ (which by definition have peak column densities greater than the threshold to be identified as fragments). +" At a distance of 6 kpc. for fragment mass of 2/8/32 ML, and =151074 ? we ect Rau,=5/10/2y"" aand plow=2.1/1.2/0.6« ονP. respectively."," At a distance of 6 kpc, for fragment mass of 2/8/32 $_{\odot}$ and $ + =1.5\times10^{21}$ $^{-2}$ we get $_{\rm min}=5/10/20$ and $\rho_{\rm c}^{\rm low} =2.4/1.2/0.6\times10^3$ $^{-3}$, respectively." + For the same given mass there is also an upper density Bit which corresponds to the point where the size of the fragment becomes smaller than the resolution of the observations., For the same given mass there is also an upper density limit which corresponds to the point where the size of the fragment becomes smaller than the resolution of the observations. +" This provides an upper lait on the deusitv. pj""=O75«Alyο "," This provides an upper limit on the density, $\rho_{\rm + c}^{\rm up}=0.75\times M_{lim}/(\pi R_{res}^3)$ ." +For the 3 masses discussed before we get p?!=O.L/L.7/6.8«101 ci5m, For the 3 masses discussed before we get $\rho_{\rm c}^{up} =0.4/1.7/6.8\times10^5$ $^{-3}$. + To calculate the density aud mss of the IRDCs and fragments requires a distance for each object., To calculate the density and mass of the IRDCs and fragments requires a distance for each object. + Two different approaches to statistically attribute a particular distance to a particular cloud have been adopted., Two different approaches to statistically attribute a particular distance to a particular cloud have been adopted. + The first is to simply assign a unique distance to all clouds., The first is to simply assign a unique distance to all clouds. + Doing this. the physical size distribution of IRDC's and fragments will be exactly the same as the angular size distribution.," Doing this, the physical size distribution of IRDCs and fragments will be exactly the same as the angular size distribution." + Given the well peaked distribution of distances for clouds with mcasured distances (Fig. 1).," Given the well peaked distribution of distances for clouds with measured distances (Fig. \ref{dist}) )," + this should be a reasonable first approxination., this should be a reasonable first approximation. + Ilowever. a more sophisticated approach is to make use of the distributiou of distances (Gather than just its poak position).," However, a more sophisticated approach is to make use of the distribution of distances (rather than just its peak position)." + To do this we adopt a distance distribution for +the IRDCs aud then raudoimilv assign a distance drawn from this distribution to each cloud., To do this we adopt a distance distribution for the IRDCs and then randomly assign a distance drawn from this distribution to each cloud. + Doing this for the whole sample of clouds repeatedly provides a statistical sampling of the distance distribution., Doing this for the whole sample of clouds repeatedly provides a statistical sampling of the distance distribution. + The final physical size distribution is the convolution of the true physical size distribution bv the chosen distance distribution., The final physical size distribution is the convolution of the true physical size distribution by the chosen distance distribution. + Towever this does not have a crucial Hupact on the interpretation of the plysical size distribution if the dispersion of the distance distribution is much sinaller than the angular size distribution., However this does not have a crucial impact on the interpretation of the physical size distribution if the dispersion of the distance distribution is much smaller than the angular size distribution. + This is clearly the case since the angular sizes. both for IRDCs aud fragments. extends over 2 order of maenitudes while IRDC distances span only over a factor of 3 at imost.," This is clearly the case since the angular sizes, both for IRDCs and fragments, extends over 2 order of magnitudes while IRDC distances span only over a factor of 3 at most." + Tn other words. the dispersion iu distance has relatively little effect on the final physical size distribution (see Appendix A).," In other words, the dispersion in distance has relatively little effect on the final physical size distribution (see Appendix A)." + To assign clistances to the clouds using this sampling technique we adopt a Gaussian distribution of distances with a peak at Likpe aud a dispersion of 1 kpc. consistent with observed distance distributions (Fie. L)).," To assign distances to the clouds using this sampling technique we adopt a Gaussian distribution of distances with a peak at 4 kpc and a dispersion of 1 kpc, consistent with observed distance distributions (Fig. \ref{dist}) )." + Mass distributions of molecular cloud structures have been extcusively studied in the past. therefore they represcut a good point of comparison for this current study.," Mass distributions of molecular cloud structures have been extensively studied in the past, therefore they represent a good point of comparison for this current study." +"We defined lass as: where «Ng,> is the average cohuuu density across the IRDC or fragment aud Πιο its equivaleut radius CPEQOO).",We defined mass as: where $$ is the average column density across the IRDC or fragment and $R_{\rm eq}$ its equivalent radius (PF09). + Figure 8 shows the mass distributions for IRDCs aud fragments calculated adopting a sinele distance of Uspe (filled square svinbols) aud for randomly attributed clistances as described iu Section 5.1.., Figure \ref{mass} shows the mass distributions for IRDCs and fragments calculated adopting a single distance of 4kpc (filled square symbols) and for randomly attributed distances as described in Section \ref{sec:size}. + The shaded baud on the figures shows the range (3 times the dispersion) πράσα o» the 100 ciffereut distance realizations aud he open triuegles the mean for the different realizatious., The shaded band on the figures shows the range (3 times the dispersion) spanned by the 100 different distance realizations and the open triangles the mean for the different realizations. + The completeness limits are showu w the dashed lines., The completeness limits are shown by the dashed lines. + For comparison the powcr-aw slopes of the CO clump mass function (slope = (1.7) aud the Salpeter mass function. (slope = 1.35) are also shown., For comparison the power-law slopes of the CO clump mass function (slope $= -0.7$ ) and the Salpeter mass function (slope $= -1.35$ ) are also shown. + Using the MPFITS IDL owckage (Alarkwardt 2009) we have fitted the two distributions above their respective completeness nuits., Using the MPFITS IDL package (Markwardt 2009) we have fitted the two distributions above their respective completeness limits. +" For the IRDCs we find a limear function Gu a log-log plot) provides a good fit with dNMppcfdlogSeM=M."" with a=0.85+ OUT. The mass distribution of fragimieuts is better fitted by a lognormal function defined as", For the IRDCs we find a linear function (in a log-log plot) provides a good fit with $dN_{\rm{IRDC}}/d\log M=M^{-\alpha}$ with $\alpha=0.85 \pm 0.07$ The mass distribution of fragments is better fitted by a lognormal function defined as +We will examine it further in Sec. 3.2..,We will examine it further in Sec. \ref{ssec:metallicity}. +" North of this alignment, we can see that there is a prominent dust lane."," North of this alignment, we can see that there is a prominent dust lane." +" In the same alignment, we can see a tidal tail extending to the West."," In the same alignment, we can see a tidal tail extending to the West." + The smooth change of the brightness of the tail starting from the interacting galaxies suggests that it contains significant quantities of stars stripped from the parent galaxies which is confirmed by the fact that the tail is clearly seen in the near- in 2MASS images., The smooth change of the brightness of the tail starting from the interacting galaxies suggests that it contains significant quantities of stars stripped from the parent galaxies which is confirmed by the fact that the tail is clearly seen in the near--infrared in 2MASS images. +" Another, more prominent, tidal tail"," Another, more prominent, tidal tail" + 2=2.56. —1 (Maeaiuetal.1988): (I&nceibetal.L998:I&neib.Alloin.&Pello1998).. Ulazardctal.198," $z$ $\sim$ $''$ \citep{Magain_etal_1988}; \citep{Kneib_etal_1998, +Kneib_Alloin_Pello_1998}. \citep{Hazard_etal_1984}." + (Ny>LO?cm7) Wangetal.(2000). 0 (Chartas—2000).," $N_{\rm H} > +10^{23} {\rm cm}^{-2}$ \citet{Wang_etal_2000} \citet{Elvis_2000} $\sigma$ \citep{Chartas_2000}." +.. 120°C. (~2” , $-120^{\circ}$ $\sim$ $''$ + , +Since the redshift number density of these absorbers has also been shown to have roughly no evolution. these results agree with the Tinkeretal.(2010) model in which only the gas racius of haloes evolves with redshift.,"Since the redshift number density of these absorbers has also been shown to have roughly no evolution, these results agree with the \citet{Tinker10} model in which only the gas radius of haloes evolves with redshift." + Within this model. the gas radii of haloes expand with increasing redshift such that the haloes at ΖΞ1 have a gas radius that is ~40% larger in units of the DAL halo virial radius. compared to z=0.6.," Within this model, the gas radii of haloes expand with increasing redshift such that the haloes at z=1 have a gas radius that is $\sim$ larger in units of the DM halo virial radius, compared to z=0.6." + However. the errors on our bias measurement are still too large to rule out other halo evolution models in which the halo mass also evolves with redshift.," However, the errors on our bias measurement are still too large to rule out other halo evolution models in which the halo mass also evolves with redshift." + We measure the covering fraction. of strong absorption to be f.—0.5 within 60 tkpe around. DEEDP2 galaxies., We measure the covering fraction of strong absorption to be $f_{c}$ =0.5 within 60 $^{-1}$ kpc around DEEP2 galaxies. + We find no absorber host-galaxy pairs on scales larger than 37 tkpe. suggesting that the cllective gas racius of strong absorption around. DEEP? ealaxics may be as small as ~40h *kpe.," We find no absorber host-galaxy pairs on scales larger than 37 $^{-1}$ kpc, suggesting that the effective gas radius of strong absorption around DEEP2 galaxies may be as small as $\sim$ $^{-1}$ kpc." + In our sample. we identify just one candidate absorber host galaxv. which exhibits no evidence of ongoing star formation.," In our sample, we identify just one candidate absorber host galaxy, which exhibits no evidence of ongoing star formation." + Despite the small sample. size. this finding suggests that absorbers with similar equivalent widths S28 LLSA)) may not preferentially trace galaxies with high star formation rates at z~l.," Despite the small sample size, this finding suggests that absorbers with similar equivalent widths $_{r}^{\lambda2796}\sim$ ) may not preferentially trace galaxies with high star formation rates at $\sim$ 1." + However. we stress that a much larger sample would be required to fully test. this result.," However, we stress that a much larger sample would be required to fully test this result." + A larger overlapping survey of quasars ancl galaxies will be necessary to better constrain measurements of the typical environments of absorbers as well as the cold gas covering fraction of twpical galaxies at 21., A larger overlapping survey of quasars and galaxies will be necessary to better constrain measurements of the typical environments of absorbers as well as the cold gas covering fraction of typical galaxies at $\ga$ 1. + Surveys such as the SDSS-LLL Baryon Oscillation Spectroscopic Survey (BOSS). will soon provide the higher densities of quasars necessary to achieve this required: precision.," Surveys such as the SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS), will soon provide the higher densities of quasars necessary to achieve this required precision." + Follow-up spectroscopy of already. identified. quasars at higher resolution or signal-to-noise could. acdcditionallv produce the numbers of absorbers in. deep galaxy survey footprints needed to vastly. improve our understanding of the distribution of cold gas in dark matter haloes in the near future., Follow-up spectroscopy of already identified quasars at higher resolution or signal-to-noise could additionally produce the numbers of absorbers in deep galaxy survey footprints needed to vastly improve our understanding of the distribution of cold gas in dark matter haloes in the near future. + We would like to thank the referee. Jeremy Vinker. for helpful. discussions. ancl comments. which have greatly improved this work.," We would like to thank the referee, Jeremy Tinker, for helpful discussions and comments, which have greatly improved this work." + We also thank JT for providing| us with his model predictions. presented in Figure 5.," We also thank JT for providing us with his model predictions, presented in Figure 5." + We are also grateful to Pushpa Ixhare. and Jean Quashnock or helpful discussions anc to many others. who have contributed to the construction of the SDSS DRT quasar absorption line catalog of Yorkctal.(2011).," We are also grateful to Pushpa Khare and Jean Quashnock for helpful discussions and to many others, who have contributed to the construction of the SDSS DR7 quasar absorption line catalog of \citet{York11}." +. Funding for he SDSS and SDSS-IL has been provided. by the Alfred > Sloan Foundation. the U.S.. Department of Energy. 10 National Acronautics and Space Administration. the Japanese Monbukagakusho. the Max. Planck Society. and he Lieher Education. Funding Council for Eneland.," Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the U.S. Department of Energy, he National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England." + The SDSS Web Site is httpwww.sdss.org/., The SDSS Web Site is http://www.sdss.org/. +order in perturbation theory and found. the result. to. be a third. order polvnomial in 0.,order in perturbation theory and found the result to be a third order polynomial in $\theta$. + More recently. 2. found a relation between 6 and 9 using the spherical collapse model.," More recently, \citet{2008MNRAS.391.1796B} found a relation between $\theta$ and $\delta$ using the spherical collapse model." + In all of these relations. the dependence on cosmological »uwameters was found. to be extremely weak (??).. ," In all of these relations, the dependence on cosmological parameters was found to be extremely weak \citep{1992ApJ...390L..61B, Bouchet:1994xp}." +The velocity divergence depends on ο and ον. in a standard ACDAL cosmology. only through the linear growth rate. f (?)," The velocity divergence depends on $\Omega_m$ and $\Omega_{\Lambda}$, in a standard $\Lambda$ CDM cosmology, only through the linear growth rate, $f$ \citep{Scoccimarro:1999ed}." + We showed in the previous section that. including he velocity. divergence auto and cross power spectrum accurately reprocluces the redshift space power spectrum for a range of dark energy models onscales where the Ixaiser ormula fails., We showed in the previous section that including the velocity divergence auto and cross power spectrum accurately reproduces the redshift space power spectrum for a range of dark energy models onscales where the Kaiser formula fails. + The quantities in Eqs., The quantities in Eqs. + 14. and 10. can be calculated if we exploit the relationship between the velocity and density field., \ref{dm} and \ref{SM} can be calculated if we exploit the relationship between the velocity and density field. + In Fig., In Fig. + 7 we plot the velocity divergence auto (left panel) and cross (right panel) power spectrum as a function of the matter power spectrum for ACDAL and the three quintessence dark energy models., \ref{allmodels} we plot the velocity divergence auto (left panel) and cross (right panel) power spectrum as a function of the matter power spectrum for $\Lambda$ CDM and the three quintessence dark energy models. + We find that the density velocity relationship is very similar for each mocel at the redshifts considered. with only a slight difference for the SUCGILA model at high. redshifts and at small scales.," We find that the density velocity relationship is very similar for each model at the redshifts considered, with only a slight difference for the SUGRA model at high redshifts and at small scales." + The departure of the SUGRA mocdel from the general density velocity relation is due to shot noise. which alfects the power spectrum most at these scales in the SUCILUX mocdel as it has the lowest amplitude.," The departure of the SUGRA model from the general density velocity relation is due to shot noise, which affects the power spectrum most at these scales in the SUGRA model as it has the lowest amplitude." + We have verified that this effect is due to shot noise by sampling half the particles in the same volume. thereby doubling the shot noise. and repeating the P(k) measurement to find an even larger departure.," We have verified that this effect is due to shot noise by sampling half the particles in the same volume, thereby doubling the shot noise, and repeating the $P(k)$ measurement to find an even larger departure." + Fig., Fig. + 7 shows the independence of thedensity velocity relation not only of the values of cosmological parameters. as found in previous works. 7.. but. also a lack of dependence on the cosmological expansion history and initial power spectrum.," \ref{allmodels} shows the independence of thedensity velocity relation not only of the values of cosmological parameters, as found in previous works, \citet{1992ApJ...390L..61B}, but also a lack of dependence on the cosmological expansion history and initial power spectrum." + Fitting over the range 0.01.« A(h/Mpesc:0.3))]. we lind the following function accurately describes the relation between the non-linear velocity clivergence and matter power spectrum at z=0 to better than 5% on scales A< +. where £55 is the non-linear matter power spectrum.," Fitting over the range $0.01$ $^{40}$ X-ray source, and the counterintuitive trend of fitted parameters against count rate." + As noted earlier. the high ancl variable values of the X-ray absorber in the absorbed blackhody fits relt rend)) require the absorber to be in the vicinity of iltself.," As noted earlier, the high and variable values of the X-ray absorber in the absorbed blackbody fits \\ref{trend}) ) require the absorber to be in the vicinity of itself." + Whereas the presence of such intva- or cireum-binary material is expected. due to the Copious mass loss from (he supergiant mass donor. it is likely to be highly ionized on average (see. e.g.. Wojdowskietal. 2000)). even when the luminosity is a few times 10 |: much more so if the bolometric luminosity is near LOM|.," Whereas the presence of such intra- or circum-binary material is expected, due to the copious mass loss from the supergiant mass donor, it is likely to be highly ionized on average (see, e.g., \citealt{Wea2000}) ), even when the luminosity is a few times $^{38}$ ; much more so if the bolometric luminosity is near $^{41}$." + While high density chumps with lower (han average ionization are expected. we need extreme clumping to explain the observed absorber.," While high density clumps with lower than average ionization are expected, we need extreme clumping to explain the observed absorber." + For example. for a chunp “em from a LO! ssource {ο have £<1. a density greater than LO’ em? is recuired: for such a clump to be responsible [or the observed. X-ray absorption of ~2x10?!7. ib must have a length of only ~2x109 em.," For example, for a clump $^{13}$ cm from a $^{41}$ source to have $\xi < 1$, a density greater than $^{15}$ $^{-3}$ is required; for such a clump to be responsible for the observed X-ray absorption of $\sim 2 \times 10^{21}$, it must have a length of only $\sim 2 \times 10^6$ cm." + A clump at a distance of 1012 cm needs a density >LO! ? and a length of ~2x10 om., A clump at a distance of $^{15}$ cm needs a density $> 10^{11}$ $^{-3}$ and a length of $\sim 2 \times 10^{10}$ cm. + That is. for such a chump to remain neutral. it must have a high overdensity factor. ancl hence a small filling factor.," That is, for such a clump to remain neutral, it must have a high overdensity factor, and hence a small filling factor." + We therefore consider (he inferred neutrality of the X-ray absorber to be a severe problem [for the absorbed blackbody interpretation., We therefore consider the inferred neutrality of the X-ray absorber to be a severe problem for the absorbed blackbody interpretation. + This model also leads to a counterintuitive trend with observed count rate rend: rendtab)). whereas our alternative spectral model does not suffer from this problem.," This model also leads to a counterintuitive trend with observed count rate \\ref{trend}; \\ref{trendtab}) ), whereas our alternative spectral model does not suffer from this problem." + We do not necessarily claim (hat our model is the correct. physical description ofl., We do not necessarily claim that our model is the correct physical description of. +. Nevertheless. it is comforting to note that a simple analvtcal model. with a physical interpretation (relaiivistic emission line from (he accretion disk) can fit the collection of hieh state spectra without requiring an anti-correlation between observed count rate and bolometrie luminosity. or the presence of a neutral absorber within an ULXsvstem.," Nevertheless, it is comforting to note that a simple analytical model, with a physical interpretation (relativistic emission line from the accretion disk) can fit the collection of high state spectra without requiring an anti-correlation between observed count rate and bolometric luminosity, or the presence of a neutral absorber within an ULXsystem." + [t is «quite possible that other models can be found that can fit the available data equally well., It is quite possible that other models can be found that can fit the available data equally well. +"by Bardecu. Bond and Efstathiou ?"".. then applied. for the by-uow dead 17 keV neutrino by Boud and Efstathiouστ...","by Bardeen, Bond and Efstathiou \cite{bardeen}, then applied for the by-now dead 17 keV neutrino by Bond and Efstathiou \cite{bond}." +" After the CODE data. it was first considered by Chun ὃν, aud this idea was later applied to νο by others 77."," After the COBE data, it was first considered by Chun \cite{ckk}, and this idea was later applied to $\nu_\tau$ by others \cite{others}." + For the structure formation. the radiationanatter equality poiut Ree is iuportant.," For the structure formation, the radiation-matter equality point $R_{EQ}$ is important." + At Ree the structure scale Age is given by A lighto axino decays to an axion aud a oeravitino via the interaction ogiven in Eq.| (, At $R_{EQ}$ the structure scale $\lambda_{EQ}$ is given by A light axino decays to an axion and a gravitino via the interaction given in Eq. ( +7).,7). + Normally. one would expect] a couplingpling supressedsuj by MjAfp. but the Goldstino conrponeut dominates whose coupling is supressed by Fs.," Normally, one would expect a coupling supressed by $M_P$, but the Goldstino component dominates whose coupling is supressed by $F_S$ ." + Naimcly. the eravitino coupling is of the form (1PVoft where J is the supercurrenut.," Namely, the gravitino coupling is of the form $(1/F_S)(\partial_\mu\xi) +J^\mu$ where $J^\mu$ is the supercurrent." + In this case. the axino lifetime is eiven iu Eq. (," In this case, the axino lifetime is given in Eq. (" +8).,8). + The detail οπσον deusities of respective species are eiven in Fie., The detail energy densities of respective species are given in Fig. + 2., 2. + When the cosmic scale factor exceeds Reo. 0 dominates the mass deusity of the universe.," When the cosmic scale factor exceeds $R_{EQ1}$, $\tilde a$ dominates the mass density of the universe." + The cold axion dominates the energy density of the universe after the scale factor exceeds ego»., The cold axion dominates the energy density of the universe after the scale factor exceeds $R_{EQ2}$. + In Fig., In Fig. + 3. Ree is the radiatiou- matter equality point inthe CDM model.," 3, $R_{EQ}$ is the radiation- matter equality point inthe CDM model." + Thus. the axino-eravitino cosmology extends," Thus, the axino-gravitino cosmology extends" +While recent studies based on the molecular line data of the GRS have generated a census of molecular clouds in the Galactic plane (e.g..Jacksonetal.2006:Rathborne2009;Roman-Duvaletal. 2010).. the dust extinction maps cat provide a mass tracer for these clouds extending over a clearly wider dynamical range than the CO data.,"While recent studies based on the molecular line data of the GRS have generated a census of molecular clouds in the Galactic plane \citep[e.g.,][]{jac06, rat09, rom10}, the dust extinction maps can provide a mass tracer for these clouds extending over a clearly wider dynamical range than the CO data." + Most importantly. the dynamical range will overlap with that of higher columi density tracers (especially thermal dust emission). allowing combining the information from the two tracers.," Most importantly, the dynamical range will overlap with that of higher column density tracers (especially thermal dust emission), allowing combining the information from the two tracers." + Such ar approach ean provide column density data extending from low column density envelope material to gravitationally dominatec objects in the clouds., Such an approach can provide column density data extending from low column density envelope material to gravitationally dominated objects in the clouds. + Thereby. the data sets together can be used to reveal the detailed mass distributions surrounding the progenitors of high-mass stars. and we will continue towards deriving such data in forthcoming work.," Thereby, the data sets together can be used to reveal the detailed mass distributions surrounding the progenitors of high-mass stars, and we will continue towards deriving such data in forthcoming work." + In this paper. we examined the feasibility of NIR dust extinction mapping technique in tracing low-to-intermediate column density structures surrounding prospective birthplaces of high-mass stars. re. IRDCs.," In this paper, we examined the feasibility of NIR dust extinction mapping technique in tracing low-to-intermediate column density structures surrounding prospective birthplaces of high-mass stars, i.e., IRDCs." + We used the data from the UKIDSS/Galactic Plane Survey to derive dust extinction through 10 cloud complexes at thedistances between ~2.5—8 kpe. harboring altogether hundreds of IRDCs.," We used the data from the UKIDSS/Galactic Plane Survey to derive dust extinction through 10 cloud complexes at thedistances between $\sim 2.5-8$ kpc, harboring altogether hundreds of IRDCs." + We compared the derived NIR extinction. maps to the CO molecular line data from the Boston University-FCRAO Galactic Ring Survey. 8 jm dust opacity data from a recently published Spitzer IRDC catalogue by Peretto&Fuller(2009).. and to 870 jum dust emission data from the ATLASGAL survey (Schulleretal. 2009)..," We compared the derived NIR extinction maps to the $^{13}$ CO molecular line data from the Boston University-FCRAO Galactic Ring Survey, 8 $\mu$ m dust opacity data from a recently published Spitzer IRDC catalogue by \citet{per09}, and to 870 $\mu$ m dust emission data from the ATLASGAL survey \citep{sch09}. ." + The conclusions of our work are as follows., The conclusions of our work are as follows. +"outputs (E-,is,) that are 1-2 orders of magnitude larger than that of theSwift bursts ","outputs $E_{\gamma,iso}$ ) that are 1-2 orders of magnitude larger than that of the bursts (Figure \ref{fig:eiso}) )." +"Given the well known correlations between Ej«4; (Figureand 8)). (??),, and the hardness of LAT GRB spectra required Ey,isofor them to be detected by LAT at all, their large Ej,;,5's are not surprising."," Given the well known correlations between $E_{peak}$ and $E_{\gamma,iso}$ \citep{amati02,amati06}, and the hardness of LAT GRB spectra required for them to be detected by LAT at all, their large $E_{\gamma,iso}$ 's are not surprising." + This suggests to us that the LAT is preferentially detecting extremely energetic GRBs compared to previous GRB experiments., This suggests to us that the LAT is preferentially detecting extremely energetic GRBs compared to previous GRB experiments. +" The sensitivity, large field of view, and large energy range of the LAT make it especially sensitive to hard bursts."," The sensitivity, large field of view, and large energy range of the LAT make it especially sensitive to hard bursts." +" While the physical origin of the Amati relation is not well understood, the energetic LAT bursts seem to qualitatively follow the same relationship."," While the physical origin of the Amati relation is not well understood, the energetic LAT bursts seem to qualitatively follow the same relationship." +" Applying our characterizations of the optical and X-ray light curves and SEDs to the energetics, we can infer jet half-opening angles and collimation-corrected -ray energy outputs or limits when all observations were either pre- or (E),post-jet break."," Applying our characterizations of the optical and X-ray light curves and SEDs to the energetics, we can infer jet half-opening angles and collimation-corrected $\gamma$ -ray energy outputs $E_{\gamma}$ ), or limits when all observations were either pre- or post-jet break." +" Again, the methods used in these calculations and jet break determination are described in detail in ?.."," Again, the methods used in these calculations and jet break determination are described in detail in \cite{racusin09}." +" Using the XRT and UVOT data alone, most of the LAT GRB afterglow light curves discussed below) are best characterized by single(exceptions power laws, with relatively flat slopes (ao;< 1.8), with the exception of the poorly sampled GRB 100414A which may have had a break in the large gap between observations, and the short GRB 090510 which shows an early break to a steep - a behavior suggestive of a “naked” short hard burst decay(?) that indicates the turnoff of the prompt emission in a low environment with either an afterglow too faint to densitydetect or no afterglow at all."," Using the XRT and UVOT data alone, most of the LAT GRB afterglow light curves (exceptions discussed below) are best characterized by single power laws, with relatively flat slopes $\alpha_{o,x}\lesssim 1.8$ ), with the exception of the poorly sampled GRB 100414A which may have had a break in the large gap between observations, and the short GRB 090510 which shows an early break to a steep decay - a behavior suggestive of a “naked” short hard burst \citep{kumar00} that indicates the turnoff of the prompt emission in a low density environment with either an afterglow too faint to detect or no afterglow at all." +" However, ?| discussed the possibility that the break in the optical and X-ray light curves of GRB 090510 at ~2000 seconds is an early jet break, rather than a naked afterglow (i.e. steep fall off is either high latitude emission or post-jet break)."," However, \cite{depasquale10} discussed the possibility that the break in the optical and X-ray light curves of GRB 090510 at $\sim +2000$ seconds is an early jet break, rather than a naked afterglow (i.e. steep fall off is either high latitude emission or post-jet break)." +" The following calculations use the jet break assumption, but we recommend caution when examining the energetics of this GRB."," The following calculations use the jet break assumption, but we recommend caution when examining the energetics of this GRB." +" The LAT optical light curves, where sampled well, show shallow behavior or contamination at late times by the host galaxy or nearby sources."," The LAT optical light curves, where sampled well, show shallow behavior or contamination at late times by the host galaxy or nearby sources." + This is consistent with the idea that most of the LAT afterglow observations are pre-jet break the exceptions noted above)., This is consistent with the idea that most of the LAT afterglow observations are pre-jet break (with the exceptions noted above). +" Several recent papers (with(??7)| suggest that when using other broadband observations (including deep late optical/NIR observations), some of these bursts do hint at jet breaks, but theSwift data alone are insufficient to constrain jet breaks."," Several recent papers \citep{mcbreen10,cenko10,swenson10} suggest that when using other broadband observations (including deep late optical/NIR observations), some of these bursts do hint at jet breaks, but the data alone are insufficient to constrain jet breaks." + We will discuss the differences in jet breaks and energetics between this paper and those of ??? further in Section 4..," We will discuss the differences in jet breaks and energetics between this paper and those of \cite{mcbreen10,cenko10,swenson10} further in Section \ref{sec:disc}." +" If we assume all of the LAT GRBs are pre-jet break (except for GRB 100414A, which may be post jet break,"," If we assume all of the LAT GRBs are pre-jet break (except for GRB 100414A, which may be post jet break," +with pseudostates (RAIPS. 73) approaches.,"with pseudostates (RMPS, \citealt{0953-4075-29-1-015}) ) approaches." + The advantage of the CCC aethod is that. at least for collision systems with two electrons. it has heen shown o vield convergent results as basis size is increased: rowever. it has the disadvantage of requiug cousiderable computational effort.," The advantage of the CCC method is that, at least for collision systems with two electrons, it has been shown to yield convergent results as basis size is increased; however, it has the disadvantage of requiring considerable computational effort." + The advantage of the RAIPS method is that the R-matrix is calculated once aud then results or mnanyv collision energies can be caleulated with little additional effort., The advantage of the RMPS method is that the $R$ -matrix is calculated once and then results for many collision energies can be calculated with little additional effort. + This is particularly imiportaut for the study of resonances requiring dense euergv ericls., This is particularly important for the study of resonances requiring dense energy grids. +" The disadvantage, however. is that convergence with basis size can be slower resulting iu the appearance of pseudo-FOROMALLECS."," The disadvantage, however, is that convergence with basis size can be slower resulting in the appearance of pseudo-resonances." +" ? have published data frou extensive L-state CCC calculations for trausitious with »<3 and »zx L and inchide senu-enrpirieal cross sections for àsΞ-|. vos|,"," \citet{CCC} have published data from extensive 45-state CCC calculations for transitions with $n\le 3$ and $n^\prime \le 4$ , and include semi-empirical cross sections for $n=4$, $n^\prime=4$." + The calculations show good agreement with experiaenuts where available. and analytic fits to the cross section data are provided.," The calculations show good agreement with experiments where available, and analytic fits to the cross section data are provided." + ? have done calculations uxiug a 55-state RAIPS approach resultingin cross section data for alb transitions with no-— 27=0 aud ο d.," \cite{Griffin2001} have done calculations using a 55-state RMPS approach resultingin cross section data for all transitions with $n=2$, $l=0$ and $n^\prime \le$ 4." +" Ther caleulatious demonstrate the importance of including the coupling to the target continu via pseudostates; particularly at collidouns energies greater thau the lonizatlon enerev. he. 25.45.1] eV where the effects are σα] for 2s»2p. but become significant for 2s>3M and even greater for 2s.»141,"," Their calculations demonstrate the importance of including the coupling to the target continuum via pseudostates, particularly at collisions energies greater than the ionization energy, i.e. $> 5.4$ eV, where the effects are small for $2s\rightarrow 2p$, but become significant for $2s\rightarrow 3l$ and even greater for $2s\rightarrow 4l$." + The cross sections are in good agreement with the CCC and experiuenutal results where compared., The cross sections are in good agreement with the CCC and experimental results where compared. + Since there is a possibility that resonances at low collision euergies are unresolved ly the CCC caleulatious aud. could contribute significantly to the rate coefficients. we performed our own RAIPS caleulatious foy p< Landa’€ IL and »'/=Ss. which eives the additional advantage of an iudepenudoeut check.," Since there is a possibility that resonances at low collision energies are unresolved by the CCC calculations and could contribute significantly to the rate coefficients, we performed our own RMPS calculations for $n \le$ 4 and $n^\prime \le$ 4 and $n^\prime l^\prime = 5s$, which gives the additional advantage of an independent check." + These calculations are described below in Sect., These calculations are described below in Sect. + 2.1.1. aud compared with the existing data in Sect. 2.1.2., \ref{sect:rmat} and compared with the existing data in Sect. \ref{sect:res}. + As mentioned above. the rate coefficieuts. calculated we? have been used du iuost calculations of nou-LTE formation of Li I lines in cool stars (7277?7).. so hey represent an important basis for comparison in this work.," As mentioned above, the rate coefficients calculated by \citet{Park1971} have been used in most calculations of non-LTE formation of Li I lines in cool stars \citep{1984A&A...130..319S,1994A&A...288..860C, Lind2009,2010A&A...522A..26S,2005PASJ...57...45T}, so they represent an important basis for comparison in this work." + ? replaced the data of the important 2s}2p transition with that of 7.., \citet{1984A&A...130..319S} replaced the data of the important $2s\rightarrow 2p$ transition with that of \citet{1962ApJ...136..906V}. + Both these sources are oed on Born approximation calculations. which are well known to be valid only at hieh impact cuereics aud to substantially overestimate the cross sections near hreshold.," Both these sources are based on Born approximation calculations, which are well known to be valid only at high impact energies and to substantially overestimate the cross sections near threshold." + Thus. enipirical corrections determined frou various experiments are applied.," Thus, empirical corrections determined from various experiments are applied." + Based on comparison with the experumeuts. both works conclude that the calculated rates are not likely to be iu error by more than a factor of two.," Based on comparison with the experiments, both works conclude that the calculated rates are not likely to be in error by more than a factor of two." + We mace a 3l-state RAIPS calculation ofthe excitation by electron impacts. using existing freely available computer codes.," We made a 34-state RMPS calculation ofthe excitation by electron impacts, using existing freely available computer codes." + These calculations will now be described., These calculations will now be described. + For the initial atomic structure calculations we used he code (??:: see also 2)). which is an adaptation of (?) that allows the construction of polarization o»eudostates;," For the initial atomic structure calculations we used the code \citealt{civpol_thesis,CIVPOL}; see also \citealt{2004JPhB...37.2979P}) ), which is an adaptation of \citep{CIV3} that allows the construction of polarization pseudostates." + Such pseudostates are used to account for coupling to the target coutinuuu aud are needed: to obtain a correct description of the dipole polarization and lus the long-range interaction potential., Such pseudostates are used to account for coupling to the target continuum and are needed to obtain a correct description of the dipole polarization and thus the long-range interaction potential. + They have beeu shown by ? to be inmportaut at intermediate cuergics., They have been shown by \citet{Griffin2001} to be important at intermediate energies. + and use the configuration iuteraction (CT) uethod auc the radial parts of the (pseudo) orbitals are represcuted by Slater-tvpe orbitals: for details sec and ὃν, and use the configuration interaction (CI) method and the radial parts of the (pseudo) orbitals are represented by Slater-type orbitals; for details see and \cite{CIVPOL}. + The atomic structure of the target Li Twas built bv optinisiug spectroscopic orbitals with all allowed 5» values up tow=Sf: the 15 aud 2s orbitals were Hartrec-Fock orbitals taken fromο, The atomic structure of the target Li I was built by optimising spectroscopic orbitals with all allowed $nl$ values up to $nl=5f$; the $1s$ and $2s$ orbitals were Hartree-Fock orbitals taken from. +"ν, The energies obtained for the ten lowest-lving spectroscopic states are compared with experimental values taken from the NIST. Atomic Spectra Database (2). in Table 1.. and the agreement is satisfactory."," The energies obtained for the ten lowest-lying spectroscopic states are compared with experimental values taken from the NIST Atomic Spectra Database \citep{NIST} in Table \ref{energy}, and the agreement is satisfactory." +" Ouce the spectroscopic orbitals (aud states) were calculated. we added 09= 66s.p. d) aud. T(s. p.d) pseudo-orbitals to describe the polarization of the erouud aud first excited state. respectively,"," Once the spectroscopic orbitals (and states) were calculated, we added $n=6$ $s,p,d$ ) and $s,p,d$ ) pseudo-orbitals to describe the polarization of the ground and first excited state, respectively." + To test the quality of he polarization pseudostates. we compared the static dixe polarizabilities obtained with experimental and heoretical values found iu the literature. see Table 2..," To test the quality of the polarization pseudostates, we compared the static dipole polarizabilities obtained with experimental and theoretical values found in the literature, see Table \ref{polar}." + For the polarization of the erounc state there is good agreement between OUL results and those frou the iterature., For the polarization of the ground state there is good agreement between our results and those from the literature. + In the case of the polarizability of the first excited state. we found only one otherheoretical result (2).. where the polarizability is calculated in the Coulonib approximation.," In the case of the polarizability of the first excited state, we found only one othertheoretical result \citep{PolThe-a}, , where the polarizability is calculated in the Coulomb approximation." + The computed orbitals were then used in a RAIPS calculation of the clectrou-impact excitation cross sectious., The computed orbitals were then used in a RMPS calculation of the electron-impact excitation cross sections. + The code (2). was used for the internal region problem. and for the external region problem we," The code \citep{InnerRmatrix} was used for the internal region problem, and for the external region problem we" +officicney ΟΕ=0.05 the mass accretion rate is estimated to be AL~0.0035 ovear i. 10% of the Eddinetou accretion rate.,"efficiency $\eta^{\rm BOL} = 0.05$ the mass accretion rate is estimated to be $\dot{M} \simeq 0.0035$ $_\odot$ $^{-1}$, $\sim 10$ of the Eddington accretion rate." +" For such high accretion rates the transition from thin disk to an advection-dominated accretion flow may occur anywhere up to a radius of ~2000r, (7) aud so our fitted radius is consisteut with sucli à scenario.", For such high accretion rates the transition from thin disk to an advection-dominated accretion flow may occur anywhere up to a radius of $\sim 2000 r_g$ \citep{narayan98a} and so our fitted radius is consistent with such a scenario. + If features ou the truncated edge of the disk are steady in fux. as found for the Bine in NCC 1051. heu Galactic biuaries would also be expected o show such lines iu the low flux state aud the absence of such would cistavor the txuucated disk oriein for the lines.," If features on the truncated edge of the disk are steady in flux, as found for the line in NGC 4051, then Galactic binaries would also be expected to show such lines in the low flux state and the absence of such would disfavor the truncated disk origin for the lines." + While similar lines have not oen reported to date for Galactic black hole vnaries (see7.forareview)... constraints on such ies have not vet been explored in that source class. leaving this au open question.," While similar lines have not been reported to date for Galactic black hole binaries \citep[see][for a review]{done07b}, constraints on such lines have not yet been explored in that source class, leaving this an open question." + Tn an alternative ποσο]. the fact that the specific euergev of the line is coincident with Ίνα Cluission from neutral Cr kkeV) prompts a renewed iuterest in the spallation of Fe as a mechanisin for cuhancine otherwise weak Lincs. especially since PCA is consistent with a common origin for the new line and the neutral compoucut of Fe.," In an alternative model, the fact that the specific energy of the line is coincident with $\alpha$ emission from neutral Cr keV) prompts a renewed interest in the spallation of Fe as a mechanism for enhancing otherwise weak lines, especially since PCA is consistent with a common origin for the new line and the neutral component of Fe." + Tn à companion paper. ?).. explore in detail the spallation imterpretation of the new result. extending the work of ?) in the light of new nuderstanding about the cuvirous of active nuclei.," In a companion paper, \citet{turner09c}, explore in detail the spallation interpretation of the new result, extending the work of \citet{skibo97} in the light of new understanding about the environs of active nuclei." + 7) fined the observed abundance eubaucemoent o be high auc that these extreme cuhaucement effects are most likely to be achieved iu gas out of he plane of the accretion disk., \citet{turner09c} find the observed abundance enhancement to be high and that these extreme enhancement effects are most likely to be achieved in gas out of the plane of the accretion disk. + In such a picture. he timescale for spallation may be as short as a ‘ew vears if the cosmic ray output is comparable o the bolometric output of the nucleus;," In such a picture, the timescale for spallation may be as short as a few years if the cosmic ray output is comparable to the bolometric output of the nucleus." + ο) also estimate the expected radio aud >reg fiux from he proposed spallation process iu NGC 1051 and fund preciictions to be consistent with current fiux neasurements iu those bauds., \citet{turner09c} also estimate the expected radio and $\gamma-ray$ flux from the proposed spallation process in NGC 4051 and find predictions to be consistent with current flux measurements in those bands. + Our analvsis of data fom NGC 1051 aken during 2005 and 2008 has revealed line cluission at S.likkeV iu the rest-frame of the ealaxv., Our analysis of data from NGC 4051 taken during 2005 and 2008 has revealed line emission at keV in the rest-frame of the galaxy. + We have established. the reality of the ine at >99.9% confidence in data from 2005. supported by Monte Carlo simulations that show he probability. of the Lue beiug a statistical diuctuation is p<3.310L," We have established the reality of the line at $>99.9\%$ confidence in data from 2005, supported by Monte Carlo simulations that show the probability of the line being a statistical fluctuation is $p < 3.3 \times 10^{-4}$." + The possibility of the line arising from a statistical fluctuation in the spectral data has been firmly ruled out by establishing its detection iu time-sliced data., The possibility of the line arising from a statistical fluctuation in the spectral data has been firmly ruled out by establishing its detection in time-sliced data. + Further to this. we have confirmed the line to be evident in all three NIS units independently. aud established that the observed line is inconsistent with arising from the X-ray background.," Further to this, we have confirmed the line to be evident in all three XIS units independently, and established that the observed line is inconsistent with arising from the X-ray background." + The source spectrum varies with flux. aud the low state is donuünated by a hard spectral form with the new line plus the neutral comiponeut of Fe Ίνα emission superimiposed upon that. suggestive of a conmion origin for both.," The source spectrum varies with flux, and the low state is dominated by a hard spectral form with the new line plus the neutral component of Fe $\alpha$ emission superimposed upon that, suggestive of a common origin for both." + The line has au equivalent width during 2005 of about 15 eV while he Fe Ko line is measured at 195 eV. These reprocessed signatures show up prominently in tle source low state when the coutinuua is suppressed x the highest covering fraction of absorption., The line has an equivalent width during 2005 of about 45 eV while the Fe $\alpha$ line is measured at 195 eV. These reprocessed signatures show up prominently in the source low state when the continuum is suppressed by the highest covering fraction of absorption. + As disk hotspot emission would be expected ο vary in flux and energy over relatively short iuescales. the Linits on line variability disfavor lis particulay originOo althoughC» the data remain consistent with enmüssion from a special location such as the innermost radius of the accretion disk.," As disk hotspot emission would be expected to vary in flux and energy over relatively short timescales, the limits on line variability disfavor this particular origin although the data remain consistent with emission from a special location such as the innermost radius of the accretion disk." + The alternative picture. that the lue is Cr Ka cluission following spallation of Fe is also found to bea good explanation of the data: that possibility and its duplications are explored in a companion paper.," The alternative picture, that the line is Cr $\alpha$ emission following spallation of Fe is also found to be a good explanation of the data: that possibility and its implications are explored in a companion paper." + TIT acknowledges NASA evant NNNOSALHSOC. LM acknowledges STFC erant προ PP/EO001111/1., TJT acknowledges NASA grant NNX08AL50G. LM acknowledges STFC grant number PP/E001114/1. + We are grateful to the anonvinous referee whose conumnents significantly improved this manuscript: we also thank the operatious team for performing this observation aud providing software auc calibration for the data analysis., We are grateful to the anonymous referee whose comments significantly improved this manuscript: we also thank the operations team for performing this observation and providing software and calibration for the data analysis. + This research has also made use of data obtained from the ITigh Encreyv Astrophysics Scicuce Archive Research Center IIEASARCG). provided by NASA’s Coddard Space Flight Ceuter.," This research has also made use of data obtained from the High Energy Astrophysics Science Archive Research Center (HEASARC), provided by NASA's Goddard Space Flight Center." +"can be described as where B, is the dipole magnetic field strength of the neutron star at the magnetic pole, R, is the radius of the neutron star, Q is the angular frequency of radiation at t=0, y=L6x s is the corresponding spin-down timescale1018 of 4,0,theLs magnetar,[ο and I~109gcm? is the typical moment of inertia of the magnetar (Pacini 1967; Gunn Ostriker 1969).","can be described as where $B_{\rm p}$ is the dipole magnetic field strength of the neutron star at the magnetic pole, $R_{\rm s}$ is the radius of the neutron star, $\Omega$ is the angular frequency of radiation at $t=0$, $\tau_{\rm 0}=1.6\times 10^4 B_{\rm p,14}^{-2} \Omega_4^{-2}I_{45} +R_{\rm s,6}^{-6}$ s is the corresponding spin-down timescale of the magnetar, and $I\sim 10^{45}~{\rm g~cm^2}$ is the typical moment of inertia of the magnetar (Pacini 1967; Gunn Ostriker 1969)." +" Here the convention Qn=Q/10"" is adopted in cgs units.", Here the convention $Q_{\rm n}= Q/10^{\rm n}$ is adopted in cgs units. + One then has Laip~constfort«το and Laiyxt?fort>το.," One then has $L_{\rm dip} \sim {\rm +const}~{\rm for} ~ t\ll \tau_{\rm 0}$ and $L_{\rm dip} \propto +t^{-2}~{\rm for} ~t\gg \tau_{\rm 0}$." +" An abrupt drop in the X-ray flux with a slope steeper than t-? may be interpreted as a decrease of radiation efficiency, or the collapse of the neutron star into a black hole, possibly by losing the angular momentum or by accreting materials."," An abrupt drop in the X-ray flux with a slope steeper than $t^{-2}$ may be interpreted as a decrease of radiation efficiency, or the collapse of the neutron star into a black hole, possibly by losing the angular momentum or by accreting materials." +" Within such a model, the fact that would require (Bp,14,Q4,I4s,P)~(30,0.06,1,1)."," Within such a model, the fact that would require $(B_{\rm p,14},~\Omega_4,~I_{45},~R_{\rm s,6}) \sim +(30,~0.06,~1,~1)$." + This is a slow (P~10 ms) magnetar (By~3x1015 G)., This is a slow $P \simeq 10$ ms) magnetar $B_{\rm p} \simeq 3\times 10^{15}$ G). + The composition of this spindown-powered outflow is likely Poynting-flux-dominated., The composition of this spindown-powered outflow is likely Poynting-flux-dominated. +" Besides the magnetar argument (which naturally gives a highly magnetized outflow), another argument would be the lack of a bright thermal component with a temperature kT~ from the outflow photosphere as"," Besides the magnetar argument (which naturally gives a highly magnetized outflow), another argument would be the lack of a bright thermal component with a temperature $kT \sim 10~{\rm keV}~L_{47}^{1/4}R_{0,9}^{-1/2}$ from the outflow photosphere as" +decaving population of SN la is more common in carly-tvpe galaxies (Llamuy 1996: Ivanov. 2000).,decaying population of SN Ia is more common in early-type galaxies (Hamuy 1996; Ivanov 2000). + This diversity should. be reflected in the abundance vields with the brighter SN Ia. producing more Ni and less Si-group elements than the fainter ones., This diversity should be reflected in the abundance yields with the brighter SN Ia producing more Ni and less Si-group elements than the fainter ones. + Based on carly work withNewton. Finoguenov (2002) argue that the diversity in the SN Ia population would explain the distribution of chemical elements in the Virgo Cluster.," Based on early work with, Finoguenov (2002) argue that the diversity in the SN Ia population would explain the distribution of chemical elements in the Virgo Cluster." + The variation of the peak brightness. which correlates with the production of 6 dj and anti-correlates with the production of Si-eroup elements. can also be explained in the framework of the celaved detonation models by a variation of the dellagration-to-detonation transition density (transition from subsonic to supersonic [lame velocities).," The variation of the peak brightness, which correlates with the production of $^{56}$ Ni and anti-correlates with the production of Si-group elements, can also be explained in the framework of the delayed detonation models by a variation of the deflagration-to-detonation transition density (transition from subsonic to supersonic flame velocities)." + Fie., Fig. + S presents the expected. vields for a variety of SNIa explosion models from καποιο (1999). with the WDDI. WDD2. WDD3 and W7 mocels on the x-axis.," \ref{fig:div} presents the expected yields for a variety of ${\rm SN\;Ia}$ explosion models from Iwamoto (1999), with the WDD1, WDD2, WDD3 and W7 models on the x-axis." + We assume a constant relative fraction. of SNla. f.=0.15.," We assume a constant relative fraction of ${\rm SN\;Ia}$, $f=0.15$." + The WY model represents a pure dellagration explosion mechanism., The W7 model represents a pure deflagration explosion mechanism. + The WDD models represent delaved-detonation explosions and the last digit indicates the density at which the Blame. velocity. becomes supersonic (dellagration-to-detonation transition densitv) in units of 10) & 7., The WDD models represent delayed-detonation explosions and the last digit indicates the density at which the flame velocity becomes supersonic (deflagration-to-detonation transition density) in units of $10^7$ g $^{-3}$. + This transition density is likely dependent on the composition of the progenitor (see Jackson 2010)., This transition density is likely dependent on the composition of the progenitor (see Jackson 2010). + Alatching our observed οιο and S/Ee profiles. given the existing. SNIa. vields. would. require that. the centre of the galaxy has been enriched. almost solely by NDDI supernovae while the outer regions almost solely by WDD3.," Matching our observed Si/Fe and S/Fe profiles, given the existing ${\rm SN\;Ia}$ yields, would require that the centre of the galaxy has been enriched almost solely by WDD1 supernovae while the outer regions almost solely by WDD3." + The contribution by SN la with longer delay times and larger Si/Lle ratio would be the largest in the centre of the galaxy. out any realistic enrichment scenario predicts an enrichment v a mixture of dillerent types of SN la at all radii.," The contribution by SN Ia with longer delay times and larger Si/Fe ratio would be the largest in the centre of the galaxy, but any realistic enrichment scenario predicts an enrichment by a mixture of different types of SN Ia at all radii." + This model predicts a large central increase in the Ar/Ie and Ca/be abundance ratios that seem to be in conflict with he observed relatively Dat. profiles., This model predicts a large central increase in the Ar/Fe and Ca/Fe abundance ratios that seem to be in conflict with the observed relatively flat profiles. + The predicted: Mg/Ie xofile is relatively Dat in agreement with observations., The predicted Mg/Fe profile is relatively flat in agreement with observations. + The strongest prediction of this model is the ~30 per cent rise in he Ni/Fe abundance ratio with the increasing radius., The strongest prediction of this model is the $\sim30$ per cent rise in the Ni/Fe abundance ratio with the increasing radius. + Our observed. Ni/Fe profile. which is unfortunately dominated ov svstematic uncertainties. suggests a relatively [lat racial clistribution.," Our observed Ni/Fe profile, which is unfortunately dominated by systematic uncertainties, suggests a relatively flat radial distribution." + The O/Fe ratio of 0.60+0.03 Solar determined in. the centre of M ST with the Rellection Cirating Speetrometers (Werner ct al., The O/Fe ratio of $0.60\pm0.03$ Solar determined in the centre of M 87 with the Reflection Grating Spectrometers (Werner et al. + 200Gb: these data resolve the line anc the individual lines of the Fe-L complex) is significantly lower than the values. predicted. by the proposed. enrichment scenarios., 2006b; these data resolve the line and the individual lines of the Fe-L complex) is significantly lower than the values predicted by the proposed enrichment scenarios. + These best ft ΟΡο ratios are consistent with the values determined. using the CCD tvpe detectors on (Matsushita et al., These best fit O/Fe ratios are consistent with the values determined using the CCD type detectors on (Matsushita et al. + 2003)., 2003). + Either the measurements strongly uncerestimate the O abundance or some Κον aspect of the chemical enrichment of the hot LOAL/ESAL is not understood., Either the measurements strongly underestimate the O abundance or some key aspect of the chemical enrichment of the hot ICM/ISM is not understood. + Using the recently updated AtomDB atomic database. the best fitting O/Le ratios are 50 per cent larger compared to the previous version. indicating that at least part. of the cliscrepancy might be a modeling issue.," Using the recently updated AtomDB atomic database, the best fitting O/Fe ratios are 50 per cent larger compared to the previous version, indicating that at least part of the discrepancy might be a modeling issue." + Furthermore. all of our proposed enrichment scenarios are incompatible with the rising O/Te abundance profile reported from (Bobhringer ot al.," Furthermore, all of our proposed enrichment scenarios are incompatible with the rising O/Fe abundance profile reported from (Böhhringer et al." + 2001. Finoguenov et al.," 2001, Finoguenov et al." + 2002. Matsushita ect al.," 2002, Matsushita et al." + 2003)., 2003). + However. measurements of the line emission at Lo0.65 keV with CCD detectors suller from. significant systematic uncertainties due to à combination of limited spectral resolution. residual gain uncertainties. coupled with incomplete. modelling. of the detector oxygen. οσο aud possible incomplete subtraction of the [ine emission from the Galactic. foreground. (whieh could. bias the ο) abundance measurement in the outskirts of AL 87. high).," However, measurements of the line emission at $E\sim0.65$ keV with CCD detectors suffer from significant systematic uncertainties due to a combination of limited spectral resolution, residual gain uncertainties, coupled with incomplete modelling of the detector oxygen edge and possible incomplete subtraction of the line emission from the Galactic foreground (which could bias the O abundance measurement in the outskirts of M 87 high)." + These svstematic uncertainties force us to treat all current O abundance measurements with caution., These systematic uncertainties force us to treat all current O abundance measurements with caution. + More. robust measurements of the O/Fe profile will be possible with the calorimeters on the satellite., More robust measurements of the O/Fe profile will be possible with the calorimeters on the satellite. + Using a deep (574 ks)Chandra observation of ALSST. we performed the best measurements to date of the radial distributions of metals in the ambient central LOCAL of the Virgo Cluster.," Using a deep (574 ks) observation of 87, we performed the best measurements to date of the radial distributions of metals in the ambient central ICM of the Virgo Cluster." + We conclude that: We thank RoC. Morris. for computational support., We conclude that: We thank R.G. Morris for computational support. + We thank «ον. Irwin and J. de Plaa for stimulating discussions., We thank J.A. Irwin and J. de Plaa for stimulating discussions. + We thank the anonymous referee for the important sugeestions which significantlv improved. the paper., We thank the anonymous referee for the important suggestions which significantly improved the paper. + N. Werner. anc AL Simionescu were supported by the National Aeronautics and Space Administration. through Chandra/Iinstein Postdoctoral Fellowship Aware) Number PES-90056 and PE9-O0070 issued by the Chandra: X-ray, N. Werner and A. Simionescu were supported by the National Aeronautics and Space Administration through Chandra/Einstein Postdoctoral Fellowship Award Number PF8-90056 and PF9-00070 issued by the Chandra X-ray +breaking phase transition al the erand unified scale.,breaking phase transition at the grand unified scale. +" Such transitions lead to the formation of an unstable topological defect known as ""global texture."""," Such transitions lead to the formation of an unstable topological defect known as “global texture.""" +" Carroll- points. out that [or. some purposes it. is. useful. to pretend that the —ha724,7> term in the Friedmann equation represents an effective ""energy densitv in curvature. and define. py —(3h/8aG.—RajaPDs>>."," Carroll points out that for some purposes it is useful to pretend that the $-ka^{-2} R_0^{-2}$ term in the Friedmann equation represents an effective “energy density in curvature”, and define $\rho_k$ $-(3k / 8\pi GR_0^2) a^{-2}$." + Caldwell (1999 astro-ph 8163) remarks (hat most observations are consistent wilh models rght up to the w= 1 or cosmological constant limit. ancl so it is natural to ask what lies on the other side at w « 1.," Caldwell (1999 astro-ph 8168) remarks that most observations are consistent with models right up to the w = –1 or cosmological constant limit, and so it is natural to ask what lies on the other side at w $<$ –1." + He termed this phantom energy., He termed this phantom energy. + In this paper we outline how a dark energv program will constrain these elements and. in particular. how thev affect the measurement of the IIubble Constant. by means of the anisotropy in the cosmic microwave background.," In this paper we outline how a dark energy program will constrain these elements and, in particular, how they affect the measurement of the Hubble Constant by means of the anisotropy in the cosmic microwave background." +" Section 2 extends the Friedinann equation: $3 shows that supernova data are currently tolerant of small values of O4 and 03: 34 explores the degeneracies in CMD data: 65 examines how matter density experiments like 2dE (Peacock 2001) are affected: $6 broadly explores the parameter space of £2, as il applies to SN and CMDB data.", Section 2 extends the Friedmann equation; $\S$ 3 shows that supernova data are currently tolerant of small values of $\Omega_1$ and $\Omega_2$; $\S$ 4 explores the degeneracies in CMB data; $\S$ 5 examines how matter density experiments like 2dF (Peacock 2001) are affected; $\S$ 6 broadly explores the parameter space of $\Omega_n$ as it applies to SN and CMB data. + Our conclusions are in the final section., Our conclusions are in the final section. + An observer conlrontecd with data like that in Figure 1 might respond bv fitting a polynomial to the expansion rate as a function of redshilt., An observer confronted with data like that in Figure 1 might respond by fitting a polynomial to the expansion rate as a function of redshift. + But a plivsical equation already exists. namely the Friedimann equation.," But a physical equation already exists, namely the Friedmann equation." + From the point of view ol fitting the data (he observer might be surprised at the emphasis placed by physics on the higher order coefficients., From the point of view of fitting the data the observer might be surprised at the emphasis placed by physics on the higher order coefficients. + This was not rectified until the discovery of dark energy. based on earlier versions of Figure 1 bv the High z Supernova and Supernova Cosmology teams. although the zeroth order coefficient. was considered ancl discarded. by Einstein.," This was not rectified until the discovery of dark energy, based on earlier versions of Figure 1 by the High z Supernova and Supernova Cosmology teams, although the zeroth order coefficient was considered and discarded by Einstein." + According to Gooding (1992) the textures source term is, According to Gooding (1992) the textures source term is +"were the start density 3x105cm 3?, the upper limit on the number of accelerated electrons is increased tenfold.","were the start density $\times$ $^{8}$ $^{-3}$, the upper limit on the number of accelerated electrons is increased tenfold." +" The detection thresholds from the previous section can be used again: For X-ray detection through RHESSI lightcurves, a coronal electron beam would require about x 10?? electrons above 10 keV over 4 s, or about 4x 10?? electrons above 10 keV over a few minutes."," The detection thresholds from the previous section can be used again: For X-ray detection through RHESSI lightcurves, a coronal electron beam would require about $\times$ $^{35}$ electrons above 10 keV over 4 s, or about $\times$ $^{35}$ electrons above 10 keV over a few minutes." + RHESSI characterization by imaging requires at least 3x10°° 036 electrons above 10 keV. The fact that no clear spatial and temporal correlation of Type III radio burst and X-ray emission beyond the limb has ever been established is already an indicator that electron beams must have typically less than these numbers of electrons., RHESSI characterization by imaging requires at least $\times$ $^{36}$ electrons above 10 keV. The fact that no clear spatial and temporal correlation of Type III radio burst and non-thermal X-ray emission beyond the limb has ever been established is already an indicator that electron beams must have typically less than these numbers of electrons. + A systematic search using data from the Nancaay Radioheliograph and RHESSI will be initiated shortly., A systematic search using data from the Nançaay Radioheliograph and RHESSI will be initiated shortly. +" The best case so far of such an event has been discussed in?,, and mentionned briefly in the conclusion."," The best case so far of such an event has been discussed in, and mentionned briefly in the conclusion." +" (1)Strong escaping (“up”) beams, i.e. with fluxes comparable to the usual chromospheric HXR-producing flare electrons (21035 electrons above 10 keV), should easily be detectable and imageable with RHESSI, provided any chromospheric footpoint is occulted."," (1) escaping (“up”) beams, i.e. with fluxes comparable to the usual chromospheric HXR-producing flare electrons $\gtrsim$ $^{38}$ electrons above 10 keV), should easily be detectable and imageable with RHESSI, provided any chromospheric footpoint is occulted." +" The absence of such observations supports the scenario established so far, ie. that escaping electrons are fewer in number than a few tenths of a percent of those hitting the chromosphere."," The absence of such observations supports the scenario established so far, i.e. that escaping electrons are fewer in number than a few tenths of a percent of those hitting the chromosphere." + in turns hints at asymmetries in the overall standard acceleration scenario., This in turns hints at asymmetries in the overall standard acceleration scenario. +" Possible explanations can range from (a) the presence of a “collapsing trap” mechanism that enhances the number of accelerated flare electrons, but not the escaping electrons on open field lines, (b) the possibility that the main acceleration actually takes place elsewhere than in the high corona, such as in the footpoints, as suggested by?,, (c) the possibility that escaping electron beams are a secondary energy release phenomenon, triggered by electromagnetic waves from the flare electrons(?),, or (d) the presence of a secondary reconnection process higher up in the corona, where particle densities are much lower, connecting to open field lines?"," Possible explanations can range from (a) the presence of a “collapsing trap” mechanism that enhances the number of accelerated flare electrons, but not the escaping electrons on open field lines, (b) the possibility that the main acceleration actually takes place elsewhere than in the high corona, such as in the footpoints, as suggested by, (c) the possibility that escaping electron beams are a secondary energy release phenomenon, triggered by electromagnetic waves from the flare electrons, or (d) the presence of a secondary reconnection process higher up in the corona, where particle densities are much lower, connecting to open field lines." +).. |(2) GOES is not expected to observe anything of note fromweak beams (beams with <10°° electrons above 10 keV)., (2) GOES is not expected to observe anything of note from beams (beams with $\lesssim$ $^{36}$ electrons above 10 keV). +" Escapingweak beams appear to be just below RHESSI’s imaging capabilities (even with footpoints occulted), marginally within Hinode/XRT's imaging capabilities, but well within FOXSI’s."," Escaping beams appear to be just below RHESSI's imaging capabilities (even with footpoints occulted), marginally within Hinode/XRT's imaging capabilities, but well within FOXSI's." +were classified as lil. flare aud splutter im Cuaeiner ct al. (,"were classified as lull, flare and splutter in Greiner et al. (" +1996). aud each of these states last for a few huudred seconds;,"1996), and each of these states last for a few hundred seconds." + Simular N-rayv elt curves were analyzed in detail bv Belloni ct al. (, Similar X-ray light curves were analyzed in detail by Belloni et al. ( +L997a: 1997b) who classified them as “outbursts”: they found that the source shows distinct aud differeut spectral and temporal characteristics during the “quiescence” and outburst.,1997a; 1997b) who classified them as “outbursts”; they found that the source shows distinct and different spectral and temporal characteristics during the “quiescence” and outburst. + Taam. Chen. aud Swank (1997) detected a wide rauge of trausieut activity including regular bursts with a recurrence time of about oue minute and regular bursts.," Taam, Chen, and Swank (1997) detected a wide range of transient activity including regular bursts with a recurrence time of about one minute and irregular bursts." + Belloni et al. (, Belloni et al. ( +19971) made a detailed spectral analysis during a sequence of “bursts” and discovered a strong correlation between the quiescent phase and burst duration.,1997b) made a detailed spectral analysis during a sequence of “bursts” and discovered a strong correlation between the quiescent phase and burst duration. + Paul ct al. (, Paul et al. ( +1998a) detected several types of bursts using the INAE data aud ound evidence for matter disappearing mto the event rorizon of the black hole.,1998a) detected several types of bursts using the IXAE data and found evidence for matter disappearing into the event horizon of the black hole. + Yadav et al. (, Yadav et al. ( +1999) made a systematic analysis of these bursts and classified them sed on the recurrence time.,1999) made a systematic analysis of these bursts and classified them based on the recurrence time. + Yadav et al. (, Yadav et al. ( +1999) presented a comprehensive picture or the origin of these bursts in the light of the recent heories of advective accretion disk.,1999) presented a comprehensive picture for the origin of these bursts in the light of the recent theories of advective accretion disk. + It was sugeested that he peculiar bursts are characteristic of the change of state of the source., It was suggested that the peculiar bursts are characteristic of the change of state of the source. + The source cau switch back and forth )etween the low-hard state aud the high-soft state near critical accretion rates in a very short time scale. ceiving rise to the irregular and quasiregular bursts.," The source can switch back and forth between the low-hard state and the high-soft state near critical accretion rates in a very short time scale, giving rise to the irregular and quasi-regular bursts." + The fast time scale for the transition of the state is explained by invoking he appearance and disappearance of the advective disk in its viscous time scale., The fast time scale for the transition of the state is explained by invoking the appearance and disappearance of the advective disk in its viscous time scale. + The periodicity of the regular musts is explained by matching the viscous time scale with he cooling time scale of region bevoud a shock frout ora centrifugal barrier (Chakrabarti Titarchuk 1995)., The periodicity of the regular bursts is explained by matching the viscous time scale with the cooling time scale of region beyond a shock front or a centrifugal barrier (Chakrabarti Titarchuk 1995). + Iu this paper we prescut the results of a study of the iue variability and spectral characteristics of the source GRS 1915|105 duiug the irregular bursts., In this paper we present the results of a study of the time variability and spectral characteristics of the source GRS 1915+105 during the irregular bursts. + We show that during these bursts the source males distinct transitions )eteen the two spectral states ina few seconds., We show that during these bursts the source makes distinct transitions between the two spectral states in a few seconds. + Iu section 2 we present results obtained from an analysis of the data obtained from the Proportional Counter Arrav (PCA) of he Rossi N-vav Thine Explorer (RXTE)., In section 2 we present results obtained from an analysis of the data obtained from the Proportional Counter Array (PCA) of the Rossi X-ray Timing Explorer (RXTE). + In section 3 we discuss the importance of our results and in the last section a παν of the results is elven., In section 3 we discuss the importance of our results and in the last section a summary of the results is given. + GRS 19151105 was in a low-hard state diving 1996 December to 1997 March when the lard N-rav spectral index (~2.0) aud the soft N-rayv flux. (300 - 500 τιςνα) were low (αποetal.1998: J)., GRS 1915+105 was in a low-hard state during 1996 December to 1997 March when the hard X-ray spectral index $\sim$ 2.0) and the soft X-ray flux (300 - 500 mCrab) were low \cite{grei:98}; \cite{trud:98}) ). + The source started a new outburst around 1997 Aprib-May when the soft N-arav flux started iucreasing and the X-ray spectrum became soft (spectral iudex increased to 3 D., The source started a new outburst around 1997 April-May when the soft X-ray flux started increasing and the X-ray spectrum became soft (spectral index increased to 3 $-$ 4). + It reached the hiel-soft state in August 1997., It reached the high-soft state in August 1997. + The 1.3 to 12.2 keV Χαν light curve of the source obtained from the RATE ASAI archives is shown in Figure 1. from 1997. Jaunary to 1997 September.," The 1.3 to 12.2 keV X-ray light curve of the source obtained from the RXTE ASM archives is shown in Figure 1, from 1997 January to 1997 September." + Iudividual dwell data (see Levine et al., Individual dwell data (see Levine et al. + 1996) are plotted against the ASM day numbers (which is equal to ALJD - 19353)., 1996) are plotted against the ASM day numbers (which is equal to MJD - 49353). + A few dates (Gu 1997) are marked on the top of the figure., A few dates (in 1997) are marked on the top of the figure. + There are about 20 dwells on the source per daw. lasting for about 90 s. Data are in ASM counts «τς Crab 2 75 ASM counts +).," There are about 20 dwells on the source per day, lasting for about 90 s. Data are in ASM counts $^{-1}$ (1 Crab = 75 ASM counts $^{-1}$ )." + The RNTE public archive contains several observations on GRS 1915|105 using the RATE PCA (Jahoda et al., The RXTE public archive contains several observations on GRS 1915+105 using the RXTE PCA (Jahoda et al. + 1996)., 1996). + These observations typically last for a few thousand seconds and the start times of these observations are narked as circles in Figure 1., These observations typically last for a few thousand seconds and the start times of these observations are marked as circles in Figure 1. + Several of these observations are analyzed and reported im the literature aud these are uarked with vertical arrows im the figure., Several of these observations are analyzed and reported in the literature and these are marked with vertical arrows in the figure. +" The observation ines of the regular bursts reported as ‘rings’ iu the PCA color-color diagrams by Villa Nevalainen (1998) are uarked with acy in the fieure and the ""imregular bursts reported by Belloni et al. (", The observation times of the regular bursts reported as `rings' in the PCA color-color diagrams by Vilhu Nevalainen (1998) are marked with a `v' in the figure and the `irregular bursts' reported by Belloni et al. ( +19975) is marked as “BY.,1997b) is marked as `B'. +" The eculiar repeated observation of the ""kink iu the leht curve followed by a Iul and then riugimg flares reported w Eikeuberry et al. (", The peculiar repeated observation of the `kink' in the light curve followed by a `lull' and then ringing flares reported by Eikenberry et al. ( +1998) is marked by au E.,1998) is marked by an `E'. + Similar episodes of flares have seen by Alarkwardt et al. (, Similar episodes of flares have seen by Markwardt et al. ( +1999) and it is marked with au AU.,1999) and it is marked with an `M'. + The remaining observations which are reported in the literature are from Trudolvyubov. Churazov. Cülfanov (1999) aud Muno et al. (," The remaining observations which are reported in the literature are from Trudolyubov, Churazov, Gilfanov (1999) and Muno et al. (" +1999).,1999). + The observation times of CRS 1915|105 by the PPCs ou board IXAE (Paul cl al., The observation times of GRS 1915+105 by the PPCs on board IXAE (Paul el al. + 19982: Yadav et al., 1998a; Yadav et al. + 1999) ave marked as stars in Fieure 1., 1999) are marked as stars in Figure 1. + It can be seen from the figure that the source was in a stable low-hard state wp to 1997 April 25 (dav uuuber 1210) when the average ASM count was 20 1., It can be seen from the figure that the source was in a stable low-hard state up to 1997 April 25 (day number 1210) when the average ASM count was 20 $^{-1}$. + Barring hnree episodes of dippiug behaviors (which could be absorption dips seeu in other black hole caucidate sources ike IU 1630-17 - see Ίνακος et al., Barring three episodes of dipping behaviors (which could be absorption dips seen in other black hole candidate sources like 4U 1630-47 - see Kuulkers et al. + 1998). the source fux was stable with a riis deviation of15%.," 1998), the source flux was stable with a rms deviation of." +. It should be roted here that the ASM data. with a dwell time of 90 5 and about 20 dwells per dav. is inseusitive to short term varlabilitics.," It should be noted here that the ASM data, with a dwell time of 90 s and about 20 dwells per day, is insensitive to short term variabilities." + The spectral ancl temporal behavior during he low-harcd state was stable characterized by a hard spectrum (with the power-law iudex of ~2. and the total fux in the power-law component being ~s80% }) and 0.5 10 Tz QPOs (Irudolvubov et al.," The spectral and temporal behavior during the low-hard state was stable characterized by a hard spectrum (with the power-law index of $\sim$ 2, and the total flux in the power-law component being $\sim$ ) and 0.5 – 10 Hz QPOs (Trudolyubov et al." + 1999: Nuno et al., 1999; Muno et al. + 1999)., 1999). + The fact that the canonical low-hard states of black hole candidate sources have a negligible thermal component (Chituis et al., The fact that the canonical low-hard states of black hole candidate sources have a negligible thermal component (Chitnis et al. + 1998) prompted Trudolyubov et al. (, 1998) prompted Trudolyubov et al. ( +"1999) to characterize this state as an ""interinediate state” aud they couclude that with the lowering of the accretion rate the source should eo to the canonical hard state.",1999) to characterize this state as an “intermediate state” and they conclude that with the lowering of the accretion rate the source should go to the canonical hard state. + Since the source was iu simular state on several occasions (1996 July-August: 1997 October: 1998 Septemiber-October). we treat this state as the “low-hard state” of GRS-1915|105.," Since the source was in similar state on several occasions (1996 July-August; 1997 October; 1998 September-October), we treat this state as the “low-hard state” of GRS-1915+105." + After 1997 April 25 the source started a steady increase in its N-rav emission with an average increase in the ASAI count rate of 0.65 3 + and reaching a count rate of τος+ in the middle of July (day πο. 1290)., After 1997 April 25 the source started a steady increase in its X-ray emission with an average increase in the ASM count rate of 0.65 $^{-1}$ $^{-1}$ and reaching a count rate of 76 $^{-1}$ in the middle of July (day number 1290). + The variability. as cau be deduced from the ASAD count rates and measured as the fraction of runs to mean. steadily increased from to," The variability, as can be deduced from the ASM count rates and measured as the fraction of rms to mean, steadily increased from to." + It should be noted that during the low-hard state of 1996 July-August the source showed simular variability behavior: the rius variation was low (5 - 104)) during the low-lard state aud it was ~LO% just before and after this state (Paul ct al., It should be noted that during the low-hard state of 1996 July-August the source showed similar variability behavior: the rms variation was low (5 - ) during the low-hard state and it was $\sim$ just before and after this state (Paul et al. + 19051)., 1998b). + The variability. however. decreased to <15% around 1997 June (Dav uuuber 1260).," The variability, however, decreased to $<$ around 1997 June (Day number 1260)." + Divine this period the source showed evidences of continous “rineiue” fares (Villian aud Novalainen 1998: Yadav ct al., During this period the source showed evidences of continuous “ringing” flares (Vilhu and Nevalainen 1998; Yadav et al. + 1999). with time scales of 30 60 s and these will not be evident in the ASM data.," 1999), with time scales of 30 – 60 s and these will not be evident in the ASM data." + The variability increased again from June cud (Day muuber 1275) aud the faring state continued for about 20 more days with the ASAI variability being 30-1054., The variability increased again from June end (Day number 1275) and the flaring state continued for about 20 more days with the ASM variability being 30 -. +. The source reached a steady state with low variability (~10%})., The source reached a steady state with low variability $\sim$ ). + The ringing flares started again iu the beginning of 1997 August (Yadav ct al., The ringing flares started again in the beginning of 1997 August (Yadav et al. + 1999) and towards the cud of this state, 1999) and towards the end of this state +To determine the new proper motion for NLTT 20316 we used positions available through USNO-A2.0. USNO-D1.0. GSC 2.2. 2ATASS. and an ISPI image taken on 05 April 2010 ειν 2:2: 2h).,"To determine the new proper motion for NLTT 20346 we used positions available through USNO-A2.0, USNO-B1.0, GSC 2.2, 2MASS, and an ISPI image taken on 08 April 2010 \citealt{2003AJ....125..984M}, \citealt{1998usno.book.....M}; \citealt{2008AJ....136..735L}; \citealt{2003tmc..book.....C}) )." + The total baseline between the first aud ια] epoch used was ~59 vears., The total baseline between the first and final epoch used was $\sim$ 59 years. +" NLTT 20316 is uot resolved iu auy of the epochs as the 2"" separation. seeing coucditious aud plate scale of each detector caused the A and DB components to appear bleuded."," NLTT 20346 is not resolved in any of the epochs as the $\arcsec$ separation, seeing conditions and plate scale of each detector caused the A and B components to appear blended." + We simulated the PSF for the A and D component of NLTT 20316 ou cach of the detectors to estimate the nucertaity due to blending., We simulated the PSF for the A and B component of NLTT 20346 on each of the detectors to estimate the uncertainty due to blending. + We added this additional nucertaity in quadrature to the catalog uncertainties and used these in the proper motion measurement., We added this additional uncertainty in quadrature to the catalog uncertainties and used these in the proper motion measurement. + The absolute astrometric position from cach catalog (with correspouding epochs) were used to solve for the proper motion using a least squares weighted solution., The absolute astrometric position from each catalog (with corresponding epochs) were used to solve for the proper motion using a least squares weighted solution. + There is an SDSS image taken on 06 January 2006 and an ISPI nuage taken on 27 February 2010 with sub-arcseconc seeing where both componucuts are resolved., There is an SDSS image taken on 06 January 2006 and an ISPI image taken on 27 February 2010 with sub-arcsecond seeing where both components are resolved. + Using these two epochs with a -—1 vear baseline. we caleulatec the proper motion of cach component.," Using these two epochs with a $\sim$ 4 year baseline, we calculated the proper motion of each component." + These resolve values are cousisteut with the motion calculated from the blended source along a 59 vear baseline., These resolved values are consistent with the motion calculated from the blended source along a 59 year baseline. + This iudicates that orbital motion is not effecting the total motion of the system., This indicates that orbital motion is not effecting the total motion of the system. +" For NLTT 20316 we calculated p, —-17248 mas yr and 52-5026 mas | (usus all catalog positions) and for 2MASS JOs50|1057 we calculated 45, I6 nias η", For NLTT 20346 we calculated $\mu_{\alpha}$ $\pm$ 8 mas $^{-1}$ and $\mu_{\delta}$ $\pm$ 6 mas $^{-1}$ (using all catalog positions) and for 2MASS J0850+1057 we calculated $\mu_{\alpha}$ $\pm$ 6 mas $^{-1}$ and $\mu_{\delta}$ $\pm$ 6 mas $^{-1}$. + NLTT 20316 —-11Ehas two published proper motion values iu the LSPALN and New Luvteu 73) catalogues aud. as stated in section 3d. 2MASS JOs50|1057 has previous proper motion values reported in 7? and 7? (sco Table 1).," NLTT 20346 has two published proper motion values in the LSPM-N and New Luyten \citealt{1979lccs.book.....L}) ) catalogues and, as stated in section 3.1, 2MASS J0850+1057 has previous proper motion values reported in \citet{2004AJ....127.2948V} and \citet{2002AJ....124.1170D} (see Table \ref{PM}) )." +" Our astrometric results are consistent within 20 of previous published results aud using the new values. both the μι, and pps values for the potential companious are within 20 of cach other."," Our astrometric results are consistent within $\sigma$ of previous published results and using the new values, both the $\mu_{\alpha}$ and $\mu_{\delta}$ values for the potential companions are within $\sigma$ of each other." + Alone with the predicted distance measurement of the primary (see section [1 below). aud the new parallax measurement for 24MASS. 10550|1057 of 3548 mas or 29-47 pc. this svstein is a strong wideconrpainion COMMMOL proper notion candidate.," Along with the predicted distance measurement of the primary (see section 4.1 below), and the new parallax measurement for 2MASS J0850+1057 of $\pm$ 8 mas or $\pm$ 7 pc, this system is a strong widecompanion common proper motion candidate." + NLTT 20316 was identified asa potential companion to 2MÀSS σος1057. through a connuon proper motion search of the Brown Dwarf Kinematics Project (DDKDP) catalog (2)) and the Lepine-Shara Proper Motion North (LSPALN) and Hipparcos catalogs ο 7))., NLTT 20346 was identified asa potential companion to 2MASS J0850+1057 through a common proper motion search of the Brown Dwarf Kinematics Project (BDKP) catalog \citealt{2009AJ....137....1F}) ) and the Lepine-Shara Proper Motion North (LSPM-N) and Hipparcos catalogs \citealt{2002AJ....124.1190L}; \citealt{1997A&A...323L..49P}) ). + Several other svstems were detected and detailed analysis was presented in ?.., Several other systems were detected and detailed analysis was presented in \citet{2009AJ....137....1F}. + In that work. an augular separation of up to 10 arciuuutes and a proper motion matcl criterion of better than 26 in both right ascension (RA) and declination (DEC) between the svsteui components was required to determine common proper motion candidates.," In that work, an angular separation of up to 10 arcminutes and a proper motion match criterion of better than $\sigma$ in both right ascension (RA) and declination (DEC) between the system components was required to determine common proper motion candidates." + The average uncertaiutv for objects im the DDKD catalog is 15 amas | (in both directions) so proper motion agreenieut was typically required to be < J03nas | between the stellar companion aud ultracool dwart (UCD)., The average uncertainty for objects in the BDKP catalog is 15 mas $^{-1}$ (in both directions) so proper motion agreement was typically required to be $<$ 30 mas $^{-1}$ between the stellar companion and ultracool dwarf (UCD). + 7. also required a distance match between colponcuts of better than 20 or typically better than 10 pe., \citet{2010AJ....139..176F} also required a distance match between components of better than $\sigma$ or typically better than 10 pc. + The system containing NLTT 20316 was not investigated in 7— because proper motion components were sliehtlv outside of the 26 requirement., The system containing NLTT 20346 was not investigated in \citet{2010AJ....139..176F} because proper motion components were slightly outside of the $\sigma$ requirement. + However. after follow-up aging aud re-analysis of the astromoetry of both compoucuts we found strong evidence for colpaiouship (see Section 3.2).," However, after follow-up imaging and re-analysis of the astrometry of both components we found strong evidence for companionship (see Section 3.2)." + To quautifv the probability that NLTT 20516 nieht be a chance aliguiment with 2\LASS JO0850|1057. we ran a Moute Carlo simulation of all stars iu the LSPALN aud Ilipparcos catalogs that shared a common proper motion. but not necessarily distance or position. with the brown chwart (to within 20 see? for details).," To quantify the probability that NLTT 20346 might be a chance alignment with 2MASS J0850+1057, we ran a Monte Carlo simulation of all stars in the LSPM-N and Hipparcos catalogs that shared a common proper motion, but not necessarily distance or position, with the brown dwarf (to within $\sigma$ –see \citealt{2009AJ....137....1F} for details)." + There were 156 stars in the Iipparcos catalog aud 632 stars in the LSPALN catalog with matching proper motion compoucuts., There were 156 stars in the Hipparcos catalog and 632 stars in the LSPM-N catalog with matching proper motion components. +" After 10000 iterations we found the likelihood that NLTT 20316 is a chance coincidence with 2\LASS JO0850|1057 (at an angular seperation of 218 "") is < L.0%..", After 10000 iterations we found the likelihood that NLTT 20346 is a chance coincidence with 2MASS J0850+1057 (at an angular seperation of 248 $\arcsec$ ) is $<$ . + From the MagE data for NETT. 20316 we classified, From the MagE data for NLTT 20346 we classified +We find that lower redshift SMCs appear to have lower rest-frame W-band luminosities. suggesting that galaxy ‘downsizing (Vhomas et al..,"We find that lower redshift SMGs appear to have lower rest-frame K-band luminosities, suggesting that galaxy 'downsizing' (Thomas et al.," + 2005) is at work in the SMCG population., 2005) is at work in the SMG population. + This is an expected. result. in the generally assumed. picture of SALGs being a stage in the evolution of elliptical ealaxies., This is an expected result in the generally assumed picture of SMGs being a stage in the evolution of elliptical galaxies. + Several of our SMCs are found. to either be multiple sources with two or more components. or to lie in groups or clusters.," Several of our SMGs are found to either be multiple sources with two or more components, or to lie in groups or clusters." + However an analysis of the photomoetric-redshift distributions of all sources within LO” of SMCs finds no statistically significant number of companions compared to non-SALG objects.," However an analysis of the photometric-redshift distributions of all sources within 10"" of SMGs finds no statistically significant number of companions compared to non-SMG objects." + This work represents the first stage of analysing the miucd-to-far-LR SEDs of the SILADISS submillimetre galaxies., This work represents the first stage of analysing the mid-to-far-IR SEDs of the SHADES submillimetre galaxies. + The SILADES field in Lockman was observed by the Spitzer GTO teams with somewhat deeper integrations and is being ciseussed. elsewhere (Dye et al.," The SHADES field in Lockman was observed by the Spitzer GTO teams with somewhat deeper integrations and is being discussed elsewhere (Dye et al.," + 2007) while specific subpopulations such as NlIi-selected. sources are also being investigated (Takagi et al..," 2007) while specific subpopulations such as NIR-selected sources are also being investigated (Takagi et al.," +. 2007)., 2007). + Examination of Spitzer counterparts to non-racdio-detected: sources in the SXDE anc Lockman SILXDES fields is also underway (Oliver et al.," Examination of Spitzer counterparts to non-radio-detected sources in the SXDF and Lockman SHADES fields is also underway (Oliver et al.," + in. preparation: Dye et al.," in preparation; Dye et al.," + in. preparation). along with stacking analvsis to produce population averages for uncletected sources (Serjeant et al;," in preparation), along with stacking analysis to produce population averages for undetected sources (Serjeant et al.," + in preparation)., in preparation). + Thanks to Jeff. Wage anc Marcos Trichas for useful comments., Thanks to Jeff Wagg and Marcos Trichas for useful comments. + DLC is funded by PPARCYSTEC. LRS is supported by the Roval Society.," DLC is funded by PPARC/STFC, IRS is supported by the Royal Society." + The JCAIP is supported by the United. NineclomAs Science and. Technology. Facilities Council (STEC). the National Research Council Canada (NI). and the Netherlands Organization for Scientific Research (NWO): it is overseen by the JCAL Board.," The JCMT is supported by the United KingdomÕs Science and Technology Facilities Council (STFC), the National Research Council Canada (NRC), and the Netherlands Organization for Scientific Research (NWO); it is overseen by the JCMT Board." + We acknowledge funding support. from PPARC/STEC. NRC and NASA.," We acknowledge funding support from PPARC/STFC, NRC and NASA." + The authors would. like to thank the stall at the JOAVP for their typically excellent! support, The authors would like to thank the staff at the JCMT for their typically excellent support +Jaikumar 2005) similar to wlal has been suggestedMOD in the superuova case (Chevalier1989).,Jaikumar 2005) similar to what has been suggested in the supernova case \citep{Chev89}. +. The deusity of the fallback matter. represeltaive of the crust material of the parent. neutron star. is estituated to be of the order «E105 eon7.," The density of the fallback matter, representative of the crust material of the parent neutron star, is estimated to be of the order of $10^6~{\rm g~cm}^{-3}$." + Note that our MHD equaious (1))-€1 ) are uou-relativistic., Note that our MHD equations \ref{Eq-continuity}) \ref{Eq-entropy}) ) are non-relativistic. + While near the surface of the quark star sole aspects of the plivsiος will be cosiderably cliauged by relativistic ellects. we expect that the overall dyuaimics will not be vastly cilerent in a more realistic calculation.," While near the surface of the quark star some aspects of the physics will be considerably changed by relativistic effects, we expect that the overall dynamics will not be vastly different in a more realistic calculation." +" All figures shown here a'e for resolutiou 128"".", All figures shown here are for resolution $128^3$. + We have run simulations at higher resolution. but fouud that they differ little as lar ase lereetics aud evolution are concerned.," We have run simulations at higher resolution, but found that they differ little as far as energetics and evolution are concerned." + Figures 2-—3 show the evolution of the exterior magnetic field as it adjusts to the p., Figures \ref{fig:xz_plane}- \ref{fig:xy_plane} show the evolution of the exterior magnetic field as it adjusts to the vortex-confined . +" The couplicated struct weoftie surface magnetic field is clearly seen in the autimatious driveu by the freqient neieuetic ""ec'Onnecious as the surface ield tries to align itself with the interior one (rotation axis).", The complicated structure of the surface magnetic field is clearly seen in the animations driven by the frequent magnetic reconnections as the surface field tries to align itself with the interior one (rotation axis). + Tlese PalleloLL reconection events woud bear many similarities to tlie initial events those jear / . butI we expect them to be less energetic as the magnetic field slowly decays alid weakens.," These random reconnection events would bear many similarities to the initial events those near $t=0$ ), but we expect them to be less energetic as the magnetic field slowly decays and weakens." + Eveitually. tlthe nagetic field evolves itto a stable configuration (see FieoO. 2))," Eventually, the magnetic field evolves into a stable configuration (see Fig. \ref{fig:xz_plane}) )" + after which the sar euters a eJes‘ent phase., after which the star enters a quiescent phase. + The restructuriug of tje. fielc in the trausition 'egion leads to an approximatey spherical Allvénn wave traveling oitwards (see Fie., The restructuring of the field in the transition region leads to an approximately spherical Alfvénn wave traveling outwards (see Fig. + 2 [o .4 auc is more prominent lu sunuatious with a stronger maguetic field stnaller 3)., \ref{fig:xz_plane} for $t=1$ ) and is more prominent in simulations with a stronger magnetic field smaller $\beta$ ). + As dje wave travels outwards it amplifies the magnetic field in certain regions causing them to uidereο reconnection. which boαμ distorts te wave aud eveutually damps it out.," As the wave travels outwards it amplifies the magnetic field in certain regions causing them to undergo reconnection, which both distorts the wave and eventually damps it out." +" Furthermore. the regious that underwent. recoluection appear to slow slow oscillatory motious between the reconiecticin site aud the surrounding gas (""breatune”)."," Furthermore, the regions that underwent reconnection appear to show slow oscillatory motions between the reconnection site and the surrounding gas (“breathing”)." + This can be seen in the series of diminishiug pu]ses in Fig., This can be seen in the series of diminishing pulses in Fig. + 6 and the frequercy of the puses renuallis uearly coustaut (see Fig. 7))., \ref{fig:intensity_time} and the frequency of the pulses remains nearly constant (see Fig. \ref{fig:fft}) ). + We note tha these pulses appear more prominently in simulations with lower 3 and do wot arise in simulations wl hol., We note that these pulses appear more prominently in simulations with lower $\beta$ and do not arise in simulations with $\beta > 1$. + The magnetic energy released iu the organization is shown in Fig., The magnetic energy released in the organization is shown in Fig. + 6 aud cau be cast into a simple equation.," \ref{fig:intensity_time} and can be cast into a simple equation," +2002).. so we [lix 3=1.5. which is consistent with the linding of Dunne&Eales(2001). for local galaxies ancl with the values obtained. for carbonite ancl silicate grains from laboratory measurements (Aeladzeetal.1994).,", so we fix $\beta=1.5$, which is consistent with the finding of \citet{Dunne} for local galaxies and with the values obtained for carbonite and silicate grains from laboratory measurements \citep{Agladze}." +.. This leaves two free parameters to be fitted: Za and the SED normalisation., This leaves two free parameters to be fitted: $T_\mathrm{d}$ and the SED normalisation. +" ln practice we work in terms of theapparent dust temperature, Ty=Lif|z) and [it the data for eachach galaxy to Wwf2lPexp(hοπήvanaslITA)1].. where several:i factors of (1|z) have been absorbed into theapparcn/ normalisation. «Ll."," In practice we work in terms of the dust temperature, $T_\mathrm{A}=T_\mathrm{d}/(1+z)$ and fit the data for each galaxy to $A\nu_\mathrm{obs}^{3+\beta}/[\mathrm{exp}(h\,\nu_\mathrm{obs}/k\,T_\mathrm{A})-1]$, where several factors of $(1+z)$ have been absorbed into the normalisation, $A$." + Assuming that the redshift is known. the restfranc dust temperature can be recovered. and. the luminosity of the SMG. can be determined. by integrating the SED.," Assuming that the redshift is known, the restframe dust temperature can be recovered and the luminosity of the SMG can be determined by integrating the SED." + In cases where the spectroscopic redshift is ambiguous. the most reliable or probable spectroscopic. redshift) available from the literature has been chosen and is listed in Table 5..," In cases where the spectroscopic redshift is ambiguous, the most reliable or probable spectroscopic redshift available from the literature has been chosen and is listed in Table \ref{tab:tdm}." + For sources with only a 90 per cent confidence photometric redshift lower limit. the redshift is taken at this limit. (see ‘Table 4)).," For sources with only a 90 per cent confidence photometric redshift lower limit, the redshift is taken at this limit (see Table \ref{tab:sharc_photom}) )." + We characterise the shape of the SEDs independently of the photometric redshifts because we do not use the radio data in our fits to the SED. and where photometric redshifts are used they have been determined. using all available FL and radio photometry (except for the 350jim data from this oper).," We characterise the shape of the SEDs independently of the photometric redshifts because we do not use the radio data in our fits to the SED, and where photometric redshifts are used they have been determined using all available FIR and radio photometry (except for the $350\,\mathrm{\mu m}$ data from this paper)." +" Alore complex, SED modelling was not attempted (c... fitting two-temperature cust components as in Dunne&Eales 2001)). since this would require more [re xwameters than can be constrained using the typically 23 photometric points which exist for cach of our SALGs."," More complex SED modelling was not attempted (e.g., fitting two-temperature dust components as in \citealt{Dunne}) ), since this would require more free parameters than can be constrained using the typically 2--3 photometric points which exist for each of our SMGs." +" The Wien side of the spectrum is sometimes also mocilied ww a power-law of the form S,x7"" to account for the increase in optical depth in this part of the spectrum and o provide a better fit to observational cata (see. Blain.Barnard&Chapman 2003)).", The Wien side of the spectrum is sometimes also modified by a power-law of the form $S_{\nu} \propto \nu^{-\alpha}$ to account for the increase in optical depth in this part of the spectrum and to provide a better fit to observational data (see \citealt{BlainBarnard}) ). + We neglect such elaborations rere (see also Kovacsetal. 2006)). since the Wien side of the spectrum. is not sampled with our data.," We neglect such elaborations here (see also \citealt{Kovacs}) ), since the Wien side of the spectrum is not sampled with our data." + 24ji photometry are available for SILXDISZS sources but are complicated to interpret since this band samples PALL and stellar emission," $24\,\mathrm{\mu m}$ photometry are available for SHADES sources but are complicated to interpret since this band samples PAH and stellar emission" +Figure 1. for the range of coronal plasma temperatures 6.010.! times that of the brightest line (Fe XXIII A23.363) are listed in Table 4..," The full list of lines in the CHIANTI database within $5\sigma$ of the O $\alpha$ wavelength range $\pm 0.05$ from $23.37\pm +0.02$ ) with intensities $\ge 10^{-4}$ times that of the brightest line (Fe XXIII $\lambda 23.363$ ) are listed in Table \ref{t:5sigma}." + The NIST Atomic Spectra Database (version 3.1.2: 2007)) also lists two other transitions within the 5o range from Ti XIII and Se XIV., The NIST Atomic Spectra Database (version 3.1.2; ) also lists two other transitions within the $5\sigma$ range from Ti XIII and Sc XIV. + Neither ol these are expected to be of any significance since (heir solar abundances according to the GS assessment are 300 and 21000 lower than that of Fe. respective=," Neither of these are expected to be of any significance since their solar abundances according to the GS assessment are 300 and 21000 lower than that of Fe, respectively." + The equivalent width (EW) of the O Ixa line relative to coronal [norescing spectra with GS abundances is illustrated in Figure 3. for a range of isothermal plasma. temperatures and different photospheric O abundances., The equivalent width (EW) of the O $\alpha$ line relative to coronal fluorescing spectra with GS abundances is illustrated in Figure \ref{f:ew} for a range of isothermal plasma temperatures and different photospheric O abundances. + The Monte Carlo sampling error on the computed EWs is estimated to be no larger than 7%., The Monte Carlo sampling error on the computed EWs is estimated to be no larger than . +.. One striking leature of the trend of EW with T lov all compositions is the sharp decline with rising temperature for log7356.6: this contrasts with both Ne Ίνα and Fe Ίνα. whose EWs exhibit a steady. monotonic rise with increasing LT (Papers 1 II). corresponding (o a commensurate increase in the number of ionising photons.," One striking feature of the trend of EW with $T$ for all compositions is the sharp decline with rising temperature for $\log T\la 6.6$: this contrasts with both Ne $\alpha$ and Fe $\alpha$, whose EWs exhibit a steady, monotonic rise with increasing $T$ (Papers I II), corresponding to a commensurate increase in the number of ionising photons." + The different behaviour of O Ίνα arises because. for coronal plasmas with logT'S6.6 and solar composition. K-shell photoionisation of oxvgen is due mostly to line rather than continuum radiation.," The different behaviour of O $\alpha$ arises because, for coronal plasmas with $\log T\la 6.6$ and solar composition, K-shell photoionisation of oxygen is due mostly to line rather than continuum radiation." + Toward hotter temperatures. (he important emitting photoionising species. including O VII and O VILI. become ionised. and continuum contributions begin to dominate.," Toward hotter temperatures, the important line-emitting photoionising species, including O VII and O VIII, become ionised, and continuum contributions begin to dominate." + Regarcing sensitivitv to O abundance. Figure 3. illustrates that the EW changes by a smaller [actor (han expected based on a proportional relation with the photospheric the O abundance.," Regarding sensitivity to O abundance, Figure \ref{f:ew} illustrates that the EW changes by a smaller factor than expected based on a proportional relation with the photospheric the O abundance." + As discussed by and in Paper 1. this is à result of the the O photoionisation cross-section being a significant component of the total opacily near threshold: for verv large O abundances where O begins (o dominate the opacity. the EW will tend to a constant value dictatedsimply by equipartition of ionising photons between O Ix-and L-shells.," As discussed by and in Paper I, this is a result of the the O K-shell photoionisation cross-section being a significant component of the total opacity near threshold: for very large O abundances where O begins to dominate the opacity, the EW will tend to a constant value dictatedsimply by equipartition of ionising photons between O K-and L-shells." + Nevertheless. for “normal” ranges of O abundance the O Ίνα line variations," Nevertheless, for “normal” ranges of O abundance the O $\alpha$ line variations" +the Jeans length. itself could be significantly. increased due to the weakening of gravity in certain models by a large value of the JBD field in the early universe.,the Jeans length itself could be significantly increased due to the weakening of gravity in certain models by a large value of the JBD field in the early universe. + Nevertheless. a strong (first order) inflationary phase transition in extended inflation models. driven. by the JBD field (La&Stein-1993:Majumcdar1997). naturally leads to unnucleated and trapped false vacuum regions ancl topological defects such as domain walls anc wormboles that could. easily. collapse into black holes. and could also create super-horizon density perturbations.," Nevertheless, a strong (first order) inflationary phase transition in extended inflation models driven by the JBD field \citep{extended2,asm11,asm12,asm13} naturally leads to unnucleated and trapped false vacuum regions and topological defects such as domain walls and wormholes that could easily collapse into black holes, and could also create super-horizon density perturbations." + The formation of super-horizon scale PBIIs in the expanding FRW background has been studied. recently (ανασα&Carr2005b)., The formation of super-horizon scale PBHs in the expanding FRW background has been studied recently \citep{harada3}. +. In the present. analysis we will not take recourse to any particular formation mechanism for PBUs. but rather study their cosmological evolution in JBD theory. assuming that there exist PBIIs in such scenarios.," In the present analysis we will not take recourse to any particular formation mechanism for PBHs, but rather study their cosmological evolution in JBD theory, assuming that there exist PBHs in such scenarios." + We now consider the evolution of PBIIs in. the cosmological background. governed. by the above solutions (5)).06)) and (7)), We now consider the evolution of PBHs in the cosmological background governed by the above solutions \ref{rdsoln1}) \ref{rdsoln2}) ) and \ref{rdsoln3}) ). + We assume that the PDII density. is low enough to ensure radiation domination., We assume that the PBH density is low enough to ensure radiation domination. + For a PBIL immersed in the radiation field. the accretion of radiation leads to the increase of its mass with the rate given by ἀπ bay where req=2Mo is the black hole radius. and. f. ds the accretion elliciencv.," For a PBH immersed in the radiation field, the accretion of radiation leads to the increase of its mass with the rate given by = f _R where $r_{BH}=2M/\phi$ is the black hole radius, and $f$ is the accretion efficiency." + Using the solution for ó given by I2q.(6))with the assumption of Ja;|«1. and using pi=(3M) (32s17)]. one obtains where B=(3f)(287 M5. ]5q.(9))," Using the solution for $\phi$ given by \ref{rdsoln2}) )with the assumption of $|\omega_i| \ll 1$, and using $\rho_R = [(3M_{pl}^2)/(32\pi t^2)]$ , one obtains = where $B=(3f)/(2\xi^2M_{pl}^2t_i)$ . \ref{accr2}) )" + is integrated. to vield | with AJ; being the initial mass of the PDII at time πι, is integrated to yield = with $M_i$ being the initial mass of the PBH at time $t_i$. +" Since the logarithmic growth rate for a PDII given by LEq.(10)) is subdominant to the linear growth of the horizon mass Mg4 (since a~ 117), once a PBLL is formed. it is indeed: possible for it to grow in size by accreting the radiation energv within its cosmological horizon."," Since the logarithmic growth rate for a PBH given by \ref{accr3}) ) is subdominant to the linear growth of the horizon mass $M_H \sim t$ (since $a \sim t^{1/2}$ ), once a PBH is formed, it is indeed possible for it to grow in size by accreting the radiation energy within its cosmological horizon." + Fora complete picture of PBL evolution. one needs also to consider the Hawking evaporation process. whose rate is eiven by ἀπό o1 where 7=6/(SrAL) is the Hawking temperature. e theStelan-Boltzmann constant and g is the elfective number of degrees of freedom of the particles emitted by the black hole.," For a complete picture of PBH evolution, one needs also to consider the Hawking evaporation process, whose rate is given by = - g ^2 T^4 where $T=\phi/(8\pi M)$ is the Hawking temperature, $\sigma$ theStefan-Boltzmann constant and $g$ is the effective number of degrees of freedom of the particles emitted by the black hole." +" The solution for ó given by Eq.(6)) Leads to where ef=(gotΑμ,(25677).", The solution for $\phi$ given by \ref{rdsoln2}) ) leads to = where $A = (g \sigma \xi^2 M_{pl}^4 t_i)/(256\pi^3)$. + The complete evolution for the PBIL is thus described bv the combination of Eqs.(9)) and (12)): | ]t is apparent [rom l.2q.(13)) that. for PBIIs with initial mass AM;<<(ASB). the rate. of evaporation exceeds that of acerction.," The complete evolution for the PBH is thus described by the combination of \ref{accr2}) ) and \ref{evap2}) ): = + It is apparent from \ref{bheq}) ) that for PBHs with initial mass $M_i << (A/B)^{1/4}$, the rate of evaporation exceeds that of accretion." + For such a case. accretion soon becomes negligible and. black holes lose energy at a rate given cllectively by Eq.(12)).," For such a case, accretion soon becomes negligible and black holes lose energy at a rate given effectively by \ref{evap2}) )." + Note that though the rate of evaporation decreases with time. it is still higher than the corresponding rate in standard. cosmology.," Note that though the rate of evaporation decreases with time, it is still higher than the corresponding rate in standard cosmology." + “Phis is because the Hawking temperature 2—óf(S2À) is larger for JBD PDlls for large o., This is because the Hawking temperature $T=\phi/(8\pi M)$ is larger for JBD PBHs for large $\phi$. + Hence. a PBI with initial mass M;CA/D)E4 experience monotonic growth with accretion dominating over evaporation throughout the period of validity of Eq.(18)). Le. throughout the radiation. dominated. era. q.(13))," Hence, a PBH with initial mass $M_i < (A/B)^{1/4}$ evaporates out much quicker, with a lifetime $t_{evap}$ given by = ] However, PBHs with initial mass $M_i > (A/B)^{1/4}$ experience monotonic growth with accretion dominating over evaporation throughout the period of validity of \ref{bheq}) ), i.e., throughout the radiation dominated era. \ref{bheq}) )" + can be integrated exactly and leads to the following mass-time relationship for the PDlIs: with €'=A/B., can be integrated exactly and leads to the following mass-time relationship for the PBHs: ) = ) - + with $C=A/B$. +" Aceretion of radiation can proceed ellectively till the universe stays raciation dominated. Ίο. up to the cra of matter radiation equality /,,."," Accretion of radiation can proceed effectively till the universe stays radiation dominated, i.e., up to the era of matter radiation equality $t_{eq}$." + Phis result is qualitatively different. [rom the widely accepted: picture in the standard. cosmological evolution. where accretion of radiation in the radiation dominated. era. seems to he inelfective (Carr2003).., This result is qualitatively different from the widely accepted picture in the standard cosmological evolution where accretion of radiation in the radiation dominated era seems to be ineffective \citep{pbh}. +. The domination of accretion over evaporation is observed also in other modified. gravity theories. such. asin the braneworlc scenario (Majumcar 2005)...," The domination of accretion over evaporation is observed also in other modified gravity theories, such asin the braneworld scenario \citep{brane1,brane2,brane3,brane4}. ." + Phe maximum mass achieved by a PBI of initial mass AJ; is given by MiB In the matter dominated cra. pur~e and p= 0.A set of solutions for the JBD cosmological equations (2)). 03)) wacl (4)) is given by (Sahoo&Singh2002.2003) a(t)," The maximum mass achieved by a PBH of initial mass $M_i$ is given by In the matter dominated era, $\rho_M \sim a^{-3}$ and $p=0$ A set of solutions for the JBD cosmological equations \ref{fe}) ), \ref{eqmotion}) ) and \ref{enconv}) ) is given by \citep{sahoo1,sahoo2} + a(t) =" +between plauetesimals become destructive.,between planetesimals become destructive. + Such collisions eject umimerous fragments. which collide with cach other to produce further znaller bodies.," Such collisions eject numerous fragments, which collide with each other to produce further smaller bodies." + Planctesimals are therefore ground down through such successive collisions (collision cascade)., Planetesimals are therefore ground down through such successive collisions (collision cascade). + The randoni velocities of small bodies are strongly damped by eas drag and thereby the collisiona cascade no longer occurs for fragments with radii =1 l0im.," The random velocities of small bodies are strongly damped by gas drag and thereby the collisional cascade no longer occurs for fragments with radii $\la 1$ $10\,{\rm m}$." + In the end such fragmoeuts drift iis due fo gas drag and are lost around enibrvos., In the end such fragments drift inward due to gas drag and are lost around embryos. + The collisional cascade combined with the loss of fragmicnts reduces the solid surface density au ence final enibryo lasses., The collisional cascade combined with the loss of fragments reduces the solid surface density and hence final embryo masses. +" Large planctesimals. which are relatively hard o be broken collisionally, oxoduce massive final eiibryos."," Large planetesimals, which are relatively hard to be broken collisionally, produce massive final embryos." + collisional fragmientatiou nales it difficult to orn giant plaucts along the lines of the core-aceretion model starting from αι lauetesuuals. planetary cuabrvos cau reach the critical core mass for gas accretion ouly inside LAAU iu a disk that is 10 times more massive han the MMSN model.," collisional fragmentation makes it difficult to form giant planets along the lines of the core-accretion model; starting from km-sized planetesimals, planetary embryos can reach the critical core mass for gas accretion only inside AU in a disk that is 10 times more massive than the MMSN model." +The motion of fragments < Lum is coupled with eas.,The motion of fragments $\la 1$ m is coupled with gas. + The drift timescale of such fragiuecuts are relatively] loue., The drift timescale of such fragments are relatively long. + EKeuvouY&Bromley(2009): proposed⋅:↴ thati. enibrvosuM: may AVOO⊲↽≜↦⋅accre a larec αλλο! of such fragments., \citet{kenyon09} proposed that embryos may accrete a large amount of such fragments. + However. the strong eas drag iu the Stokes reguue is dominant for fragments < θά and damps the relative velocities to. halt collision. cascade at qo Oni asac mentioned above.," However, the strong gas drag in the Stokes regime is dominant for fragments $\la 100$ m and damps the relative velocities to halt collision cascade at $1$ $10\,$ m as mentioned above." + Therefore. oulv à πα. amouit of: coupled bodies: are produced. aud. hence. they hardly coutribute: to embryo erowth↜ (Ixobavashi-:etal.al2010)2," Therefore, only a small amount of coupled bodies are produced and hence they hardly contribute to embryo growth \citep{kobayashi+10}." + ∙∙ Mauy authors have investigated embryo erowth with N-body. statistical. and lybricl siuulatious (KokuboA.€&Ida1996.oten1998.Αλὃν2000.-2002:In—-M: un ↕∖⊲≽↴⋝⋮↕⋮↖↽⋮↕⋝↕↓↕⋠∖↾⋮↕↕∙⋮∩↓↭∙∙⋎⋯⋯∏⋮↴∙↜↕," Many authors have investigated embryo growth with $N$ -body, statistical, and hybrid simulations \citep{kokubo96,kokubo98,kokubo00,kokubo02,inaba99,inaba01,inaba03,weidenschilling97,weidenschilling05,weidenschilling08,kenyon04,kenyon08,chambers06,chambers08,kobayashi+10}." +↓⋯⋅↭↖↽↕⋠∏∐⋮↴∙⋡∐⊲⋋∖↴ :accurate dynamical:ὲ results.sults. N-bodyV- simulations:ὲ have difiiculty in producing numerous fragmieuts and following their fate.," Although providing most accurate dynamical results, $N$ -body simulations have difficulty in producing numerous fragments and following their fate." + The fragmentation effec on enibrvo erowth las thus not been treated in detail iu spite of its importance., The fragmentation effect on embryo growth has thus not been treated in detail in spite of its importance. + Recently. Levison ct al. (," Recently, Levison et al. (" +2010) included fraginent production in their N-body simulation.,2010) included fragment production in their $N$ -body simulation. + However. it is still dificult to treat fragment collisions.," However, it is still difficult to treat fragment–fragment collisions." + Such successive collisions are essential in the collision cascade (e.g...Ikobavashi&Tanaka2010).," Such successive collisions are essential in the collision cascade \citep[e.g.,][]{kobayashi10}." + Therefore. statistical simulations are a better method to accurately investigate planet formation with fragmentation.," Therefore, statistical simulations are a better method to accurately investigate planet formation with fragmentation." +" Iu the statistical simulation. the collisional mass evolution of bodies is calculated within a ""particle-iu-a-box approximation."," In the statistical simulation, the collisional mass evolution of bodies is calculated within a ``particle-in-a-box'' approximation." + Bodies have horizoutal and vertical compoucuts of random velocity relative to a circular orbit that are determined by heir eccentricities aud inclinations. respectively.," Bodies have horizontal and vertical components of random velocity relative to a circular orbit that are determined by their eccentricities and inclinations, respectively." + These velocities are changed by gravitational interactions between the bodies aud hence affected w their mass spectrum. while the collision rates vetween the bodies depend on the velocitics.," These velocities are changed by gravitational interactions between the bodies and hence affected by their mass spectrum, while the collision rates between the bodies depend on the velocities." + Therefore. the coupled mass aud velocity evolution reeds to be solved (Wetherill&Stewart1993).," Therefore, the coupled mass and velocity evolution needs to be solved \citep{wetherill93}." +" While the statistical method has advantages. its weak poiut is the inability to track the individual vositions of planctesimals,"," While the statistical method has advantages, its weak point is the inability to track the individual positions of planetesimals." + However. progress m dlanctary dyvuaiic theory (Creenzweig&Lissauerart&Ida2000:Olitsukietal.2002) has helped to this problemi.," However, progress in planetary dynamic theory \citep{greenzweig92,ida89,Ohtsuki99,stewart00,Ohtsuki02} + has helped to overcome this problem." + For example. Greenzweigovercome&Lissancr(1992) and Ida&Nakazawa(1989) provided'ovided detailed expressions for the probability of ⋯∐↴∖↴↕∪∐↴∖↴↴⋝↸∖↑↖↖↽↸∖↸∖∐≻↕⋜⊔∐∖↑↸∖↴∖↴↕↕⊔⋜↧↴∖↴∪↥⋅⋝↕↑↕↕∩⊾⋜⊓⊳↸∖∐⊓⋅⋜↧↕ e star. while Stewart&Ida(2000). and Ohtsulàetal(2002) derived improved equations for ↸⊳⋜⊓⊳∏↕⋜↧↑↕∐∶↴∙⊾↑∐↸∖↸∖↖⇁∪↕∏↑↕∪∐∪↕⋟↥⋅⋜⋯≼↧∪⊔↻↕⋜∐∐∖↑↸∖↴∖↴↕⋯⋜↧↕ velocities∙∙ caused bv gravitational∙∙ iuteractions.," For example, \citet{greenzweig92} and \citet{ida89} provided detailed expressions for the probability of collisions between planetesimals orbiting a central star, while \cite{stewart00} and \citet{Ohtsuki02} derived improved equations for calculating the evolution of random planetesimal velocities caused by gravitational interactions." +∙ ∙ . ⊡⋯∐↖⇁∙↕↑∐⋜↧↴∖↴↴⋝↸∖↸∖∐↴∖↴∐∪↖↖⇁∐↑∐⋜↧↑∐↸∖↥⋅↸∖↸⊳↸∖∐↑↕↖↽ developed.leveloped statistic:statistical codesdes can6 describedescri sonen miaspects of the psplanetary Ufaccumulationv 1processes with the same accuracy as N-body simulations∙ ⋖↕∐⋜⊔⋜⊔∖↑⋜↧↕∙⊇∣∩↓∶↕↘∪⋝⋜↧∙↖↽⋜↕," Finally, it has been shown that the recently developed statistical codes can describe some aspects of the planetary accumulation processes with the same accuracy as $N$ -body simulations \citep{inaba01,kobayashi+10}." +↴∖↴↕∐↸∖↑⋜↧↕∙⊇∩↓↭∙∙ Since the timescale of collision cascade strongly affects the fiual mass of planetary embryos (IKobavasliietal. 2010).. fraginentation outcome models are essential DUfor embryo erowth.," Since the timescale of collision cascade strongly affects the final mass of planetary embryos \citep{kobayashi+10}, , fragmentation outcome models are essential for embryo growth." + Collisional. fraguicutation. includes∙ several uucertain∙ parameters., Collisional fragmentation includes several uncertain parameters. + Robavashi‘: consta ∖simple ∖⊳⋅⋠⋅⋉∖⊀⋅fragincutation model which is consistent with ctodalaboratory experiments (Fujiwaractal.1977:Takaeiet1981:Tol and hydrodyuanücal simulatious (Benz&Asphaug1999) aud analvtically clarified," \citet{kobayashi10} + constructed a simple fragmentation model which is consistent with laboratory experiments \citep{fujiwara,takagi,holsapple} and hydrodynamical simulations \citep{benz99} and analytically clarified" +must move at the speed. of light opposite the rotation of the DIL just in order to stay still.,must move at the speed of light opposite the rotation of the BH just in order to stay still. + Inside the creosphere. the space-time itself is dragged in the direction of the BIL rotation: Le.. nothing can stay there at rest with respect to distant observers. but it must orbit the DII in the same direction in which the DII rotates.," Inside the ergosphere, the space-time itself is dragged in the direction of the BH rotation; i.e., nothing can stay there at rest with respect to distant observers, but it must orbit the BH in the same direction in which the BH rotates." + This process is called the drageing of inertial frames (e.g..?)..," This process is called the dragging of inertial frames \citep[e.g.,][]{mtw73}." + The DBII-disc magnetic connection. first mentioned. by Zeldovich Schwartzman ancl quoted.in. 2.. can occur and change the encrev-angular-momentum balance of the accreting gas in the dise (e.g.2???)," The BH-disc magnetic connection, first mentioned by Zel'dovich Schwartzman and quotedin \citet{t74}, can occur and change the energy-angular-momentum balance of the accreting gas in the disc \citep[e.g.,][]{mt,membrane,bland99,vanPutten99}." + ??7 derived the equations for the energy and angular momentum transferred rom a lIxerr. BI to a geometrically-thin accretion disc (which consists of a hiehly-concducting ionised eas) by magnetic connection. and we shall use these equations. ," \citet{li00a,li00b,li02} derived the equations for the energy and angular momentum transferred from a Kerr BH to a geometrically-thin accretion disc (which consists of a highly-conducting ionised gas) by magnetic connection, and we shall use these equations. [" +See also the work by 2.],See also the work by \citet{wang02}. .] + As the DIE rotates relative to he disc. an electromotive force is generated.," As the BH rotates relative to the disc, an electromotive force is generated." + This drives a poloidal electric current flowing through the BII and the disc ancl produces an additional power on the disc., This drives a poloidal electric current flowing through the BH and the disc and produces an additional power on the disc. + From he conservation laws of energy and angular momentum for a hin Ixeplerian accretion disc torqued by a BLL. 2. caleulated he radiation Hux. the internal viscous torque and the total »ower of the disc. and found that the disc can radiate even without accretion.," From the conservation laws of energy and angular momentum for a thin Keplerian accretion disc torqued by a BH, \citet{li02} calculated the radiation flux, the internal viscous torque and the total power of the disc, and found that the disc can radiate even without accretion." + ? also looked. for observational signatures of the Bll-clise magnetic connection as more energy is raciated away from the disc and showed that the magnetic connection can produce a very steep emissivity compared to the standard. thin-aceretion disc model.," \citet{li02L} also looked for observational signatures of the BH-disc magnetic connection as more energy is radiated away from the disc and showed that the magnetic connection can produce a very steep emissivity compared to the standard, thin-accretion disc model." + 77 obtained the numerical solution of the Cirad-Shafranov equation for a Bll-clise magnetie-connection configuration in the case of both Sehwarzschild ancl Werr 1115.," \citet{uzdensky04,uzdensky05} obtained the numerical solution of the Grad-Shafranov equation for a BH-disc magnetic-connection configuration in the case of both Schwarzschild and Kerr BHs." + The Crad-Shafranov equation is a non-linear. partial differential equation that. describes the magnetic Lux distribution of plasma in an axisvmmetric svstem.," The Grad-Shafranov equation is a non-linear, partial differential equation that describes the magnetic flux distribution of plasma in an axisymmetric system." + Uzdensky found that this Bll-clise magnetic connection can only be maintained very close to the DII (see in the next section)., Uzdensky found that this BH-disc magnetic connection can only be maintained very close to the BH (see in the next section). + In recent vears. a number of models that also include the Bll-cise magnetic connection have been developed.," In recent years, a number of models that also include the BH-disc magnetic connection have been developed." + A DII magnetic field. configuration with both open and closed: magnetic [eld lines was considered. by 2.. who described. the Ποιά configuration by the hall-opening angle of the magnetic [ux tube on the horizon. which is determined by the mapping relation between the angular coordinate on the BL horizon and the radial coordinated on the accretion disc.," A BH magnetic field configuration with both open and closed magnetic field lines was considered by \citet{lei05}, who described the field configuration by the half-opening angle of the magnetic flux tube on the horizon, which is determined by the mapping relation between the angular coordinate on the BH horizon and the radial coordinated on the accretion disc." + ?. proposed a tov model for the magnetic connection. in which case a poloidal magnetic field is generated by a single electric current flowing in the equatorial plane around a Werr BIL.," \citet{wang} proposed a toy model for the magnetic connection, in which case a poloidal magnetic field is generated by a single electric current flowing in the equatorial plane around a Kerr BH." + ? derived the energv and angular momentum Iluxes for a Were DII surrounded by an aclvection-clominatecl accretion disc., \citet{ma07} derived the energy and angular momentum fluxes for a Kerr BH surrounded by an advection-dominated accretion disc. + “To solve the equations of the aceretion [low. they used a pseudo-Newtonian potential.," To solve the equations of the accretion flow, they used a pseudo-Newtonian potential." + 7. solved the cvnamic equations for à disc-corona system. and. simulated. its N-rav spectra by using the Monte Carlo method., \citet{gan09} solved the dynamic equations for a disc-corona system and simulated its X-ray spectra by using the Monte Carlo method. + ?/— studied the magnetic field. configuration. generated. by a toroidal clistributed continuously in a thin aceretion disc. as well as the role of magnetic reconnection in the cise το produce quasi-periodic oscillations in DII binaries.," \citet{zhao09} studied the magnetic field configuration generated by a toroidal distributed continuously in a thin accretion disc, as well as the role of magnetic reconnection in the disc to produce quasi-periodic oscillations in BH binaries." + In the context of GIAMLILD. ? presented a 22D (ΑΔΗΠΟ result of jet formation driven by à magnetic field produced by a current loop near à rapidly-rotating DII. in which case the magnetic Lux tubes connect the region between the BIL ergosphere and a co-rotating accretion disc.," In the context of GRMHD, \citet{shinji06} presented a 2-D GRMHD result of jet formation driven by a magnetic field produced by a current loop near a rapidly-rotating BH, in which case the magnetic flux tubes connect the region between the BH ergosphere and a co-rotating accretion disc." + Furthermore. relativistic Povnting jets driven from the inner region of an accretion disc that is initially threaded by a dipole-like magnetic field were studied by ον.," Furthermore, relativistic Poynting jets driven from the inner region of an accretion disc that is initially threaded by a dipole-like magnetic field were studied by \citet{lovelace03}." +" Their model is derived. from the special relativistic equation for a force-[ree electromagnetic Ποιά, ", Their model is derived from the special relativistic equation for a force-free electromagnetic field. [ +See also το.),"See also \citet{lynden-bell96,lynden-bell03}. .]" + In this paper. we propose a model for launching relativistic jets from a (geometricallv-thin) disc inside the ergosphere as an οσοι of the rotation of the space-time.," In this paper, we propose a model for launching relativistic jets from a (geometrically-thin) disc inside the ergosphere as an effect of the rotation of the space-time." + We consider here the Bll-cdise magnetic connection. whose main role is to provide the source of energy for the jets when the mass accretion rate is very low.," We consider here the BH-disc magnetic connection, whose main role is to provide the source of energy for the jets when the mass accretion rate is very low." + We use the general relativistic form of the conservation laws for the matter in à thin accretion disc to describe the disc structure when both the DBlI-disc magnetic connection and the jet formation are considered., We use the general relativistic form of the conservation laws for the matter in a thin accretion disc to describe the disc structure when both the BH-disc magnetic connection and the jet formation are considered. + The mocdel is based on the calculations of ?.. and 2.. being mainly inlluenced by the work of 7. and ?.. ," The model is based on the calculations of \citet{nt}, \citet{pt} and \citet{li02}, being mainly influenced by the work of \citet{znajek78} and \citet{mt}. [" +Some incipient ideas which are at the base of this model were exposed in. 22..],"Some incipient ideas which are at the base of this model were exposed in \citet{eu04,eu05}. .]" + Vhis is the first work that studies the »ocess of jet launching from a gcometrically-thin accretion disc inside the DII ergosphere when the energy and angular momentum: are transferred. (rom the DII to this region of he accretion disce via closed magnetic field lines. within the ramework of general relativity.," This is the first work that studies the process of jet launching from a geometrically-thin accretion disc inside the BH ergosphere when the energy and angular momentum are transferred from the BH to this region of the accretion disc via closed magnetic field lines, within the framework of general relativity." + An important result of the model. with impact on observation of the AGN jets. is tha he power of the jets does not depend linearly on the mass accretion rate all the wav down to very low accretion rates or Bs of a given mass.," An important result of the model, with impact on observation of the AGN jets, is that the power of the jets does not depend linearly on the mass accretion rate all the way down to very low accretion rates for BHs of a given mass." + This result is cillerent from that of 7.. who found a linear dependence between the power of the jet and the mass aceretion rate by considering a spherica Doncdi-tvpe accretion on to DlIs (in which case the accreting matter has zero or very low angular momentum).," This result is different from that of \citet{allen06}, who found a linear dependence between the power of the jet and the mass accretion rate by considering a spherical Bondi-type accretion on to BHs (in which case the accreting matter has zero or very low angular momentum)." + In their calculations. the power of the jet is estimated. from. the energy and time scale required to inflate the cavity observed in the surrounding X-ray emitting gas.," In their calculations, the power of the jet is estimated from the energy and time scale required to inflate the cavity observed in the surrounding X-ray emitting gas." +" Phe model proposed here combines two regimes associated with the driving of the jets. an accretion power regime and a (DII) spin-down power regime. where the switeh from the former to the latter regime corresponds to à mass accretion rate of ii—10.17,"," The model proposed here combines two regimes associated with the driving of the jets, an accretion power regime and a (BH) spin-down power regime, where the switch from the former to the latter regime corresponds to a mass accretion rate of $\dot{m}\sim 10^{-1.8}$." + In the aceretion power regime. the power of the jets is linearly dependent on the mass aceretion rate. whereas in the spin-down power regime the power of the jets depends very weakly on the mass aceretion rate.," In the accretion power regime, the power of the jets is linearly dependent on the mass accretion rate, whereas in the spin-down power regime the power of the jets depends very weakly on the mass accretion rate." + In the accretion power regime. the energy and. angular momentum. are extracted and transported away from the dise inside the DII ergosphere by both the kinetic Dux of particles and Povnting lux in the [orm of jets.," In the accretion power regime, the energy and angular momentum are extracted and transported away from the disc inside the BH ergosphere by both the kinetic flux of particles and Poynting flux in the form of jets." + Instead. in the spin-down power regime the energv and angular momentum are extracted. and. carried away [rom the dise inside the ergosphere. predominantly in the form of Poynting flux. with just little. amount of kinetic Dux of particles.," Instead, in the spin-down power regime the energy and angular momentum are extracted and carried away from the disc inside the ergosphere predominantly in the form of Poynting flux with just little amount of kinetic flux of particles." + The work presented in this paper is different from that of 2.. in whieh the production. of 'ovnting Hux jets is associated. with a combination of the BlanclordZnajek mechanism. the Bll-cise connection and he Blandford.Payne mechanism.," The work presented in this paper is different from that of \citet{wang08}, in which the production of Poynting flux jets is associated with a combination of the Blandford–Znajek mechanism, the BH-disc connection and the Blandford–Payne mechanism." + Furthermore. we argue hat the accretion. which is initially at either close to the I5ddington rate or at low rates. can be driven in à non- geometrically thin ancl quasi-Ixeplerian cise inside he BIL cregosphere by the external jet. torque.," Furthermore, we argue that the accretion, which is initially at either close to the Eddington rate or at low rates, can be driven in a non-radiant, geometrically thin and quasi-Keplerian disc inside the BH ergosphere by the external jet torque." + “Phis is distinctly different from optically thin. adyection-dominated accretion flow models (c.g.. 2).. in which the accretion at ow rates is advection-dominated. (i.c.. the thermal energy generated via viscous dissipation is mostlv retained by the acereted mass [low rather than being racliated. and the," This is distinctly different from optically thin, advection-dominated accretion flow models \cite[e.g.,][]{narayan94}, , in which the accretion at low rates is advection-dominated (i.e., the thermal energy generated via viscous dissipation is mostly retained by the accreted mass flow rather than being radiated, and the" +get an even better formula which works very well for /j<0.3.,get an even better formula which works very well for $\fll<0.3$. +" Thus we find an approximation: . and tin 15 found from Aya, and equation 5..", Thus we find an approximation: where and $\umin$ is found from $\Amax$ and equation \ref{eqn:u_of_a}. +" In using this formula, one typically starts with measured values of {ως A5,,. and an initial guess of Aj; and uses different (unknown) values of fj, to find the corresponding underlying Ana, and /p."," In using this formula, one typically starts with measured values of $\tep$, $\Amaxp$ , and an initial guess of $\Amax$ and uses different (unknown) values of $\fll$, to find the corresponding underlying $\Amax$ and $\te$." +" Ifthe value of 4,444 found using the new fitting formula is smaller than 3, then one should use the HDE formula instead."," If the value of $\Amax$ found using the new fitting formula is smaller than 3, then one should use the HDE formula instead." +" The new filing formula is shown as the solid line in Figure 2 and does better than HDE or WP lor A4,>3.", The new fitting formula is shown as the solid line in Figure 2 and does better than HDE or WP for $\Amax>3$. +" Over the range 0.0132 and A’Wax>1.31. while the old HDE formula works better for low values of μις and / Aj."," In summary, we tested the HDE formula, and (WP) formulas and Equation \ref{eqn:quadfitnum} over a wide range of parameters and found the new fitting function works better than HDE for all values of $\fll$ when $\Amax>3$ and $\Amaxp>1.34$, while the old HDE formula works better for low values of $\Amax$ and $\Amaxp$ ." +" The WP large Aas formula gives/j within only for large fj 0.5), and large «μμ. while the other WP formula is not useful except forA4,< L3"," The WP large $\Amax$ formula gives$\te$ within only for large $\fll (>0.5$ ), and large $\Amax$ , while the other WP formula is not useful except for$\Amax \ll 1.34$ ." +"limit of £44,> 4+ Myr for the expansion time (Tomisaka Ikeuchi 1988).",limit of $t_\mathrm{exp} >$ 4 Myr for the expansion time (Tomisaka Ikeuchi 1988). + We estimate the mechanical energy input by the starburst into the superbubble from the emitted Ha radiation using the shock model by Binette et al. (, We estimate the mechanical energy input by the starburst into the superbubble from the emitted $\alpha$ radiation using the shock model by Binette et al. ( +1985).,1985). +" They calculated the radiative cooling mechanism of shock-heated gas. emitting optical line radiation. and found that Lj,z μαι."," They calculated the radiative cooling mechanism of shock-heated gas, emitting optical line radiation, and found that $L_\mathrm{H\alpha} \approx$ $^{-2} L_\mathrm{mech}$ ." +" With Ly, 26.610! erg 1 for NGC 4410 (MB93) this leads to Lua~ ere |.", With $L_\mathrm{H\alpha}$ = erg $^{-1}$ for NGC 4410 (MB93) this leads to $L_\mathrm{mech} \approx$ erg $^{-1}$. + Applying 10°! erg for the energy release per and taking into account that roughly only is converted into mechanical luminosity we derive a rate of 10 |., Applying $^{51}$ erg for the energy release per and taking into account that roughly only is converted into mechanical luminosity we derive a rate of $\sim$ 1.0 $^{-1}$. + Under the simplified consideration of a spherically expanding gas one can estimate its density., Under the simplified consideration of a spherically expanding gas one can estimate its density. + With the scaling factor of the RS model and setting the electron density equal to the hydrogen density we get the following expression for the electron density of the hot gas: where JNjs is the scaling factor. D ts the distance to the source. ris the radius of the superbubble and f is a filling factor taking into account that the hot gas is not distributed homogeneously but broken up into separate bubbles.," With the scaling factor of the RS model and setting the electron density equal to the hydrogen density we get the following expression for the electron density of the hot gas: where $N_{RS}$ is the scaling factor, $D$ is the distance to the source, $r$ is the radius of the superbubble and $f$ is a filling factor taking into account that the hot gas is not distributed homogeneously but broken up into separate bubbles." + With the parameters of D = 97 Mpe. r = 4 kpe. Nga = em? and an assumed filling factor of 0.1 one obtains an electron density of 0.03 ?.," With the parameters of $D$ = 97 Mpc, $r$ = 4 kpc, $N_{RS}$ = $^5$ and an assumed filling factor of 0.1 one obtains an electron density of 0.03 $^{-3}$." + Changing the filling factor to f = 0.9 leads to η = 0.01 5m , Changing the filling factor to $f$ = 0.9 leads to $n_e$ = 0.01 $^{-3}$ . +An expansion time of 10* yr with a halo gas density of 0.01 ? leads to an X-ray luminosity of the shell of eres. 1., An expansion time of $^7$ yr with a halo gas density of 0.01 $^{-3}$ leads to an X-ray luminosity of the shell of erg $^{-1}$. + A lower rate of 0.5 + and a slightly smaller expansion time of yr reduce the obtained X-ray luminosity to erg ! in the ROSAT band., A lower rate of 0.5 $^{-1}$ and a slightly smaller expansion time of yr reduce the obtained X-ray luminosity to erg $^{-1}$ in the ROSAT band. +" The derived plasma temperature of 10"" K lies at the upper bound of the range with log T = 6.0 — 6.9 found by S94 for the (0.1—2.2) keV band.", The derived plasma temperature of $^{7}$ K lies at the upper bound of the range with log $T$ = 6.0 – 6.9 found by S94 for the (0.1–2.2) keV band. + For a Salpeter IMF. a activity between 10 and 100 and a SN rate of 0.5 ! the star formation rate results to —95 M. +.," For a Salpeter IMF, a activity between 10 and 100 $_{\sun}$ and a SN rate of 0.5 $^{-1}$ the star formation rate results to $\sim$ 95 $_{\sun}$ $^{-1}$." + Depending on the fraction of the mechanical energy release of a this value can increase up to a factor of 5., Depending on the fraction of the mechanical energy release of a this value can increase up to a factor of 5. + Each galaxy and. in particular. mergers. galaxy pairs or SB galaxies are unique systems.," Each galaxy and, in particular, mergers, galaxy pairs or SB galaxies are unique systems." + In order to get an insight on whether NGC 4410 and its derived structures are somehow typical for close encounters. we compare the derived X-ray luminosity in the ROSAT band with other disturbed and isolated SB galaxies.," In order to get an insight on whether NGC 4410 and its derived structures are somehow typical for close encounters, we compare the derived X-ray luminosity in the ROSAT band with other disturbed and isolated SB galaxies." + The peculiar galaxy NGC 2782 e.g. is thought to be a merger of two disk galaxies of unequal mass and has Ly 24 eres ! (Schulz et al., The peculiar galaxy NGC 2782 e.g. is thought to be a merger of two disk galaxies of unequal mass and has $L_\mathrm{X}$ = erg $^{-1}$ (Schulz et al. + 1998)., 1998). + Another galaxy with disturbed morphology and comparable X-ray luminosity (Lx = eres. !) is NGC 1808., Another galaxy with disturbed morphology and comparable X-ray luminosity $L_\mathrm{X}$ = erg $^{-1}$ ) is NGC 1808. + In contrast the PSPC data of this object do not show any X-ray outflow out of the central source into the halo., In contrast the PSPC data of this object do not show any X-ray outflow out of the central source into the halo. + But one has to mention that NGC 1808 has a SFR of only IOM ; + (Junkes et al., But one has to mention that NGC 1808 has a SFR of only 10 $_{\sun}$ $^{-1}$ (Junkes et al. + 1995)., 1995). + Relatively isolated systems without any companion. like e.g. NGC 253 (Fabbiano et al.," Relatively isolated systems without any companion, like e.g. NGC 253 (Fabbiano et al." + 1992). NGC 2903 and NGC 4569 (Junkes et al.," 1992), NGC 2903 and NGC 4569 (Junkes et al." + in preparation). contain X-ray luminosities of a few 10 erg !. emphasizing the importance of interaction for star-forming activity.," in preparation), contain X-ray luminosities of a few $^{40}$ erg $^{-1}$, emphasizing the importance of interaction for star-forming activity." +" PC96 found a significant difference in the Lx/Ly, ratio between pure AGN. pure SBs and galaxies with circumnuclear star-forming rings with an active nucleus."," PC96 found a significant difference in the $L_\mathrm{X}/L_\mathrm{H\alpha}$ ratio between pure AGN, pure SBs and galaxies with circumnuclear star-forming rings with an active nucleus." + The pure active nuclei show log(Lxζει) between 0.00 and 1.68. while the pure SBs in the sample lie between -1.46 and -0.36.," The pure active nuclei show $L_\mathrm{X}/L_\mathrm{H\alpha}$ ) between 0.00 and +1.68, while the pure SBs in the sample lie between -1.46 and -0.36." + The three galaxies with combined X-ray emission from AGN and SB have values of -0.26 (NGC 1097). +0.16 (NGC 1068) and +0.63 (NGC 7469). indicating a continuous decrease from AGN to SB.," The three galaxies with combined X-ray emission from AGN and SB have values of -0.26 (NGC 1097), +0.16 (NGC 1068) and +0.63 (NGC 7469), indicating a continuous decrease from AGN to SB." +" From this tendency one would expect a Lx/Li, «0 for the RS+PO model for NGC 4410.", From this tendency one would expect a $L_\mathrm{X}/L_\mathrm{H\alpha}$ $<$ 0 for the RS+PO model for NGC 4410. +" Our results. however yields 0.77 thereby. approximately the same as for a single PO model with Lx/Lj, ) = 40.81."," Our results, however yields +0.77 thereby, approximately the same as for a single PO model with $L_\mathrm{X}/L_\mathrm{H\alpha}$ ) = +0.81." +" The fraction of Zip, from the SB relative to the total Ha luminosity amounts to98%.. and for NGC 1097. NGC 1068 and NGC 7469. respectively."," The fraction of $L_\mathrm{H\alpha}$ from the SB relative to the total $\alpha$ luminosity amounts to, and for NGC 1097, NGC 1068 and NGC 7469, respectively." + Comparing only the contributions from the SB to the Ha and X-ray luminosity. PC96 found log(Lx/Li) = -0.99. -0.70 and -0.36 for NGC 1097. NGC 1068 and NGC 7469. respectively.," Comparing only the contributions from the SB to the $\alpha$ and X-ray luminosity, PC96 found $L_\mathrm{X}/L_\mathrm{H\alpha}$ ) = -0.99, -0.70 and -0.36 for NGC 1097, NGC 1068 and NGC 7469, respectively." +" If we concider the fraction of Ha. luminosity from the SB in these galaxies. and assume that of the total Ha luminosity originates from the SB within NGC 4410a. Γι, would result in erg Land Lx/ Lj) = 40.36. which is quite high compared to the sample analysed by PC96."," If we concider the fraction of $\alpha$ luminosity from the SB in these galaxies, and assume that of the total $\alpha$ luminosity originates from the SB within NGC 4410a, $L_\mathrm{H\alpha}$ would result in erg $^{-1}$ and $L_\mathrm{X}/L_\mathrm{H\alpha}$ ) = +0.36, which is quite high compared to the sample analysed by PC96." + We observed the interacting pair of galaxies NGC 4410 with the ROSAT HRI and PSPC., We observed the interacting pair of galaxies NGC 4410 with the ROSAT HRI and PSPC. + Spectral investigations of NGC 4410 suggest that the integral X-ray emission (Lx = ere |) can be decomposed into a thermal component (deseribed by a RS spectrum) and a component from the AGN (described by a power-law spectrum)., Spectral investigations of NGC 4410 suggest that the integral X-ray emission $L_\mathrm{X}$ = erg $^{-1}$ ) can be decomposed into a thermal component (described by a RS spectrum) and a component from the AGN (described by a power-law spectrum). + The HRI image reveals an extended X-ray halo related to NGC 4410a with an extension of ffrom the nucleus of NGC 4410a to the southeast., The HRI image reveals an extended X-ray halo related to NGC 4410a with an extension of from the nucleus of NGC 4410a to the southeast. + Combining spatial and spectral informations reveals an X-ray luminosity of the halo gas of Ly = ere | (1/3 of the total X-ray emission)., Combining spatial and spectral informations reveals an X-ray luminosity of the halo gas of $L_\mathrm{X}$ = erg $^{-1}$ (1/3 of the total X-ray emission). + The companion galaxy NGC 4410b houses only a very faint central point-like source below the 3c level. corresponding to an upper limit of erg + for the X-ray luminosity.," The companion galaxy NGC 4410b houses only a very faint central point-like source below the $\sigma$ level, corresponding to an upper limit of erg $^{-1}$ for the X-ray luminosity." + As a reasonable model we can assume that the tidal interaction 1n the pair of galaxiesNGC 4410 has two effects on the one partner. the face-on pec Sab galaxy NGC (I) A central monster iseither formed due to. this interaction or has already existed before and is now fed by infalling gas during the merging event. producing AGN signatures.," As a reasonable model we can assume that the tidal interaction in the pair of galaxiesNGC 4410 has two effects on the one partner, the face-on pec Sab galaxy NGC (1) A central monster iseither formed due to this interaction or has already existed before and is now fed by infalling gas during the merging event, producing AGN signatures." + Evidence for an existing AGN comes from the ROSAT X-ray spectrum supported by the spatially correlated, Evidence for an existing AGN comes from the ROSAT X-ray spectrum supported by the spatially correlated +a free parameter in our mociels. aud assume that the wind undergoes free expansion interior to this radius.,"a free parameter in our models, and assume that the wind undergoes free expansion interior to this radius." + Ieuce cach solution will consist of a region of supersonic wind with no mass loading aud an adjacent region with mass loadiug., Hence each solution will consist of a region of supersonic wind with no mass loading and an adjacent region with mass loading. +" One can imagine two possible causes for ΠΠ ""unxassloadius radius", One can imagine two possible causes for this minimum `mass-loading' radius. + Ta one scenario the clumps could rave been ejected at low velocity from the ceutral star at an earlier evolutionary stage., In one scenario the clumps could have been ejected at low velocity from the central star at an earlier evolutionary stage. + The ejection of clumps then abruptly stopped. so that a the ine of observation they rad travelled a finite distance from the ceutral star.," The ejection of clumps then abruptly stopped, so that at the time of observation they had travelled a finite distance from the central star." + By his process a ceutral region clear of clamps surrounded by a chunpy region can be generated., By this process a central region clear of clumps surrounded by a clumpy region can be generated. + A second possibility is hat chuups interior to the mass-loading radius have beeu conipletelv destroved by the wind., A second possibility is that clumps interior to the mass-loading radius have been completely destroyed by the wind. + It ποσα» reasonable o suppose that clamps located closest to the ceutral star will be destroved first. since they will have been subjected to the wind from the ceutral star for the lougest iue.," It seems reasonable to suppose that clumps located closest to the central star will be destroyed first, since they will have been subjected to the wind from the central star for the longest time." + Then as the bubble or nebula evolves. clamps at ever jucreasing distance from the central star will be destroved.," Then as the bubble or nebula evolves, clumps at ever increasing distance from the central star will be destroyed." + T-—uescales for the destruction of claps by ablation cau ve estimated frou Iartquist (1986)) and Iwleim (199 1)., Timescales for the destruction of clumps by ablation can be estimated from Hartquist\cite{HDPS1986}) ) and Klein \cite{KMC1994}) ). + Estimated destruction timescales vary from significantly less than to ereater than the age of the bubble/PNe. in accord with the different spatial distribution of clamps in objects of differing age.," Estimated destruction timescales vary from significantly less than to greater than the age of the bubble/PNe, in accord with the different spatial distribution of clumps in objects of differing age." + Reeardless of which of the above scenarios is respousible for the existence of such a qt niass-loading radius. this radius will physically increase with time.," Regardless of which of the above scenarios is responsible for the existence of such a minimum mass-loading radius, this radius will physically increase with time." + Our similarity solution requires that it increases in the same wav as that of the contact discontiuuitv raeTAM shore A is the radial dependence of the uiass-loading).," Our similarity solution requires that it increases in the same way as that of the contact discontinuity $r \propto t^{2/(5+\lambda)}$, where $\lambda$ is the radial dependence of the mass-loading)." + For most of the solutions preseuted iu this paper. the minim mass-loacding radius scales with or close to f.," For most of the solutions presented in this paper, the minimum mass-loading radius scales with or close to $t$." + Since on plivsical erounds we might expect it to scale as f. our solutions closely match this requirement.," Since on physical grounds we might expect it to scale as $t$, our solutions closely match this requirement." + Tn our solutions au inner shock may or may nof ye present - in the latter case the mass-loaded wind directly comnects to the contact discontinuty. aud the uas loading nav be strong enough for the wind to vecolme subsonic with respect to the chumps before the contact discontiuuitv is reached.," In our solutions an inner shock may or may not be present - in the latter case the mass-loaded wind directly connects to the contact discontinuity, and the mass loading may be strong enough for the wind to become subsonic with respect to the clumps before the contact discontinuity is reached." + If au iuner shock is oxeseut. the postshock flow is by definitiou subsonic with respect to the shock. but may still be supersonic with respect to the clumps.," If an inner shock is present, the postshock flow is by definition subsonic with respect to the shock, but may still be supersonic with respect to the clumps." + In this case a mmuber of different xofiles for the Mach umuber are possible before. the contact discontinuity is reached., In this case a number of different profiles for the Mach number are possible before the contact discontinuity is reached. + At the center of the bubble prior to the onset of mass loading. we solve oulv the continuity aud momoeutun equations. with the implicit assumption that the thermal enerev of the flow is neslieible. whilst iu the mass loading regions we additionally solve the cuecrey equation. aud include a source terii for nass injection iu the continuity equation.," At the center of the bubble prior to the onset of mass loading, we solve only the continuity and momentum equations, with the implicit assumption that the thermal energy of the flow is negligible, whilst in the mass loading regions we additionally solve the energy equation, and include a source term for mass injection in the continuity equation." + For a 5=5/3 eas. the equations for the loaded flow are: Tu these equationsvo the sviubols have their usual meanines.," For a $\gamma = 5/3$ gas, the equations for the mass-loaded flow are: In these equations the symbols have their usual meanings." + Iu the next sections we discuss appropriate similarity variables for these equations. our treaticut of the boundary conditions. and the scaling relationships to normalize the resulting solutions.," In the next sections we discuss appropriate similarity variables for these equations, our treatment of the boundary conditions, and the scaling relationships to normalize the resulting solutions." + The reader is again referred to PDII for a amore in-depth discussion of the cletails., The reader is again referred to PDH for a more in-depth discussion of the details. + Let the interchump ambicut medimm have a deusitv of the form p=pyr. and let us consider the caseiu which the imass-ablation rate is also radially dependent: p=Oral!5 for subsonic ablation (AL<1). aud p=Ors for Supersonic ablation (AL21) ITartquist 1986)).," Let the interclump ambient medium have a density of the form $\rho = \rho_{0} r^{\beta}$, and let us consider the casein which the mass-ablation rate is also radially dependent: $\dot{\rho} = Q + r^{\lambda} M^{4/3}$ for subsonic ablation $M<1$ ), and $\dot{\rho} = Q + r^{\lambda}$ for supersonic ablation $M>1$ ) Hartquist \cite{HDPS1986}) )." + A siuilavity solution demands that A=(2.5)/3. and the “physical parameters r.p.04 and £ may be expressed in ternis ofthe dimeusiouless similarity variables ον fle). gc). aud Ate) where Upon substituting the above similarity variables. the lydrodvuaiic equations for the region of freely expaudiug wind become: where a prime denotes derivation withrespect to x. For the flow in the mass-loaded region we obtain: where the Mach umber. Af=gνο (LOA).," A similarity solution demands that $\lambda = (2\beta - 5)/3$, and the `physical' parameters $r, \rho, u$ and $\varepsilon$ may be expressed in terms of the dimensionless similarity variables $x$, $f(x)$, $g(x)$, and $h(x)$ where Upon substituting the above similarity variables, the hydrodynamic equations for the region of freely expanding wind become: where a prime denotes derivation withrespect to x. For the flow in the mass-loaded region we obtain: where the Mach number, $M = g \sqrt{9f/(10h)}$ ." + It is simple to rearrange these equations to find. 7’. g'. and h which may then be integrated to obtain solutions.," It is simple to rearrange these equations to find $f'$ , $g'$ , and $h'$ which may then be integrated to obtain solutions." +Adcling these gives the full density perturbation: [t is important to understand. in a qualitative sense. tlie amplituce of the deusity perturbation in equation (31).,"Adding these gives the full density perturbation: It is important to understand, in a qualitative sense, the amplitude of the density perturbation in equation (31)." + The relative perturbation. pi/po. created by a simple point mass (a monopole) is ol order rji/r. according to equation (21).," The relative perturbation, $\rho_1/\rho_0$, created by a simple point mass (a monopole) is of order $r_{\rm in}/r$, according to equation (24)." + However. our oscillating deusity perturbation is quadrupolar.," However, our oscillating density perturbation is quadrupolar." + Thus. the monopole result must be multiplied by two powers of &«i4.," Thus, the monopole result must be multiplied by two powers of $k\,a_{\rm tot}$." + The amplitude in equation (31) is indeed of order)., The amplitude in equation (31) is indeed of order. +. As expected. the perturbation is an acoustic wave that travels racially outward with phase velocityc.," As expected, the perturbation is an acoustic wave that travels radially outward with phase velocity." + At any time. the phase of the wave is also dependent on ©.," At any time, the phase of the wave is also dependent on $\phi$." + In fact. equation (31) reveals that tlie disturbance may also be viewed as a trailing. two-armed spiral wave. with a amplitude that peaks at the equatorπρ).," In fact, equation (31) reveals that the disturbance may also be viewed as a trailing, two-armed spiral wave, with a latitude-dependent amplitude that peaks at the equator." + Since1.. the spiral is tightly wrapped. with a relatively small pitch augle.," Since, the spiral is tightly wrapped, with a relatively small pitch angle." + Figure 3 illustrates the basic geometry of tlie wave., Figure 3 illustrates the basic geometry of the wave. + Shown are wavefrouts (surfaces of constaut phase) for the two spiral arius in the equatorial plane., Shown are wavefronts (surfaces of constant phase) for the two spiral arms in the equatorial plane. + If. we trace oue arm around the circle. the radius of the [ront increases by2z/k.," If we trace one arm around the circle, the radius of the front increases by." +. However. because a second arm is interleaved. the actual radial wavelength of the disturbance is A/2. with an associated wavenumber of 24.," However, because a second arm is interleaved, the actual radial wavelength of the disturbance is $\lambda/2$, with an associated wavenumber of $2\,k$." + The perturbations angular frequency is δω. so the outward velocity is againc.," The perturbation's angular frequency is $2\,\omega$, so the outward velocity is again." +.. We uext determine the velocity created in the gas by the passing wave., We next determine the velocity created in the gas by the passing wave. + Taking the curl of the momenttun equation (3). we fiud tliat Thus. the induced vorticity is indepeucent of time. and is zero for oscillatory motion.," Taking the curl of the momentum equation (3), we find that Thus, the induced vorticity is independent of time, and is zero for oscillatory motion." + It.follows that the velocity may be written as where ey is the velocity potential., Itfollows that the velocity may be written as where $\psi_1$ is the velocity potential. + From the mass coutinuity equation (1). ey obeys If we assume that zw depends on the same phase as py. then the dominant. contribution to Vere in the far-field limit is simply —147 es.," From the mass continuity equation (4), $\psi_1$ obeys If we assume that $\psi_1$ depends on the same phase as $\rho_1$, then the dominant contribution to $\nabla^2\psi_1$ in the far-field limit is simply $-4\,k^2\,\psi_1$ ." + Using py(4) from equation (31). we find that," Using $\rho_1 (t)$ from equation (31), we find that" +We thank $. Gillessen and the referee for comments.,We thank S. Gillessen and the referee for comments. +Lt has usually been thought that the disc in spiral galaxies extends to radii well bevond the optical disc.,It has usually been thought that the disc in spiral galaxies extends to radii well beyond the optical disc. + rotation curves have ↸⋠⋠⊀therefore led to extensive studies of the clark| matter clistribution at large radii↔, rotation curves have therefore led to extensive studies of the dark matter distribution at large radii. +" Llowever. suggested that. dilluse.u optical. emission2. could in. principle2. be found: at radii"" larger than the disc."," However, suggested that diffuse optical emission could in principle be found at radii larger than the disc." +: They initially suggested that bevond a certain radius. cold gas could no longer support itself. against. ionization⋠⊀⊲ bv the ambient. raciation field.," They initially suggested that beyond a certain radius, cold gas could no longer support itself against ionization by the ambient radiation field." + To test this theory. they. obtained very deep optical spectra for one of the brightest Sculptor eroup galaxies. NGC 253. and succeeded in detecting ionized gas (lla and. Nu]) bevond the dise.," To test this theory, they obtained very deep optical spectra for one of the brightest Sculptor group galaxies, NGC 253, and succeeded in detecting ionized gas $\alpha$ and ]) beyond the disc." + The rotation curve they derived also showed signs of a possible decline., The rotation curve they derived also showed signs of a possible decline. + Llowever. their. results led them to. conclude. that the existence. of ⋅⊀this extended. ionized⊀⊀ gas was not due to the ambient. radiationD. field.. but more likely: clue to hot. voung stars in. the central regions. of⋅ the galaxy ionizing⊀↔ the outer disc. through a strong warp present in. the ealaxy’s ↼∢disc.," However, their results led them to conclude that the existence of this extended ionized gas was not due to the ambient radiation field, but more likely due to hot young stars in the central regions of the galaxy ionizing the outer disc through a strong warp present in the galaxy's disc." + Detecting dilfuse ionized gas can therefore. not. only provide insight as to the kinematics of a galaxy at large radii. but. also provide strong constraints on the source of its ionization.," Detecting diffuse ionized gas can therefore not only provide insight as to the kinematics of a galaxy at large radii, but also provide strong constraints on the source of its ionization." + In this context. carried. out a deep La ," In this context, carried out a deep $\alpha$ " +its mark on the phase-space structure of the halos.,its mark on the phase-space structure of the halos. + Indeed. hese dark halo streams are a major source of attention in oresent clay studies of the formation of our Galaxy (Πο&White1999:οι 2000).," Indeed, these dark halo streams are a major source of attention in present day studies of the formation of our Galaxy \citep{helmi99,helmi00}." +. ]t remains an interesting question as to whether we can ind evidence for these merging events in the Fundamental fane., It remains an interesting question as to whether we can find evidence for these merging events in the Fundamental Plane. + González-CGiarcía&vanMbacda(2003) look into he effects of major mergers on the Fundamental. Plane and found that the Fundamental Plane does remain Iargelv intact in the case of two merging ellipticals., \cite{cesar03a} look into the effects of major mergers on the Fundamental Plane and found that the Fundamental Plane does remain largely intact in the case of two merging ellipticals. + Llowever. what he effects will be of an incessant bombarcment of a halo »v material in its surroundings has not been studied in much detail.," However, what the effects will be of an incessant bombardment of a halo by material in its surroundings has not been studied in much detail." + Given that this is a sensitive function of the cosmological scenario. we will study the influence on FP yaramcters and thickness in more detail.," Given that this is a sensitive function of the cosmological scenario, we will study the influence on FP parameters and thickness in more detail." +" In this paper we address the specific question as to whether we can trace an inllucnce of cosmic parameters in the scaling relations for simulated. clusters. and in particular the influence of the cosmic density. parameter $2, and the cosmological constant A."," In this paper we address the specific question as to whether we can trace an influence of cosmic parameters in the scaling relations for simulated clusters, and in particular the influence of the cosmic density parameter $\Omega_m$ and the cosmological constant $\Lambda$." + We use a set of clissipationtless A’-body simulations involving open. Lat and closed. Universes.," We use a set of dissipationless $N$ -body simulations involving open, flat and closed Universes." +" All the simulations are variants of the cold dark. matter. (CDM). scenario. representing: cillerent cosmologies. concerning both cillerent values for the mass density O,,. for dark energy € and for the implied. power spectrum of density perturbations and the related. merging and accretion history of the clusters."," All the simulations are variants of the cold dark matter (CDM) scenario, representing different cosmologies, concerning both different values for the mass density $\Omega_{m}$, for dark energy $\Omega_{\Lambda}$ and for the implied power spectrum of density perturbations and the related merging and accretion history of the clusters." + The organization of this paper is as follows., The organization of this paper is as follows. + In section 2 we describe the simulations and the definitions of the various parameters we use., In section \ref{sec5:sim} we describe the simulations and the definitions of the various parameters we use. + In section 3. we present a general deseription of the scaling relations which we investigate in this study before specifving the way in which we analyze them from the cluster-sized. halos in our simulation., In section \ref{sec5:background} we present a general description of the scaling relations which we investigate in this study before specifying the way in which we analyze them from the cluster-sized halos in our simulation. + We investigate the scaling relations of galaxy clusters in different cosmologies at 2=0 in section 4.., We investigate the scaling relations of galaxy clusters in different cosmologies at $z=0$ in section \ref{sec5:scaling}. + Section 5 aclelresses the evolution of the scaling relations as a Function of redshift and cosmic time., Section \ref{sec5:evol_scaling} addresses the evolution of the scaling relations as a function of redshift and cosmic time. + We also investigate the dependence of merging and accretion on the scaling relations. which we discuss in section 6..," We also investigate the dependence of merging and accretion on the scaling relations, which we discuss in section \ref{sec5:mergacc}." + The interpretation of our results on the Fundamental Plane within the context of the virial theorem is cliseussec in section 7.., The interpretation of our results on the Fundamental Plane within the context of the virial theorem is discussed in section \ref{sec5:reconcile}. + Conclusions are presented in section &.., Conclusions are presented in section \ref{sec5:conclusions}. + We perform. thirteen. N-body. simulations that. follows the dvnamices of No=256 particles in a periodic box of size L—2005. !Mpe., We perform thirteen N-body simulations that follows the dynamics of $N=256^{3}$ particles in a periodic box of size $L=200h^{-1}$ Mpc. + The initial conditions are generated. with identical phases for Fourier. components of the Gaussian random field., The initial conditions are generated with identical phases for Fourier components of the Gaussian random field. + In this way. cach cosmological model contains the same morphological structures.," In this way, each cosmological model contains the same morphological structures." + For. all models we chose the same Llubble parameter. {0.7. and the same normalization of the power spectrum. Tx 0.5.," For all models we chose the same Hubble parameter, $h=0.7$, and the same normalization of the power spectrum, $\sigma_{8}=0.8$ ." +" The principa dillerences between the simulations are the values of the matter density and vacuum energy. density xumeters. f2,, anc Q4."," The principal differences between the simulations are the values of the matter density and vacuum energy density parameters, $\Omega_{m}$ and $\Omega_{\Lambda}$." + By combining these parameters. we get. modes describing the three possible geometries of he Universe: open. Hat and closed.," By combining these parameters, we get models describing the three possible geometries of the Universe: open, flat and closed." + The effect of having the same Hubble xuameter and dilferent cosmological constants ranslates Late» having different cosmic times., The effect of having the same Hubble parameter and different cosmological constants translates into having different cosmic times. + Fable 1. lists he values of the cosmological parameters and the cosmic imes at whic1 the data is analysed., Table \ref{table5:paramsim} lists the values of the cosmological parameters and the cosmic times at which the data is analysed. + Phe initial conditions are evolved. up to the present ine (2 ) using the massive parallel tree N-bocly code GADGET? (Springel2005)., The initial conditions are evolved up to the present time $z=0$ ) using the massive parallel tree N-body code GADGET2 \citep{springel05}. +. Phe Plumumer-cquivalent softening was set at eu;=15h. tkpe in physical units from D-—2102-—) while itwas taken to be fixed in comoving units at. high« voredshifts.," The Plummer-equivalent softening was set at $\epsilon_{pl}=15h^{-1}$ kpc in physical units from $z=2$ to $z=0$, while itwas taken to be fixed in comoving units at higher redshifts." +" For cach cosmological model we wrote the out of 100 snapshots. from ap,=0.2 (2Ξ 4) to the presen tine. (vu,lfs 0). equally spaced. in loger)."," For each cosmological model we wrote the output of 100 snapshots, from $a_{exp}=0.2$ $z=4$ ) to the present time, $a_{exp}=1$$z=0$ ), equally spaced in $\log(a)$ ." + We use the HOP algorithm (Eisenstein.&Llut1998) to extract the groups present in the simulations., We use the HOP algorithm \citep{eisenstein98} to extract the groups present in the simulations. + OP, HOP +"For the relativistic electrons (1.6., {ο— 1), eq.(8)) and eq.(11)) take the simplified forms where €2hw'/(y',mec”?), be=21—0)»hue /(mec”), and hui,0.", The polarized radiation flux is The polarization degree of the EIC emission is One can see that a non-zero net polarization is expected as long as $\theta_{\rm v}>0$. +" In the numerical example, we assume that the seed photons have a thermal spectrum (as suggested in the photosphere model) where KT""zzkT/2I; is the temperature (measured in the rest frame of the emitting region) of thethermal emission."," In the numerical example, we assume that the seed photons have a thermal spectrum (as suggested in the photosphere model) where $kT'\approx kT/2\Gamma_{\rm i}$ is the temperature (measured in the rest frame of the emitting region) of thethermal emission." +" In the calculation we take I;~300 and kT’~100 keV. The electron distributionis taken as Ny,comparisonox?/;6?x4/;??e for 4/,>2, otherwise Ny,=0."," In the calculation we take $\Gamma_{\rm i} \sim 300$ and $kT \sim +100$ keV. The electron distribution is taken as $N_{\gamma_{\rm e}} +\propto {\gamma'}_{\rm e}^{-(1+p)} \propto {\gamma'}_{\rm e}^{-3.5}$ for ${\gamma'}_{\rm e}>2$, otherwise $N_{\gamma_{\rm e}} =0$." +" For purpose we also consider the case of Ny,oxy, ? "," For comparison purpose we also consider the case of $N_{\gamma_{\rm e}} +\propto {\gamma'}_{\rm e}^{-2}$ ." +The numerical results are presented in Fig.5.., The numerical results are presented in \ref{fig:Pol-1}. + One can see that the polarization degrees expected in these two representative cases are only slightly different., One can see that the polarization degrees expected in these two representative cases are only slightly different. +" We also find that a moderate linear polarization level (P;,grc> 10%) is achievable only for 0,76;+1/(313)."," We also find that a moderate linear polarization level $P_{\rm \nu,EIC}>10\%$ ) is achievable only for $\theta_{\rm +v}\gtrsim \theta_{\rm j}+1/(3\Gamma_{\rm i})$." + Currently the prompt emission consists of a thermal and a non-thermal components., Currently the prompt emission consists of a thermal and a non-thermal components. + The thermal component with the flux Ενει is expected to be unpolarized while the nonthermal EIC component may have a high linear polarization level.," The thermal component with the flux $F_{\rm +\nu,th}$ is expected to be unpolarized while the nonthermal EIC component may have a high linear polarization level." + The observed polarization degree should be strongly frequency-dependent., The observed polarization degree should be strongly frequency-dependent. +" Roughly speaking, the linear polarization degree is anti-correlated with the weight of the thermal component."," Roughly speaking, the linear polarization degree is anti-correlated with the weight of the thermal component." +" With an energy ~ kT’, the emission is dominated by the thermal component and Pyrobs is low."," With an energy $\sim kT$ , the emission is dominated by the thermal component and $P_{\rm kT,obs}$ is low." +" For hv> kT, theemission is dominated by the EIC component and νους» Pic, as illustrated in Fig.6.."," For $h\nu \gg kT$ , theemission is dominated by the EIC component and $P_{\nu,\rm obs} \sim P_{\nu,\rm EIC}$ , as illustrated in \ref{fig:Pol-2}. ." + This unique, This unique +"pressure, fuapx=Px/Pair, and compare it to what would be if all the wind energy was confined.","pressure, $f_{\rm trap,X} = P_{\rm X}/P_{\rm dir}$, and compare it to what $f_{\rm trap,X}$ would be if all the wind energy was confined." +" We firap,.xcan calculate the trapped-wind value using the wind-luminosity relation (??),, which indicates that the momentum flux carried by winds from a star cluster is about half that carried by the radiation field if the cluster the entire IMF’."," We can calculate the trapped-wind value using the wind-luminosity relation \citep{kud,rep}, which indicates that the momentum flux carried by winds from a star cluster is about half that carried by the radiation field if the cluster samples the entire IMF." +" Written quantitatively, 0.5Lpo1/¢samples=Myvw, where My is the mass flux from the winds that launched at a velocity vy."," Written quantitatively, $0.5 L_{\rm bol}/c = \dot{M_{\rm w}} v_{\rm w}$, where $\dot{M_{\rm w}}$ is the mass flux from the winds that launched at a velocity $v_{\rm w}$." +" The mechanical energy loss L4, of the winds is then given by and the mechanical energy of the winds is simply Lt, where t is the time since the winds were launched."," The mechanical energy loss $L_{\rm w}$ of the winds is then given by and the mechanical energy of the winds is simply $E_{\rm w} = L_{\rm w} t$ , where $t$ is the time since the winds were launched." +" Putting these relations together, the trapped X-ray gas pressure PxT is where Vu is the volume of the HII region."," Putting these relations together, the trapped X-ray gas pressure $P_{\rm X,T}$ is where $V_{\rm HII}$ is the volume of the HII region." +" Given that Pair=Lya/(ArRigo), then frrap,x is where we have set Egn/t=v, the velocity of the expanding shell."," Given that $P_{\rm dir} = L_{\rm bol}/(4 \pi R_{\rm HII}^2 c)$, then $f_{\rm trap,X}$ is where we have set $R_{\rm HII}/t = v_{\rm sh}$, the velocity of the expanding shell." +" Finally, we put M, in terms of Ly.) and Uw, 80 that Eq."," Finally, we put $\dot{M_{\rm w}}$ in terms of $L_{\rm bol}$ and $v_{\rm w}$, so that Eq." +" 10 reduces to We use the above equation to obtain an order-of-magnitude estimate of ftrap,x if all the wind energy is confined by the shell."," \ref{eq:ftrap} reduces to We use the above equation to obtain an order-of-magnitude estimate of $f_{\rm trap,X}$ if all the wind energy is confined by the shell." +" We assume a wind velocity Uy~1000 km s-! escape velocity from a O6 V star; a reasonable order-of-magnitude(the estimate, since O3 stellar winds are faster and WR winds would be slower than this value)."," We assume a wind velocity $v_{\rm w} \sim 1000$ km $^{-1}$ (the escape velocity from a O6 V star; a reasonable order-of-magnitude estimate, since O3 stellar winds are faster and WR winds would be slower than this value)." +" If we set uj~ 25 km s! (the expansion velocity over 30 Doradus given by optical spectroscopy; 7), then ~ 20."," If we set $v_{\rm sh} \sim$ 25 km $^{-1}$ (the expansion velocity over 30 Doradus given by optical spectroscopy; \citealt{chu94}) ), then $f_{\rm trap,X} \sim$ 20." +" We can firap,Xcompare this to our observed values for the regions closest to the ftrap,xshell ones along the rim of our 441 squares in Fig. (the"," We can compare this $f_{\rm trap,X}$ to our observed values for the regions closest to the shell (the ones along the rim of our 441 squares in Fig. \ref{fig:regions}) );" +Figure 13 shows the histogram of our observed 5)); values.," Figure \ref{fig:hist} shows the histogram of our observed $f_{\rm trap,X}$ values." +" We find a mean and median ftrap,x of 0.30 and ftrap,x0.27, respectively, for our outermost regions."," We find a mean and median $f_{\rm trap,X}$ of 0.30 and 0.27, respectively, for our outermost regions." +" Over 30 Doradus, the highest values of ftrap,x are near the supernova remnant N157B in the southwest corner of 30 Doradus (see Figure 14)), where hot gas is being generated and has not had time to vent."," Over 30 Doradus, the highest values of $f_{\rm trap,X}$ are near the supernova remnant N157B in the southwest corner of 30 Doradus (see Figure \ref{fig:ftrapcheck}) ), where hot gas is being generated and has not had time to vent." +" Other locations where ftrap,x is elevated are regions with strong X-ray emission and weak Ha emission."," Other locations where $f_{\rm trap,X}$ is elevated are regions with strong X-ray emission and weak $\alpha$ emission." +" Morphologically, these areas could be where the hot gas is blowing out the 30 Doradus shell."," Morphologically, these areas could be where the hot gas is blowing out the 30 Doradus shell." + The observed values are 1-2 orders of magnitude below what ftrapxxthey would be if the wind was fully confined.," The observed $f_{\rm trap,X}$ values are 1–2 orders of magnitude below what they would be if the wind was fully confined." +" As a consequence, we find that Px of our regions is too low to be completely trapped in the HII region (the Castor et al."," As a consequence, we find that $P_{\rm X}$ of our regions is too low to be completely trapped in the HII region (the Castor et al." +" model), and the X-ray gas must be leaking through pores in the shell."," model), and the X-ray gas must be leaking through pores in the shell." +" This result is consistent with the Harper-Clark Murray model of partial confinement of the hot gas, and the weakness of Px relative to Pai, suggests the hot gas does not play a significant role in the dynamics of the HII region."," This result is consistent with the Harper-Clark Murray model of partial confinement of the hot gas, and the weakness of $P_{\rm X}$ relative to $P_{\rm dir}$ suggests the hot gas does not play a significant role in the dynamics of the HII region." + We note here that our rim regions in this analysis are, We note here that our rim regions in this analysis are +proportional to (defdr)|.,proportional to $(dv/dr)^{-1}$. + Deuce. a sinaller teriunal velocity will automatically result im a παο calculated line acceleration.," Hence, a smaller terminal velocity will automatically result in a smaller calculated line acceleration." + Tn earlier sections we have demonstrated that the mass loss around the bistability jump inereases., In earlier sections we have demonstrated that the mass loss around the bi-stability jump increases. + As we have used.observed values for the ratio v4/Vese da our model calculations. we have not vet provided a seclf&cousistent explanation of the observed bi-stabilitv Πο in va/vosc.," As we have used values for the ratio $\ratio$ in our model calculations, we have not yet provided a self-consistent explanation of the observed bi-stability jump in $\ratio$." + As a cousisteucy test of our calculations aud an attempt to explain the observed jump in the ratio Vrνο. we procecded to solve the momeutuu equation of line driven wind models around the bistabilitv jump.," As a consistency test of our calculations and an attempt to explain the observed jump in the ratio $\ratio$, we proceeded to solve the momentum equation of line driven wind models around the bi-stability jump." + The approach we take is to combine predicted force multiplier paralcters & and a (see below) frou the Monte. Carlo calculation with the analytical solution of line driven winds frou CAIs., The approach we take is to combine predicted force multiplier parameters $k$ and $\alpha$ (see below) from the Monte Carlo calculation with the analytical solution of line driven winds from CAK. + We calculated the lue acceleration gp for several models with differcut T;g usine the Monte Carlo method., We calculated the line acceleration $g_{\rm L}$ for several models with different $\teff$ using the Monte Carlo method. + The values of gp were expressed iu terms of the force nuutiplicr AZ(f£) (Eq. 8))., The values of $g_{\rm L}$ were expressed in terms of the force multiplier $M(t)$ (Eq. \ref{eq:CAK}) ). + Following CAIN we tried. to express M(f) iu terms of a power-law fit of he optical depth parameter £ (Eq. 9))., Following CAK we tried to express $M(t)$ in terms of a power-law fit of the optical depth parameter $t$ (Eq. \ref{eq:tCAK}) ). + We found that in the rauge 20 000 1 will be assumed."," Furthermore, $\Gamma \gg 1$ will be assumed." +" The observed intensity is then where y=TYie is the Lorentz factor of the radiating electrons as measured in the observers frame, τ is the synchrotron optical depth and m is the mass of the electron."," The observed intensity is then where $\gamma \equiv \Gamma \gamma_{\rm me}'$ is the Lorentz factor of the radiating electrons as measured in the observers frame, $\tau$ is the synchrotron optical depth and $m$ is the mass of the electron." + It will be assumed that the emission is produced at a distance R from the neutron star., It will be assumed that the emission is produced at a distance $R$ from the neutron star. + Radiation from the streaming electrons is observed from a surface of size απ;/T?., Radiation from the streaming electrons is observed from a surface of size $a \pi R^2 / \Gamma^2$. + The value of a is unity for radially streaming electrons and a spherically symmetric source., The value of $a$ is unity for radially streaming electrons and a spherically symmetric source. +" In many cases, the value of a is likely to be smaller than unity, either due to an actual source size smaller than R/T or the source geometry."," In many cases, the value of $a$ is likely to be smaller than unity, either due to an actual source size smaller than $R/\Gamma$ or the source geometry." + The observed flux can then be written, The observed flux can then be written +circular annulus with mean radius 2° (11 kkpe) centered on NGC 1101 is most likely due to the fact that such a circular region contains cooler raim-pressure stripped gas Crom the trailing side of NGC L101 (the debris tall) as well as the Foruax ICM.,circular annulus with mean radius $2'$ $11$ kpc) centered on NGC 1404 is most likely due to the fact that such a circular region contains cooler ram-pressure stripped gas from the trailing side of NGC 1404 (the debris tail) as well as the Fornax ICM. + A single temperature APEC model provides a poor fit to the data inside the edge. as shown in Table L..," A single temperature APEC model provides a poor fit to the data inside the edge, as shown in Table \ref{tab:spectra}." + This is not surprising since a second component is warranted to model the coutributiou [rom foreground cluster emission., This is not surprising since a second component is warranted to model the contribution from foreground cluster emission. + We model this emission with a separate APEC component with abundance aud temperature fixed at the best fit cluster values., We model this emission with a separate APEC component with abundance and temperature fixed at the best fit cluster values. + We find a temperature for the kkeV⋅⋅ ⋅∥∣∣∡∣∣ −⋅∣⊔⋅⇁⊳⊳with an⋅⋅ abundance 0.73. 45; Z..∑∸⋜↕⋜∥∙⋃∢∙≺⇂∐⋃⊳∖≺↵∑≟⋜↕⊳∖⋯⊳∖∐⇂↩∐≺↵≺↵≺∟≺∸≺↵∩⊔≻⋅⋅≻," We find a temperature for the galactic diffuse gas inside the edge of $0.55^{+0.01}_{-0.02}$ keV with an abundance $0.73^{+0.65}_{-0.16}\,\Zs$." +⋅≻Thefit is n inchauged ib the cluster component. temperature is allowed to vary. although the errors on the ⋅ ↥≺↵≺⇂∢∙∐⇂⊳∖≺↵↕⋅↕↩⋯↥↽≻≺↵⋅⋜⋯⊔⋅↩↸⊥⋅↓↖∖∎∣ ∣↽⋝∣∣∡⊇ ≽↓≽⊔⊊≺↵∖⋝⋜⋃⋅≺↵↥⋜↕⋅∑≟≺↵⋅⊺∐≺↵↕≺↵⋯↥≻≺↵↕⋅⋜⋯⊔⋅≺↵∖∖↽≺↵∐↕," The fit is unchanged if the cluster component temperature is allowed to vary, although the errors on the fitted cluster temperature $1.48^{+0.24}_{-0.22}$ keV) are large." +≺↵⋜↕⊳∖⋃⋅≺↵↥∩↓⋅∪∐⇂⊳∖≺↵∑≟⋜↕⊳∖; ⋅⋋ ∎↥↓∖⊽∁↽∶⊂⊲↽⊔∩↓↕⊳∖∐↕∑∸∩⋯⇂⋜↕∑≟↕⋅≺↵↩⊔≺↵∐↕∖∖↽∐∐↥↽∐⋅≺↵∖⊽↥∩⋃⊳∖∐≺↵⋜↕⊳∖⋯⋅≺↲⋯≺↵∐↕⊳∖∑⇁⋡↥∖⊽≺↵↥↕↕∐≺↵≺↥∐⇀≺↵↕⋅≺↵⊓∙≺↵⊳∖↥∐↕≺↵⊔∩⊓↲↥⊳∖ ⋜↕∐⇂⊳∖↥↽≻≺↵∢∙↕⋅⋜↕↥≺↵⊸∖⋃⋅⋜↕∢∙↕∩∐↕⋅≺↵∑≟↕∩, The temperature we measure for diffuse gas in NGC 1404 is in good agreement with previous measurements given the differences in the models and spectral extraction regions. +∐⊳∖⋅⇂⊽⊳∖↥∐∑≟∐⋃∺⇀−∖⊺↥⋟∺↥⋟∁≺⇂⋜↕↕⋜↕⋅∙∣∩⊔≺↵⊳∖≺↵↕⋜↕⋅↸↣∐∫∪⊤⊔∎⋯��∐⋜↕∐↕≺↵⋜↕∐ emperature for NGC 1101 of 0.65Mn kkeV: while O'Sullivan (2003) fouud a temperature orolile consistent with isothermal with AT=0.640.01 for radii r<1.6. similar to that [ound » Scharl (2001) using; ACIS-I data.," Using ROSAT PSPC data, Jones (1997) found a mean temperature for NGC 1404 of $0.65^{+0.02}_{-0.01}$ keV; while O'Sullivan (2003) found a temperature profile consistent with isothermal with $kT = 0.6 \pm +0.01$ for radii $r \lesssim 1'.6$, similar to that found by Scharf (2004) using ACIS-I data." + We find. however. an abundance A significantly higher hau that [ο by most previous authors C4~O.11Z.. Loewenstein 199[: d—0.16Z... Jones 1997: A~0.35. O'Sullivan 2003). aud more consistent with solar or super- abuudauces expected [or elliptical galaxies (Buote 2002: Brigheuti Mathews 1999).," We find, however, an abundance $A$ significantly higher than that found by most previous authors $A \sim 0.14\,\Zs$, Loewenstein 1994; $A \sim 0.16\,\Zs$ , Jones 1997; $A \sim 0.35$, O'Sullivan 2003), and more consistent with solar or super-solar abundances expected for elliptical galaxies (Buote 2002; Brighenti Mathews 1999)." + This discrepancy is probably due to a combination of limited statistics. large heterogeneousextraction," This discrepancy is probably due to a combination of limited statistics, large heterogeneousextraction" +relatively dense. material in the fireball will be able to cool rapidly down to this temperature before the cooling rate stalls.,relatively dense material in the fireball will be able to cool rapidly down to this temperature before the cooling rate stalls. + We approximate a racliatively cooling fireball by maintaining a hot core region which cools acliabatically as it expands., We approximate a radiatively cooling fireball by maintaining a hot core region which cools adiabatically as it expands. + Once gas elements cross the boundary. to this region. we assume them to cool immediately to the effective temperature of the photosphere and thereafter adiabatically.," Once gas elements cross the boundary to this region, we assume them to cool immediately to the effective temperature of the photosphere and thereafter adiabatically." + We derive the radius of the photospheric surface below. using the blackbody luminosity and the thermal energy. of the central region.," We derive the radius of the photospheric surface below, using the blackbody luminosity and the thermal energy of the central region." +" Yo lind the photospheric radius rj=(0:25, in our radiative model we calculate the total thermal energy in a sphere of radius η, Lenec. dillerentiating. Racliative cooling at fixed elective temperature 7j, gives and so. using we have the dillerential equation for the core radius as a function of time where We solve. equation (31)) numerically anc plot. the xhaviour for typical parameters in Fig. 2.."," To find the photospheric radius $r_{\rm p}=a_{0} \beta \eta_{\rm p}$ in our radiative model we calculate the total thermal energy in a sphere of radius $r_{\rm p}$ Hence, differentiating, Radiative cooling at fixed effective temperature $T_{\rm p}$ gives and so, using we have the differential equation for the core radius as a function of time where We solve equation \ref{eqn:cordiff}) ) numerically and plot the behaviour for typical parameters in Fig. \ref{fig:tempbnd}." + We see how. in he Lagrangian coordinate 4. the boundary migrates inward continually.," We see how, in the Lagrangian coordinate $\eta$, the boundary migrates inward continually." + In. Eulerian coordinates. plotted in Fig. 3..," In Eulerian coordinates, plotted in Fig. \ref{fig:abstempbnd}," + he boundary is initially acvectecd outwards with the Low., the boundary is initially advected outwards with the flow. + When the inward migration exceeds the expansion rate. the ohotosphere turns around. and. begins to collapse.," When the inward migration exceeds the expansion rate, the photosphere turns around and begins to collapse." +" In both lots the initial conditions for my, have relatively little impact on the behaviour at [ate times.", In both plots the initial conditions for $\eta_{\rm p}$ have relatively little impact on the behaviour at late times. + Models with ijjz4 initially are indistinguishable as they rapidly: converge on the same curve., Models with $\eta_{\rm p}\ga4$ initially are indistinguishable as they rapidly converge on the same curve. +" Lower initial values for rj, also converge. albeit more σον]. on the same evolution."," Lower initial values for $\eta_{\rm p}$ also converge, albeit more slowly, on the same evolution." + We plot the temperature profiles at different. times for the radiative model in Fig. 4.., We plot the temperature profiles at different times for the radiative model in Fig. \ref{fig:tprof}. + Phe profiles show how the material outside the core region cools very rapidly with distance away from the boundary., The profiles show how the material outside the core region cools very rapidly with distance away from the boundary. + As a result. the shell of material with significant temperature outside the core is very thin.," As a result, the shell of material with significant temperature outside the core is very thin." + For computational convenience we set a mininimum temperature for any of the gas at 1000 1. In the LPE approximation. the density. and. temperature determine the ionization state of the eas at each point. in space and time through the solution of a network of Saha equations.," For computational convenience we set a minimum temperature for any of the gas at $1~000$ K. In the LTE approximation, the density and temperature determine the ionization state of the gas at each point in space and time through the solution of a network of Saha equations." + Atomic level populations are similarly determined through Boltzmann factors and. partition. functions., Atomic level populations are similarly determined through Boltzmann factors and partition functions. + Lor purely adiabatie cooling. the temperature retains its initial uniform spatial profile. but decreases with time.," For purely adiabatic cooling, the temperature retains its initial uniform spatial profile, but decreases with time." + The LEE ionization is therefore higher in the outer low-clensity regions which also move fastest., The LTE ionization is therefore higher in the outer low-density regions which also move fastest. + Thus in the LYE mocdel high ionization emission lines are predicted. to have broader velocity. profiles., Thus in the LTE model high ionization emission lines are predicted to have broader velocity profiles. + Once we have determined the evolution of 7 and p with time. we can follow the evolution of the ionization structure," Once we have determined the evolution of $T$ and $\rho$ with time, we can follow the evolution of the ionization structure" +When comparing models of star-forming regions to observations. it is important to understand how our incomplete understanding of the regions may affect such comparison.,"When comparing models of star-forming regions to observations, it is important to understand how our incomplete understanding of the regions may affect such comparison." + Often. the star formation history is poorly constrained. but may be important considering the relatively short timescales of interest of ~10 Myr.," Often, the star formation history is poorly constrained, but may be important considering the relatively short timescales of interest of $\sim10$ Myr." + In figure 3. we show the time profiles of kinetic energy ejection from the stellar winds and supernova explosions and of the interstellar mass of ΑΙ., In figure \ref{fig:onecluster} we show the time profiles of kinetic energy ejection from the stellar winds and supernova explosions and of the interstellar mass of $^{26}$ Al. + Lines show the three different star formation histories described in section 35 (model D. (model D) and the (model ID.," Lines show the three different star formation histories described in section \ref{sec:models}: (model I), (model I) and the (model II)." + The results of all three models are surprisingly. similar: Values for the current and future times are the same within <10%.., The results of all three models are surprisingly similar: Values for the current and future times are the same within $\lesssim$. + Some differences appear in the past values. increasing towards the time of formation of subgroup OBId (12 Myr ago).," Some differences appear in the past values, increasing towards the time of formation of subgroup OB1d (12 Myr ago)." + We conclude that the properties investigated in this paper are not sensitive to the exact star formation history for regions with ages above 5-6 Myr. and they cannot be used to constrain earlier star formation. accordingly.," We conclude that the properties investigated in this paper are not sensitive to the exact star formation history for regions with ages above 5-6 Myr, and they cannot be used to constrain earlier star formation, accordingly." + Shaded areas in figure 3 show the Io (dark grey) and 2c (light grey) statistical variations., Shaded areas in figure \ref{fig:onecluster} show the $\sigma$ (dark grey) and $\sigma$ (light grey) statistical variations. +" These are derived through random sampling of the mass function (seee.g.Cervino&Luridiana 2006).. and are large because both the kinetic energy of the winds and the ejection of ""AI strongly depend on the ZAMS mass of the stars."," These are derived through random sampling of the mass function \citep[see e.g.][]{Cervino2006}, and are large because both the kinetic energy of the winds and the ejection of $^{26}$ Al strongly depend on the ZAMS mass of the stars." + It is clear that these variations are larger than the uncertainties in the star formation history., It is clear that these variations are larger than the uncertainties in the star formation history. + We note that the lines indicate the values. and that these probability distributions are strongly asymmetric for small numbers of stars (seeVossetal.2009).," We note that the lines indicate the values, and that these probability distributions are strongly asymmetric for small numbers of stars \citep[see][]{Voss-popsyn}." + In figure + we compare the results of three different stellar evolution models and supernova yields. that are considered representative of the spread in theoretical predictions.," In figure \ref{fig:fivecluster} we compare the results of three different stellar evolution models and supernova yields, that are considered representative of the spread in theoretical predictions." + For all three models the subgroups were modelled individually (model ID)., For all three models the subgroups were modelled individually (model II). + A spread in current values of ~20—30% can be seen. yet much smaller than the statistical variation.," A spread in current values of $\sim20-30$ can be seen, yet much smaller than the statistical variation." + The main differences at early times are between the stellar evolution models including rotation and the ones without. with both more energy and *°Al being ejected from the stars in their wind phases than from their supernovae.," The main differences at early times are between the stellar evolution models including rotation and the ones without, with both more energy and $^{26}$ Al being ejected from the stars in their wind phases than from their supernovae." + This difference i$ mainly caused by two effects: the somewhat higher ages of the sub-groups inferred by the stellar models including rotation (e.g. the 2 Myr higher age of subgroup ΟΒΙα) and the enhanced wind ejection caused by stellar rotation., This difference is mainly caused by two effects: the somewhat higher ages of the sub-groups inferred by the stellar models including rotation (e.g. the 2 Myr higher age of subgroup OB1a) and the enhanced wind ejection caused by stellar rotation. + in the For densities. below the critical density. the mean interparticle distance is smaller than the Debve raclius.," in the For densities below the critical density, the mean interparticle distance is smaller than the Debye radius." + llence. when analyzing the possibility that an ion carries a bound electron. the Debye length. is not relevant.," Hence, when analyzing the possibility that an ion carries a bound electron, the Debye length is not relevant." + 1n Πο., In fig. + 5 we show the run of the density. and. temperature in the Sun along with the critical density (calculated. for the actual temperature ancl composition)., \ref{fig:the-sun-rho-crit} we show the run of the density and temperature in the Sun along with the critical density (calculated for the actual temperature and composition). + Fig., Fig. + 6. depicts the domains of Ry=£r; For three values of the hydrogen mass fraction. 0.35. 0.5 and 0.7.," \ref{fig:rho-T-plane} depicts the domains of $R_{D}=\langle r_{s} \rangle $ for three values of the hydrogen mass fraction, 0.35, 0.5 and 0.7." + One finds that through most of the volume of the Sun. the density is always below the critical one and. hence the analysis of the structure of the electronic leves must take into account the nearby ion rather than the DebsὉ radius.," One finds that through most of the volume of the Sun, the density is always below the critical one and hence the analysis of the structure of the electronic levels must take into account the nearby ion rather than the Debye radius." + Ouly close to the surface does the situation change. the Debve radius becomes smaller than the mean interparicle distance and the critical density becomes smaller than t1ο actual density.," Only close to the surface does the situation change, the Debye radius becomes smaller than the mean interparticle distance and the critical density becomes smaller than the actual density." + When one evaluates the pressure ionization for metals al 2=0. one assumes the Wiener Seitz cell.," When one evaluates the pressure ionization for metals at $T=0$, one assumes the Wigner Seitz cell." + Phe rational for using it at higher temperatures is the fact that the speed of the electron in the bound state is so much greater than the speed of the ions. such that the ions can be assumed to be at rest.," The rational for using it at higher temperatures is the fact that the speed of the electron in the bound state is so much greater than the speed of the ions, such that the ions can be assumed to be at rest." + The use of the ion-sphere for opacity calculations was examined by 2.., The use of the ion-sphere for opacity calculations was examined by \citet{Roz92}. + We used the variational principle method and trial functions of two tvpes., We used the variational principle method and trial functions of two types. + The first type is taken from 2... namely a polvnomial in r times an exponential function (the simple bound state). while the second tvpe is a Padé approximation.," The first type is taken from \citet{Rous74}, namely a polynomial in $r$ times an exponential function (the simple bound $s$ -state), while the second type is a Padé approximation." + The results for Hydrogen obtained using the two tvpes of trial functions are compared ancl found to be practically the same to within a relative accuracy of 10. or better., The results for Hydrogen obtained using the two types of trial functions are compared and found to be practically the same to within a relative accuracy of $10^{-2}$ or better. + Additional trials with other functions and. parameters.7 did not improve the results bevond the second significant digit., Additional trials with other functions and parameters did not improve the results beyond the second significant digit. +" Interestinely. with our definition of rz). the energy level is only a function. of frz3/Re(Z) and it is shown in lig. Ἐν,"," Interestingly, with our definition of $ \langle r_{Z} \rangle$, the energy level is only a function of $ \langle r_{Z} \rangle /R_{B}(Z)$ and it is shown in fig. \ref{fig:E(hxi)}." + Complete pressure ionization is found. to occur ab irz)=L945Re(Z) respective of Z. To obtain the results for a particular ion. one has to find its rz) for the composition. temperature and density under consideration.," Complete pressure ionization is found to occur at $ \langle r_{Z} \rangle=1.945R_{B}(Z)$ irrespective of Z. To obtain the results for a particular ion, one has to find its $ \langle r_{Z} \rangle$ for the composition, temperature and density under consideration." + The results for Z7=0 are shown in fig. S.., The results for $T=0$ are shown in fig. \ref{fig:Schr-coul-finite-rz}. + We stress that these results are obtained for 7=0 and do not. depend on the Debve radius (and hence do not depend on the temperature indirectly)., We stress that these results are obtained for $T=0$ and do not depend on the Debye radius (and hence do not depend on the temperature indirectly). + We conclude that neither Ne. nor species with a higher Z. are fully ionized in the solar core.," We conclude that neither ${\rm Ne}^{20}$, nor species with a higher Z, are fully ionized in the solar core." + The above results are. easily translated. into. the conditions in the Sun., The above results are easily translated into the conditions in the Sun. + In fig. 9..," In fig. \ref{fig:the-sun1}," + we plot the run of the erouncl state binding energy of Be’ throughout the Sun., we plot the run of the ground state binding energy of ${\rm Be}^{7}$ throughout the Sun. + This calculation indicates that Bervllium is fully ionized in the Sun below a solar mass fraction of 0.66., This calculation indicates that Beryllium is fully ionized in the Sun below a solar mass fraction of 0.66. +the spectrum of relativistic protons may be substantially mocified in the energv range 1 GeV - 100 GeV due to the resonant interaction with MIID Alfvénnie turbulence.,the spectrum of relativistic protons may be substantially modified in the energy range 1 GeV - 100 GeV due to the resonant interaction with MHD Alfvénnic turbulence. + This is à consequence of the fact that the acceleration. time for protons is minimum at these energies (see Fig., This is a consequence of the fact that the acceleration time for protons is minimum at these energies (see Fig. + 16 in Paper D., 16 in Paper I). +" Indeed. at smaller scales. (which. resonate with smaller values of the proton energy) τι72»70, and the acceleration time should. decrease with particles momentum as (from Eqs. ὃ-"," Indeed, at smaller scales (which resonate with smaller values of the proton energy) $\tau_s>>\tau_d$ and the acceleration time should decrease with particle's momentum as (from Eqs. \ref{dpp}-" + 9 51): while at lareer scales (which resonate with more energetic protons) Ts*7; and the acceleration time should increase with the momentum of the particles (from Eqs. ὃ-, \ref{kres} \ref{wk_2}) ): while at larger scales (which resonate with more energetic protons) $\tau_s << \tau_d$ and the acceleration time should increase with the momentum of the particles (from Eqs. \ref{dpp}- + 9 49)) as: In Fig., \ref{kres} \ref{wk_1}) ) as: In Fig. + 1 we also mark the tvpical regions of the spectrum of the hadrons which approximatively contribute to the injection of the secondary. electrons. ancl positrons witha given Lorentz factor., \ref{fig:protons} we also mark the typical regions of the spectrum of the hadrons which approximatively contribute to the injection of the secondary electrons and positrons with a given Lorentz factor. + Phe consequence of the decrease of the ellicieney of Alfvenn acceleration. with increasing proton energv is that only the amount of secondary clectrons/positrons injected at 4~10° is expected to be significantly increased., The consequence of the decrease of the efficiency of Alfvénn acceleration with increasing proton energy is that only the amount of secondary electrons/positrons injected at $\gamma \sim 10^2-10^3$ is expected to be significantly increased. + On the other hand. the injection rate of secondary electrons. and. positrons with +~101. which emit the svachrotron radiation at 0.3.1.4 Cillz. is not expected to be substantially modified: (at. least not. more than a factor of 23) by the Alfvénn acceleration process.," On the other hand, the injection rate of secondary electrons and positrons with $\gamma \sim 10^4$, which emit the synchrotron radiation at 0.3–1.4 GHz, is not expected to be substantially modified (at least not more than a factor of 2–3) by the Alfvénn acceleration process." + The main point of this paper is to include the effect of the reacceleration of the secondary electrons ancl positrons. as generated in hadronic interactions of a time-dependent spectrum of protons.," The main point of this paper is to include the effect of the reacceleration of the secondary electrons and positrons, as generated in hadronic interactions of a time-dependent spectrum of protons." + This phenomenon has a twofold elfect on the observable non thermal radiation from a cluster: first. the secondary electrons. ancl positrons add to the pool of (primary) electrons that can suller the re-energization due to coupling with waves.," This phenomenon has a twofold effect on the observable non thermal radiation from a cluster: first, the secondary electrons and positrons add to the pool of (primary) electrons that can suffer the re-energization due to coupling with waves." + Second. energy is channelled [rom waves to protons. therefore causing an increase with time of the relative weight of secondary electrons and. positrons with respect to relic electrons.," Second, energy is channelled from waves to protons, therefore causing an increase with time of the relative weight of secondary electrons and positrons with respect to relic electrons." + The evolution of the spectra of particles. (protons and electrons) and Alfvénn waves is obtained. by solving numerically Eqs. 10.. 11..," The evolution of the spectra of particles (protons and electrons) and Alfvénn waves is obtained by solving numerically Eqs. \ref{elettroni}, \ref{protoni}," +" and 12 with ἐν,/) given by Iq. 36.."," and \ref{turbulence} + with $Q_e(p_e,t)$ given by Eq. \ref{qepm2}." + The spectrum of the secondary electrons anc positrons at the beginning of the acceleration period is computed from. the FokkerPlank equation (eq. LO.," The spectrum of the secondary electrons and positrons at the beginning of the acceleration period is computed from the Fokker–Plank equation (Eq. \ref{elettroni}," + with the source term given by Eq. 36)), with the source term given by Eq. \ref{qepm2}) ) + uncer stationary conditions and assuming {2—0 (e.g.. Dolag Ensslin 2000): Our seneral [indings. illustrated in Fig. 2.," under stationary conditions and assuming $D_{pp}=0$ (e.g., Dolag Ensslin 2000): Our general findings, illustrated in Fig. \ref{fig:3panels}," + are summarized. below., are summarized below. + As in the case of the reacecleration of relic primary electrons. (Paper D). the ellicienev for lepton acceleration decreases with increasing energv of relativistic hadrons in the ICM.," As in the case of the reacceleration of relic primary electrons (Paper I), the efficiency for lepton acceleration decreases with increasing energy of relativistic hadrons in the ICM." + As a consequence. the prominence of the bump of accelerated: particles that appears in Fig.," As a consequence, the prominence of the bump of accelerated particles that appears in Fig." + 2) is expected to decrease when the energy content in the form of hadrons increases., \ref{fig:3panels} is expected to decrease when the energy content in the form of hadrons increases. + A pronounced. feature appears in the spectrum. of leptons. due to the reacceleration process. namely a sharp drop in the spectrum. followed by a flattening.," A pronounced feature appears in the spectrum of leptons, due to the reacceleration process, namely a sharp drop in the spectrum, followed by a flattening." + The drop can be easily understood in terms of balance between energy, The drop can be easily understood in terms of balance between energy +inertial-wave ravs. which are characteristics of the Poincaré equation.,"inertial-wave rays, which are characteristics of the Poincaré equation." + ltelatively simple wave attractors exist in this range of frequencies., Relatively simple wave attractors exist in this range of frequencies. + The symmetrical pair of attractors involving four rellections on the outer boundary. illustrated. in. the upper part of Fig. Ll.," The symmetrical pair of attractors involving four reflections on the outer boundary, illustrated in the upper part of Fig. \ref{f:attractors}," + exists lor 1.076. 0. we search for a perturbative solution in the approximation of small 8. so we set rj2Ro+é and y,= yore. with 0<&«Ro and [e|« qo."," To treat the general case of $\theta \ge 0$ , we search for a perturbative solution in the approximation of small $\theta$ , so we set $r_1 = R_0 + \xi$ and $\varphi_1 = \varphi_0 +\varepsilon$ , with $0 < \xi \ll R_0$ and $|\varepsilon| \ll \varphi_0$ ." + By substituting in Eqs. (B3)).," By substituting in Eqs. \ref{eq:V1_eqs}) )," +The principal aim of this work is to present the simplest model that permits a largely analytical exploration of the m=| counterrotating instability in a shot” nearly Weplerian dise of collisionless self.gravitating matter.,The principal aim of this work is to present the simplest model that permits a largely analytical exploration of the $m=1$ counter–rotating instability in a “hot” nearly Keplerian disc of collisionless self–gravitating matter. + To this end. we have considered. a twocomponent softened eravitv disc. and. performed a linearised WIXD. analysis of both local and global modes.," To this end we have considered a two–component softened gravity disc, and performed a linearised WKB analysis of both local and global modes." + We derive an analytical expression for local WIND. waves for arbitrary m. which turns out to be quartic in the frequency w.," We derive an analytical expression for local WKB waves for arbitrary $m$, which turns out to be quartic in the frequency $\omega$ ." +" Specialising to m= ol. we show that w is smaller than the (Ixeplerian) orbital frequency by the small quantitity ¢=Al,/AL (the ratio of the disc mass to the mass of the central object): in other words. the m=1 modes aremodes."," Specialising to $m=1$ , we show that $\omega$ is smaller than the (Keplerian) orbital frequency by the small quantitity $\varepsilon = M_d/M$ (the ratio of the disc mass to the mass of the central object); in other words, the $m=1$ modes are." + “The dispersion relation now reduces to a quaclratie equation in a., The dispersion relation now reduces to a quadratic equation in $\omega$. + llence the criteria for stability. instability and. overstability can be readily derived. in simple analytical forms.," Hence the criteria for stability, instability and overstability can be readily derived in simple analytical forms." + For a onecomponent disc (which does not have any counter the m.=l modes are stable. consistent. with the results of ‘Tremaine(2001).," For a one–component disc (which does not have any counter--rotation), the $m=1$ modes are stable, consistent with the results of \citet{tre01}." +. Equal mass in the two counterrotating Components Corresponds to the case of not net rotation., Equal mass in the two counter–rotating components corresponds to the case of not net rotation. + In this case we find that the local modes are purely unstable (i.e. not overstable). consistent with Araki(1994):Lovelaceetal.(L997):Touma (2002).," In this case we find that the local modes are purely unstable (i.e. not overstable), consistent with \citet{ara87, pp90, sm94, ljh97, tou02}." +. However the eencral case of arbitrary mass ratio in the two counterrotating components corresponds to overstabilitv. ancl we show analvticallv that the clises must be unrealistically hot to avoid an overstabilitv.," However the general case of arbitrary mass ratio in the two counter--rotating components corresponds to overstability, and we show analytically that the discs must be unrealistically hot to avoid an overstability." + We finally contructed global WIxXD modes. numerically. for the case ofa Ixuzmindiscfor the case of no net rotation. by using BohrSommoerfeld quantisation.," We finally contructed global WKB modes, numerically, for the case of a Kuzmindiscfor the case of no net rotation, by using Bohr–Sommerfeld quantisation." +time (iudicated by the dotted lines) over much of the disk. so we should see the effects of these torques in a large number of observed galaxies. consistent. with observational fincdines (Briges 1990. heshetnikovy Combes 1998).,"time (indicated by the dotted lines) over much of the disk, so we should see the effects of these torques in a large number of observed galaxies, consistent with observational findings (Briggs 1990, Reshetnikov Combes 1998)." +" We study the reaction of a disk to these torques by performing numerical. N-body simulations of a massive Milky Way type galactic disk (maximuun circular velocity (may,=233 kin/s. scale leneth ry=8.5 kpe. vertical scale height 4.=325 pe) subject to the torques fouud iu section 2.."," We study the reaction of a disk to these torques by performing numerical N-body simulations of a massive Milky Way type galactic disk (maximum circular velocity $v_{\rm max}=233\,$ km/s, scale length $r_d=3.5\,$ kpc, vertical scale height $h_z=325\,$ pc) subject to the torques found in section \ref{torque +section}." + Equilibrium disk models of disk mass 1x1019A£.. 3xLOMALS. and 5.6xLOMALL in a static spherically-syuunetric NEW. halo potential (Navarro. Frenuk White 1997) with concentration parameter c=15 and a virial velocity of cag)=175 kin/s are constructed using the method of Hernquist (1993).," Equilibrium disk models of disk mass $1\times 10^{10}\> M_\odot$, $3\times 10^{10}\> M_\odot$, and $5.6\times 10^{10}\> M_\odot$ in a static spherically-symmetric NFW halo potential (Navarro, Frenk White 1997) with concentration parameter $c=15$ and a virial velocity of $v_{200}=175\,$ km/s are constructed using the method of Hernquist (1993)." + Each disk contains 16381 particles., Each disk contains 16384 particles. + The moclels were evolved using GRAPESPH (Steinmetz 1996) for 2 Cyr. which took 5000-7000 timesteps depending on the model.," The models were evolved using GRAPESPH (Steinmetz 1996) for 2 Gyr, which took 5000–7000 timesteps depending on the model." + A plumuner softening of 0.3 kpe has been used., A plummer softening of 0.3 kpc has been used. + Figure 2aa shows the simulation of a disk subjected to a torque for 1 Cyr., Figure \ref{simulation disk}a a shows the simulation of a disk subjected to a torque for 1 Gyr. + The disk was aligned with the :cy-plaue at /=0., The disk was aligned with the $xy$ -plane at $t=0$. + The iuuer yart ol the disk is flat and clearly tilted toward the positive z--axis., The inner part of the disk is flat and clearly tilted toward the positive x -axis. + Bevoud 11 kpe. the disk warps wack toward the original plane.," Beyond 11 kpc, the disk warps back toward the original plane." + It. distiuctly resembles observed: warped galaxies., It distinctly resembles observed warped galaxies. + The particles of he sinulated galaxy were biuned into spherical shells 2 kpc wide. aud the minor axis of each bi was [ος from the moment of inertia teusor.," The particles of the simulated galaxy were binned into spherical shells 2 kpc wide, and the minor axis of each bin was found from the moment of inertia tensor." + Figure 2bb plots the tilt angle of each ring from the initial. plane of the disk., Figure \ref{simulation disk}b b plots the tilt angle of each ring from the initial plane of the disk. + The flat region shows up clearly as the inner rings which are all tilted a uniform from the initial plane. while beyond Ll kpe (the radius) the disk warps back toward the initial plane.," The flat region shows up clearly as the inner rings which are all tilted a uniform from the initial plane, while beyond 11 kpc (the ) the disk warps back toward the initial plane." + A imassless disk. in contrast. does not exhibit an inner Hat region and is warped at all adii as shown by the solicl line in Figure 2bb. The self-gravity of the massive disk maiutaius its," A massless disk, in contrast, does not exhibit an inner flat region and is warped at all radii, as shown by the solid line in Figure \ref{simulation disk}b b. The self-gravity of the massive disk maintains its" +where The variation of the caleulated value of the interior anguar velocity as a function of the width of the gap ὁΞruaMn is presented in Fig 3..,where and The variation of the calculated value of the interior anguar velocity as a function of the width of the gap $\delta = \rout-\rin$ is presented in Fig \ref{fig:ocdelta}. + Lt can be seen that the simulations. represented by the black squares. fit well the analytical predictions provided that the Ekman number is small enough (ic. below LO”).," It can be seen that the simulations, represented by the black squares, fit well the analytical predictions provided that the Ekman number is small enough (i.e. below $10^{-6}$ )." + Lt is also interesting to note. as an aside. that for gap width of about of the radiative zone's radius (which corresponds to the width of the solar tachocline). the interior angular velocity is of the equatorial velocity. which is very close to the value observed.," It is also interesting to note, as an aside, that for gap width of about of the radiative zone's radius (which corresponds to the width of the solar tachocline), the interior angular velocity is of the equatorial velocity, which is very close to the value observed." + I is not clear whether this intcresting match is a mere fortuitous coincidence or the result. of some more subtle physical processes., It is not clear whether this interesting match is a mere fortuitous coincidence or the result of some more subtle physical processes. + Another wav of comparing the results of the simulations to analvtical predictions is through the construction of 1e Ekman spiral. which is à parametric representation of 1e azimuthal velocity against the [atitudinal velocity às a function of radius. at a fixed co-Iatitude 8.," Another way of comparing the results of the simulations to analytical predictions is through the construction of the Ekman spiral, which is a parametric representation of the azimuthal velocity against the latitudinal velocity as a function of radius, at a fixed co-latitude $\theta$." + Fig., Fig. +" 4. compares 1o results of the asymptotic solution and the true numerical solution for a slightlv ciflerent simulation. in which the angular-velocitv. profile imposed. on the outer boundary. is hosen to be constant with value O4=Qe|10.7. and the angular velocity of the inner core is simply Qi,=OQ. (the no-torque condition is dropped)."," \ref{fig:ekmspir} compares the results of the asymptotic solution and the true numerical solution for a slightly different simulation, in which the angular-velocity profile imposed on the outer boundary is chosen to be constant with value $\Omega_{\rm +out} = \Omega_{\rm c} + 10^{-5}$, and the angular velocity of the inner core is simply $\Omega_{\rm in} = \Omega_{\rm c}$ (the no-torque condition is dropped)." + Note how the fit of the asymptotic analytical prediction o the numerical solution is valid only. provided the Ekman number is small enough., Note how the fit of the asymptotic analytical prediction to the numerical solution is valid only provided the Ekman number is small enough. + For Lager Ekman numbers. Viscosity plavs a non-negligible role in the dvnamies of the luiel outside the boundary. lavers. invalidating Proudman's asvmptotic analysis.," For larger Ekman numbers, viscosity plays a non-negligible role in the dynamics of the fluid outside the boundary layers, invalidating Proudman's asymptotic analysis." + This result has been obtained. already w Dormy. Cardin Jault (L998) who studied the non-magnetic case extensively.," This result has been obtained already by Dormy, Cardin Jault (1998) who studied the non-magnetic case extensively." + Phe good agreement between he analytical asvmptotic solutions and the simulations validates the numerical procedure., The good agreement between the analytical asymptotic solutions and the simulations validates the numerical procedure. + The influence of the magnetic field. on the [uid depends essentially on two parameters: the field. strength. ancl the maenctic cdilfusivitv., The influence of the magnetic field on the fluid depends essentially on two parameters: the field strength and the magnetic diffusivity. +" In this section. three regimes are presented for varving Elsasser number at fixed. (L..£,,)."," In this section, three regimes are presented for varying Elsasser number at fixed $(\Enu,\Eeta)$ ." + The Elsasser number is then fixed. and in Section 4.2. the dependence of the solution on the magnetic Ekman numberis presentecd.," The Elsasser number is then fixed, and in Section \ref{sec:intfield2} the dependence of the solution on the magnetic Ekman numberis presented." +"Παρόν, we then discarded measurements with discrepant values of flux. background. « aud y positious using a 6 uedian clipping (5o for the flux aud 100 for the other xuanmeters). aud the resulting values were averaged. the xXiotonmietre error being taken as the error on the average flux measurement.","images, we then discarded measurements with discrepant values of flux, background, $x$ and $y$ positions using a $\sigma$ median clipping $\sigma$ for the flux and $\sigma$ for the other parameters), and the resulting values were averaged, the photometric error being taken as the error on the average flux measurement." + At this stage. a 506 slippiug median clipping was used ou the resulting light curve to discard otally discrepaut fluxes.," At this stage, a $\sigma$ slipping median clipping was used on the resulting light curve to discard totally discrepant fluxes." + Figure l shows the resulting raw lieht curve. aud the ine-seres for the background aud the c aud y positions.," Figure 1 shows the resulting raw light curve, and the time-series for the background and the $x$ and $y$ positions." + As can be seen in Fie., As can be seen in Fig. + 1 and Fig., 1 and Fig. + 2. the measured vackeround showed an unusual evolution durus the run.," 2, the measured background showed an unusual evolution during the run." + It remained stable during ~3.5 hrs. then it mereased abruptly of a few and finally its scatter mereased arecly.," It remained stable during $\sim$ 3.5 hrs, then it increased abruptly of a few, and finally its scatter increased largely." + Such a behavior is most probably of iustruucutal origin., Such a behavior is most probably of instrumental origin. + We included this iustrumental effect m our data uodeliug (see below)., We included this instrumental effect in our data modeling (see below). + The IRAC 3.6 and L5 jui detectors are composed of IuSb arravs that show a strong iutrapixel quanti efficiency (QE) variabilitv. the QE being maximal in the middle of the pixel and decreasing towards the edges.," The IRAC 3.6 and 4.5 $\mu$ m detectors are composed of InSb arrays that show a strong intrapixel quantum efficiency (QE) variability, the QE being maximal in the middle of the pixel and decreasing towards the edges." + The fullwidth at half maxinuun (FEWIIM) of the poiut-spread function (PSF) is ~1.7 pixels., The full-width at half maximum (FWHM) of the point-spread function (PSF) is $\sim$ 1.7 pixels. + This uudersauipliug of the PSF combined with the QE iutrapixel variability leads to a strong depeudauce of the measured stellar fux on the exact location of the PSF ceuter in a pixel., This undersampling of the PSF combined with the QE intrapixel variability leads to a strong dependance of the measured stellar flux on the exact location of the PSF center in a pixel. + As Spitzers pointing wobbles with an amplitude of —0.1 pixel and a, As 's pointing wobbles with an amplitude of $\sim$ 0.1 pixel and a +limiting surlace brightness ‘iin0.35 mJy.,limiting surface brightness $\Sigma_{\rm min}=0.35$ mJy. + This. vields Dui=5.7 nG. Figure ο plots the distribution. of magnetic field strengths., This yields $B_{\rm min} = 5.7$ $\mu$ G. Figure \ref{fig:Bdist} plots the distribution of magnetic field strengths. + Phese were obtained by binnine the Fitt Alexander galaxies in stellar mass. ancl convolving this distribution withthe results of Figure 5..," These were obtained by binning the Fitt Alexander galaxies in stellar mass, and convolving this distribution withthe results of Figure \ref{fig:BvsMstars}." + Our mocdel (left panel) provides a good match to the data at. low. and intermediate magnetic field strengths. corresponding to low and intermediate mass galaxies.," Our model (left panel) provides a good match to the data at low and intermediate magnetic field strengths, corresponding to low and intermediate mass galaxies." + Lhe model overpredicts the counts at the bright end. primarily due to the expected peak in D at ~2.]0H (Figure 5)).," The model overpredicts the counts at the bright end, primarily due to the expected peak in $B$ at $\sim 2 \times 10^{11}$ (Figure \ref{fig:BvsMstars}) )." + A model with ci. a factor of 3 higher than in our best fit model is included for comparison (right panel)., A model with $\epsilon_{\rm grav}$ a factor of 3 higher than in our best fit model is included for comparison (right panel). + Counts at low values of D are significantly underprecdieted. consistent with this model predicting higher values of. D al a given stellar mass than found by πι Alexander (Figure 5)).," Counts at low values of $B$ are significantly underpredicted, consistent with this model predicting higher values of $B$ at a given stellar mass than found by Fitt Alexander (Figure \ref{fig:BvsMstars}) )." + Svochrotron luminosity is the most straightforward observational manifestation of magnetic fields., Synchrotron luminosity is the most straightforward observational manifestation of magnetic fields. + Following Longair (1994). assuming equipartition this luminosityis eiven by where V. is the volume of the emitting region ancl jj the ratio between proton and. electron. energy. densities.," Following Longair (1994), assuming equipartition this luminosityis given by where $V$ is the volume of the emitting region and $\eta_{\rm p}$ the ratio between proton and electron energy densities." +" Consistent with observations of our Galaxy (Longair 1994 ancl references therein) we adopt im,=100.", Consistent with observations of our Galaxy (Longair 1994 and references therein) we adopt $\eta_{\rm p} = 100$. + The constant Ca) depends weakly on spectral index à. and the minimum and maximum energy culolls zi and Muay.," The constant $G(\alpha)$ depends weakly on spectral index $\alpha$, and the minimum and maximum energy cutoffs $\nu_{\rm min}$ and $\nu_{\rm max}$ ." +" For an electron power-law distribution IN(/£)xE ""where p= 2.5. we have"," For an electron power-law distribution $N(E) \propto E^{-p}$ where $p=2.5$ , we have" +This work is partly based on research done in collaboration with Sidney Bluchuan (Univ.,This work is partly based on research done in collaboration with Sidney Bludman (Univ. + Pennsylvania and DESY) and was supported by the Departament of Energy. under. Grant Nos., Pennsylvania and DESY) and was supported by the Department of Energy under Grant Nos. + DE-FGO6-90ER40561 at the Institute for Nuclear Theory (Univ., DE-FG06-90ER40561 at the Institute for Nuclear Theory (Univ. + Washington) and DE-FGO2-97ERAL029 at the Institute for Fundamental Theory (Univ., Washington) and DE-FG02-97ER41029 at the Institute for Fundamental Theory (Univ. + Florida). and by the Eppley Foundation for Research.," Florida), and by the Eppley Foundation for Research." + The author is also grateful to the Aspen Center lor Physics for its hospitality., The author is also grateful to the Aspen Center for Physics for its hospitality. +careful reading and his constructive Conuments and suggestions.,careful reading and his constructive comments and suggestions. + We thank Maura MeLaughlin for comments on the manuscript., We thank Maura McLaughlin for comments on the manuscript. +all important reactions up to 77 Mg. in particular all à reactions and the complete hot (-limited) CNO evele.,"all important reactions up to $^{25}$ Mg, in particular all $\alpha$ reactions and the complete hot $\beta$ -limited) CNO cycle." + The reaction rates were taken from the Thielemann nuclear reactions library (provided by IV. C. Cannon) The changes in chemical composition and the energy density due to the nuclear burning are updated: after cach time step in the hyelrocnamical calculation., The reaction rates were taken from the Thielemann nuclear reactions library (provided by R. C. Cannon) The changes in chemical composition and the energy density due to the nuclear burning are updated after each time step in the hydrodynamical calculation. + To prevent nuclear burning in the ambient medium. we assumed that the ambient medium contained neither HE nor He in these particular calculations. (," To prevent nuclear burning in the ambient medium, we assumed that the ambient medium contained neither H nor He in these particular calculations. (" +For further details we refer to LP.),For further details we refer to IP.) + The boundary. conditions in the code. which describe the characteristics of the inllowing stream. are the internal and external Mach numbers. Mg and Moa: the ratio between the central density in the stream and the ambient density at the outer boundary 5: the initial inclination angle of the stream 6 (i.c. the angle between the initial How direction and the direction of the primary).," The boundary conditions in the code, which describe the characteristics of the inflowing stream, are the internal and external Mach numbers, $M_{\rm int}$ and $M_{\rm ext}$; the ratio between the central density in the stream and the ambient density at the outer boundary $\eta_{\rho}$; the initial inclination angle of the stream $\theta$ (i.e. the angle between the initial flow direction and the direction of the primary)." + For the chemical composition of the eas in the stream we use the abundances of the secondary., For the chemical composition of the gas in the stream we use the abundances of the secondary. + The boundary conditions for the rest of the box in the racial direction are outflow boundaries (except in the gas inflow zone) where the condition of hydrostatic equilibrium has been imposed for ghost cells., The boundary conditions for the rest of the box in the radial direction are outflow boundaries (except in the gas inflow zone) where the condition of hydrostatic equilibrium has been imposed for ghost cells. + Ehe boundary condition in the azimuthal cireetion also assumes outflow conditions (sve used a evicl which normally covers an angle z)., The boundary condition in the azimuthal direction also assumes outflow conditions (we used a grid which normally covers an angle $\pi$ ). +" As Courant number we used Nope,=0.650.8.", As Courant number we used $N_{\rm CFL } = 0.6 \div 0.8$. + A further parameter is the angular velocity with which the coordinate svstem rotates (most calculations were performed. in the frame rotating with the primary core)., A further parameter is the angular velocity with which the coordinate system rotates (most calculations were performed in the frame rotating with the primary core). + Figure 1. shows the initial interaction of a stream with a massive core and. illustrates the development. of a stationary stream., Figure \ref{fig:initial} shows the initial interaction of a stream with a massive core and illustrates the development of a stationary stream. + The parameters for this simulation are characteristic for a sstar filling its Roehe lobe inside the envelope of a very evolved red supergiant. (after helium core burning)., The parameters for this simulation are characteristic for a star filling its Roche lobe inside the envelope of a very evolved red supergiant (after helium core burning). + Ehe panels on the left show the hyelrogen abundance. while the panels on the right show the divergence. of the velocity field.," The panels on the left show the hydrogen abundance, while the panels on the right show the divergence of the velocity field." + The Eter was chosen because it shows shock structures particularly clearly., The latter was chosen because it shows shock structures particularly clearly. +" The top panels show the stream just before its ""impact with the core (569ss alter the beginning of the simulation). while the second. set of. panels is close to the point. of impact (at 778ss: note the bow shock in the right panels)."," The top panels show the stream just before its `impact' with the core s after the beginning of the simulation), while the second set of panels is close to the point of impact (at s; note the bow shock in the right panels)." + Immediately after the impact. stream matter bounces olf the core. where most of it is just rellected by the core and continues to move in the forward. direction. (ie. counter-clockwise). but some of it is pushed. backwards. attaining an angular velocity component opposite to the rotation of the core.," Immediately after the impact, stream matter bounces off the core, where most of it is just reflected by the core and continues to move in the forward direction (i.e. counter-clockwise), but some of it is pushed backwards, attaining an angular velocity component opposite to the rotation of the core." + As material that has been stopped. by the core is pushed by material in the stream following from behind. it starts to Dow up again. driving two powerful shocks on the front and. back side of the stream into the envelopes.," As material that has been stopped by the core is pushed by material in the stream following from behind, it starts to flow up again, driving two powerful shocks on the front and back side of the stream into the envelopes." + These shocks compress the stream significantly., These shocks compress the stream significantly. + Once they have left the domain of the caleulation. the stream. has attained essentially a stationary configuration. where the point of deepest. penetration. (2x2104 em) and. the stream shape no longer change significantly.," Once they have left the domain of the calculation, the stream has attained essentially a stationary configuration, where the point of deepest penetration $R\simeq 2\times10^{10}\,$ cm) and the stream shape no longer change significantly." + The overall Dow pattern also becomes more-or-less stationary. where all the matter leaving the stream in the core impact region Lows up again. being vigorously mixed with helium from the core in the process.," The overall flow pattern also becomes more-or-less stationary, where all the matter leaving the stream in the core impact region flows up again, being vigorously mixed with helium from the core in the process." + The main objective of our calculation is to determine how deep the stream can penetrate into the core of à massive star rather than the initial transient behaviour., The main objective of our calculation is to determine how deep the stream can penetrate into the core of a massive star rather than the initial transient behaviour. + In the quasi-stationary situation this depends mainly on the entropy that is generated in the stream-core interaction., In the quasi-stationary situation this depends mainly on the entropy that is generated in the stream-core interaction. + While the stream is in lateral pressure balance with the ambient matter at an carly stage of infall. i becomes increasingly unbalanced as the velocity increases and becomes significantly. supersonic relative to the ambient medium.," While the stream is in lateral pressure balance with the ambient matter at an early stage of infall, it becomes increasingly unbalanced as the velocity increases and becomes significantly supersonic relative to the ambient medium." + The interaction between the stream and. the ambient matter due to the jump in pressure can be treated in a simplified way as a Riemann problem (see e.g. LeVeque et 11905). a solution of which is a combination of shock ancl rarclaction waves.," The interaction between the stream and the ambient matter due to the jump in pressure can be treated in a simplified way as a Riemann problem (see e.g. LeVeque et 1998), a solution of which is a combination of shock and rarefaction waves." + In the case where the stream expancds. the rarefaction wave. propagating into the stream material. does not change the stream entropy.," In the case where the stream expands, the rarefaction wave, propagating into the stream material, does not change the stream entropy." + Llowever. compression of the stream by the ambient matter. in the Form of shocks moving into the stream. generates entropy inside the shocks.," However, compression of the stream by the ambient matter, in the form of shocks moving into the stream, generates entropy inside the shocks." + For a strong shock. where the pressure jump Pusfl. 4. the coefficient. of entropy change. Le. the ratio of the entropy of the shocked stream material. 5... to the initial entropy in the stream. SL. can be estimated as S/S. (Zeldovich1966)..," For a strong shock, where the pressure jump $P_{\rm amb }/P_{\rm s } +\gg 4$ , the coefficient of entropy change, i.e. the ratio of the entropy of the shocked stream material, $S_{\rm ss}$, to the initial entropy in the stream, $S_{\rm s}$, can be estimated as = / \cite{Zeld}." + In our case. we rather expect the development of weak shocks.," In our case, we rather expect the development of weak shocks." + Then an estimate for /vys can be written as l| ΜΜ... (Zeldovich1966).., Then an estimate for $K_{\rm S } $ can be written as 1 + ) ^2 -1)^3 \cite{Zeld}. + Phe pressure jump {μιf/f changes with the distance to the primary core., The pressure jump $P_{\rm amb }/P_{\rm s }$ changes with the distance to the primary core. + In the case of a power- parametrisation of the ambient. pressure. equation (22)) predicts that. models with smaller power-law indices will result in smaller pressure jumps for the same initial stream properties ancl hence smaller values for AS and that this cocllicient increases as the power-law index increases.," In the case of a power-law parametrisation of the ambient pressure, equation \ref{eq:ks}) ) predicts that models with smaller power-law indices will result in smaller pressure jumps for the same initial stream properties and hence smaller values for $K_{\rm S}$ and that this coefficient increases as the power-law index increases." + In Figure 2. we present some of the kev characteristics of a stream with the same parameters as in Figure 1.. once a more-or-less stationary [low pattern has been established.," In Figure \ref{fig:pr_disc} we present some of the key characteristics of a stream with the same parameters as in Figure \ref{fig:initial}, once a more-or-less stationary flow pattern has been established." + Note in thetop two panels that the entropy. in the core of the stream is initially constant and thatall the entropy, Note in thetop two panels that the entropy in the core of the stream is initially constant and thatall the entropy +approaches when / is small.,approaches when $f^d$ is small. + IE f is sufficiently small for linearization to be appropriate. under sole conditions. significant gains in computational efficiency can be achieved by taking the following into consideration.," If $f^d$ is sufficiently small for linearization to be appropriate, under some conditions, significant gains in computational efficiency can be achieved by taking the following into consideration." +" Under linear conditions. for the present model. we can write where w=ΠωςΠρ— land ó=T),./Ty)1."," Under linear conditions, for the present model, we can write where $\omega=n_{loc}/n_0-1$ and $\phi=T_{loc}/T_0-1$." + This representation can be very useful [or proving the computational efficiency. of update (9))., This representation can be very useful for improving the computational efficiency of update \ref{add}) ). + For example. for isothermal constant density flows. particles can be generated Irom a combination of a normal distribution and analviic inversion of the cumulative distribution function. which is significantly more efficient than acceplance-rejection.," For example, for isothermal constant density flows, particles can be generated from a combination of a normal distribution and analytic inversion of the cumulative distribution function, which is significantly more efficient than acceptance-rejection." + Alternatively. (13)) provides a means of obtaining tight bounds for FUEEF and (hus reducing the number of rejections if (he acceptance-rejection route is followed.," Alternatively, \ref{lin}) ) provides a means of obtaining tight bounds for $|f^{loc}-F|$ and thus reducing the number of rejections if the acceptance-rejection route is followed." + We have presented an efficient. variauce-reduced particle method for solving the Bolizmaun equation in the relaxation-time approximation., We have presented an efficient variance-reduced particle method for solving the Boltzmann equation in the relaxation-time approximation. + The method combines simplicity with a number of desirable properties associated with particle methods. such as robust capture of traveling discontinuities in (he distribution function ancl efficient. collision operator evaluation using importance sampling [9].. without the high relative statistical uncertainty associated with traditional particle methods in low-signal problems.," The method combines simplicity with a number of desirable properties associated with particle methods, such as robust capture of traveling discontinuities in the distribution function and efficient collision operator evaluation using importance sampling \cite{pof2005}, without the high relative statistical uncertainty associated with traditional particle methods in low-signal problems." + In particular. the method presented here can capture arbitrarily small deviations from equilibrium for constant computational cost.," In particular, the method presented here can capture arbitrarily small deviations from equilibrium for constant computational cost." + More sophisticated techniques with spatially variable underlying equilibrium distribution |13.14]. are expected to increase computational efficiency. by reducing the number of deviational particles required (o," More sophisticated techniques with spatially variable underlying equilibrium distribution \cite{thomas1,thomas2} are expected to increase computational efficiency by reducing the number of deviational particles required to" + (e.g..Sandersetal.1988:Hopkinsetal.2008).. (e.g.. (e.g..Tremaineetal.2002)..," \citep[e.g.,][]{Sanders_etal_1988,Sanders_Mirabel_1996,Canalizo_Stockton_2001, +Hopkins_etal_2008}, \citep[e.g.,][]{Hernquist_1989}. \citep[e.g.,][]{Toomre_Toomre_1972}. \citep[e.g.,][]{Tremaine_etal_2002}. \citep[e.g.,][]{Wyithe_Loeb_2003,Hopkins_etal_2008,Shen_2009}." + dynamical processes within quasar hosts is intrinsic quasar absorption lines., dynamical processes within quasar hosts is intrinsic quasar absorption lines. +" Historically most of the focus has been on broad absorption lines (BALs. usually defined as absorption troughs broader than 2000kms7!). which are undoubtedly intrinsic to the quasar,"," Historically most of the focus has been on broad absorption lines (BALs, usually defined as absorption troughs broader than $2000\,{\rm km\,s^{-1}}$ ), which are undoubtedly intrinsic to the quasar." +" Here we focus on another class of narrow absorption lines. called associated absorption lines (AALS). whose absorption velocity is close to the systemic velocity of the background quasar (z,52Sem)."," Here we focus on another class of narrow absorption lines called associated absorption lines (AALs), whose absorption velocity is close to the systemic velocity of the background quasar $z_{ab}\approx +z_{em}$ )." + AALS are traditionally defined as narrow absorption troughs (=S00kms! ) with a velocity offset vo within +3000kms7! of the systemic redshift of the quasar?.," AALs are traditionally defined as narrow absorption troughs $\la +500\,{\rm km\,s^{-1}}$ ) with a velocity offset $v_{\rm off}$ within $\pm +3000\,{\rm km\,s^{-1}}$ of the systemic redshift of the quasar." +. Strong (EW>0.6À)) low-ionization aassociated absorbers are present in a few percent of the entire quasar population (e.g..VandenBerketal.2008).," Strong ${\rm EW}>0.6\,$ ) low-ionization associated absorbers are present in a few percent of the entire quasar population \citep[e.g.,][]{Vanden_Berk_etal_2008}." +. These absorption systems are generally believed to be close to the quasar and are explained by either (or à combination) of the following scenarios: absorption by external galaxies clustering around the quasar (e.g..Weymannetal.1979;Wildetal. 2008):; absorption by halo clouds of the quasar host galaxy (e.g..Heckmanetal.1991): absorption by material from a starburst wind of the quasar host (e.g..Heekmanetal. 1990): or originating from the vicinity of the black hole (=--—200 ppe) based on partial coverage analysis or variability studies (e.g..Hamannetal.1995;Barlow&Sargent1997).," These absorption systems are generally believed to be close to the quasar and are explained by either (or a combination) of the following scenarios: absorption by external galaxies clustering around the quasar \citep[e.g.,][]{Weymann_etal_1979,Wild_etal_2008}; absorption by halo clouds of the quasar host galaxy \citep[e.g.,][]{Heckman_etal_1991}; absorption by material from a starburst wind of the quasar host \citep[e.g.,][]{Heckman_etal_1990}; or originating from the vicinity of the black hole $\la 200$ pc) based on partial coverage analysis or variability studies \citep[e.g.,][]{Hamann_etal_1995,Barlow_Sargent_1997}." +". On the other hand. classical intervening. absorber systems (with wp« z4,) are not physically associated. with the quasar and are absorptions due to cosmologically intervening foreground galaxies along the quasar line-of-sight (LOS) (Baheall&Spitzer1969:Bergeron 1986).."," On the other hand, classical intervening absorber systems (with $z_{ab}\ll z_{em}$ ) are not physically associated with the quasar and are absorptions due to cosmologically intervening foreground galaxies along the quasar line-of-sight (LOS) \citep{1969ApJ...156L..63B,1986A&A...155L...8B}. ." + The strength of these intervening absorbers is shown to correlate with the associated star formation rate. measured within 10 kpe," The strength of these intervening absorbers is shown to correlate with the associated star formation rate, measured within 10 kpc" +"ds? dt? 22005yydF2, with Eq. (3))","ds^2 ) ), with Eq. \ref{etamunu}) )" + remaining valid at “spatial iufuitv., remaining valid at “spatial infinity.” + Such a modification is pertectly justified because of the linearity of the weak-field limit (where one is able to formulate the plivsies in terms of the additive eravitational potentials)., Such a modification is perfectly justified because of the linearity of the weak-field limit (where one is able to formulate the physics in terms of the additive gravitational potentials). +" Within the considered framework aud approximations. the space-time curvatures derived fro gp, and Cy are identical."," Within the considered framework and approximations, the space-time curvatures derived from $g_{\mu\nu}$ and $\psi_{\mu\nu}$ are identical." + The reported incompleteness in the theory of general relativity for the description of eravitation reveals certain simüluities to the Aharouoyv-Bolin effect? Indeed. in the Aharonoyv-Bolun effect an observable pliase arises iu a region with vanishing field streneth tensor FY’Cr). (ie. im a region with vanishing Leurl of the gauge poteutial 4 (7)).," The reported incompleteness in the theory of general relativity for the description of gravitation reveals certain similarities to the Aharonov-Bohm \cite{AB} Indeed, in the Aharonov-Bohm effect an observable phase arises in a region with vanishing field strength tensor $F^{\mu\nu}(\vec r)$, (i.e. in a region with vanishing $4$ -curl of the gauge potential $A^{\mu}(\vec r)$ )." + Ii the effect reported here. an observable phase arises in a region where the contributions of the oc; νο constant potcutials to the curvature tensor RHeeNo) vanish.," In the effect reported here, an observable phase arises in a region where the contributions of the $\phi_{GA}$ -type constant potentials to the curvature tensor $R^{\mu\nu\sigma\lambda}(\vec r)$ vanish." +" Both of the effects mentioned above. illustrate the circumstance that im quantum mechanical processes the gauge field AMC?) aud the gravitational potential gf!”(7) may be favored over the corresponding fields streugth tensor £""(7). aud the curvature tensor RETAp) . respectively."," Both of the effects mentioned above, illustrate the circumstance that in quantum mechanical processes the gauge field $A^\mu(\vec r)$ and the gravitational potential $g^{\mu\nu}(\vec r)$ may be favored over the corresponding fields strength tensor $F^{\mu\nu}(\vec r)$, and the curvature tensor $R^{\mu\nu\sigma\lambda}(\vec r)$ , respectively." +" However. since the umber of the independent degrees of freedom of A""(7) is quite different from that of g""(7). the analogy between the Ahavonov-Boluu effect and the one considered here is not complete."," However, since the number of the independent degrees of freedom of $A^\mu(\vec r)$ is quite different from that of $g^{\mu\nu}(\vec r)$, the analogy between the Aharonov-Bohm effect and the one considered here is not complete." + Iu sunuuarx. the local galactic cluster. the Gveat attractor. enibeds us iu a dimensionless eravitational potential of about ον10.7.," In summary, the local galactic cluster, the Great attractor, embeds us in a dimensionless gravitational potential of about $- 3 \times +10^{-5}$." + Tn the solar svsteu this poteutial is coustaut to about 1 part iu 104., In the solar system this potential is constant to about $1$ part in $10^{11}$. + Consequently. plauctary orbits remain unaffected.," Consequently, planetary orbits remain unaffected." + However. this is uot so for the flavor-oscillation clocks.," However, this is not so for the flavor-oscillation clocks." + Iu a terrestrial free fall the eravitationally induced accelerations vanish. but +ιο eravitationally induced plases of the Savor-oscillation clocks do not.," In a terrestrial free fall the gravitationally induced accelerations vanish, but the gravitationally induced phases of the flavor-oscillation clocks do not." + We argued that there exists an clement ofiicoiipleteness in the geucral-relativistic description of gravitation., We argued that there exists an element of incompleteness in the general-relativistic description of gravitation. + The arrived incoupletcuess may be subjected to au experiuental test by verifviug the inequality derived here., The arrived incompleteness may be subjected to an experimental test by verifying the inequality derived here. +" The origin of the reported iuconipleteness lies in the mnüplicit eeneral-relativistic asstuuption on the equivalence of the space-time metric as nieasured by a freely falling observer in the vicinity of a eravitating source (which iu tur is clnbedded in a $e; y-type constant eravitational potential) aud the metric as measured by an observer at the ""spatial iufiuitv.""", The origin of the reported incompleteness lies in the implicit general-relativistic assumption on the equivalence of the space-time metric as measured by a freely falling observer in the vicinity of a gravitating source (which in turn is embedded in a $\Phi_{GA}$ -type constant gravitational potential) and the space-timemetric as measured by an observer at the “spatial infinity.” +Table 2 provides the key parameters of the actual PACS AOR implementations for each field.,Table \ref{tab:aor} provides the key parameters of the actual PACS AOR implementations for each field. + No significant source variability is expected for the dust-dominated emission of almost all detected sources., No significant source variability is expected for the dust-dominated emission of almost all detected sources. + For this reason no timing contraints needed to be applied in the scheduling., For this reason no timing contraints needed to be applied in the scheduling. +" For practical reasons scheduling of all AORs of a field during a visibility period was aimed for, and was typically but not always achieved."," For practical reasons scheduling of all AORs of a field during a visibility period was aimed for, and was typically but not always achieved." +" For fields near the plane of the ecliptic (COSMOS), asteroid passages may introduce another time dependent factor, as clearly demonstrated in mid-infrared detections during oobservations of the COSMOS field (Sanders et al. 2007))."," For fields near the plane of the ecliptic (COSMOS), asteroid passages may introduce another time dependent factor, as clearly demonstrated in mid-infrared detections during observations of the COSMOS field (Sanders et al. \cite{sanders07}) )." + The contrast between galaxies and asteroids is more favourable in the far-infrared., The contrast between galaxies and asteroids is more favourable in the far-infrared. +" Still, bright asteroids would be detectable in individual maps if present but were not identified when differencing our individual COSMOS maps from a coaddition."," Still, bright asteroids would be detectable in individual maps if present but were not identified when differencing our individual COSMOS maps from a coaddition." + SPIRE maps for most of the PEP fields are obtained in coordinated observations by the HerMES key program (Oliver et al. 2011))., SPIRE maps for most of the PEP fields are obtained in coordinated observations by the HerMES key program (Oliver et al. \cite{oliver11}) ). +" For the two z~1 clusters we implemented within PEP simple 10'x10' “‘large’ SPIRE scanmaps in nominal scan speed, spatially dithering between five concatenated independent repetitions."," For the two $\sim$ 1 clusters we implemented within PEP simple $\times$ `large' SPIRE scanmaps in nominal scan speed, spatially dithering between five concatenated independent repetitions." +" For scanning instruments with detectors that have a significant 1/f low frequency noise component, map creation usually follows one of two alternative routes."," For scanning instruments with detectors that have a significant 1/f low frequency noise component, map creation usually follows one of two alternative routes." +" One is using full ‘inversion’ algorithms as widely applied by the cosmic microwave background community and the other uses highpass filtering of the detector timelines and subsequent direct projection, frequently used for MMIPS 70 or 160 um reductions."," One is using full `inversion' algorithms as widely applied by the cosmic microwave background community and the other uses highpass filtering of the detector timelines and subsequent direct projection, frequently used for MIPS 70 or 160 $\mu$ m reductions." + An algorithm of the first ‘inversion’ type is available in the HCSS ddata processing in the form of an implementation and adaption to Herschel of a version of the MadMap code (Cantalupo et al. 2010))., An algorithm of the first `inversion' type is available in the HCSS data processing in the form of an implementation and adaption to Herschel of a version of the MadMap code (Cantalupo et al. \cite{cantalupo10}) ). + The alternative option that we adopt and describe in more detail below is using highpass filtering of the detector timelines and a direct ‘naive’ mapmaking., The alternative option that we adopt and describe in more detail below is using highpass filtering of the detector timelines and a direct `naive' mapmaking. +" This choice is made because for our particular case of deep field observations, MadMap presently does not reach the same point source sensitivity, and the preservation of diffuse emission is not important for our science case."," This choice is made because for our particular case of deep field observations, MadMap presently does not reach the same point source sensitivity, and the preservation of diffuse emission is not important for our science case." +" As noted, the cross-linked design of the PEP observations however does permit the future application of such inversion codes."," As noted, the cross-linked design of the PEP observations however does permit the future application of such inversion codes." + Our reduction first proceeds on a per AOR level and is based on scanmap scripts for the PACS photometer pipeline (Wieprecht et al. 2009)), Our reduction first proceeds on a per AOR level and is based on scanmap scripts for the PACS photometer pipeline (Wieprecht et al. \cite{wieprecht09}) ) +" in HCSS, with parameter settings and additions optimized for our science case."," in HCSS, with parameter settings and additions optimized for our science case." +" After retrieving PACS data and satellite pointing information we apply the first reduction steps to the time-ordered PACS data frames, identifying functional blocks in the data, flagging bad pixels, flagging any saturated data, converting detector signals from digital units to volts and the chopper position from digital units to physical angle."," After retrieving PACS data and satellite pointing information we apply the first reduction steps to the time-ordered PACS data frames, identifying functional blocks in the data, flagging bad pixels, flagging any saturated data, converting detector signals from digital units to volts and the chopper position from digital units to physical angle." +" After adding to the time-ordered data frames the instantaneous pointing obtained from the Herschel pointing product, we apply ‘recentering’ corrections."," After adding to the time-ordered data frames the instantaneous pointing obtained from the Herschel pointing product, we apply `recentering' corrections." + These are derived by comparing PACS maps obtained in a separate first, These are derived by comparing PACS maps obtained in a separate first +A large fraction of Sevfert 1 galaxies show significant reddening of their continua and emission lines due (o an intrinsic column of dust. (Ward et al.,A large fraction of Seyfert 1 galaxies show significant reddening of their continua and emission lines due to an intrinsic column of dust (Ward et al. + 1987)., 1987). + X-ray observations ol a number of these galaxies show that the column density of neutral hydrogen is much, X-ray observations of a number of these galaxies show that the column density of neutral hydrogen is much +FO Aqe is an intermediate polar (1). à magnetic variant of he cataclvsmic-variable class of binary stars.,"FO Aqr is an intermediate polar (IP), a magnetic variant of the cataclysmic-variable class of binary stars." + Phese svstenis consist. of a Roche-Iobe-filling. late-type secondary and a white-dwarl primary. the latter having a strong magnetic ield 1110 AIG). inclined to the rotational axis of the star.," These systems consist of a Roche-lobe-filling, late-type secondary and a white-dwarf primary, the latter having a strong magnetic field 1–10 MG), inclined to the rotational axis of the star." + Phe in-falling matter forms an aceretion disc which is runcated at the magnetospheric boundary. where it threads onto the white dwarl’s magnetic field.," The in-falling matter forms an accretion disc which is truncated at the magnetospheric boundary, where it threads onto the white dwarf's magnetic field." + Phe material is then channeled into ‘accretion curtains’ which guide the material owards the poles. at which stand-olf shocks form. heating material. to 1107 SaIx. (soe. Patterson L994 for⋅ an in-depth. review)," The material is then channeled into `accretion curtains' which guide the material towards the poles, at which stand-off shocks form, heating material to $^8$ K (see Patterson 1994 for an in-depth review)." + The accretion geometry of FO Aqr has been the subject of much debate Lblellicr 1991: Norton 11992: Ποιος 1993: DBeardmore 11998: the last three hereafter referred to as N92. 1193 and. BOS respectively). but it is now generally accepted that the system shows disc-overflow accretion. with most of the material accreting via. disc-fed accretion curtains (causing à pulse at the 20.9-min. spin cycle). and a component of the accretion stream overflowing the disc and coupling to the magnetic field directly (causing a pulsation at the beat period between the spin and 4.85-hr orbital eveles).," The accretion geometry of FO Aqr has been the subject of much debate Hellier 1991; Norton 1992; Hellier 1993; Beardmore 1998; the last three hereafter referred to as N92, H93 and B98 respectively), but it is now generally accepted that the system shows disc-overflow accretion, with most of the material accreting via disc-fed accretion curtains (causing a pulse at the 20.9-min spin cycle), and a component of the accretion stream overflowing the disc and coupling to the magnetic field directly (causing a pulsation at the beat period between the spin and 4.85-hr orbital cycles)." + Whereas many LPs have quasi-sinusoical spin pulses. FO Aqr shows a more complex pulse. including a broader dip and a narrow Ποιο) feature. both of which are variable over time (N92. BOS).," Whereas many IPs have quasi-sinusoidal spin pulses, FO Aqr shows a more complex pulse, including a broader dip and a narrow `notch' feature, both of which are variable over time (N92, B98)." + Our aim here is to use the superior spectroscopic capability of the satellite to investigate the spin pulse and thus the way in which material leaves the accretion disc and threads onto field lines., Our aim here is to use the superior spectroscopic capability of the satellite to investigate the spin pulse and thus the way in which material leaves the accretion disc and threads onto field lines. +" The white cwarf in FO Aqr was spinning down during the 1980s (Shafter AIMaery 1987).. but Steiman-C'ameron.... Imamura SSteiman-Cameron> (1950)∖/ reportedpo that the !period-,lengthening had. almost stopped by the time of their 1987 observations."," The white dwarf in FO Aqr was spinning down during the 1980s (Shafter Macry 1987), but Steiman-Cameron, Imamura Steiman-Cameron (1989) reported that the period-lengthening had almost stopped by the time of their 1987 observations." + Osborne Alukai (L989) and Patterson (L998) found. that FO Aqr then began spinning up. which is confirmed by the most recent ephemeris by. Williams (2003).," Osborne Mukai (1989) and Patterson (1998) found that FO Aqr then began spinning up, which is confirmed by the most recent ephemeris by Williams (2003)." + However. these ephemerices sulfer from significant O—C' jitter and develop a Cvcle-count ambiguity for times later than £998 (Williams 2003).," However, these ephemerides suffer from significant $O-C$ jitter and develop a cycle-count ambiguity for times later than 1998 (Williams 2003)." + Thus we cannot compare the phasing of our data (rom 2001) with previous reports with any confidence., Thus we cannot compare the phasing of our data (from 2001) with previous reports with any confidence. + FO Aqr was observed by the satellite (Jansen et al., FO Aqr was observed by the satellite (Jansen et al. + 2001) for 37 ks on 2001 May. Nei12., 2001) for 37 ks on 2001 May 12. + Ehe. X-ray MOS-1.," The X-ray MOS-1," +large liniting maenitude of the IES survey (2B<17.5).,large limiting magnitude of the HES survey $B <17.5$ ). + When uniform distribution of the stellar halo is assumed. ( of the eiaut EMP survivors iu the Milky Wav halo are expected to be detected.," When uniform distribution of the stellar halo is assumed, $\sim 5\%$ of the giant EMP survivors in the Milky Way halo are expected to be detected." + In the following figures. we plot the predicted umber of stars which are expected to be in the WES sample. asstuing a uniform stellar halo.," In the following figures, we plot the predicted number of stars which are expected to be in the HES sample, assuming a uniform stellar halo." + When de Vaucouleurs density distribution is assed. detection frequency decreases by a factor of 5. since may undetectable stars should be distributed in the inner part of the Galactic halo from the solar orbit.," When de Vaucouleurs density distribution is assumed, detection frequency decreases by a factor of 5, since many undetectable stars should be distributed in the inner part of the Galactic halo from the solar orbit." + For clemental abundance ratio. we adopt data compiled bv the SAGA database(Sudaetal.2010).," For elemental abundance ratio, we adopt data compiled by the SAGA \citep{Suda10}." +. Figure 3. shows distributions of O. Na. Me. Si. Cr. aud Zu abuudauces relative to iron against ," Figure \ref{XFeobs} shows distributions of O, Na, Mg, Si, Cr, and Zn abundances relative to iron against $\feoh$." +We select lieh-resolutiou sample of R=20000., We select high-resolution sample of $R\geq20000$. + We [Fe/TI].note that. since SAGA compiles data from many sources. scatter of the abundances by the SAGA dataset can be larecr than the iutrisic scatter of the stellar abuucdances.," We note that, since SAGA compiles data from many sources, scatter of the abundances by the SAGA dataset can be larger than the intrinsic scatter of the stellar abundances." + To see the systematic difference between literatures. three subsamples analysed by ciffercut authors are plotted by different svinbols with error bars.," To see the systematic difference between literatures, three subsamples analysed by different authors are plotted by different symbols with error bars." + Blue trianeles(A) iu Fig., Blue $(\triangle)$ in Fig. + 3. denote data analysed bv the First Stars project (IBll(2002) aud other 13 papers of the seres)., \ref{XFeobs} denote data analysed by the First Stars project \citet{Hill02} and other 13 papers of the series). + Creeu squares(1) denote data of which first author of source paper is W.Aoki (Aokietal.(2002) and other 15 papers iu cutry list of SAGA)., Green $\square$ ) denote data of which first author of source paper is W.Aoki \citet{Aoki02} and other 15 papers in entry list of SAGA). + Alagenta inverted triaugle (V) shows sauple of IToudaetal.(2004.2007).," Magenta inverted triangle $(\triangledown)$ shows sample of \citet{Honda04, Honda07}." +. These three subsaniples are analysed assunninug a plane parallel stellar atmosphere (1D) aud local thermal equilibria (LTE) but there are systematic difference in the abuudauce ratio owing to difference iu model atinospheres. parameters used during the analysis. aud lines used in analysis.," These three subsamples are analysed assuming a plane parallel stellar atmosphere (1D) and local thermal equilibrium (LTE) but there are systematic difference in the abundance ratio owing to difference in model atmospheres, parameters used during the analysis, and lines used in analysis." + Other stars are plotted with red plus sigus (1) aud vellow CLOSSCS «) for eiuits(Tiag0.5$ are not plotted because their surface is thought to be polluted by binary mass transfer. + LNomivaoetal.(2007) show hat carbon on these stars originates mn he imtermediate uassive conipaundon stars and their surace abundances of O. Na aud Meg are also affected wv binary mass rausfer (Nishimuraetal.2009).," \citet{Komiya07} show that carbon on these stars originates in the intermediate massive companion stars and their surface abundances of O, Na and Mg are also affected by binary mass transfer \citep{Nishimura09}." +". Receutly. abundance deteriuuatious with a non-LTE scheme,eB.Masliouk-inactal2008:Andrevskywetal.2010) or with 3D nodel atimosplicres(e.e.AsplundGarcÁaPA2001:ConzAjlezIernAjudezetal.2008) are carried out."," Recently, abundance determinations with a non-LTE \citep[e.g.][]{Mashonkina08,Andrievsky10} or with 3D model \citep[e.g.][]{Asplund01,Gonzalez08} are carried out." + Difference of abuudances determined with these models from LD LITE iodels is often of order ~0.5 dex., Difference of abundances determined with these models from 1D LTE models is often of order $\sim 0.5$ dex. + They possibly dimunish the shift between elaut aud turnoff stars and decrease ο... of the abundance distribution., They possibly diminish the shift between giant and turnoff stars and decrease dispersion of the abundance distribution. + We conunent about 3D/uouLTE effects for sole elemieuts in next section with comparison to model results., We comment about 3D/nonLTE effects for some elements in next section with comparison to model results. + Figure |— shows resultant ietallicity distribution functions (MDEs) for three models ning different IMEs., Figure \ref{IMFMDF} shows resultant metallicity distribution functions (MDFs) for three models using different IMFs. + Solid red. dashed ereeu aud dotted blue Lues denote Models KI. LI. aud CIS. respectively.," Solid red, dashed green and dotted blue lines denote Models KK, LK, and CK, respectively." + All three models predict similar patterns of the NDEs but quite differcut total uunber of EXIP survivors., All three models predict similar patterns of the MDFs but quite different total number of EMP survivors. + This is because fractious of low-mass stars are differcut., This is because fractions of low-mass stars are different. + As seen in Fie. L..," As seen in Fig. \ref{IMFMDF}," + Model KI with the hieh mass ΤΝΤ is consistent witli observations but other models with the lower mass IMEs predict many more EMP survivors., Model KK with the high mass IMF is consistent with observations but other models with the lower mass IMFs predict many more EMP survivors. + We may overestima5 the efficiency. of the identification of EXP survivors by the TIES survey. because we assiune homogencity of the Galactic stellar halo aud the TES survey reaches the outer eud of the Galactic halo.," We may overestimate the efficiency of the identification of EMP survivors by the HES survey, because we assume homogeneity of the Galactic stellar halo and the HES survey reaches the outer end of the Galactic halo." + However. as seenin Fie. L.," However, as seen in Fig. \ref{IMFMDF}," + the predicted mmuber of EXIP survivors for Models Lis and CI is ~1001000 times larger than observations and this laree discrepancy cannot be explained by spatial inhomogencity of the stellar halo and/or iusufüciency of the survey., the predicted number of EMP survivors for Models LK and CK is $\sim 100-1000$ times larger than observations and this large discrepancy cannot be explained by spatial inhomogeneity of the stellar halo and/or insufficiency of the survey. + This indicates that typical mass of EMP population stars is segnificautlv higher than nearby Pop., This indicates that typical mass of EMP population stars is significantly higher than nearby Pop. + I stars. as shown m our earlier studies.," I stars, as shown in our earlier studies." + Figure 5. shows dependence on the SN viclds., Figure \ref{yieldMDF} shows dependence on the SN yields. + Solid red. loue-dashed ereen. short-dashed blue aud dotted magenta lines denote results of Models IKK. IW. KE. and KC. respectively.," Solid red, long-dashed green, short-dashed blue and dotted magenta lines denote results of Models KK, KW, KF, and KC, respectively." + All model results are similar iu the total nuuber of EMP survivors., All model results are similar in the total number of EMP survivors. + ΑΤΙΤΟΤΗ=3. the patterus of the àDF differ.," At $\feoh \lesssim -3$, the patterns of the MDF differ." + These extremely ietal deficicut stars are verycarly generations of stars formed with metal ejectedbv only one or a few SN progenitor(s) in their host halos., These extremely metal deficient stars are very early generations of stars formed with metal ejected by only one or a few SN progenitor(s) in their host halos. + A MDEF at [Fe/H|<3 is sensitive to individual SN yields., A MDF at $\feoh\lesssim-3$ is sensitive to individual SN yields. + The MDEF of Model II has a lauup at [Fe/II|~ 3.6., The MDF of Model KK has a hump at $\feoh\sim -3.6$ . + This is because iron vields of normal SNe Tare tuned to 0.07AL. in Ikobavashictal.(2006) and imetallicity of primordial uiini-halo with typical mass becomes [Fe/TI]|a~3.6 by a singleSN., This is because iron yields of normal SNe II are tuned to $0.07\msun$ in \citet{Kobayashi06} and metallicity of a primordial mini-halo with typical mass becomes $\feoh\sim-3.6$ by a singleSN. + We see a smaller lump at [Fe/TI| to 3 in other models. too.," We see a smaller hump at $\feoh=-4$ to $-3$ in other models, too." + In Model KEIN. since cuereetic," In Model KK, since energetic" +classify our sources as Classical Doubles (CD). Jetted sources (J) or Fat Doubles (FD).,"classify our sources as Classical Doubles (CD), Jetted sources (J) or Fat Doubles (FD)." + In terms of their Fanaroll-Riley classification (Fanaroll Riles 1974). Classical Doubles are always identified with FRIL-type sources whilst Fat Doubles are identified as ΕΙ or FRILL radio galaxies and Jetted: sources are generally identified: with FRI-type sources.," In terms of their Fanaroff-Riley classification (Fanaroff Riley 1974), Classical Doubles are always identified with FRII-type sources whilst Fat Doubles are identified as FRII or FRI/II radio galaxies and Jetted sources are generally identified with FRI-type sources." + Qur classifications can be found in Table 1 and full details can be found in Mitchell (2006)., Our classifications can be found in Table \ref{table:sample} and full details can be found in Mitchell (2006). +" In Figure 2 we show D, (4000) versus the low-frequeney radio Luminosity at 151 Mllz. Liz. for our galaxies. wit1 symbols corresponding to their spectral classification."," In Figure \ref{heglegplot} we show $_{n}$ (4000) versus the low-frequency radio luminosity at 151 MHz, $_{151}$, for our galaxies, with symbols corresponding to their spectral classification." + Moivated by figure 6 of Kaullmann et al. (, Motivated by figure 6 of Kauffmann et al. ( +"2003). we include a ashed line at D, (4000) 1.6 in order to illustrate dillerences in star formation.","2003), we include a dashed line at $_{n}$ (4000) = 1.6 in order to illustrate differences in star formation." +" Objects with D,,(4000) < 1.6 may have formed a noticeable fraction or greater) of heir stellar. mass in recent star. bursts in the moclels of ναπαπα ct al. (", Objects with $_{n}$ (4000) $<$ 1.6 may have formed a noticeable fraction or greater) of their stellar mass in recent star bursts in the models of Kauffmann et al. ( +2003).,2003). +" On the other hand. objects wit 1D, (4000) 7 1.6 show little or no evidence for recent star formation."," On the other hand, objects with $_{n}$ (4000) $>$ 1.6 show little or no evidence for recent star formation." +" This division at D,,(4000) = 1.6 therefore represents a conservative division. between objects which may have evidence of recent star formation. and those which do not."," This division at $_{n}$ (4000) = 1.6 therefore represents a conservative division between objects which may have evidence of recent star formation, and those which do not." + We reiterate that since we are unable to measure L9 [or our objects we are unable to be more specific as regards the star formation histories of our galaxies., We reiterate that since we are unable to measure $\delta$ for our objects we are unable to be more specific as regards the star formation histories of our galaxies. + Alindful of this note of caution. it is still. reaclily apparent that the galaxies form two distinct. populations.," Mindful of this note of caution, it is still readily apparent that the galaxies form two distinct populations." + One population. with lower radio luminosities (Lis.<1077 WV d ly is composed. exclusively ο| LEGs.," One population, with lower radio luminosities $_{151} < 10^{25.3}$ W $^{-1}$ $^{-1}$ ), is composed exclusively of LEGs." +" The galaxies in this population have systematically. higher D, (4000) indices ancl thus older stellar. populations.", The galaxies in this population have systematically higher $_{n}$ (4000) indices and thus older stellar populations. +" The second population. at higher radio luminosities (List10777? AN tse 4) and smaller D, (40)0) indices (vounger stellar. populations) consists mainly o “LEGS. altrough a [ow LECs are also present in this population."," The second population, at higher radio luminosities $_{151} > 10^{25.3}$ W $^{-1}$ $^{-1}$ ) and smaller $_{n}$ (4000) indices (younger stellar populations), consists mainly of HEGs, although a few LEGs are also present in this population." + 6C'0825|3407 and τς051919415 could belong to οἱher population (as cliscussecl in Section ?2?))., 6C0825+3407 and 7C0213+3418 could belong to either population (as discussed in Section \ref{d4000-em}) ). + We illustrate he clivision ονου the two populations by the vertical dashed line in Figure 2.., We illustrate the division between the two populations by the vertical dashed line in Figure \ref{heglegplot}. + Phe traditional division between FRE type anc ΙΙΙ tvpe radio galaxies falls at biz;=1y22.25 W xd and motivates our population division al this value., The traditional division between FRI type and FRII type radio galaxies falls at $_{151} = 10^{25.3}$ W $^{-1}$ $^{-1}$ and motivates our population division at this value. + “Phis is also the radio luminosity at which there is an apparent divergence in the evolution with redshift. the higher luminosity racio sources tending to evolve more strongly than the lower luminosity sources (Clewley Jarvis 2004: Sadler et al.," This is also the radio luminosity at which there is an apparent divergence in the evolution with redshift, the higher luminosity radio sources tending to evolve more strongly than the lower luminosity sources (Clewley Jarvis 2004; Sadler et al." + 2007)., 2007). +" Performing a two sided K-S test on the D, (4000) indices for the two populations enables us to reject at a significance of that the two populations are drawn from the same distribution.", Performing a two sided K-S test on the $_{n}$ (4000) indices for the two populations enables us to reject at a significance of that the two populations are drawn from the same distribution. + We also perform a Mann- (MWW) test on the two populations and, We also perform a Mann-Whitney-Wilcoxon (MWW) test on the two populations and +combined with this result derived from H emission observations at larger linear seales indicates that there is no significant change in the slope of the power spectrum over 45 orders of magnitude in linear scale.,combined with this result derived from H emission observations at larger linear scales indicates that there is no significant change in the slope of the power spectrum over $4-5$ orders of magnitude in linear scale. + This spectrum is significantly shallower than the Kolmogorov spectrum (with power law index of 11/3) expected from an incompressible turbulent medium (Kolmogorov1941)., This spectrum is significantly shallower than the Kolmogorov spectrum (with power law index of $11/3$ ) expected from an incompressible turbulent medium \citep{ko41}. + This may be because of the fact that the turbulence in H is compressible and magnetohydrodynamic in nature (seeRoy2009.fordiscussiononthis issue).," This may be because of the fact that the turbulence in H is compressible and magnetohydrodynamic in nature \citep[see][for discussion on this +issue]{nr09}." + If the density fluctuation is small compared to the mean density. then for gas in pressure equilibrium. the slope of the opacity fluctuation power spectrum will be nearly the same as that of —the density fluctuation power spectrum (Deshpandeetal. 2000).," If the density fluctuation is small compared to the mean density, then for gas in pressure equilibrium, the slope of the opacity fluctuation power spectrum will be nearly the same as that of the density fluctuation power spectrum \citep{de00}." +. However. fluctuations in both the density and velocity fields contribute to the observed H opacity fluctuations.," However, fluctuations in both the density and velocity fields contribute to the observed H opacity fluctuations." +" It can be shown that for the power spectrum estimated from ""thick slices”. i.e. those with velocity width larger than the turbulent velocity dispersion. the contribution is only from the density fluctuations. and all velocity information get averaged out (Lazarian&Pogosyan2000)."," It can be shown that for the power spectrum estimated from “thick slices”, i.e. those with velocity width larger than the turbulent velocity dispersion, the contribution is only from the density fluctuations, and all velocity information get averaged out \citep{lp00}." +". So. for ""thick slices"". the intensity fluctuation is dominantly due to density fluctuation and the observed power law index 1 is expected to be same as the index of the density fluctuation power spectrum."," So, for “thick slices”, the intensity fluctuation is dominantly due to density fluctuation and the observed power law index $n$ is expected to be same as the index of the density fluctuation power spectrum." +" On the other hand. for ""thin slices"". the power law index of the observed power spectrum is |2/2. where «7 is the power law index of the velocity structure function."," On the other hand, for “thin slices”, the power law index of the observed power spectrum is $n + \beta/2$, where $\beta$ is the power law index of the velocity structure function." + Hence. it is possible to decouple the density and velocity fluctuations from the power spectra derived from “thin” and “thick” velocity channels.," Hence, it is possible to decouple the density and velocity fluctuations from the power spectra derived from “thin” and “thick” velocity channels." + Lazarian&Pogosyan2000) reported a near-Kolmogorov power law index for both density and velocity fluctuations power spectra for the Milkv Way and the Small Magellanie Cloud by applying this technique to the H emission data (Green1993:Stanimiroviéetal.1999).," \citet{lp00} reported a near-Kolmogorov power law index for both density and velocity fluctuations power spectra for the Milky Way and the Small Magellanic Cloud by applying this technique to the H emission data \citep{gr93,st99}." +. For our data. we find that though there is à very weak trend of smaller à for arger channel width. the observed change of a by about 0.1 for a change of velocity width from — 0.4to —12.8 kms. + is within 18 10 error bar.," For our data, we find that though there is a very weak trend of smaller $\alpha$ for larger channel width, the observed change of $\alpha$ by about $-0.1$ for a change of velocity width from $\sim +0.4$ to $\sim 12.8$ km $^{-1}$ is within the $1~\sigma$ error bar." +" Since à remains unchanged for ""thin slices” with velocity width as small as 0.4 km 7. ie. much smaller than the ypical value of 4.0 kms. ο forturbulent dispersion in Galactic cold H rcRadhakrishnanetal.1972).. we can constrain to be 0.20.6 (3n error)."," Since $\alpha$ remains unchanged for “thin slices” with velocity width as small as $\sim 0.4$ km $^{-1}$ , i.e. much smaller than the typical value of $4.0$ km $^{-1}$ for turbulent dispersion in Galactic cold H \citep{ra72}, we can constrain $\beta$ to be $0.2 \pm 0.6$ $3\sigma$ error)." + This is consistent with the value of ;7=3j2/3 predicted or turbulence in an incompressible medium (Kolmogorov[941)., This is consistent with the value of $\beta = 2/3$ predicted for turbulence in an incompressible medium \citep{ko41}. +. In this work. we have studied the H 21 em opacity fluctuation towards Cas A. A simple but robust method of directly estimating the power spectrum from the observed visibilities is outlined.," In this work, we have studied the H 21 cm opacity fluctuation towards Cas A. A simple but robust method of directly estimating the power spectrum from the observed visibilities is outlined." + In this analysis we avoid the complications of imaging the bright. extended continuum source. of subtracting the continuum and of making optical depth image for channels with H absorption.," In this analysis we avoid the complications of imaging the bright, extended continuum source, of subtracting the continuum and of making optical depth image for channels with H absorption." + We have found that the H1 opacity fluctuation power spectrum can be modelled as a power law with an index of 2.856+0.10 (30 error)., We have found that the H opacity fluctuation power spectrum can be modelled as a power law with an index of $-2.86 \pm 0.10$ $3\sigma$ error). + This is consistent with earlier observational results., This is consistent with earlier observational results. + We lave not found any significant difference of the power law index between velocity channels with absorption produced by the gas rom the Perseus arm and the Local arm., We have not found any significant difference of the power law index between velocity channels with absorption produced by the gas from the Perseus arm and the Local arm. + We have also checked. by smoothing the visibility data for adjacent channels. if there is variation of the power law index with the velocity width of channels.," We have also checked, by smoothing the visibility data for adjacent channels, if there is variation of the power law index with the velocity width of channels." + It is found that. within the estimation errors. the power aw index remains constant for a wide range of velocity widths.," It is found that, within the estimation errors, the power law index remains constant for a wide range of velocity widths." + We can not. however. rule out contribution of velocity fluctuations o the observed opacity fluctuations if the power law index of the velocity structure function is 0.2+0.6 (eq error).," We can not, however, rule out contribution of velocity fluctuations to the observed opacity fluctuations if the power law index of the velocity structure function is $0.2 \pm 0.6$ $3\sigma$ error)." + We plan to apply. in future. this visibility based method to study the opacity fluctuations for other lines of sight in different regions of the Galaxy.," We plan to apply, in future, this visibility based method to study the opacity fluctuations for other lines of sight in different regions of the Galaxy." + We thank the staff of the GMRT who have made these observations possible., We thank the staff of the GMRT who have made these observations possible. + PD would like to acknowledge HRDG CSIR and SRIC. IIT. Kharagpur for providing financial support.," PD would like to acknowledge HRDG CSIR and SRIC, IIT, Kharagpur for providing financial support." + S.B. would like to acknowledge financial support from. BRNS. DAE through the project 2007/37/1I/BRNS/357.," S.B. would like to acknowledge financial support from BRNS, DAE through the project 2007/37/11/BRNS/357." + We are grateful to Rajaram Nityananda and Sanjit Mitra for many helpful comments., We are grateful to Rajaram Nityananda and Sanjit Mitra for many helpful comments. +We are also grateful to the anonymous referee for prompting us into substantially improving this paper.,We are also grateful to the anonymous referee for prompting us into substantially improving this paper. +arises against this component. this would require a fairly high optical depth (τ2 0.5).,"arises against this component, this would require a fairly high optical depth $\tau \ga 0.5$ )." + The 21em absorption is thus most likely to arise against the brighter components A. B. C and D (and perhaps the arc of radio emission between A and B). each of which have flux densities 2100 mJy at 1.7 GHz.," The 21cm absorption is thus most likely to arise against the brighter components A, B, C and D (and perhaps the arc of radio emission between A and B), each of which have flux densities $\ga 100$ mJy at 1.7 GHz." + We note that component A also shows evidence for scatter broadening at frequencies below 5 GHz while D is the most strongly reddened of the source components: on the other hand. B is the bluest of all components and shows no evidence for scatter broadening in the VLBA images (W03).," We note that component A also shows evidence for scatter broadening at frequencies below 5 GHz while D is the most strongly reddened of the source components; on the other hand, B is the bluest of all components and shows no evidence for scatter broadening in the VLBA images (W03)." + This suggests that there is relatively less dust and gas along the line of sight to component B; the two main 21em features thus appear most likely to arise from absorption against components A and D. We have explored these possibilities with a simple kinematic model using a differentially rotating disk absorber., This suggests that there is relatively less dust and gas along the line of sight to component B; the two main 21cm features thus appear most likely to arise from absorption against components A and D. We have explored these possibilities with a simple kinematic model using a differentially rotating disk absorber. + The modelling does not produce a unique result. but rather succeeds in demonstrating that a single. massive galaxy could indeed be responsible for the 21em absorption profile.," The modelling does not produce a unique result, but rather succeeds in demonstrating that a single, massive galaxy could indeed be responsible for the 21cm absorption profile." + If a more complex. multi-galaxy system were to be invoked. there would be ample free parameters to fit the integral spectrum reported here.," If a more complex, multi-galaxy system were to be invoked, there would be ample free parameters to fit the integral spectrum reported here." + Further observational progress will require radio interferometry to separate the absorption along different lines of sight., Further observational progress will require radio interferometry to separate the absorption along different lines of sight. + The philosophy of modelling the 21em profile shape is based on the assumption that narrow absorption features occur in the spectrum when à compact. high-surface brightness image of the background radio source “selects” a small patch from an extended. smooth velocity field of a rotating galaxy.," The philosophy of modelling the 21cm profile shape is based on the assumption that narrow absorption features occur in the spectrum when a compact, high-surface brightness image of the background radio source “selects” a small patch from an extended, smooth velocity field of a rotating galaxy." + Thus. the two mam narrow 21em features of Fig.," Thus, the two main narrow 21cm features of Fig." + | are expected to be associated with specific source components of the background source. once VLBI observations are conducted in the 21 em line.," \ref{fig:lowres} are expected to be associated with specific source components of the background source, once VLBI observations are conducted in the 21 cm line." + The modelling uses the source structure obtained from the 1.7 GHz VLBA maps of W03 for the compact radio components. with a scaling in flux to both match the relative flux densities of the components in the higher frequency bands. and still produce the integral flux density measured at 805 MHz by our WSRT observations.," The modelling uses the source structure obtained from the 1.7 GHz VLBA maps of W03 for the compact radio components, with a scaling in flux to both match the relative flux densities of the components in the higher frequency bands, and still produce the integral flux density measured at 805 MHz by our WSRT observations." + The more extended components C and E had to be supplemented with diffuse gaussian components to account for the flux missing from the VLBA map., The more extended components C and E had to be supplemented with diffuse gaussian components to account for the flux missing from the VLBA map. + The two models discussed here (and shown in Fig. 2[{[, The two models discussed here (and shown in Fig. \ref{fig:models}[ [ +B]) are representative of two broad classes which can reproduce the observed 21cm profile.,B]) are representative of two broad classes which can reproduce the observed 21cm profile. + It should be emphasized. however. that neither class is able to account for the observations simultaneously. including the scatter broadening and reddening of different source. components.," It should be emphasized, however, that neither class is able to account for the observations simultaneously, including the scatter broadening and reddening of different source components." + Both models are axially symmetric. planar systems with rotation curves that are flat at Vi in the outer regions. with a linear rise from the centre to Αι.," Both models are axially symmetric, planar systems with rotation curves that are flat at $V_{\rm rot}$ in the outer regions, with a linear rise from the centre to $R_{\rm c}$." +" The systemic velocity of the galaxy is offset from 805 MHz (z= 0.76448) by Voy. and the galaxy centroid is specified by the projected positional offsets AX (west). AY (north) relative to image D. The HI optical depth profile for each pixel is broadened by a velocity dispersion of «e,=7 km s! before computing that pixel’s contribution to the integral absorption spectrum."," The systemic velocity of the galaxy is offset from 805 MHz $z=0.76448$ ) by $V_{\rm off}$, and the galaxy centroid is specified by the projected positional offsets $\Delta X$ (west), $\Delta Y$ (north) relative to image D. The HI optical depth profile for each pixel is broadened by a velocity dispersion of $\sigma_{\rm v}=7$ km $^{-1}$ before computing that pixel's contribution to the integral absorption spectrum." + Models belonging to class I are motivated by the need to inflict heavy reddening on image D without reddening B. coupled with accounting for the scatter broadening of A and C. However. this model does not account for the scatter," Models belonging to class I are motivated by the need to inflict heavy reddening on image D without reddening B, coupled with accounting for the scatter broadening of A and C. However, this model does not account for the scatter" +colliding is somewhat steeper than those observed for molecular clouds.,colliding is somewhat steeper than those observed for molecular clouds. + However this distribution of gas is an extreme case. as in general the gas would be comprised. of multiple clumps of various sizes.," However this distribution of gas is an extreme case, as in general the gas would be comprised of multiple clumps of various sizes." + We now consider many collisions and. calculate the average velocity. dispersion. at each size scale., We now consider many collisions and calculate the average velocity dispersion at each size scale. + In all the collisions. we still assume 2 clumps collide. and fix the radius of the first clump to 1.," In all the collisions, we still assume 2 clumps collide, and fix the radius of the first clump to 1." + However both the impact parameter b and the second clump radius. ro. can be varied.," However both the impact parameter $b$ and the second clump radius, $r_{2}$, can be varied." + We show 3 dilferent possibilities for the collisions of clumps in Fig., We show 3 different possibilities for the collisions of clumps in Fig. + 17., 17. + Firstly we vary b randomly. assuming a probability clistribution function of f(b)=1. Q$ 2 clumps collide simultaneously, or 2 clumps collide with each other before colliding with further material in the shock." + The latter is evident in the simulations. where lavers of clumps enter the shock and interact with each other.," The latter is evident in the simulations, where layers of clumps enter the shock and interact with each other." + This is again likely to produce a shallower relation compared. with the caleulations in this section., This is again likely to produce a shallower relation compared with the calculations in this section. + Overall. for the most. structured. distribution of 2 olfset clumps colliding. the resulting velocity size-scale relation is steep. @xrt.," Overall, for the most structured distribution of 2 offset clumps colliding, the resulting velocity size-scale relation is steep, $\sigma \propto r^1$." + For the least. structured clistribution. ic. uniform gas. the velocity size-scale relation of the shock is Hat.," For the least structured distribution, i.e. uniform gas, the velocity size-scale relation of the shock is flat." + In reality. the distribution of gas. ancl therefore the gradient of the velocity size-scale relation. is likely to lie within these two extremes.," In reality, the distribution of gas, and therefore the gradient of the velocity size-scale relation, is likely to lie within these two extremes." + We have presented. simulations and analysis of shocks for initial clistributions of uniform. clumps. and fractal gas.," We have presented simulations and analysis of shocks for initial distributions of uniform, clumpy and fractal gas." + We lind an increasing velocity size scale relation in all our results similar to that observed. except for the uniform shocks.," We find an increasing velocity size scale relation in all our results similar to that observed, except for the uniform shocks." + For example. for a 2.2 D fractal distributionrepresentative of the [SAL the velocity size-scale. relation is approximately axe’Oot 7)," For example, for a 2.2 D fractal distributionrepresentative of the ISM, the velocity size-scale relation is approximately $\sigma \propto r^{0.4}$ \citet{Falgarone2005})" + For example. for a 2.2 D fractal distributionrepresentative of the [SAL the velocity size-scale. relation is approximately axe’Oot 7):," For example, for a 2.2 D fractal distributionrepresentative of the ISM, the velocity size-scale relation is approximately $\sigma \propto r^{0.4}$ \citet{Falgarone2005})" +be supplied by an BO.5 ZAMS star with a Iuminositv of 1.1x10!L..,be supplied by an B0.5 ZAMS star with a luminosity of $1.1\times10^4$. +. The FIR luminosity of the region inferred [rom the URAS observations is. however. 1.0x10° (Sricharan et al.," The FIR luminosity of the region inferred from the IRAS observations is, however, $1.0\times 10^5$ (Sridharan et al." + 2002)., 2002). + The most likely explanation for (he discrepancy in (he luminosities inlerred from the radio and FUR observations is that. due to the coarse angular resolution of the IRAS observations. the FIR luminosity includes the contribution of the star or stars ionizing the large cometary LI] region located NW of the dense core (see Fig.," The most likely explanation for the discrepancy in the luminosities inferred from the radio and FIR observations is that, due to the coarse angular resolution of the IRAS observations, the FIR luminosity includes the contribution of the star or stars ionizing the large cometary HII region located NW of the dense core (see Fig." + 5)., 5). + This cometary HII region has a flix density of ~20 mJv. which requires a D0.5 ZAMS star with a luminosity of 2.0x1011. ito maintain its ionization.," This cometary HII region has a flux density of $\sim$ 20 mJy, which requires a B0.5 ZAMS star with a luminosity of $2.0\times 10^4$ to maintain its ionization." + Another contributing effect could be absorption of UV photons by dust within the hvpercompact HII region., Another contributing effect could be absorption of UV photons by dust within the hypercompact HII region. + There is no archive Spitzer data for this source., There is no archive Spitzer data for this source. + We made 7 mim. high-angular resolution. continuum observations. using the VLA. towards (hiree regions of massive star formation thought to be in early stages of evolution.," We made 7 mm, high-angular resolution, continuum observations, using the VLA, towards three regions of massive star formation thought to be in early stages of evolution." + These regions are associated. with energetic molecular outflows and two of them were not previously detected in radio continuum observations with the VLA., These regions are associated with energetic molecular outflows and two of them were not previously detected in radio continuum observations with the VLA. + The main objective was to search [ον the presence of disks ancl/or hyvpercompact regions of ionized gas., The main objective was to search for the presence of disks and/or hypercompact regions of ionized gas. + Our main results aud conclusions are as follows., Our main results and conclusions are as follows. + Emission al 7 mm was detected toward the three regions., Emission at 7 mm was detected toward the three regions. + Towards IRAS 18470-0044 we detected (wo objects with spectral indices between 4.8 and 43.4 GIIz of ~—0.1. indicating that the emission is Iree-free radiation arising [rom optically (hin II] regions excited bv stars with spectral tvpes BO.5.," Towards IRAS 18470-0044 we detected two objects with spectral indices between 4.8 and 43.4 GHz of $\sim-0.1$, indicating that the emission is free-free radiation arising from optically thin HII regions excited by stars with spectral types B0.5." + We conclude that these small HID regions are embedded within massive and dense cores aud have already. reached. pressure. equilibrium with (heir dense and turbulent molecular surroundings., We conclude that these small HII regions are embedded within massive and dense cores and have already reached pressure equilibrium with their dense and turbulent molecular surroundings. + In the case of RAS 192174-1651 we detect (wo components: component A is a hypercompact I] region that is optically thick below 15 Gllz. while component D is optically thin in the 8.1 to 22.5 Gllz range.," In the case of IRAS 19217+1651 we detect two components: component A is a hypercompact HII region that is optically thick below 15 GHz, while component B is optically thin in the 8.4 to 22.5 GHz range." + We discuss if component B could be ionized gas oulllowing from component A but conclude that each component has its own ionizing star., We discuss if component B could be ionized gas outflowing from component A but conclude that each component has its own ionizing star. +" Towards IAS 23151+5912 we detected à hvpercompact WI] region that can be modeled as a source with a radius of 3x10.| pe (or 57 AU) and an emission measure of 2.3x10? pe ο,", Towards IRAS 23151+5912 we detected a hypercompact HII region that can be modeled as a source with a radius of $3\times10^{-4}$ pc (or 57 AU) and an emission measure of $2.3\times10^9$ pc $^{-6}$. + We conclude that IRAS 2315145912 is indeed a massive star lorming region in a very early stage of evolution. with the hvpercompact III region being formed while the suspected hot molecular core around it is still probably undergoing accretion.," We conclude that IRAS 23151+5912 is indeed a massive star forming region in a very early stage of evolution, with the hypercompact HII region being formed while the suspected hot molecular core around it is still probably undergoing accretion." +Furthermore. ofthe ELALS N2 area is covered by the parent sample of the quasar. ic. only about of the total LELAIS area.,"Furthermore, of the ELAIS N2 area is covered by the parent sample of the quasar, i.e., only about of the total ELAIS area." +" The total number of random associations in the overlap region is therefore only z 1 "". eiving strong support for the reality of the PLLOT-quasar association."," The total number of random associations in the overlap region is therefore only $\approx$ 1 $\times$ $^{-3}$, giving strong support for the reality of the PHOT-quasar association." + The quasar does not appear in the ESC or FSR catalogues., The quasar does not appear in the FSC or FSR catalogues. + To test the reliability of our PILOT detection. we made ADDSCANS of the source. as well as of 15 galaxies with reliable 90 detections at similar flux densities (60-80. mJv) from the Paper HIE catalogue. anc 16 control positions at random 20 ollsets from the targe »ositions.," To test the reliability of our PHOT detection, we made ADDSCANs of the source, as well as of 15 galaxies with reliable 90 detections at similar flux densities (60-80 mJy) from the Paper III catalogue, and 16 control positions at random $'$ offsets from the target positions." + We found our ΠΟΣΤ 90 data to be not wel reproduced by the ADDSCAN LOO measurements. although most of the Dux densities were »ositive.," We found our PHOT 90 data to be not well reproduced by the ADDSCAN 100 measurements, although most of the flux densities were positive." + However. the control fields gave values distribute around zero as expected. from. which we derived a zz de ADDSCAN detection of our. PIIO'T. source.," However, the control fields gave values distributed around zero as expected, from which we derived a $\approx$ $\sigma$ ADDSCAN detection of our PHOT source." + This confirms he reality ofthe source. but we also conclude that it is too faint to reliably measure the Dux density with ADDSCANS.," This confirms the reality of the source, but we also conclude that it is too faint to reliably measure the flux density with ADDSCANs." + We only consider in the following upper limits from the FSC., We only consider in the following upper limits from the FSC. + Optical spectroscopy was obtained. at the Nordic Optical Telescope. using z 700) in. non- S. . ↓≻⇂↥∪⋯⊔↓∢⋅↿↓⋅⊔⇍≼⇍∪⊔∠⊔↿↓∪⊔⊳∖⋜⋯∠⇂⊳∖⋖⋅⋖, Optical spectroscopy was obtained at the Nordic Optical Telescope using $\approx$ 700) in non-photometric conditions and seeing of $''$. +⋅↓⊔⋏∙≟∪⇂↓⊳⋅↱≻⊳∖∖⋖⊾⊔⊳∖⋖⋅∠⇂⋜↧↓⊳⇉− ⋅∕∕⇁ ∕∕ ∖∖⋰⊔⇂∢⋅⊳∖∐↿∪↓⋅⊲↓∢⊾⊔⋖⋅∠⊔⊲⇀⊲∖∖, We used a $''$ -wide slit oriented EW. +⊽⊳↾↓∖⇂⊔⊾⋖⋅⇀∖↓≻∪⊳∖⊔↓⋅⋖⋅↿↕⊔↓∢⊾∖∖⋎⋜↧⊳∖∶∫≻≼⋗∪∪⊳∖⊳ The spectrum. was reduced. using standard. routines and is shown in Figure 2., The exposure time was 3 $\times$ 900 s. The spectrum was reduced using standard routines and is shown in Figure 2. + We derive a redshift:ς = 1.099 + 0.002., We derive a redshift: = 1.099 $\pm$ 0.002. + This value is consistent with previous estimates (Crampton. Cowley. Lartwick 1989). and is used in the Following.," This value is consistent with previous estimates (Crampton, Cowley, Hartwick 1989), and is used in the following." + Table 1l gives the relative line Huxes. EWs. and ENIMS.," Table 1 gives the relative line fluxes, EWs, and FWHMs." + ‘Table 2 summarizes the available photometric cata for this selclomestuclieck object., Table 2 summarizes the available photometric data for this seldom-studied object. + New sub-min observations (see Farrah 2001) were carried out with the Submillimetre Comnmon-User. Bolometer Array (SCUBA) at. the. James Clerk Maxwell. “Telescope CCMIT) in. photometry mode., New sub-mm observations (see Farrah 2001) were carried out with the Submillimetre Common-User Bolometer Array (SCUBA) at the James Clerk Maxwell Telescope (JCMT) in photometry mode. + Data reduction was performed. using thestandard. SURE pipeline software., Data reduction was performed using thestandard SURF pipeline software. + Lhe source is undetected. both at 450 ancl SSOμα. with 30 upper limits of S1.6 and 6.96 nilv. respectively.," The source is undetected both at 450 and 850, with $\sigma$ upper limits of 81.6 and 6.96 mJy, respectively." + The region surrounding the HyvLIG has unfortunately not been observed as part of the radio survey of the northern IELAIS areas (Ciliegi 1999). but the available racio flux limits imply that this quasar is raclio-quiet. (Sopp Alexander 1991).," The region surrounding the HyLIG has unfortunately not been observed as part of the radio survey of the northern ELAIS areas (Ciliegi 1999), but the available radio flux limits imply that this quasar is radio-quiet (Sopp Alexander 1991)." + Following Vérron-Cetty Vérron (2000). we obtain: My z 26.0 mag.," Following Vérron-Cetty Vérron (2000), we obtain: $M_{\rm B}$ $\approx$ – 26.0 mag." + The SED is displaved in Figure 3., The SED is displayed in Figure 3. + Assuming that the host galaxy is similar to coeval quasars (e.g.. AleLure 1999). we used the radio galaxy relation of Eales (1997) to estimate the host galaxy near-I0t magnitude. obtaining: A = 17.0 τε 0.4 mag.," Assuming that the host galaxy is similar to coeval quasars (e.g., McLure 1999), we used the radio galaxy relation of Eales (1997) to estimate the host galaxy near-IR magnitude, obtaining: $K$ = 17.0 $\pm$ 0.4 mag." + As can be seen in Fig.3. the contribution of the host galaxy to the SED is negligible.," As can be seen in Fig.3, the contribution of the host galaxy to the SED is negligible." + In order to estimate the energy. budgets to the It luminosity. we mocelled the SED by simultaneously considering mocdels for dust-enshrouded ACGNs (Efstathiou Rowan-Robinson 1995) and starbursts (Efstathiou. Rowan-Robinson. Sichenmoregen 20000).," In order to estimate the energy budgets to the IR luminosity, we modelled the SED by simultaneously considering models for dust-enshrouded AGNs (Efstathiou Rowan-Robinson 1995) and starbursts (Efstathiou, Rowan-Robinson, Siebenmorgen 2000b)." + Although we do not claim to have exhaustively explored the possible physical parameter space of these models. we found that the SED is most naturally explained by a combination of these two components.," Although we do not claim to have exhaustively explored the possible physical parameter space of these models, we found that the SED is most naturally explained by a combination of these two components." + Pure AGN models have dilliculties in accounting for the far-LHi emission., Pure AGN models have difficulties in accounting for the far-IR emission. + We achieve a satisfactory fit to the SED (see Fig.3) by assuming roughly similar contributions from dust. &rains heated by the nuclear UV/optical continuum (Lay a 5.2 107? 5.2 L. ) and by a starburst (Lrz 5.0 « 1077 f. E.), We achieve a satisfactory fit to the SED (see Fig.3) by assuming roughly similar contributions from dust grains heated by the nuclear UV/optical continuum $L_{\rm IR}^{\rm AGN}$ $\approx$ 5.2 $\times$ $^{12}$ $h_{65}^{-2}$ $_{\odot}$ ) and by a starburst $L_{\rm IR}^{\rm SB}$$\approx$ 5.0 $\times$ $^{12}$ $h_{65}^{-2}$ $_{\odot}$ ). + The dilliculties in fitting the region around 3-7 might be related to uncertainties in the ISOCAM absolute calibration aper LH)., The difficulties in fitting the region around 3-7 might be related to uncertainties in the ISOCAM absolute calibration (Paper II). +" The fofed rest-frame LI. luminosity we derive: Lip, 1000 yam) zm 1.02 1055 ο65E L.. is slightly above the iweshold for a LIVLIC classification in the scheme of Iti."," The rest-frame IR luminosity we derive: $L_{\rm IR}$ (1-1000 $\mu$ m) $\approx$ 1.02 $\times$ $^{13}$ $h_{65}^{-2}$ $_{\odot}$ , is slightly above the threshold for a HyLIG classification in the scheme of RR." +evel L.,level 4. +" Above the horizon the tail of downeoing unous is visiblο,", Above the horizon the tail of downgoing muons is visible. + However. where at eut level 2 and 3 a background of fakes is present below t1ο horizon. a cluster of upeoing tracks appears which is separated frou the downgoing ~ackeround.," However, where at cut level 2 and 3 a background of fakes is present below the horizon, a cluster of upgoing tracks appears which is separated from the downgoing background." + The 17 of L9105 eveuts which pass he highest quality cuts are concentrated at larger zenith angeles., The 17 of $4.9\cdot 10^8$ events which pass the highest quality cuts are concentrated at larger zenith angles. + The distribution iu rigif ascension is. statisticalv consistent with a random distributio1., The distribution in right ascension is statistically consistent with a random distribution. + Acose 1ispectiou of 1e spatial fopology aud the amplitudes of the 17 events shows that one of ιο 1T events is likely to be a ij initiated’ cascade or a breistra1ung event., A close inspection of the spatial topology and the amplitudes of the 17 events shows that one of the 17 events is likely to be a $\nu_e$ initiated cascade or a bremstrahlung event. + The eveut cjuracteristics of the remaimine 16 events are d1 agxOnewt with 16 expectation for upeoiug neutrino nkuced iuuons., The event characteristics of the remaining 16 events are in agreement with the expectation for upgoing neutrino induced muons. + A disav of a neutrino adidate weuch extends over a leugth o: nua through the euire ¢etector is shown by Halzen ο., A display of a neutrino candidate which extends over a length of m through the entire detector is shown by Halzen \cite{halzen}. + Tje upward moving siguature of this event is ilhstrated -1 figure 2 where the ohoton arrival times of this event are pksttoc VOrsus the depth of the seusors., The upward moving signature of this event is illustrated in figure \ref{ArrTimeVsDepth_1197960} where the photon arrival times of this event are plotted versus the depth of the sensors. + The slope maches the vertical velocity of a track recoustructec Lata zeuihn augle of 155°. which agrees with the resul of the full Chereukov cone fit.," The slope matches the vertical velocity of a track reconstructed at a zenith angle of $155^\circ$, which agrees with the result of the full Cherenkov cone fit." + Figure 2. also srows the amplitudes as a function of distance of t10 reconstiiited mou track., Figure \ref{ArrTimeVsDepth_1197960} also shows the amplitudes as a function of distance of the reconstructed muon track. + The observed photon deusity is high for sensors οose to the rack., The observed photon density is high for sensors close to the track. +" A full simulation of atmospheric neutrinos has been performed which predicts that 21 1,i aud 7;"" events pass the level cuts.", A full simulation of atmospheric neutrinos has been performed which predicts that 21 $\nu_\mu$ and $\overline{\nu_\mu} $ events pass the level 4 cuts. + Fieuree 3. shows the zenith aueleoO distribution of all eveuts at level 1 along with the prediction of the atmospheric, Figure \ref{level4_zenith_overlay_cos} shows the zenith angle distribution of all events at level 4 along with the prediction of the atmospheric +context has been realised in pioneering works early on ??7).. ,"context has been realised in pioneering works early on \citep[e.g.][]{Bekenstein1973, Blandford1979, + Kapoor1985}." +"More recently, analytical and numerical studies (e.g.173) have found that globular clusters and dwarf galaxies are the prime targets for getting depleted of their central BHs."," More recently, analytical and numerical studies \citep[e.g.][]{Merritt2004, Boylan2004, Madau2004, Micic2006} have found that globular clusters and dwarf galaxies are the prime targets for getting depleted of their central BHs." +" Moreover, recoiled BHs which do not escape their host galaxies are likely to induce stellar cores through repeated passages close to the centre."," Moreover, recoiled BHs which do not escape their host galaxies are likely to induce stellar cores through repeated passages close to the centre." +" In the case of purely stellar systems, accurate N-body simulations (forarecentstudysee7) have led to a good understanding how gravitationally recoiled BHs orbit in spherical systems and what their typical return timescales for different kick velocities are."," In the case of purely stellar systems, accurate N-body simulations \citep[for + a recent study see][]{Gualandris2008} have led to a good understanding how gravitationally recoiled BHs orbit in spherical systems and what their typical return timescales for different kick velocities are." +" For systems with gas, however, only a handful of numerical studies (e.g.??7) are available."," For systems with gas, however, only a handful of numerical studies \citep[e.g.][]{Kornreich2008, + Devecchi2009, Guedes2011} are available." + These studies computed the trajectories of recoiled BHs and accounted for their possible interaction with the surrounding gas., These studies computed the trajectories of recoiled BHs and accounted for their possible interaction with the surrounding gas. +" Adopting a semi-analytical approach, BH luminosities during the wandering phase have nevertheless been estimated (e.g.????).."," Adopting a semi-analytical approach, BH luminosities during the wandering phase have nevertheless been estimated \citep[e.g.][]{VolonteriPerna2005, + Blecha2008, Fujita2009, Guedes2011}." +" Recently, ? performed simulations of BH binaries embedded in a circum-nuclear disc allowing for gas accretion, and by analytically tracing BH spin evolution, found that high recoil velocities should not be very likely."," Recently, \citet{Dotti2010} + performed simulations of BH binaries embedded in a circum-nuclear disc allowing for gas accretion, and by analytically tracing BH spin evolution, found that high recoil velocities should not be very likely." +"While observationally several candidates for recoiled BHs have been proposed (??,, but see ?1)), there is scarce evidence for luminous recoiled quasars, at least in the case of large kinematic offsets (7).","While observationally several candidates for recoiled BHs have been proposed \citet{Komossa2008, Civano2010}, but see \citet{Shields2009, Heckman2009}) ), there is scarce evidence for luminous recoiled quasars, at least in the case of large kinematic offsets \citep{Bonning2007}." +". For galaxies containing gas, the evolution of recoiled BHs can possibly vary significantly depending on the mass fraction of the gas, and its spatial distribution and thermodynamic state."," For galaxies containing gas, the evolution of recoiled BHs can possibly vary significantly depending on the mass fraction of the gas, and its spatial distribution and thermodynamic state." + This situation presents a much more complex problem than for purely stellar systems., This situation presents a much more complex problem than for purely stellar systems. +" For example, recoiled BHs might accrete some of the interstellar gas which could in return affect their trajectory."," For example, recoiled BHs might accrete some of the interstellar gas which could in return affect their trajectory." +" Also, if BH feedback effects associated with accretion are not negligible, they could provide distributed heating throughout the galaxy."," Also, if BH feedback effects associated with accretion are not negligible, they could provide distributed heating throughout the galaxy." + It is clear that a full understanding of thesepossibilities will require the exploration of a large parameter space., It is clear that a full understanding of thesepossibilities will require the exploration of a large parameter space. +" At redshifts of z~2—3, galaxy mergers are much more common in the hierarchical structure formation scenario than at the present day, and it is believed that many galaxies are gas-rich, with gas fractions of up to 50% (?,andrefer-ences therein).."," At redshifts of $z \sim 2-3$, galaxy mergers are much more common in the hierarchical structure formation scenario than at the present day, and it is believed that many galaxies are gas-rich, with gas fractions of up to $50\%$ \citep[][and references therein]{Forster2009}. ." + Massive compact ellipticals at z~2 with much smaller sizes and higher stellar densities than their local counterparts (e.g.?) are likely to be the end products of gas-rich mergers where remnant BHs would reside., Massive compact ellipticals at $z \sim 2$ with much smaller sizes and higher stellar densities than their local counterparts \citep[e.g.][]{Dokkum2008} are likely to be the end products of gas-rich mergers where remnant BHs would reside. +" This epoch also corresponds to the peak of the quasar space density, indicating that BHs are accreting gas supplied by their hosts efficiently."," This epoch also corresponds to the peak of the quasar space density, indicating that BHs are accreting gas supplied by their hosts efficiently." +" This is hence an extremely important and interesting regime, where BH mergers and recoils are expected to occur frequently and at the same time the gas component in the host systems cannot be neglected."," This is hence an extremely important and interesting regime, where BH mergers and recoils are expected to occur frequently and at the same time the gas component in the host systems cannot be neglected." +" In this paper, we present an exploratory study of the properties of recoiled BHs in gas-rich galaxies, where BH accretion and feedback processes are followed self-consistently."," In this paper, we present an exploratory study of the properties of recoiled BHs in gas-rich galaxies, where BH accretion and feedback processes are followed self-consistently." +" We first focus on studying an isolated spiral galaxy, simulated at a high resolution to understand how the inclusion of gas accretion or additional BH feedback affects the orbits of recoiled BHs, their return timescale to the centre, and their imprints on the host galaxy."," We first focus on studying an isolated spiral galaxy, simulated at a high resolution to understand how the inclusion of gas accretion or additional BH feedback affects the orbits of recoiled BHs, their return timescale to the centre, and their imprints on the host galaxy." +" We simulate kicks of different magnitude, both in the plane and perpendicular to the plane of the galaxy, to gauge the dependence of the AGN luminosity on the kick orientation and on the assumed equation of state for the interstellar gas."," We simulate kicks of different magnitude, both in the plane and perpendicular to the plane of the galaxy, to gauge the dependence of the AGN luminosity on the kick orientation and on the assumed equation of state for the interstellar gas." +" We then perform a major merger simulation of two gas-rich galaxies, each containing a supermassive BH in its centre."," We then perform a major merger simulation of two gas-rich galaxies, each containing a supermassive BH in its centre." +" After BH coalescence, we follow the evolution of the gravitationally recoiled BH and study how its growth is affected by the kick, and which consequences this has for the scatter in the BH mass-host galaxy scaling relations."," After BH coalescence, we follow the evolution of the gravitationally recoiled BH and study how its growth is affected by the kick, and which consequences this has for the scatter in the BH mass-host galaxy scaling relations." +" Note that a systematic study of recoiled BHs in merging galaxies is underway (?,privatecommunication)..", Note that a systematic study of recoiled BHs in merging galaxies is underway \citep[][private communication]{Blecha2011}. + The paper is organised as follows., The paper is organised as follows. +" In Section 2,, we outline the numerical methods we adopted."," In Section \ref{Methodology}, we outline the numerical methods we adopted." +" Most of our results are presented in Section ??,, where we discuss isolated spiral galaxies with uniform or clumpy discs (Section ??)), and major mergers of two gas-rich galaxies (Section ??))."," Most of our results are presented in Section \ref{Results}, where we discuss isolated spiral galaxies with uniform or clumpy discs (Section \ref{isolated}) ), and major mergers of two gas-rich galaxies (Section \ref{merging}) )." +" In Section 4,, we discuss our findings and draw our conclusions."," In Section \ref{Conclusions}, we discuss our findings and draw our conclusions." + In this work we perform hydrodynamical simulations with the massively parallel Tree-SPH code (lastde-scribedin ?)., In this work we perform hydrodynamical simulations with the massively parallel Tree-SPH code \citep[last described in][]{Gadget2}. +" The code computes gravitational forces acting on dark matter, gas, star and BH particles, as well as the hydrodynamical forces that affect the baryons."," The code computes gravitational forces acting on dark matter, gas, star and BH particles, as well as the hydrodynamical forces that affect the baryons." +" Gas is modelled as an optically thin plasma of hydrogen and helium, which can radiatively cool and heat."," Gas is modelled as an optically thin plasma of hydrogen and helium, which can radiatively cool and heat." +" Star formation and supernova feedback is implemented adopting a subresolution multi-phase model (?),, while BH growth and feedback is modelled as described in ????.."," Star formation and supernova feedback is implemented adopting a subresolution multi-phase model \citep{SpringelH2003}, , while BH growth and feedback is modelled as described in \citet{DiMatteo2005, + Springel2005b, Sijacki2007, Sijacki2009}." +" For completeness, webriefly summarise this model below."," For completeness, webriefly summarise this model below." +" In the simulation code, BHs are treated as collisionless sink"," In the simulation code, BHs are treated as collisionless sink" +"large beam smearing effects as in radio observations, this approximation is reasonable.","large beam smearing effects as in radio observations, this approximation is reasonable." +" However, for our data, where local velocities from strongly star forming regions as well as significant flows along the bars in the objects could significantly skew the isovelocity contours towards the bar axis (e.g, ??7), we are bound to derive misplacements between the kinematic line of nodes position angle aand the photometric counterpart"," However, for our data, where local velocities from strongly star forming regions as well as significant flows along the bars in the objects could significantly skew the isovelocity contours towards the bar axis \citep[e.g., ][]{Duval1977, Huntley1978, Buta1987}, we are bound to derive misplacements between the kinematic line of nodes position angle and the photometric counterpart." +" One step forward in treating this problem is the Φρ..expansion of the minimisation routine to the expression x?V2.X3(c2,+ s2,).", One step forward in treating this problem is the expansion of the minimisation routine to the expression $\chi^2 = V_\mathrm{los}^2 - \Sigma_{m=1}^3 (c_m^2 + s_m^2)$ . +" However, patchiness of observed field, the presence of strong dust content internal to the observed galaxy, and asymmetric drift cause considerable computational complications which are beyond the scope of this paper (e.g.,?).."," However, patchiness of observed field, the presence of strong dust content internal to the observed galaxy, and asymmetric drift cause considerable computational complications which are beyond the scope of this paper \citep[e.g., ][]{Weijmansetal2008}." + We derive the outer disk line of nodes position angle from the near infrared images presented in section 5.1 ))by using the average position angle for the outer isophotes over a 2-4 kpc range in radius., We derive the outer disk line of nodes position angle ) from the near infrared images presented in section \ref{sec:ellipticities} by using the average position angle for the outer isophotes over a 2–4 kpc range in radius. +" We compare the values with those obtained from the RC3 catalogue as well as previous studies of our sample galaxies, and find that in most cases, the photometrically derived values are in fair agreement (see Table 3)), however, for 3342, 55921, and 66946, the vvalues from the literature are based¢, on comprehensive analysis, we use these angles for deriving the pattern speeds."," We compare the values with those obtained from the RC3 catalogue as well as previous studies of our sample galaxies, and find that in most cases, the photometrically derived values are in fair agreement (see Table \ref{tab:PAvalues}) ), however, for 342, 5921, and 6946, the values from the literature are based on comprehensive analysis, we use these angles for deriving the pattern speeds." +" Furthermore, we compare the x? values for the linear fits to the (V), (X) pairs, and as it is expected that the mmethod delivers the least scatter along the correct line"," Furthermore, we compare the $\chi^2$ values for the linear fits to the $\langle V\rangle$, $\langle X\rangle$ pairs, and as it is expected that the method delivers the least scatter along the correct line" +enission observed iu Figure 3. could be explained by the preseuce of other sources iu the GC core.,emission observed in Figure \ref{fig:6553-X3-PSF} could be explained by the presence of other sources in the GC core. + Unfortunately. this short oobservation does not periit a coufideut detection of all the sources in the core.," Unfortunately, this short observation does not permit a confident detection of all the sources in the core." + Furthermore. restricting counts to the oor the eenerev ranges in docs not load to the detection of any nearbv source. sugeestine that this excess of counts above lis not due to a single source. but due to multiple faiuter sources.," Furthermore, restricting counts to the or the energy ranges in does not lead to the detection of any nearby source, suggesting that this excess of counts above is not due to a single source, but due to multiple fainter sources." + A longer high angular resolution observation of the central region of NGC 6553 would certainly shed light ou the PL tail observed in the sspectrum of the candidate qLMXD The PL component measured with hhas an absorbed flux Fx=L9«10thereea2s+ in the ange with a photon iudex T=2.1., A longer high angular resolution observation of the central region of NGC 6553 would certainly shed light on the PL tail observed in the spectrum of the candidate qLMXB The PL component measured with has an absorbed flux $\Fx=4.9\tee{-14}\cgsflux$ in the range with a photon index $\Gamma=2.1$. + Usiug/w3pinuus.htiul. the expected /ACIS-S3 count rate is L7ctsks SkeV)). which corresponds to 23.5 counts on this short oobservation.," Using, the expected /ACIS-S3 count rate is $4.7\unit{cts\perksec}$ ), which corresponds to 23.5 counts on this short observation." +" However. the bbackground subtracted count rate of an aunulus (ry,=107 and rag= 30%) coutered around the core source is τσ1ος."," However, the background subtracted count rate of an annulus $r_{\rm in}=10\arcsec$ and $r_{\rm + out}=30\arcsec$ ) centered around the core source is $7\pm14\unit{cts}$." + The non-detectiou of an excess of counts around the core source does not support the possibility that iultiple diffuse sources are responsible for the high-cnerey contamination of the sspectimm of the candidate qLAINB., The non-detection of an excess of counts around the core source does not support the possibility that multiple diffuse sources are responsible for the high-energy contamination of the spectrum of the candidate qLMXB. + This could be explained if the sources are variable., This could be explained if the sources are variable. +" Alternatively, the detected PL component could be intrinsic to the candidate qLMXD. but display some variability. as has been observed for other LAINBs."," Alternatively, the detected PL component could be intrinsic to the candidate qLMXB, but display some variability, as has been observed for other LMXBs." + This possibility is investigated by extracting counts in the iruneec., This possibility is investigated by extracting counts in the range. + With the pn camera. a countrate of O.97T+O.31Letsks+ is detected. which corresponds. to O.36etsks| expected ou the ACTS-S3 detector uxingPIALMs.. assuming a photon iudex P—2.1.," With the pn camera, a countrate of $0.97\ppm0.31\unit{cts\perksec}$ is detected, which corresponds to $0.36\unit{cts\perksec}$ expected on the ACIS-S3 detector using, assuming a photon index $\Gamma=2.1$." + We detect 1.1320.4?ctsks.+ ou the ddata in the iranse., We detect $1.13\ppm0.47\unit{cts\perksec}$ on the data in the range. + These count rates are consistent and therefore there is no observed variability. of the ligh-cucrey conrponeut (>2 keV). at the <2a level.," These count rates are consistent and therefore there is no observed variability of the high-energy component $>2\keV$ ), at the $<2\sigma$ level." + The «ρουπα of the candidate qLAINB in the core of NGC 6553. i0. inge on-axis. is extracted. from a 2755 radius cieular region to include mere than of the sourceenergv.," The spectrum of the candidate qLMXB in the core of NGC 6553, i.e., image on-axis, is extracted from a 5 radius circular region to include more than of the source." +". For the purpose of the couut rate calculation only, the backeround is extracted using a circular reeion of rradius around the source. excluding around the qLMXD itself. which eusures that >99% of the ECF is excluded."," For the purpose of the count rate calculation only, the background is extracted using a circular region of radius around the source, excluding around the qLMXB itself, which ensures that $>99\%$ of the ECF is excluded." + Due to the small wmmbers of counts. a binning of 10 counts per bin is applied for the candidate qLMXD. which ouly guarautees mareinally Gaussian uucertaiuntv in cach bin.," Due to the small numbers of counts, a binning of 10 counts per bin is applied for the candidate qLMXB, which only guarantees marginally Gaussian uncertainty in each bin." + The binned spectruii is used sinultaucously with the three EPIC spectra to evaluate the cousisteucy of the spectra., The binned spectrum is used simultaneously with the three EPIC spectra to evaluate the consistency of the spectra. + All parameters are tied between the four spectra., All parameters are tied between the four spectra. + Only thepowerlaw norm is sot to zero for the oobservation., Only the norm is set to zero for the observation. + Also. a multiplicative constant is added to the model to quantify the variation between EPIC aud ACTS-S3 spectra.," Also, a multiplicative constant is added to the model to quantify the variation between EPIC and ACIS-S3 spectra." + We find that the best-fit parameters of the four spectra are consistent with that of the EPIC spectra alone (see Table 3. aud Figure 5))., We find that the best-fit parameters of the four spectra are consistent with that of the EPIC spectra alone (see Table \ref{tab:rescore} and Figure \ref{fig:6553-X3-all}) ). + In addition. the amultiplication constant. which was left free for the ACTS-S3 spectrum. is statistically consistent with unity. Acs=O85vds.," In addition, the multiplication constant, which was left free for the ACIS-S3 spectrum, is statistically consistent with unity, $c_{\rm + ACIS}=0.85\ud{0.43}{0.26}$." + This is evideuce that. within the pAatistics of the observation. the sspectrui is consistent with the three EPIC spectra.," This is evidence that, within the statistics of the observation, the spectrum is consistent with the three EPIC spectra." +" Finally, we also perform a fit of the uuubimned spectrum alone. using Casl-statistic (7).."," Finally, we also perform a fit of the unbinned spectrum alone, using Cash-statistic \citep{cash79}." + The backeround. representing 2.5% of the extracted counts (1.2 counts out of [8 in the source extraction regio) can be neglected. as required by Cash-statistic.," The background, representing $2.5\%$ of the extracted counts (1.2 counts out of 48 in the source extraction region) can be neglected, as required by Cash-statistic." +" For colmparison purposes with the sspectral fitting. the chosen model here is alone (with fixed absorption. distance aud mass as before). which assumes that the PL component observed iu the sspectruu is not intrinsic to the candidate qLAINB. 1.6..that in the sspectrtun the PL tail is due to contaminating nearby sources,"," For comparison purposes with the spectral fitting, the chosen model here is alone (with fixed absorption, distance and mass as before), which assumes that the PL component observed in the spectrum is not intrinsic to the candidate qLMXB, i.e.,that in the spectrum, the PL tail is due to contaminating nearby sources." + The best-fit value are x4=6.6!MEkan (Mxg= LM.) and KTg=13113eV. which are in remarkable aereement with the values obtained from the oobservation.," The best-fit value are $\rns = +6.6\ud{3.2}{1.3}\km$ $\mns=1.4\msun$ ) and $\kteff = +134\ud{35}{39}\eV$, which are in remarkable agreement with the values obtained from the observation." +" The uunabsorbed fux is Fx=τον]Porean7?8 ο, ", The unabsorbed flux is $\Fx = 1.0\tee{-13}\cgsflux$ . +These results are also listed in Table 3.. for a convenieut comparison witli the sspectral fits.," These results are also listed in Table \ref{tab:rescore}, for a convenient comparison with the spectral fits." +ALXXIPOL is a bolometric. balloon-borne experiment. designed to measure the E-mode polarization anisotropy in the cosmic microwave background radiation (CALB).,"MAXIPOL is a bolometric, balloon-borne experiment designed to measure the E-mode polarization anisotropy in the cosmic microwave background radiation (CMB)." + The ALANIPOL instrument is a reimplementation of the hardware from the successful. CMB temperature anisotropy experiment ALANIALA 1.2.3].," The MAXIPOL instrument is a reimplementation of the hardware from the successful CMB temperature anisotropy experiment MAXIMA \cite{hanany,lee,stompor}." + While the MANIALA telescope and. data electronics remained. largely. unchanged. the receiver was converted into a polarimeter by retrofitting it with a rotating half-wave plate (LIN) and a fixed wire-gricl polarizer.," While the MAXIMA telescope and data electronics remained largely unchanged, the receiver was converted into a polarimeter by retrofitting it with a rotating half-wave plate (HWP) and a fixed wire-grid polarizer." + ALAXIPOL has Uown twice from NASA's National Scientific Ballooning Facility in Ft., MAXIPOL has flown twice from NASA's National Scientific Ballooning Facility in Ft. + Sumner. New Mexico.," Sumner, New Mexico." + Tho first Hight. NLANIPOL-0. launched in September 2002 and the second. NLAXIPOL-1. in May 2003.," The first flight, MAXIPOL-0, launched in September 2002 and the second, MAXIPOL-1, in May 2003." + In this paper we discuss the science goals of the experiment. the hardware implementation (Section 2)). the lights (Section 3)). the noise and. potential svsteniatic errors (Section 4)).," In this paper we discuss the science goals of the experiment, the hardware implementation (Section \ref{sec:instrument}) ), the flights (Section \ref{sec:flights}) ), the noise and potential systematic errors (Section \ref{sec:systematics}) )." + The goal of ALANIPOL is to measure the peaks in the I-mocde (1911) and tenperature-E-mocle (PE) cross correlation power spectra between (55200 and /=1000., The goal of MAXIPOL is to measure the peaks in the E-mode (EE) and temperature-E-mode (TE) cross correlation power spectra between $\ell$ =300 and $\ell$ =1000. + To accomplish this goal. ALANIPOL mapped the Z. Q and €@ Stokes parameters of 2° wide “how tic” shaped regions of the sky with 10 resolution.," To accomplish this goal, MAXIPOL mapped the $I$, $Q$ and $U$ Stokes parameters of $^{\circ}$ wide “bow tie” shaped regions of the sky with $^\prime$ resolution." + Detection of the polarization anisotropy of the CM was recently reported by DASL 4]. and WALAD 5)., Detection of the polarization anisotropy of the CMB was recently reported by DASI \cite{dasi} and WMAP \cite{wmap}. + Alany subsystems in the ALANIPOL instrument have already been thoroughly detailed in previous NLAXINLA publications d.6.7.S]..," Many subsystems in the MAXIPOL instrument have already been thoroughly detailed in previous MAXIMA publications \cite{hanany,lee_hardware,winant,rabii}." + Vhis discussion will focus primarily on the new ALAXLPOL-speeilic hardware elements that were retrofitted into the ALANIALA instrument., This discussion will focus primarily on the new MAXIPOL-specific hardware elements that were retrofitted into the MAXIMA instrument. +afterglows is described in Section 3.,afterglows is described in Section 3. +" In Section 4, we present and discuss results of the simulation and possible ways of afterglow identification."," In Section 4, we present and discuss results of the simulation and possible ways of afterglow identification." +" For the purpose of our simulation, we need to know the way Gaia will scan the sky (Lindegren"," For the purpose of our simulation, we need to know the way $\textit{Gaia}$ will scan the sky \citep{lindegren}." +" 2010).. Gaia will carry two identical telescopes, separated by the angle of 5= 106.55, as shown in Figure 1.."," $\textit{Gaia}$ will carry two identical telescopes, separated by the angle of $\beta = 106.5^{\circ}$ as shown in Figure \ref{fig1}." + The satellite will make four rotations per day around its axis (which is perpendicular to the direction in which both telescopes are pointing) with the constant angular velocity w., The satellite will make four rotations per day around its axis (which is perpendicular to the direction in which both telescopes are pointing) with the constant angular velocity $\omega$. + The direction of the axis itself is tilted by the angle 7=45° from the direction of the Sun., The direction of the axis itself is tilted by the angle $\gamma = 45^{\circ}$ from the direction of the Sun. + The axis will experience slow precession motion around the Earth-to-Sun direction with a period of 63 days (Q in Figure 1))., The axis will experience slow precession motion around the Earth-to-Sun direction with a period of 63 days $\Omega$ in Figure \ref{fig1}) ). +" Gaia will have an orbit around the L2 point and will thus experience rotation around the Sun, which is shown in Figure 1 as a rotation around the z axis."," $\textit{Gaia}$ will have an orbit around the L2 point and will thus experience rotation around the Sun, which is shown in Figure \ref{fig1} as a rotation around the $x$ axis." +" Knowing w,,7,( and p (one year orbital period around the Sun), we construct the scanning law of Gaia (see the Appendix A))."," Knowing $\omega, \Omega, \gamma, \beta$ and $\rho$ (one year orbital period around the Sun), we construct the scanning law of $\textit{Gaia}$ (see the Appendix \ref{a1}) )." + Gaia’s two telescopes will have a field of view of ~0.7?x each., $\textit{Gaia}$ 's two telescopes will have a field of view of $\sim 0.7^{\circ}\times 0.7^{\circ}$ each. + The expected limiting magnitude in broadband G magnitude (details on the photometric system of Gaia are given in Jordietal.2010)) is G = 20 mag., The expected limiting magnitude in broadband $G$ magnitude (details on the photometric system of $\textit{Gaia}$ are given in \citealt{jordi}) ) is $G$ = 20 mag. +" The specifics of scientific performance are given on the official Gaia World Wide Web and, for example, in Lindegren(2010)."," The specifics of scientific performance are given on the official $\textit{Gaia}$ World Wide Web and, for example, in \citet{lindegren}." + There will be a 7 x 9 astrometric CCD field in Gaia’s focal plane., There will be a 7 $\times$ 9 astrometric CCD field in $\textit{Gaia}$ 's focal plane. + Each source will transit over the nine CCDs and will be observed by each of them with 4.4 s integration time., Each source will transit over the nine CCDs and will be observed by each of them with 4.4 s integration time. +" First we focus on on-axis afterglows, i.e., those with their jet cones turned in our line of sight."," First we focus on on-axis afterglows, i.e., those with their jet cones turned in our line of sight." +" In such cases we can observe the GRB, which triggers a satellite and follow-up optical observations."," In such cases we can observe the GRB, which triggers a satellite and follow-up optical observations." +" Hence, we can base the initial parameters of our simulations on the actually observed GRB afterglow numbers and their characteristics."," Hence, we can base the initial parameters of our simulations on the actually observed GRB afterglow numbers and their characteristics." + Since the launch of the Swift satellite in 2004 (Gehrelsetal.2004) a large number of GRBs and their afterglows has been detected (Roamingetal., Since the launch of the $\textit{Swift}$ satellite in 2004 \citep{gehrels} a large number of GRBs and their afterglows has been detected \citep{roaming}. + 2009).. The Swift detection rate is about 100 GRBs per year., The $\textit{Swift}$ detection rate is about 100 GRBs per year. + In about half of the detected GRBs there is no bright optical afterglow detected., In about half of the detected GRBs there is no bright optical afterglow detected. +" Since the satellite covers approximately 5 of the sky, we can estimate that there are around 300 GRBs per year, for which an optical afterglow could be detected with timely observations."," Since the satellite covers approximately $\frac{1}{6}$ of the sky, we can estimate that there are around 300 GRBs per year, for which an optical afterglow could be detected with timely observations." +" To obtain their general properties, we used observations published in the Gamma Ray Burst Coordinate Network (Barthelmyetal.1995).."," To obtain their general properties, we used observations published in the Gamma Ray Burst Coordinate Network \citep{barthelmy}." + We chose GRBs detected between 2006 September and 2009 April thathad an optical afterglow detected (and reasonably well sampled)., We chose GRBs detected between 2006 September and 2009 April thathad an optical afterglow detected (and reasonably well sampled). +" In general, not many optical afterglows have been detected in the first few minutes after the initial trigger (Kannetal.2010, 2011).."," In general, not many optical afterglows have been detected in the first few minutes after the initial trigger \citep{kanna,kannb}. ." +" Consequently,we used measured R magnitudes at approximately (t—to) =0.01 day after the prompt"," Consequently,we used measured $R$ magnitudes at approximately $(t-t_0)=$ 0.01 day after the prompt" +F606W and F814W filters is also affected.,$F606W$ and $F814W$ filters is also affected. + This is shown in figure 2 where we present the color-magnitude diagram for a cooling sequence of a white dwarf of mass 0.5Ma computed using models with and without the Ly-c opacity.," This is shown in figure \ref{F2} where we present the color-magnitude diagram for a cooling sequence of a white dwarf of mass $0.5 \, M_{\sun}$ computed using models with and without the $\rm \alpha$ opacity." + Both curves deviate significantly from each other for Tay<5000K.," Both curves deviate significantly from each other for $T_{\rm eff}\rm <5000 \, K$." + As c opacity is stronger at short wavelengths. the effect is stronger in the FOOOW filter (larger horizontal shift in Fig.," As $\rm \alpha$ opacity is stronger at short wavelengths, the effect is stronger in the $F606W$ filter (larger horizontal shift in Fig." + 2)., 2). + The new models predict a turn towards the blue. caused by CIA opacity from molecular hydrogen (Saumon&Jacobson.1999;Hansen.1998:Bergeronetal.. 1995).. at lower 7.," The new models predict a turn towards the blue, caused by CIA opacity from molecular hydrogen \citep{SJ,HN98,BSW95}, at lower $T_{\rm eff}$." + This should have an impact on the astronomical parameters of NGC 6397 derived from the analysis of its white dwarf cooling sequence., This should have an impact on the astronomical parameters of NGC 6397 derived from the analysis of its white dwarf cooling sequence. + To investigate the importance of pure hydrogen white dwarf atmosphere models with Ly-c opacity in the analysis of the white dwarf cooling sequence of NGC 6397 we performed a least square 2D fit in F8l4W and F606W-F814W to the photometric data of Hansenetal.(2007);Richer(2006): their Fig.," To investigate the importance of pure hydrogen white dwarf atmosphere models with $\alpha$ opacity in the analysis of the white dwarf cooling sequence of NGC 6397 we performed a least square 2D fit in F814W and F606W-F814W to the photometric data of \citet{HN07,RI06}; their Fig." + 6 and 4 respectively., 6 and 4 respectively. + The fitting parameters were the reddening and the true distance modulus., The fitting parameters were the reddening and the true distance modulus. + The fit was performed using two grids of atmosphere models: those with Ly-c opacity and those without., The fit was performed using two grids of atmosphere models: those with $\rm \alpha$ opacity and those without. + The second set mimies the models used in the analysis of the cluster white dwarf cooling sequence conducted by Hansenetal.(2007) and Richeretal.(2006)., The second set mimics the models used in the analysis of the cluster white dwarf cooling sequence conducted by \citet{HN07} and \citet{RI06}. + Following those authors. in our derivation of the theoretical cooling sequences we assumed the mass of the white dwarf to be 0.5Me.," Following those authors, in our derivation of the theoretical cooling sequences we assumed the mass of the white dwarf to be $0.5 \, M_{\sun}$." + Our fits to the data are given in Fig. 3.., Our fits to the data are given in Fig. \ref{F3}. + We obtained perfect fits with both theoretical cooling sequences. as Is also the case in Hansenetal.(2007) and Richeral. (2006).," We obtained perfect fits with both theoretical cooling sequences, as is also the case in \citet{HN07} and \citet{RI06}." +. In addition to that work we show. for the first time. the 7. of cool white dwarfs in the globular cluster.," In addition to that work we show, for the first time, the $T_{\rm eff}$ of cool white dwarfs in the globular cluster." + Because of the difference in localization of the turn off visible in both theoretical sequences (Fig. 2)).," Because of the difference in localization of the turn off visible in both theoretical sequences (Fig. \ref{F2}) )," + both fits give different estimations of Zr for the cool end of the observed sequence localized at F814W~27.6 (Hansenetal..2007).," both fits give different estimations of $T_{\rm eff}$ for the cool end of the observed sequence localized at $\sim \, 27.6$ \citep{HN07}." +. The effective temperature estimated on the basis of atmosphere models that account for Ly-c opacity is significantly smaller. indicating that the stars at the cut off of the observed white dwarf cooling sequence are cooler and older.," The effective temperature estimated on the basis of atmosphere models that account for $\rm \alpha$ opacity is significantly smaller, indicating that the stars at the cut off of the observed white dwarf cooling sequence are cooler and older." + We will return to this problem in the next section., We will return to this problem in the next section. + As indicated in Figure 2 there Is a significant variation in the modeled maximum value of the F606W—F814W color for a white dwarf of a given mass., As indicated in Figure \ref{F2} there is a significant variation in the modeled maximum value of the $F606W-F814W$ color for a white dwarf of a given mass. + In the present case. both model curves deviates by ~0.1 magnitude. which has a direct impact on the derived value for the reddening towards NGC 6397.," In the present case, both model curves deviates by $\sim 0.1$ magnitude, which has a direct impact on the derived value for the reddening towards NGC 6397." + With models that do not account for the Ly-a opacity, With models that do not account for the $\rm \alpha$ opacity +We also checked. whether global kinematics can distinguish between bona-fide bulges and bulge-like bars.,We also checked whether global kinematics can distinguish between bona-fide bulges and bulge-like bars. + In Fig., In Fig. +" 4 we plot V,pi/& versus e, for real bulges aud lor our simulations.", \ref{fig:fig4} we plot $V_p/\bar{\sigma}$ versus $\epsilon_b$ for real bulges and for our simulations. + For real bulges. Ἐν and σ were obtained by fitting a de Vaucouleurs prolile to the bulge.," For real bulges, $V_p$ and $\bar{\sigma}$ were obtained by fitting a de Vaucouleurs profile to the bulge." + Our simulations are rather poorly fit by a de Vaucouleurs profile. which introduces a svstematic difference between. our measurements and Ixormendys (1993).," Our simulations are rather poorly fit by a de Vaucouleurs profile, which introduces a systematic difference between our measurements and Kormendy's (1993)." +" To quantilv some ofthis uncertainty. we have measured ej. V, and 6 within Ry,pp and /0,,5;/2 and used half the difference as our error estimate."," To quantify some ofthis uncertainty, we have measured $\epsilon_b$, $V_p$ and $\bar{\sigma}$ within $R_{b,eff}$ and $R_{b,eff}/2$ and used half the difference as our error estimate." +" This diagram shows that evolved bars can show. under some viewing angles. global kinematic-elongation properties (vpical not only of the cold ""pseudo-bulges"". but also those that are taken as (he bona-fide. dvnamically-hot bulges."," This diagram shows that evolved bars can show, under some viewing angles, global kinematic-elongation properties typical not only of the dynamically-cold “pseudo-bulges”, but also those that are taken as the bona-fide, dynamically-hot bulges." + These are the expected projection effects For Uüriaxial spheroids seen at high inclination (Binnev&Tremaine1987)., These are the expected projection effects for triaxial spheroids seen at high inclination \citep{bt87}. +. Thus the population of bulges which are identified by bulge/cdisk decompositions or bx kinematics may have some contribution from bars., Thus the population of bulges which are identified by bulge/disk decompositions or by kinematics may have some contribution from bars. + Although Rahaetal.(1991). only reported bar-weakening. not destruction. by the buckling instability. it has become common wisdom that buckling destrovs bars.," Although \citet{rsjk91} only reported bar-weakening, not destruction, by the buckling instability, it has become common wisdom that buckling destroys bars." + Our simulations have failed to turn up a single instance in which Che bar was destroved by buckling. although we cannot exclude Chat it is in some extreme case.," Our simulations have failed to turn up a single instance in which the bar was destroyed by buckling, although we cannot exclude that it is in some extreme case." + The channel of bulge formation by the dissipationless destruction of bars during buckling. therefore. is not viable.," The channel of bulge formation by the dissipationless destruction of bars during buckling, therefore, is not viable." + llowever. the minimal collisionless secular evolution present in our simulations mist also occur in nature. resul(ng in svstems Chat exhibit double component mass densitv profiles.," However, the minimal collisionless secular evolution present in our simulations must also occur in nature, resulting in systems that exhibit double component mass density profiles." + For certain viewing orientations. (he spread in structural parameters and kinematic properties are indistinguishable from those observed in svstems that are classified as bulges.," For certain viewing orientations, the spread in structural parameters and kinematic properties are indistinguishable from those observed in systems that are classified as bulges." + Nonetheless. the existence in nature of round bulges inside low inclination galaxies. which our simulations cannot reproduce. requires (hat other processes are also involved.," Nonetheless, the existence in nature of round bulges inside low inclination galaxies, which our simulations cannot reproduce, requires that other processes are also involved." + Possibly secular evolution including dissipative gas (Mayer&Wadslev2004) will result in rounder bulges. but this requires extended central objects with masses of ~10—20% that ol the disk (Shen&Sellwood2004).," Possibly secular evolution including dissipative gas \citep{mw04} will result in rounder bulges, but this requires extended central objects with masses of $\sim +10-20\%$ that of the disk \citep{ss04}." +. The higher interaction rate in the early universe may have triggered (he large gas inflows needed to build such objects., The higher interaction rate in the early universe may have triggered the large gas inflows needed to build such objects. + Finally. because the halos of our simulations are rigid. (he barvonic component cannot but conserve its angular momentum.," Finally, because the halos of our simulations are rigid, the baryonic component cannot but conserve its angular momentum." + In (semi-) analvtie models of disk galaxy lormation (Fall&Elfstathiou1930:Moetal.1993:LaceySilk1991:WhiteFrenkDalcantondenBosch 1993).. the distribution of disk scale-lengths. fy. is set by that of their angular momenta.," In (semi-) analytic models of disk galaxy formation \citep{fe80,mmw98,ls91,wf91,dss97,vdb98}, the distribution of disk scale-lengths, $R_d$ , is set by that of their angular momenta." + deJong&Lacev(1996) found Chat the width of the observed, \citet{djl96} found that the width of the observed +"for epoch 2006.0; we derived the expected position from the 2MASS coordinates (11 59 27.43 -52 47 18.8 at epoch 1999.36) - which are more accurate than the ROSAT coordinates - and the proper motion mmas/yr, mmas/yr) as given by ?,, leading to an expected position of RA: 11 59 26.64 and DEC: -52 47 19.7.","for epoch 2006.0; we derived the expected position from the 2MASS coordinates (11 59 27.43 -52 47 18.8 at epoch 1999.36) - which are more accurate than the ROSAT coordinates - and the proper motion mas/yr, mas/yr) as given by \cite{ham04}, leading to an expected position of RA: 11 59 26.64 and DEC: -52 47 19.7." + The detected source is the only X-ray source within from the on-axis position., The detected source is the only X-ray source within from the on-axis position. +" No other known X- source of comparable strength is located in the vicinity of IRXS J115928.5-524717, therefore the identification is unambiguous, and the observed soft X-ray spectra make an unknown extragalactic source extremely unlikely."," No other known X-ray source of comparable strength is located in the vicinity of 1RXS J115928.5-524717, therefore the identification is unambiguous, and the observed soft X-ray spectra make an unknown extragalactic source extremely unlikely." + To investigate X-ray variability of IRXS J115928.5-524717 we created light curves with kks and hh binning respectively from the photons detected in a region around the source position., To investigate X-ray variability of 1RXS J115928.5-524717 we created light curves with ks and h binning respectively from the photons detected in a region around the source position. +" In we show the thus obtained, background subtracted light curve derived from the merged EPIC data in the 11.0 keV band for two different time resolutions."," In \\ref{lc} we show the thus obtained, background subtracted light curve derived from the merged EPIC data in the 1.0 keV band for two different time resolutions." +" The light curves shown in reflec clearly confirm that the detection of IRXS J115928.5-524717 with is not caused by a single flare event, rather persistent X-ray emission is detected during the total observation, however, variability is also present at a significant level."," The light curves shown in \\ref{lc} clearly confirm that the detection of 1RXS J115928.5-524717 with is not caused by a single flare event, rather persistent X-ray emission is detected during the total observation, however, variability is also present at a significant level." +" Therefore, instead of the commonly used term quiescence, we attribute the X-ray emission to a quasi-quiescence flux level."," Therefore, instead of the commonly used term quiescence, we attribute the X-ray emission to a quasi-quiescence flux level." +" Some enhanced activity or a smaller flare might be present at the beginning of the observation, but the overall variations in X-ray brightness appear quite smooth, at least when the hh averaged light curve shown in the upper panel is considered."," Some enhanced activity or a smaller flare might be present at the beginning of the observation, but the overall variations in X-ray brightness appear quite smooth, at least when the h averaged light curve shown in the upper panel is considered." +" Otherwise, the light curve in lower panel with kks time bins indicates stronger variability, i.e. frequent smaller flares of different amplitude and duration."," Otherwise, the light curve in lower panel with ks time bins indicates stronger variability, i.e. frequent smaller flares of different amplitude and duration." +" Given the errors, both scenarios are possible and the maximum X-ray variability may be around or even less than a factor of two, but could also be easily of the order of a few as suggested from light curves with shorter time bins."," Given the errors, both scenarios are possible and the maximum X-ray variability may be around or even less than a factor of two, but could also be easily of the order of a few as suggested from light curves with shorter time bins." + We searched for spectral variations related to changes in X- brightness for the hh time bins by studying the respective hardness ratio SS) with 00.6 keV and 11.0 keV being the photon energy bands., We searched for spectral variations related to changes in X-ray brightness for the h time bins by studying the respective hardness ratio S) with 0.6 keV and 1.0 keV being the photon energy bands. +" The SNR is rather poor and we find no clear correlation between HR and count rate, linear regression resulted in a slope of 0.035+0.044."," The SNR is rather poor and we find no clear correlation between HR and count rate, linear regression resulted in a slope of $0.035 \pm 0.044$." + Therefore we performed the spectral analysis for the total observation., Therefore we performed the spectral analysis for the total observation. +" To determine the spectral properties of IRXS J115928.5-524717, we fitted the PN spectrum with spectral models consisting of one and two temperature components."," To determine the spectral properties of 1RXS J115928.5-524717, we fitted the PN spectrum with spectral models consisting of one and two temperature components." + The elemental abundances cannot be constrained with the existing dataand were set to solar values., The elemental abundances cannot be constrained with the existing dataand were set to solar values. +" We show the X-ray spectrum and both respective best fit models in refspec,, the derived spectral properties are summarised in refft."," We show the X-ray spectrum and both respective best fit models in \\ref{spec}, the derived spectral properties are summarised in \\ref{fit}." +" The model with one temperature component is technically acceptable given the errors, but results in an somewhat poorer fit."," The model with one temperature component is technically acceptable given the errors, but results in an somewhat poorer fit." +" As visible in refspec, greater discrepancies are present for this model especially around the peak of the spectrum, indicating that it is a oversimplification."," As visible in \\ref{spec}, greater discrepancies are present for this model especially around the peak of the spectrum, indicating that it is a oversimplification." +" Given the fact that a two-temperature component model is also physically more realistic, since X-ray spectra with higher SNR generally require multiple components, we adopt its results for further discussion."," Given the fact that a two-temperature component model is also physically more realistic, since X-ray spectra with higher SNR generally require multiple components, we adopt its results for further discussion." + The best fit two-temperature model corresponds to a source flux of 6.9x107? ccm? ss“! in the keV band; for the ROSAT kkeV band we derive a roughly higher flux of 8.0x107? ccm? ss!., The best fit two-temperature model corresponds to a source flux of $6.9 \times 10^{-15}$ $^{-2}$ $^{-1}$ in the keV band; for the ROSAT keV band we derive a roughly higher flux of $8.0 \times 10^{-15}$ $^{-2}$ $^{-1}$ . +" Adopting a distance of ppc for IRXS J115928.5-524717, we obtain an X-ray luminosity of Lx=1.0x1026erg/s in the 22.0 keV band, corresponding to a moderate activity level of around log Lx/Lpo= —4.1."," Adopting a distance of pc for 1RXS J115928.5-524717, we obtain an X-ray luminosity of $L_{\rm X}= 1.0 \times 10^{26}$erg/s in the 2.0 keV band, corresponding to a moderate activity level of around log $L_{\rm X}$ $L_{\rm bol} = -4.1$ ." + Our spectral modelling results in, Our spectral modelling results in +photometric uncertainty affecting our flux estimate.,photometric uncertainty affecting our flux estimate. + Given the low angular resolution at these long wavelengths it was not possible to perform a spatial decomposition similar to the one described above for the data., Given the low angular resolution at these long wavelengths it was not possible to perform a spatial decomposition similar to the one described above for the data. +" In particular, we could not determine the fraction of energy powered by the point source that dominates the monochromatic luminosity at shorter IR wavelengths."," In particular, we could not determine the fraction of energy powered by the point source that dominates the monochromatic luminosity at shorter IR wavelengths." +" However, reffig:-4panels reveals that the peak of the emission is again shifted to the South-West with respect to the center of the galaxy."," However, \\ref{fig:4panels} reveals that the peak of the emission is again shifted to the South-West with respect to the center of the galaxy." +" Within the astrometric uncertainties it coincides with the peak of emission detected at and,um,, which suggests that the luminous HII region detected in the mid-IR is also responsible for a very large fraction of the total far-IR emission of thegalaxy!?."," Within the astrometric uncertainties it coincides with the peak of emission detected at and, which suggests that the luminous HII region detected in the mid-IR is also responsible for a very large fraction of the total far-IR emission of the." +. .6cm The new image of the 9980425 host galaxy obtained in 2008 as part of this program looks very similar to the observations performed by in 2004 (LeFloc'hetal.2006)., .6cm The new image of the 980425 host galaxy obtained in 2008 as part of this program looks very similar to the observations performed by in 2004 \citep{LeFloch06}. +". Most of the MIPS/emission Spitzeroriginates from a single point-like source that appears to coincide with the WR region, while a couple of other HII regions as well as a more diffuse component are also detected toward the nucleus and in the spiral arms of the host."," Most of the emission originates from a single point-like source that appears to coincide with the WR region, while a couple of other HII regions as well as a more diffuse component are also detected toward the nucleus and in the spiral arms of the host." + We measured the total flux of the galaxy and the luminosity of the WR region using a PSF fitting decomposition and the same approach followed for the data., We measured the total flux of the galaxy and the luminosity of the WR region using a PSF fitting decomposition and the same approach followed for the data. +" We found that the unresolved component contributes to a level of 19.5+2.0 mmJy, while the total emission of the galaxy reaches 226.2+1.3mmJy."," We found that the unresolved component contributes to a level of $\pm$ mJy, while the total emission of the galaxy reaches $S_{\rm 24\mu m}$ $\pm$ mJy." +" Within the error bars these results 554,,4,—-—are fully consistent with the photometry of LeFloc’hetal.(2006).", Within the error bars these results are fully consistent with the photometry of \citet{LeFloch06}. +". The lack of temporal variations shows that if some dust heating transient emission produced after the GRB explosion has contributed to the mid-IR emission of the galaxy, this emission must either be very faint (1.6., ;1096 of the total luminosity) or decrease very slowly with time."," The lack of temporal variations shows that if some dust heating transient emission produced after the GRB explosion has contributed to the mid-IR emission of the galaxy, this emission must either be very faint (i.e., $\ltapp$ of the total luminosity) or decrease very slowly with time." +" .6cm Numerous emission lines are clearly visible in the IRS spectroscopic observations of the WR region reffig:plot,pec)).", .6cm Numerous emission lines are clearly visible in the IRS spectroscopic observations of the WR region \\ref{fig:plot_spec}) ). +Theyarecommonlyobservedinthespectralener (Figure gydis forminggalaxiesandtheyprovidevaluablein formationontheira, They are commonly observed in the spectral energy distribution of star-forming galaxies and they provide valuable information on their activity of star formation as well as on the strength and the hardness of their radiation field. +ctiv resolutionspectrumwiththeP FITtooldevelopedbySmith, To constrain the luminosity of these features we analyzed our low-resolution spectrum with the PAHFIT tool developed by \citet{Smith07}. +et al.(2 IRSEDs., This code was specifically designed for decomposing IRS spectra into the contribution of the different components that characterize galaxy mid-IR SEDs. +"ThesearethehotdustcontinuumproducedbytheV AH ery Small bandPAH features, thenarrowionicemissionlinesandtheef fecto fs andum.."," These are the hot dust continuum produced by the Very Small Grains (VSG), the broad-band PAH features, the narrow ionic emission lines and the effect of silicate absorption at and." + The result of our decomposition is displayed in Figure 4.., The result of our decomposition is displayed in Figure \ref{fig:pahfit}. +" Given the large number of individual features identified with PAHFIT, only the spectral profile corresponding to the main PAHs is represented, along with the shape of the underlying continuum (thick solid line)."," Given the large number of individual features identified with PAHFIT, only the spectral profile corresponding to the main PAHs is represented, along with the shape of the underlying continuum (thick solid line)." +" Similarly, only the position of the most prominent forbidden lines is labeled on the plot, and the total SED reconstructed from the model is shown as a blue solid line."," Similarly, only the position of the most prominent forbidden lines is labeled on the plot, and the total SED reconstructed from the model is shown as a blue solid line." + The narrow ionic lines observed between and are also clearly visible in the high-resolution104m spectrum that we obtained with IRS., The narrow ionic lines observed between and are also clearly visible in the high-resolution spectrum that we obtained with IRS. + A more accurate estimate of their luminosity was therefore obtained by, A more accurate estimate of their luminosity was therefore obtained by +The vertical distribution of the tangent poit clouds is jest represented by an exponential with a scale height h=sd0 pc (see Fieure 11)).,The vertical distribution of the tangent point clouds is best represented by an exponential with a scale height $h=800$ pc (see Figure \ref{fig:zhist}) ). + Because R-S tests are uost sensitive to the differeuces near the median of the distribution. we tested both »(5) aud »(|b[): the former eives higher weight to clouds closer to the plane. while he latter weighs more highly the higher latitude clouds.," Because K-S tests are most sensitive to the differences near the median of the distribution, we tested both $n(b)$ and $n(|b|)$: the former gives higher weight to clouds closer to the plane, while the latter weighs more highly the higher latitude clouds." + Also. fitting to »(5) is sensitive to svuuuctrics about the lane while fitting to »(|b|) is uot.," Also, fitting to $n(b)$ is sensitive to symmetries about the plane while fitting to $n(|b|)$ is not." +" For 7;—800 pe. the K-S test probability that the observed. aud. simulated clouds were drawn from the same vertical function is GL% when comparing against 0], but not acceptable when comparing against 5."," For $h=800$ pc, the K-S test probability that the observed and simulated clouds were drawn from the same vertical function is $61\%$ when comparing against $|b|$, but not acceptable when comparing against $b$." +" Scale heights between 700 aud S50 pe were acceptable for the distribution of [0], while scale heights between 950 and 1100 pe were cousisteut with the distribution of b values. with 1000 pe being the best fit. having a probability of 21%."," Scale heights between $700$ and $850$ pc were acceptable for the distribution of $|b|$, while scale heights between 950 and $1100$ pc were consistent with the distribution of $b$ values, with 1000 pc being the best fit, having a probability of $24\%$." + This discrepaucy likely iudicates that our low-latitude confusion cutoff (Figure 8)) is not couservative chough., This discrepancy likely indicates that our low-latitude confusion cutoff (Figure \ref{fig:zvdev}) ) is not conservative enough. + As this effects the distribution of b wore strongly than of [5]. we adopt the preferred value from the latter comparison. /7=800 pc.," As this effects the distribution of $b$ more strongly than of $|b|$, we adopt the preferred value from the latter comparison, $h = 800$ pc." + The physical properties of disk-halo taugeut poiut eclouds from QT aud QIV. are sumuuarized iu Table 3.., The physical properties of disk-halo tangent point clouds from QI and QIV are summarized in Table \ref{tab:p2comptable}. + Tudividual clouds iu both quadrants of the Galaxy have simular properties. which sugeests that they belong to the same population and probably have similar origins aud evolutionary histories.," Individual clouds in both quadrants of the Galaxy have similar properties, which suggests that they belong to the same population and probably have similar origins and evolutionary histories." + We defer an analysis of the physical properties of the clouds to another paper: here we note just a few trends that eive important iusight into the nature of the disk-lalo clouds., We defer an analysis of the physical properties of the clouds to another paper; here we note just a few trends that give important insight into the nature of the disk-halo clouds. + First. as the eas mass required for a cloud to be eravitationally bound is AfzrAe?/G. where rds the radius. Ac is the FWHAL aud G is the gravitational constant. the clouds fail to be sclferavitating by several orders of magnitude.," First, as the gas mass required for a cloud to be gravitationally bound is $M\approx r\Delta v^2/G$, where $r$ is the radius, $\Delta v$ is the FWHM, and $G$ is the gravitational constant, the clouds fail to be self-gravitating by several orders of magnitude." + This was noted in the discovery of the dixk-halo cloud population. aud applies not ouly to individual clouds. but also to dense clumps within clouds revealed iu ligh-resohition observations (?7?)..," This was noted in the discovery of the disk-halo cloud population, and applies not only to individual clouds, but also to dense clumps within clouds revealed in high-resolution observations \citep{2002Lockman,2009Pidopryhora}." + Secoud. there is strong evidence that clouds farther from the Galactic plane have. larecr linewidths than clouds uearer the plane (Figure 12)).," Second, there is strong evidence that clouds farther from the Galactic plane have larger linewidths than clouds nearer the plane (Figure \ref{fig:fwhmz}) )." + This confruis previous suggestions of the trend (277)..," This confirms previous suggestions of the trend \citep{2002Lockman, 2006Stil, 2008Ford}." + Moreover. given its coutimuty with it does uot appear to arise from the superposition of separate populations of clouds. but supports the hvpothesis that it reflects pressure various throughout the halo aud the fundinueutal," Moreover, given its continuity with $|z|$, it does not appear to arise from the superposition of separate populations of clouds, but supports the hypothesis that it reflects pressure variations throughout the halo and the fundamental" +associated true distribution for that set of four fields.,associated true distribution for that set of four fields. + We will test the recovery both of the underlying. universal distribution used to construct the photometric sample (re. (5)= 0.75. 8.— 0.20) and of the actual redshift distribution of the objects selected 1n à given set of fields (which will differ due to sample/cosmic variance: cf.," We will test the recovery both of the underlying, universal distribution used to construct the photometric sample (i.e. $\langle z \rangle=0.75$ , $\sigma_z=0.20$ ) and of the actual redshift distribution of the objects selected in a given set of fields (which will differ due to sample/cosmic variance; cf." + $4)., $\S\ref{sec:results}$ ). + Before we can fit for Gaussian parameters. we must account for the fact that our photometric sample has a redshift distribution which differs from a true Gaussian because the total sample we drew from (with Gaussian. probability. às a function of z) was not uniformly. distributed in. redshift.," Before we can fit for Gaussian parameters, we must account for the fact that our photometric sample has a redshift distribution which differs from a true Gaussian because the total sample we drew from (with Gaussian probability as a function of $z$ ) was not uniformly distributed in redshift." + One can think of the actual distribution of the photometric sample in a given bin as a product of three factors: the overall redshift distribution of all objects in the Universe (essentially. the rising curve in. 1): the fractional deviation from the Universal mean of the number of objects ina given field at a given redshift. te. sample/cosmie variance: and the Gaussian function used to select objects for the photometric redshift bin.," One can think of the actual distribution of the photometric sample in a given bin as a product of three factors: the overall redshift distribution of all objects in the Universe (essentially, the rising curve in \ref{fig:ndist}) ); the fractional deviation from the Universal mean of the number of objects in a given field at a given redshift, i.e. sample/cosmic variance; and the Gaussian function used to select objects for the photometric redshift bin." + The first two factors need to be removed from both the true and recovered distributions if we are to test the recovery of the third: this is implemented differently for each case., The first two factors need to be removed from both the true and recovered distributions if we are to test the recovery of the third; this is implemented differently for each case. + For the true distribution. we divide each measurement by the overall Νας of all of the objects in the four fields used in that measurement.," For the true distribution, we divide each measurement by the overall $dN/dz$ of all of the objects in the four fields used in that measurement." + This removes the overall distribution shape as well as the fluctuations due to sample variance. and gives a true distribution that closely matches the Gaussian selection function applied to construct the sample.," This removes the overall distribution shape as well as the fluctuations due to sample variance, and gives a true distribution that closely matches the Gaussian selection function applied to construct the sample." + In principle we could do the same for the recovered distribution. but that would not be practical in real applications. as we can determine the overall shape of the redshift distribution of the overall photometric sample using photometric redshifts. but photo-z errors will prevent measuring fluctuations in the numberof objects within bins," In principle we could do the same for the recovered distribution, but that would not be practical in real applications, as we can determine the overall shape of the redshift distribution of the overall photometric sample using photometric redshifts, but photo-z errors will prevent measuring fluctuations in the numberof objects within bins" +of interest.,of interest. + In cach of these detectors. the count rates are fitted with a quadratic backeround plus source models for the source of interest and cach interfering source that appears in the window.," In each of these detectors, the count rates are fitted with a quadratic background plus source models for the source of interest and each interfering source that appears in the window." + The source models cousist of T(f) and a time-dependent model count rate. derived from the ine-depenudenut detector response convolved with an assumed source spectrum.," The source models consist of $T(t)$ and a time-dependent model count rate, derived from the time-dependent detector response convolved with an assumed source spectrum." + Each source model is inultipliedby a scaling factor. aud the source Hux is then computed by a joint fit to the scaling actors across all detectors in the fit.," Each source model is multiplied by a scaling factor, and the source flux is then computed by a joint fit to the scaling factors across all detectors in the fit." + The best-fit scaling factor is then imnultiplied by the assumed source flux model iutegrated over the energy. baud o obtain the photon fiux., The best-fit scaling factor is then multiplied by the assumed source flux model integrated over the energy band to obtain the photon flux. + Up to 31 occultation steps are possible for a eiven source ina day. and these steps are sumuaed o ect a sinele daily average flux.," Up to 31 occultation steps are possible for a given source in a day, and these steps are summed to get a single daily average flux." + This technique can be used with either theNal or BOO detectors. hough the analysis preseuted here uses ouly the Nal detectors.," This technique can be used with either the NaI or BGO detectors, though the analysis presented here uses only the NaI detectors." + A more complete description of tle CGBAL implementation of the occultation technique will be eiven in Wilson-IHodegeetal.(2010)., A more complete description of the GBM implementation of the occultation technique will be given in \citet{Wilson2010}. +. Iu Wilsou-Todeeetal.(2009a).. the measured (ΟΤΙ 1250 keV helt curves are compared to the BAT 1550 keV. light curves for several sources over the sane time intervals. aud it is seen that the fluxes measured by the two dustruments compare well.," In \citet{Wilson2009a}, the measured GBM 12–50 keV light curves are compared to the BAT 15–50 keV light curves for several sources over the same time intervals, and it is seen that the fluxes measured by the two instruments compare well." + At energies above the ~195 keV upper energev dut of the 22-3nonuth catalog (Tuclleretal.2010).. however. the GDM observations provide the only wide-field monitor available for the low cnerey eamuna-rav sky.," At energies above the $\sim195$ keV upper energy limit of the 22-month catalog \citep{Tueller2010}, however, the GBM observations provide the only wide-field monitor available for the low energy gamma-ray sky." + Of the catalog sources beiug monitored with CDM. six persistent sources have been detected above 100 keVwith a statistical significance of at least To after two vears of observations. as well as two trausieut sources.," Of the catalog sources being monitored with GBM, six persistent sources have been detected above 100 keVwith a statistical significance of at least $7\sigma$ after two years of observations, as well as two transient sources." + Table l1. gives the fluxes averaged over all 730 davs from 2008 August 12 (NLID 51690. the pena of science operations) to 2010. August (NLJID 55119) for the persistent sources. aud over all of the davs of the flares for the trausieut sources.," Table \ref{Flux_table} gives the fluxes averaged over all 730 days from 2008 August 12 (MJD 54690, the beginning of science operations) to 2010 August 11 (MJD 55419) for the persistent sources, and over all of the days of the flares for the transient sources." + Also given are the siguificauces for cach euergv baud., Also given are the significances for each energy band. + The errors are statistical oulv., The errors are statistical only. + The sources are sorted by their detection siguificance in the 100.300 keV baud., The sources are sorted by their detection significance in the 100–300 keV band. + The six persistent sources Crab. Cre κ]. Cou A. GRS 1915)105. LE 1710-29. aud. Swift J1753.5-0127 are detected by (ΝΤ at cnergics above 100 keV. Iu Figures 2- 7 we show light curves for these sources eenerated from the GDM data in several broad euergy bands with five-day resolution.," The six persistent sources Crab, Cyg X-1, Cen A, GRS 1915+105, 1E 1740-29, and Swift J1753.5-0127 are detected by GBM at energies above 100 keV. In Figures \ref{Crab}- \ref{Swift} we show light curves for these sources generated from the GBM data in several broad energy bands with five-day resolution." + These persistent sources demonstrate the capabilities of the GBAL Earth occultation mouitorie., These persistent sources demonstrate the capabilities of the GBM Earth occultation monitoring. + The Crab cuiission iu the hard N-rav/low enerev eannnmua-ray regime contains a combination of pulsar and pulsar wind nebula contributions., The Crab emission in the hard X-ray/low energy gamma-ray regime contains a combination of pulsar and pulsar wind nebula contributions. + Figure 2 shows the light curves measured by GDM iu four broad energy bands from 12 keV up to 500 keV. The spectrum in this regime has been shown by analysis of BATSE occultation data (Muchetal.1996:Line&Wheaton20035). aud data from SPI ou board (Jourdain&Roques2009) to agree with the spectrum measured with other iustrumeuts at lower X-ray energies. and then to steepen near LOO keV. Results of the BATSE aualvsis eau be described by a broken power law. while results of the SPI analysis sugecst a smoothly steepeniug spectrum.," Figure \ref{Crab} shows the light curves measured by GBM in four broad energy bands from 12 keV up to 500 keV. The spectrum in this regime has been shown by analysis of BATSE occultation data \citep{Much1996,Ling2003b} and data from SPI on board \citep{Jourdain2009} to agree with the spectrum measured with other instruments at lower X-ray energies, and then to steepen near 100 keV. Results of the BATSE analysis can be described by a broken power law, while results of the SPI analysis suggest a smoothly steepening spectrum." + The BATSE analysis further noted a distinct hardening of the spectrum near 650 keV. although this has not been confined by or the COMPTEL justriment on (Ixuiperetal.2001).," The BATSE analysis further noted a distinct hardening of the spectrum near 650 keV, although this has not been confirmed by or the COMPTEL instrument on \citep{Kuiper2001}." +. The spectral iieasureinents are consistent with either a smoothly stecpening spectrum or a spectrum of the form £F=6.6«10ΕΕκο) photons ? «s! keV | where a=2.07£0.01 for E<<100 keV and a=22340.02 for E>100 keV (Jourdain&Roques 2009).," The spectral measurements are consistent with either a smoothly steepening spectrum or a spectrum of the form $ F = 6.6 \times 10^{-4} (E/100 {\rm ~keV})^{-\alpha}$ photons $^{-2}$ $^{-1}$ $^{-1}$ , where $\alpha = 2.07 \pm 0.01$ for $E < 100$ keV and $\alpha = 2.23 \pm 0.02$ for $E > 100$ keV \citep{Jourdain2009}." +".. This corresponds to a (50100 τον(1250 keV) fiux ratio of Που=0.110 for compared to 0.112£0,001 for CDM.", This corresponds to a (50–100 keV)/(12–50 keV) flux ratio of $R_{50} = 0.145$ for compared to $0.142 \pm 0.001$ for GBM. + The (100.300 keV)/(1250 keV) flux ratio 4190=KOLL correspoudiug to the spectrmu conrpares to the GDM value of 0.07640.001. and he (300.500 keV)/(1250 keV) fiux ratio A399= for corresponds to the GDM value of 0.013+ 0.001.," The (100–300 keV)/(12–50 keV) flux ratio $R_{100} = 0.041$ corresponding to the spectrum compares to the GBM value of $0.076 \pm 0.001$, and the (300–500 keV)/(12–50 keV) flux ratio $R_{300} = 0.007$ for corresponds to the GBM value of $0.013 \pm 0.001$ ." + TheCDM measurements 4eeest a somewhat flatter spectrmu than that derived fron INTEGRAL. particularlyabove 100 keV. and are best deseribedby a spectrum with," TheGBM measurements suggest a somewhat flatter spectrum than that derived from , particularlyabove 100 keV, and are best described by a spectrum with" +funes is difficult with he BSCC data due to the large gaps in the survey area coverage aud not enough overlap between adjacent CCD images (no 2 or L-fold overlap patter).,frames is difficult with the BSCC data due to the large gaps in the survey area coverage and not enough overlap between adjacent CCD images (no 2 or 4-fold overlap pattern). + Siniblulv the photometric results suffer from a weak determination of the zero-poiut per CCD frame due to the small number of available. highly accurate standard stars.," Similarly the photometric results suffer from a weak determination of the zero-point per CCD frame due to the small number of available, highly accurate standard stars." + Once a cdeuser photometric catalog than the Treho-2 becomes available. the BSCC data would benefit from a re-reduction.," Once a denser photometric catalog than the Tycho-2 becomes available, the BSCC data would benefit from a re-reduction." + The host diuportant aspect of the BSCC astrometric data is the lieh signal-to-noise data for stars at the faint UCAC eud. ie. stars around R= 15 to 16.," The most important aspect of the BSCC astrometric data is the high signal-to-noise data for stars at the faint UCAC end, i.e. stars around R = 15 to 16." + The precision of the BSCC positions is about LO amas per coordinate. while the UCAC data are ou the 70 mas level at those magnitudes.," The precision of the BSCC positions is about 40 mas per coordinate, while the UCAC data are on the 70 mas level at those magnitudes." + However. oulv a small area of the sky could be covered with this 7-vear effort.," However, only a small area of the sky could be covered with this 7-year effort." + Full-skyv coverage with high accuracy down to about R = 17.5 will hopefully be achieved soon with the URAT project (Zacharias2008)., Full-sky coverage with high accuracy down to about R = 17.5 will hopefully be achieved soon with the URAT project \citep{urat}. +. Combining URAT data with the BSCC will provide excellent proper motions for those faint stars on the 2 1as/vr level. completely based on CCD observations for early and current epoch data.," Combining URAT data with the BSCC will provide excellent proper motions for those faint stars on the 3 mas/yr level, completely based on CCD observations for early and current epoch data." + We wish to thank the former director of the Copenhagen University Observatory. Ποιο Jorgensen. who plaved a key role in the defiuition and initialization of the project.," We wish to thank the former director of the Copenhagen University Observatory, Henning rgensen, who played a key role in the definition and initialization of the project." +" This publication makes use of data products from the Two Micron. All Skv. Survey, which is a joint project of the University of Massachusetts and the Dufraved Processing aud Analysis Center/Califoruia Tustitute of Technology. fuuded by the National Aeronautics and Space Adiuiuistration aud the Nationa Science Foundation."," This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation." + Funding for the SDSS and SDSS-II has beeu provide by the Alfred P. Sloan Fouudatiou. the Participating LIustitiions. the National Science Foundation. the U.S. Departinent of Eucrgx. the Nationa Acronauties and Space Acdiuinistration. the Japanese Moubukagakusho. the Max. Planck Society. aud the ΕΠολο Education Fuudiue Council for Euglaud.," Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the U.S. Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England." + The SDSS Web Site is http:/Aww.sdss.org National Optical Astronomy Observatories (NOAO) is acknowledged for IRAE. Sunithomian Astrophysical Observatory for DS9 1nage cisplav software. aud the California Institute of Technology for thepyplot software.," The SDSS Web Site is http://www.sdss.org/. National Optical Astronomy Observatories (NOAO) is acknowledged for IRAF, Smithonian Astrophysical Observatory for DS9 image display software, and the California Institute of Technology for the software." + (ΗΕΤΟΝ bursts (GRB) are understood to depend on barvon purity., Gamma-ray bursts (GRB) are understood to depend on baryon purity. + With too much barvon contamination. their energv would end up in kinetic energy. and eventually allerelow.," With too much baryon contamination, their energy would end up in kinetic energy, and eventually afterglow." + The rather stringent requirements for baryon purity needed [or a successful GRB are consistent with (he inference that there is only about 1 GRB per 10.000 supernovae. despite the known association between the (wo phenomena.," The rather stringent requirements for baryon purity needed for a successful GRB are consistent with the inference that there is only about 1 GRB per 10,000 supernovae, despite the known association between the two phenomena." +" One might therefore ask whether there is a continuous spectrum of “semi-GRB"" that smoothly connects normal supernovae to bright GRD."," One might therefore ask whether there is a continuous spectrum of ""semi-GRB"" that smoothly connects normal supernovae to bright GRB." + Dirty fireballs aud A-vay flashes have been proposed as examples of this., Dirty fireballs and X-ray flashes have been proposed as examples of this. +" As X-ray flashes are about as numerous as standard GRB. but have much smaller values lor V5,;. the maximum value within whieh thev could have been observable at our location. their rate density is probably much higher. aud one might ask whether the total luminosity input in such semi-GRB's could dominate the total."," As X-ray flashes are about as numerous as standard GRB, but have much smaller values for $V_{max}$, the maximum value within which they could have been observable at our location, their rate density is probably much higher, and one might ask whether the total luminosity input in such semi-GRB's could dominate the total." + ThiV. is relevant to anv question connected wilh GRD calorimetry. and (otal luminosity density. e.g. the question of how much energy is available in GRB to produce ultrarelativistic cosmic rays (ULIECR).," This is relevant to any question connected with GRB calorimetry and total luminosity density, e.g. the question of how much energy is available in GRB to produce ultrarelativistic cosmic rays (UHECR)." + There is physical motivation lor asking this question as well as it constrains models of the central engine.," There is physical motivation for asking this question as well, as it constrains models of the central engine." + IF. for example. the barvon purity is a [function of disk cooling. so that barvons from a hot atmosphere do not extend. up to the slow-Alfven critical point where they are injected into a magnetocentrifugal outflow (Levinson 2006). then one might suppose that. because this injection rate varies both with position on the disk aud time. there are many GRD in which the photons are cooled by adiabatic expansion belore being released bevond the gamma rav photosphere.," If, for example, the baryon purity is a function of disk cooling, so that baryons from a hot atmosphere do not extend up to the slow-Alfven critical point where they are injected into a magnetocentrifugal outflow (Levinson 2006), then one might suppose that, because this injection rate varies both with position on the disk and time, there are many GRB in which the photons are cooled by adiabatic expansion before being released beyond the gamma ray photosphere." + In fact. popular models of GRB Irequenily. invoke a saturation radius (that is well within the photosphere. in which case the photons would cool aciabatically before escaping.," In fact, popular models of GRB frequently invoke a saturation radius that is well within the photosphere, in which case the photons would cool adiabatically before escaping." + If there is a continuous range of the extent of this adiabatic cooling. (hen one would expect a continuous range of GRB fences. and perhaps a sizable contribution to the total allskv fence from very weak. very soft. or very prolonged (i.e. low luminosity) GRD.," If there is a continuous range of the extent of this adiabatic cooling, then one would expect a continuous range of GRB fluences, and perhaps a sizable contribution to the total allsky fluence from very weak, very soft, or very prolonged (i.e. low luminosity) GRB." + Yet another parameter that seems quite variable in GRD is the opening angle., Yet another parameter that seems quite variable in GRB is the opening angle. + The larger the opening angle. the dimmer the GRB appears.," The larger the opening angle, the dimmer the GRB appears." + Very wile GRB mieht (hus escape detection. vel might dominate the total Iuminositw density of GRD.," Very wide GRB might thus escape detection, yet might dominate the total luminosity density of GRB." + Similarly. (he peripheries of “structured jets” might conceivably conten most of the GRB energy. in," Similarly, the peripheries of ""structured jets"" might conceivably contain most of the GRB energy, in" +more probable.,more probable. +" The spin tilt angle 0, is less than 30.0? with confidence.", The spin tilt angle $\theta_t$ is less than $^\circ$ with confidence. +" At the known distance, the total transverse velocity of PSR J1829+2456 at the current time is between 4 and 102 km s!, and the radial velocity between —126 and 66 km s! with confidence."," At the known distance, the total transverse velocity of PSR J1829+2456 at the current time is between 4 and 102 km $^{-1}$, and the radial velocity between $-126$ and 66 km $^{-1}$ with confidence." +" In addition, the probability that this is moving towards the Sun is ~20% higher than that it is systemmoving away from the Sun."," In addition, the probability that this system is moving towards the Sun is $\sim$ higher than that it is moving away from the Sun." + Comparing our V; and M»; results with Wang et al. (, Comparing our $V_k$ and $M_{2i}$ results with Wang et al. ( +"2006), we have more constrained limits, as they do not include any kinematic constraints.","2006), we have more constrained limits, as they do not include any kinematic constraints." +" The masses of the neutron stars are 1.37 and 1.25 Mo, where the more massive one is NS1."," The masses of the neutron stars are 1.37 and 1.25 $_\sun$, where the more massive one is NS1." +" Unlike the other 7 binaries, the observed is NS2."," Unlike the other 7 binaries, the observed pulsar is NS2." +" This implies the binary is relatively young, with a pulsarcharateristic age of 0.112 Myr only."," This implies the binary is relatively young, with a charateristic age of 0.112 Myr only." +" The neutron stars are in an orbit with a period of 0.166 days, and an orbital eccentrirctiy of 0.0853."," The neutron stars are in an orbit with a period of 0.166 days, and an orbital eccentrirctiy of 0.0853." +" At current time, this"," At current time, this" + (1986)) and Norris Da Costa (1995)) based on the unique presence of CO-strong stars;,\cite{cohe86}) ) and Norris Da Costa \cite{norr95}) ) based on the unique presence of CO-strong stars. + Morcover. the [C/Fo] abundance in the metal-poor population is about 0.7 dex according to Norris Da Costa. which is close το. 0.5 dex. theoreically expected from the vield ratios in SNe IT (Tsujimoto et al. 1995)).," Moreover, the [C/Fe] abundance in the metal-poor population is about $-$ 0.7 dex according to Norris Da Costa, which is close to $-$ 0.5 dex, theoretically expected from the yield ratios in SNe II (Tsujimoto et al. \cite{tsuj95}) )." +" Tf sav. 0.2 dex would be the ""true value of [C/T]. oue would require a considerable C-contribution frou interiiediate-ase stars. which by itself Is nof casy to undoerstaud for the first stars formed ia w Cen."," If, say, $-$ 0.2 dex would be the “true” value of [C/H], one would require a considerable C-contribution from intermediate-age stars, which by itself is not easy to understand for the first stars formed in $\omega$ Cen." + Also a mean [O/C|-valuc of approximately 1 dex. as one would read off from Norris Da Costa is close to he theoretically expected vield ratios from SNe II.," Also a mean [O/C]-value of approximately $-$ 1 dex, as one would read off from Norris Da Costa is close to the theoretically expected yield ratios from SNe II." + On the other haud. if the increasing |C|N/Fo] among he imetal-poor old population was. at least to large out. primordial. one is driven to the conclusion that he star formation process. which formed these stars. did rot took place iun a sinele burst within a wellulxed environment. but iust have heen extended m time. allowing intermediate-age populations to contribute.," On the other hand, if the increasing [C+N/Fe] among the metal-poor old population was, at least to large part, primordial, one is driven to the conclusion that the star formation process, which formed these stars, did not took place in a single burst within a well-mixed environment, but must have been extended in time, allowing intermediate-age populations to contribute." + We shall attempt to combine these abundance pattern with other properties within a consistent scenario later ou., We shall attempt to combine these abundance pattern with other properties within a consistent scenario later on. +" The Stróuuueren m, mdex also is seusible to metallicity for stars around the main sequence tui-off (MSTO) region.", The Strömmgren $m_1$ index also is sensible to metallicity for stars around the main sequence turn-off (MSTO) region. + A recent calibration has been published bv Alalvuto (1991)) which is valid iu the color ranges 422«(b.g)y<0.38 and 0.03.—mig0.22 (the above considerations regarding the C-sensitivitv do not jiecessarilv apply here since the CN-banud iuflueuce is ess dn these hotter stars).," A recent calibration has been published by Malyuto \cite{maly}) ) which is valid in the color ranges $0.22 < (b-y)_0 < 0.38$ and $0.03 < m_{1,0} < 0.22$ (the above considerations regarding the C-sensitivity do not necessarily apply here since the CN-band influence is less in these hotter stars)." + IIughes Wallerstein (1999)) applied this calibration to their Strouunercu data of w Cen and showed that the stars of different metallicity bius ardly differ iu the location a the MSTO region (see their Fie., Hughes Wallerstein \cite{hugh}) ) applied this calibration to their Strömmgren data of $\omega$ Cen and showed that the stars of different metallicity bins hardly differ in the location at the MSTO region (see their Fig. + 9 iix 103., 9 and 10). + There exists the trend that the more metal stars seciun to be blucr in average than the uctal-poor ones. in contrast to what oue would expect if all stars had the same age.," There exists the trend that the more metal-rich stars seem to be bluer in average than the metal-poor ones, in contrast to what one would expect if all stars had the same age." + Applviug Malyuto's calibralon to our data we confirm this finding. as shown in Sect.," Applying Malyuto's calibration to our data we confirm this finding, as shown in Sect." + 5.1., 5.1. + In Fie., In Fig. + 11 (right panels) the location of MSTO stars for three different metallicity bius is shown., \ref{age} (right panels) the location of MSTO stars for three different metallicity bins is shown. + Since our sample is not colplete in this magnitude range aud photometric errors are laree. we hesitate to attempt a quantitative analysis of the metallicity distribution in the MSTO veeion.," Since our sample is not complete in this magnitude range and photometric errors are large, we hesitate to attempt a quantitative analysis of the metallicity distribution in the MSTO region." + But it is apparent that the more metal-rich stars caunot be fit by old isochroucs., But it is apparent that the more metal-rich stars cannot be fit by old isochrones. +" The combination of the reducss parameter pi aad the Strouuuercn imetallicitv μμ, can be used to divide he ROB in different sub-populations aud examine their ages and thei spatial distribution iu the cluster.", The combination of the redness parameter $p_{\rm red}$ and the Strömmgren metallicity $_{\rm ph}$ can be used to divide the RGB in different sub-populations and examine their ages and their spatial distribution in the cluster. + In Fig., In Fig. +" l0. a plot of prog versus Ημ, is shown."," \ref{spar} + a plot of $p_{\rm red}$ versus $_{\rm ph}$ is shown." + As ucutioned in the previous section there exists the eeucral rond hat re reddest stars also are tho most metal/CN-vich ones as it is expected., As mentioned in the previous section there exists the general trend that the reddest stars also are tho most metal/CN-rich ones as it is expected. +" The solid diagonal Lue iu us diagram shows the expected relation between pred nd [Fe/TI|,i if the stars would behave according to the alibration of ΠΠ]κο (2000)) (""CN-nonual stars”).", The solid diagonal line in this diagram shows the expected relation between $p_{\rm red}$ and $_{\rm ph}$ if the stars would behave according to the calibration of Hilker \cite{hilk00a}) ) (“CN-normal stars”). + Besides ie asvinptotic elaut branch. three sub-populations have en selected (boxes witli solid ines) that define different warts of the eiu branch in the CMD.," Besides the asymptotic giant branch, three sub-populations have been selected (boxes with solid lines) that define different parts of the giant branch in the CMD." + Coufirmmed member stars of w Cen according to their radial velocitics are 4.xead all over the parameter space (dark dots)., Confirmed member stars of $\omega$ Cen according to their radial velocities are spread all over the parameter space (dark dots). + Heuce a separation of ΠΟΠΟΙΟ stars in this diagram is hardly possible., Hence a separation of non-member stars in this diagram is hardly possible. + Later ou. we will use further sub-selectious witlin +1¢ sub-populations (dashed aud dotted areas) to examine +ie different spatial distributious within w Coen.," Later on, we will use further sub-selections within the sub-populations (dashed and dotted areas) to examine the different spatial distributions within $\omega$ Cen." + For the identification of possibly different ages among the sub-populations of w Cen the isochroues from Berebusch VaudeuDere (1992.. in the following DV92) have been used. converted to Stromuneren colors by Crebol Roberts (1995)).," For the identification of possibly different ages among the sub-populations of $\omega$ Cen the isochrones from Bergbusch VandenBerg \cite{berg}, in the following BV92) have been used, converted to Strömmgren colors by Grebel Roberts \cite{greb95}) )." + The location of the metal-poor giants im the CMD has been used to define a refercuce isochrouc., The location of the metal-poor giants in the CMD has been used to define a reference isochrone. + Acopting their known metallicity (|Fo/II|2L.7 dex). a distance modulus. color offset. auc age las been determined.," Adopting their known metallicity $= -1.7$ dex), a distance modulus, color offset, and age has been determined." + For fitting the RGB. only stars with a photometric error less," For fitting the RGB, only stars with a photometric error less" +Astronomical objects 5cli as stars. clouds. axl galaxies have enormous clyuamic rauge both in deusity aud in size.,"Astronomical objects such as stars, clouds, and galaxies have enormous dynamic range both in density and in size." + To iustrate this enormous dyna€ range. we cousider star formation as au example.," To illustrate this enormous dynamic range, we consider star formation as an example." + Stars [orm in molecular clouds of wuch the mean density is 10° atoms cm7., Stars form in molecular clouds of which the mean density is $^3$ atoms $^{-3}$. + The nolecular clouds coηαι cocensatious named moecular coud cores. [οι1 whüch stars form owing o the sell-gravity.," The molecular clouds contain condensations named molecular cloud cores, from which stars form owing to the self-gravity." + The molecular cloud. cores have typical size of 10 cu aud typical deusity of 103 aloms 7C., The molecular cloud cores have typical size of $^{17}$ cm and typical density of $^5$ atoms $^{-3}$. +" ο1 the οἱer hand. the central «eusity of a star is 11 atoms "" at the very )eginuiug of its proostellar stage aud the preseut Sun has he central ceisity"" of""ou 1075OF atoms 3"," On the other hand, the central density of a star is $^{11}$ atoms $^{-3}$ at the very beginning of its protostellar stage and the present Sun has the central density of $^{26}$ atoms $^{-3}$." + The radius of a proostar is 1013 em when the ceitral deusity is LOY at«uus ., The radius of a protostar is $^{14}$ cm when the central density is $^{12}$ atoms $^{-3}$ . +" As the centra density ine""CASES. (je. radius decreases down to 1040 — 10? em until tje star reaches its mail sequence (Ivdrogen burning) stage."," As the central density increases, the radius decreases down to $^{10}$ – $^{12}$ cm until the star reaches its main sequence (hydrogen burning) stage." + This elormous dynamic raige restrict us to achieve Ligh spatial resolution only in the simal ‘epious of 1αἱ9185., This enormous dynamic range restrict us to achieve high spatial resolution only in the small regions of interest. + To generate finer grids iu tlie region of interest. people Lave developed valotus nesh generation methods.," To generate finer grids in the region of interest, people have developed various mesh generation methods." + Acadtive mesh refinement (AMI) anc nested grids (NC) are tyya ol the mesh gene‘ation methods developed in the past decade., Adaptive mesh refinement (AMR) and nested grids (NG) are typical of the mesh generation methods developed in the past decade. + AMR aud NC generate finer erids uerarchically in the region of iuerest., AMR and NG generate finer grids hierarchically in the region of interest. + AMB was invented by Berger&Oliger(1981). and has )eel advauced by matry researchers.," AMR was invented by \citet{berger84} + and has been advanced by many researchers." + (C ds a variant of AMR ancl generates only one sub-grid at eact jerarcical level. while AMR I€as no restriction on the number of sub-erids.," NG is a variant of AMR and generates only one sub-grid at each hierarchical level, while AMR has no restriction on the number of sub-grids." + AMR aud NG lave SULCCEECed iu similations of star ormation aud galaxy formation in which compact objects fori1 by condensation of cUse clouds., AMR and NG have succeeded in simulations of star formation and galaxy formation in which compact objects form by condensation of diffuse clouds. + SOne recent numerical simLations on star formation and cosmology apply either AMR or τν {ο achieve hieli spatial resoion., Some recent numerical simulations on star formation and cosmology apply either AMR or NG to achieve high spatial resolution. + Trueloveetal.(1997) studied οravitational collapse of a uolecuar cloud core with AMR ¢) resolve [ragmenutatiou of the ughly coidensecd cloud core., \citet{truelove97} studied gravitational collapse of a molecular cloud core with AMR to resolve fragmentation of the highly condensed cloud core. + Since hen A] is reqrently used in uLjerical simulatious of fragmeuation during gravitational collapse (Trueloveetal.1905:Bossοἱ2000).," Since then AMR is frequently used in numerical simulations of fragmentation during gravitational collapse \citep{truelove98,boss00}." +. Using NG Burkert&Bodeuheijer(1993.1996) stucliec Tagineation of a centrally condesed protostar.," Using NG \citet{burkert93,burkert96} studied fragmentation of a centrally condensed protostar." + They succeede in resolv ingsdial arius formed by he self-e[n]ravitational instability i the protoplanetary disk., They succeeded in resolving spiral arms formed by the self-gravitational instability in the protoplanetary disk. + Usiie NG Tonisaka(1008) computed gravitaioual collapse of rotating magnetized gas cloud aud fouud magueohydrodynamical driver oulllow enmuating [rom a very compact central disk., Using NG \citet{tomisaka98} computed gravitational collapse of rotating magnetized gas cloud and found magnetohydrodynamical driven outflow emanating from a very compact central disk. + NormaL&Bryan{1999) has reviewec applicaion of AMR to cosmological simulations., \citet{norman99} has reviewed application of AMR to cosmological simulations. + Though simulations based on AMB aud NG are successful. some techuical »robleiis still remain for AMR and NC.," Though simulations based on AMR and NG are successful, some technical problems still remain for AMR and NG." + One of them is a numerical algorilun for solving the Poisson equation on a gri in which a cel faces several sunaller cells., One of them is a numerical algorithm for solving the Poisson equation on a grid in which a cell faces several smaller cells. + In other wo‘ds. difficulty arises a| boundaries between the regious covered with different size cells.," In other words, difficulty arises at boundaries between the regions covered with different size cells." + For later convenulence we name {hese boundaries the eric level bouucdaries., For later convenience we name these boundaries the grid level boundaries. + In most AMR and NG of three clitjensions. a parent ceIl faces four child cells at each grid leve boundary in case of three climeusious.," In most AMR and NG of three dimensions, a parent cell faces four child cells at each grid level boundary in case of three dimensions." + When cells are uuilorm ou a eric. a simple ceural dillereuce scheiue gives us secoud order accuracy and he difference equation can be solved fast withthe multi-grkl iteration or some otler," When cells are uniform on a grid, a simple central difference scheme gives us second order accuracy and the difference equation can be solved fast withthe multi-grid iteration or some other" +Iow-Iuminosity AGN would. be expected. over the redshift range 0«0.2. where our sources with low values of qip reside. and also with 10UcLiaca f/W 5o«1071077.,"low-luminosity AGN would be expected over the redshift range $0 < z<0.2$, where our sources with low values of $q_{\rm IR}$ reside, and also with $10^{20} $, increases with increasing mass ratio since the energy that the interloper can carry away scales as $\Delta +E / E\sim m_{1}/\left(m_{0} + m_{1}\right)$ \citep{q96} and since $n_{\mathrm{enc}} \sim E / \Delta E$ for a constant eccentricity." + Energy conservation assures that every hardening event results in an increased relative velocity between the binary and the single black hole., Energy conservation assures that every hardening event results in an increased relative velocity between the binary and the single black hole. + If the velocity of the single black hole relative to the barvcenter. and thus the elobular cluster. is greater than (lie escape velocity of the cluster core = DO tforadensecluster:1985). then the single mass will be ejected from the cluster.," If the velocity of the single black hole relative to the barycenter, and thus the globular cluster, is greater than the escape velocity of the cluster core \citep[typically $v_{\mathrm{esc}} = 50 for a dense cluster;, then the single mass will be ejected from the cluster." + The average number of ejected masses per sequence. (n4). also increases with increasing mass ratio because the higher mass ratio sequences have a lareer number of encounters and because the larger mass αἱ a given semimajor axis has more energy for the interloper to tap.," The average number of ejected masses per sequence, $\left$, also increases with increasing mass ratio because the higher mass ratio sequences have a larger number of encounters and because the larger mass at a given semimajor axis has more energy for the interloper to tap." + Conservation of momentum guarantees (hat when a mass is ejected from the cluster at very. high velocity. the binary may also be ejected.," Conservation of momentum guarantees that when a mass is ejected from the cluster at very high velocity, the binary may also be ejected." + Table 2. lists (fiiia). the fraction of sequences that result in the ejection of the binary from the cluster.," Table \ref{coreresults} lists $\left$, the fraction of sequences that result in the ejection of the binary from the cluster." + As expected. the fraction decreases sharply with increasing mass such (hat virtually none of the binaries with mass greaterChan 300M. escape the cluster.," As expected, the fraction decreases sharply with increasing mass such that virtually none of the binaries with mass greaterthan $300~\msun$ escape the cluster." +"fraction and the angular size of the torus inner boundary in the previous sections above, we discuss the current expectations for the near-IR interferometric studies of the innermost region of AGN tori, and also discuss the existing measurements.","fraction and the angular size of the torus inner boundary in the previous sections above, we discuss the current expectations for the near-IR interferometric studies of the innermost region of AGN tori, and also discuss the existing measurements." +" For the sample studied in sections 2 and 3, the fractional contribution at K-band from a putative accretion disk is suggested to be only ~25% or less, so that the point-source K- flux is essentially dominated by the flux from the torus."," For the sample studied in sections 2 and 3, the fractional contribution at K-band from a putative accretion disk is suggested to be only $\sim$ or less, so that the point-source K-band flux is essentially dominated by the flux from the torus." +" On the other hand, the physical size of the near-IR emitting region in the accretion disk is expected to be much smaller than the torus inner boundary."," On the other hand, the physical size of the near-IR emitting region in the accretion disk is expected to be much smaller than the torus inner boundary." +" Assuming a simple geometrically-thin optically-thick multi-temperature blackbody disk (Shakura Sunyaev 1973), we can at least formally estimate the K-band emitting radius rap, as a radius where the disk temperature goes down to ~1500K. We obtain where 7 and [πα are the radiative efficiency (the luminosity L=Mc’; M is the mass accretion rate) and Eddington luminosity, respectively."," Assuming a simple geometrically-thin optically-thick multi-temperature blackbody disk (Shakura Sunyaev 1973), we can at least formally estimate the K-band emitting radius $r_{\rm AD,K}$ as a radius where the disk temperature goes down to $\sim$ 1500K. We obtain where $\eta$ and $L_{\rm Edd}$ are the radiative efficiency (the luminosity $L = \eta \dot{M} c^2$; $\dot{M}$ is the mass accretion rate) and Eddington luminosity, respectively." + This is shown in Fig.4 as a dashed line., This is shown in \ref{torus_pc} as a dashed line. + The effective size of the K-band emitting region might be even smaller due to the truncation of the outer part of the disk by self-gravity (e.g. Goodman 2003)., The effective size of the K-band emitting region might be even smaller due to the truncation of the outer part of the disk by self-gravity (e.g. Goodman 2003). +" Fig.6 and 7 show the simulation of interferometric observations for a simple case of a ring-like torus plus a much more compact source, corresponding to an accretion disk, with various fractional flux contributions fap."," \ref{vis_ring_1p2} and \ref{vis_ring_0p4} show the simulation of interferometric observations for a simple case of a ring-like torus plus a much more compact source, corresponding to an accretion disk, with various fractional flux contributions $\fAD$." + Fig.6 is for a ring radius of 1.2 mas corresponding to the angular size in Eq., \ref{vis_ring_1p2} is for a ring radius of 1.2 mas corresponding to the angular size in Eq. +" 2 (Rsup case), and Fig.7 is for 0.4 mas in Eq."," \ref{eq-Rsub-mas} $\rsub$ case), and \ref{vis_ring_0p4} is for 0.4 mas in Eq." +" 4 (R,, case)."," \ref{eq-Rtauk-mas} + $\Rtauk$ case)." +" Here, the FWHM w of the ring is set to 1/5 of the ring radius Frying, but the results for the spatial frequency range shown in these Figures essentially do not change as long as w 10?) with a thick torus (top left panel), Lin,agn/Dpoiaisc is slightly smaller than the bottom left panel due to the self-occultation effect."," For super-Eddington accretion $\dot{m}_{\rm BH} \geq 10^2$ ) with a thick torus (top left panel), $L_{\rm IR,AGN}/L_{\rm bol,disc}$ is slightly smaller than the bottom left panel due to the self-occultation effect." +" For sub-Eddington accretion with a thin torus (bottom right panel), Lrr,acn/Lpol,dise becomes smaller than the case of the bottom left panel, because the radiation of the accretion disc is reprocessed at the small inner surface of the torus."," For sub-Eddington accretion with a thin torus (bottom right panel), $L_{\rm IR,AGN}/L_{\rm bol,disc}$ becomes smaller than the case of the bottom left panel, because the radiation of the accretion disc is reprocessed at the small inner surface of the torus." +" Super-Eddington accretion (meu> 10?) with a thin torus (top right panel) has the smallest Lig,AGN/Lboaisc in the four panels of Fig."," Super-Eddington accretion $\dot{m}_{\rm BH} \geq 10^2$ ) with a thin torus (top right panel) has the smallest $L_{\rm IR,AGN}/L_{\rm bol,disc}$ in the four panels of Fig." + 3 due to the self-occultation effect of the disc along with the small covering factor of the torus., 3 due to the self-occultation effect of the disc along with the small covering factor of the torus. +" We here mention the effect of the inclination angle, Oops (Fig."," We here mention the effect of the inclination angle, $\theta_{\rm obs}$ (Fig." + 1)., 1). +" The observed ratio Lir,acn/Lobs,disc(Üovs) depends on Oops, but Lir,acn is independent of 0554, where Lobs,disc(9obs) is the observed disc luminosity at the viewing angle ΟΓθους."," The observed ratio $L_{\rm IR,AGN}/L_{\rm obs,disc} +(\theta_{\rm obs})$ depends on $\theta_{\rm obs}$, but $L_{\rm IR,AGN}$ is independent of $\theta_{\rm obs}$, where $L_{\rm obs,disc}(\theta_ +{\rm obs})$ is the observed disc luminosity at the viewing angle of $\theta_{\rm obs}$." +" However, the difference between θους=0° (face on) and 0,55,—30? is a factor of 3/2."," However, the difference between $\theta_{\rm obs}=0^{\circ}$ (face on) and $\theta_{\rm obs}$ $^{\circ}$ is a factor of $\sqrt{3}/2$ ." +" In contrast, in the case of 45 deg 45 deg, the IR luminosity of super-Eddington AGNSs could be similar to that of sub-Eddington AGNs."," Thus, when $\theta_{\rm obs} > +45$ deg, the IR luminosity of super-Eddington AGNs could be similar to that of sub-Eddington AGNs." +" In summary, the IR luminosity of super-Eddington AGNs is very faint for θους<45°, while it is not so faint for 45?65°), our method isuseful for exploring the candidates of super- AGNs."," Thus, even if the effect we proposed becomes significant only for relatively large $\theta_{\rm torus}$ $>65^{\circ}$), our method isuseful for exploring the candidates of super-Eddington AGNs." +" Near-IR (NIR) emission is produced by the hot dust (> 1000K) which is directly heated by the central AGNs,"," Near-IR (NIR) emission is produced by the hot dust $> 1000\,{\rm K}$ ) which is directly heated by the central AGNs," +2tpt Sudden Ionosxpleric Disturbances. Gamuna Rav Bursts. Soft Camuna Bay repeaters - Nravs and Cama Rav Astronomy 91.20.Tt. 98.70.Rz. 07.85. 82.50.INX 2tpt It is well kuown that the earth's is a gigantic detector of cucrev plenomena which are in the Cuiverse.,"24pt Sudden Ionospheric Disturbances, Gamma Ray Bursts, Soft Gamma Ray repeaters - Xrays and Gamma Ray Astronomy 94.20.Tt, 98.70.Rz, 07.85.-m, 82.50.Kx 24pt It is well known that the earth's ionosphere is a gigantic detector of high energy phenomena which are taking place in the Universe." + The ionosphereactivities such as solar flares or highgana rav bursts or other such takingeuergetic placeevents cause ionospheric disturbances which may be detected by stucving the very low frequency (VLE) radio signals which propagate inside the waveguide formed between the ionosphere aud surface of the earth., The activities such as solar flares or gamma ray bursts or other such energetic events cause ionospheric disturbances which may be detected by studying the very low frequency (VLF) radio signals which propagate inside the waveguide formed between the ionosphere and surface of the earth. + While there are may solar flares. particularly. during the solar maxima. there are only handful of cases where the gama ray bursts (CORBs) or soft eamuna rax repeaters (SCGRs) have been detected.," While there are many solar flares, particularly, during the solar maximum, there are only handful of cases where the gamma ray bursts (GRBs) or soft gamma ray repeaters (SGRs) have been detected." + This is because the GRBs are usually cosmological and the SCRs may also be very far out (~ LOkpe) even if in our own galaxy., This is because the GRBs are usually cosmological and the SGRs may also be very far out $\sim 10$ kpc) even if in our own galaxy. +" Tudiau Centre for Space Plvsics (CSP) have been monitorime the ionospheric disturbances for about a decade,", Indian Centre for Space Physics (ICSP) have been monitoring the ionospheric disturbances for about a decade. + The goals are to study solar flares |l]. meteor showers [2]. lithosphere-ionosplore coupling and precursors to earthquakes [3-6] aud. of course. sudden ionospheric disturbances due to high cucrey phenomena such as Canina Ray Bursts and Soft Gamma ray Repeaters [7-10].," The goals are to study solar flares [1], meteor showers [2], lithosphere-ionosphere coupling and precursors to earthquakes [3-6] and, of course, sudden ionospheric disturbances due to high energy phenomena such as Gamma Ray Bursts and Soft Gamma ray Repeaters [7-10]." + The, The +it appears as an attenuation in the luear propagation of density waves emitted by the vortex aud it leads to a stronger outer wave.,it appears as an attenuation in the linear propagation of density waves emitted by the vortex and it leads to a stronger outer wave. + This is a major difference with he planet case in which asvnunetric Lindblad torques acting at the sonic line are bolieved to drive planet weration., This is a major difference with the planet case in which asymmetric Lindblad torques acting at the sonic line are believed to drive planet migration. + Furthermore. since we fiud the vortex always o 1nove with the local gas velocity. there is no effect of the pressure buffer as discussed in the appendix.," Furthermore, since we find the vortex always to move with the local gas velocity, there is no effect of the pressure buffer as discussed in the appendix." + We find that wave asvuuuetrics only weakly depend on the vackeround density profile. favoring the outer wave aud herefore inward mueration.," We find that wave asymmetries only weakly depend on the background density profile, favoring the outer wave and therefore inward migration." +" However, unlike a planet. a vortex directly feels the disk and its associated density profile. which leads to an asviunuetrce vortex core as cliscussed in Sect."," However, unlike a planet, a vortex directly feels the disk and its associated density profile, which leads to an asymmetric vortex core as discussed in Sect." + 2? iu the case of a vortensity eracieut., \ref{VORTASM} in the case of a vortensity gradient. + The resulting asvuuuctric wave chussion can either counteract or reinforce inward uueration due to ecomctrical effects as discussed above., The resulting asymmetric wave emission can either counteract or reinforce inward migration due to geometrical effects as discussed above. + We also point out that since there is no gravitational interaction between disk and vortex. there are no horseshoe orbits close to corotation.," We also point out that since there is no gravitational interaction between disk and vortex, there are no horseshoe orbits close to corotation." + In the planet case. the horseshoe drag (2). is an additional source of angular moment exchange (2).. that can be strong enoueh to counteract the wave torque in non-isothermal disks (?)..," In the planet case, the horseshoe drag \citep{ward91} is an additional source of angular momentum exchange \citep{drag}, that can be strong enough to counteract the wave torque in non-isothermal disks \citep{paard10}." + lu the vortex case. we oulv have the wave torque.," In the vortex case, we only have the wave torque." + Tt cau be shown that the deusity waves described above ransport angular momentum outward (7)., It can be shown that the density waves described above transport angular momentum outward \citep{papalin95}. + Therefore. if the waves emütted by a vortex are asvuuuetric then angular momentum has to be deposited or extracted iu he vortex neighborhood.," Therefore, if the waves emitted by a vortex are asymmetric then angular momentum has to be deposited or extracted in the vortex neighborhood." + This in turn cau be liuked ο vortex nügratiou since moving a vortex from one ocation to another means sole angular momentum was exchanged between these two locatious., This in turn can be linked to vortex migration since moving a vortex from one location to another means some angular momentum was exchanged between these two locations. + This avguneut shows that one can iu principle relate the vortex uleration rate to the wave emission asvuuuetry. without showing precisely how the waves interact with the vortex structure.," This argument shows that one can in principle relate the vortex migration rate to the wave emission asymmetry, without knowing precisely how the waves interact with the vortex structure." + To quantity this effect more precisely. let us start considering the angular monientuni couscrvation equation: where F is the outward augular moment flux -F=rierOr)|ws)=Af(22r) (see equation (1))} and denotes a 4 average.," To quantify this effect more precisely, let us start considering the angular momentum conservation equation: where $\mathcal{F}$ is the outward angular momentum flux $\mathcal{F}=r\Sigma u_r (r\Omega(r)+u_\varphi)= A/(2\pi r)$ (see equation \ref{Waction}) )) and $\langle \cdot \rangle$ denotes a $\varphi$ average." + Let us assmue a vortex of size 25 is located at r=ry and endüts deusity waves asviunetricall., Let us assume a vortex of size $2s$ is located at $r=r_0$ and emits density waves asymmetrically. + Iuteeratiug the above equation between the inner and outer radius tells us the vortex is aneular momentum if (ry|s)>Floryos). Lo.df the outer wave is stronger than the imuner wave. as in the constant vorteusitv disk described above.," Integrating the above equation between the inner and outer radius tells us the vortex is angular momentum if $\mathcal{F}(r_0+s)>\mathcal{F}(r_0-s)$, i.e. if the outer wave is stronger than the inner wave, as in the constant vortensity disk described above." + Next. to relate this effect to vortex nüeration. one has to compute the aueular momentum of a vortex.," Next, to relate this effect to vortex migration, one has to compute the angular momentum of a vortex." + The aneular momentum excess(compared to an unperturbed disk) due to a single vortex is elven by: where “Ny ds the unperturbed density and the inteeration is computed between the immer and outer radius of the vortex., The angular momentum excess(compared to an unperturbed disk) due to a single vortex is given by: where $\Sigma_0$ is the unperturbed density and the integration is computed between the inner and outer radius of the vortex. + We denote the angular size of the vortex as Ay. which we expect to be ~Myfry.," We denote the angular size of the vortex as $\Delta \varphi$, which we expect to be $\sim H_0/r_0$." + It can be seen that the augular momenta of a vortex 1s made of two parts: a contribution due to the density fuctuation associated to the vortex. and a contribution due to the vortex rotation profile «&..," It can be seen that the angular momentum of a vortex is made of two parts: a contribution due to the density fluctuation associated to the vortex, and a contribution due to the vortex rotation profile $u_\varphi$." + Assuming the vortex rotation rate is w. the velocity can be approxinated bv c(roρω for rooscororg|os.," Assuming the vortex rotation rate is $\omega$, the velocity can be approximated by $u_\varphi\simeq (r-r_0)\omega$ for $r_0-sae2pPunaEHCeu/ero)inal-," In this situation, a core would be able to collapse promptly, without an extended period of ambipolar diffusion, since $t_\mathrm{AD}/t_\mathrm{ff}\left(\rho_t\right) \gtrsim \left(v_0/v_{\mathrm{A},0}\right)^{1/2}\Gamma_\mathrm{final} > \Gamma_\mathrm{final}$." + Lu GMCs. t1ο jonization fraction is dependent οι cleuuical processes. with \jg1—20 (Meleeetal. 2010)..," In GMCs, the ionization fraction is dependent on chemical processes, with $\chi_{i0}\sim 1-20$ \citep{2010ApJ...720.1612M}. ." + The turbulent [low speed will not exceed ~-10 km/sH under realisticH conditions.me and my4107>—10%Mi 7.utypically.," The turbulent flow speed will not exceed $\sim 10$ km/s under realistic conditions, and $n_0 \sim 10^2-10^3$ $^{-3}$,." + Thereore. Paina Wwill exceed. 1 (see Equation (67))) ouly if the upstream maguetic field in the direcjon parallel to the shock front is moderate. probably <10pG.," Therefore, $\Gamma_\mathrm{final}$ will exceed $1$ (see Equation \ref{GADmodel}) )) only if the upstream magnetic field in the direction parallel to the shock front is moderate, probably $\lesssim 10~\mu\mathrm{G}$." + The line-of-sight magnetic [ield Srenetlis iu 1iolecular clouds with deusity <10%Gm7. however. cau vary over ~5—25pC (Cru(her1999:Crutcheretal. 2010).. ," The line-of-sight magnetic field strengths in molecular clouds with density $\lesssim 10^3~\mathrm{cm}^{-3}$, however, can vary over $\sim 5 - 25~\mu\mathrm{G}$ \citep{1999ApJ...520..706C, 2010ApJ...725..466C}. ." +IL the total magnetic field streneth (which is always >Bros) exceecs c20g. hen in order to reach Έμμα close to 1 so that pre-collapse cores can develop efficleiuly. couvergiug flows with vp aligued <3“40 ιο Bajoug ave favored.," If the total magnetic field strength (which is always $\geq B_\mathrm{LOS}$ ) exceeds $\sim 20\mu\mathrm{G}$, then in order to reach $\Gamma_\mathrm{final}$ close to $1$ so that pre-collapse cores can develop efficiently, converging flows with $\mathbf{v}_0$ aligned $\lesssim 30^\circ$ to $\mathbf{B}_\mathrm{cloud}$ are favored." +" h addition. we note that for op,«uud awd ca,eua the 3D turbulent velocity dispersion and lueali-ield. Alfvén speed in a cloud. a gravitatioually-bouud (or virialized) cloud has so that The strougest shocks will have ei~σα. εἰ."," In addition, we note that for $\sigma_\mathrm{3D,~cloud}$ and $v_{\mathrm{A},~\mathrm{cloud}}$ the 3D turbulent velocity dispersion and mean-field Alfvénn speed in a cloud, a gravitationally-bound (or virialized) cloud has so that The strongest shocks will have $v_0\sim\sigma_\mathrm{3D,~cloud}$ ." +" Lhese regions will be able to reach Vein,~ Lil the cloud is sufficiently supercritical (ο2 1). the ionization fraction is sufficiently low (x;0o 1). and/or the magnetic field parallel to the shock [ront isweaker than the mean field threacing the cloud CBua/Bo>1)."," These regions will be able to reach $\Gamma_\mathrm{final} \sim 1$ if the cloud is sufficiently supercritical $\Gamma_\mathrm{cloud} \gg 1$ ), the ionization fraction is sufficiently low $\chi_{i0} \sim 1$ ), and/or the magnetic field parallel to the shock front isweaker than the mean field threading the cloud $B_\mathrm{cloud} / B_0 > 1$)." + Again. with realistic yyy aud Paga: themost favorable cireuimistaice for," Again, with realistic $\chi_{i0}$ and $\Gamma_\mathrm{cloud}$ , themost favorable circumstance for" +"1998), and 0.099735 Debye for the fundamental ro-vibrational transition (Pineetal. 1985).","1998), and 0.099735 Debye for the fundamental ro-vibrational transition \cite{pin85} 1985)." +" For HCl, we used 1.109 and 1.139 Debye for the v=0 and v=1 states, respectively (DeLeeuw&Dymanus 1971; Kaiser 1970), while for the v=1-0 vibrational band we adopted 0.072961 Debye for H??CI and 0.073049 Debye for H*’Cl (Pineetal. 1985)."," For HCl, we used 1.109 and 1.139 Debye for the $v=0$ and $v=1$ states, respectively \cite{del71} 1971; \cite{kai70} 1970), while for the $v=1-0$ vibrational band we adopted 0.072961 Debye for $^{35}$ Cl and 0.073049 Debye for $^{37}$ Cl \cite{pin85} 1985)." +" State-to-state rate constants for rotational de-excitation of HF through inelastic collisions with para and ortho H» were taken from Guillonetal. (2011), whose calculations cover the first seven rotational levels of HF and extend up to a temperature of 200 K. An ortho-to-para ratio of 3 was adopted for H2."," State-to-state rate constants for rotational de-excitation of HF through inelastic collisions with para and ortho $_2$ were taken from \cite{gui11} (2011), whose calculations cover the first seven rotational levels of HF and extend up to a temperature of 200 K. An ortho-to-para ratio of 3 was adopted for $_2$." +" For HF- collisions, we adopted the values calculated by Reeseetal. (2005), covering the first ten levels of HF up to 300 K. The use of collision rate constants with H5, which are larger than with He by up to one order of magnitude, is critical for the excitation analysis of HF."," For HF-He collisions, we adopted the values calculated by \cite{ree05} (2005), covering the first ten levels of HF up to 300 K. The use of collision rate constants with $_2$, which are larger than with He by up to one order of magnitude, is critical for the excitation analysis of HF." +" We did not extrapolate the rate constants in temperature, based on the small variation in the collision cross sections for temperatures above 200-300 K (see Guillonetal. 2008, 2011)."," We did not extrapolate the rate constants in temperature, based on the small variation in the collision cross sections for temperatures above 200-300 K (see \cite{gui08} 2008, 2011)." +" As rate constants for collisions of HCl and H5, we adopted the values calculated by Neufeld&Green (1994) up to 300 K with He as collider, scaled up by a factor of 1.35 and without extrapolating in temperature."," As rate constants for collisions of HCl and $_2$, we adopted the values calculated by \cite{neu94} (1994) up to 300 K with He as collider, scaled up by a factor of 1.35 and without extrapolating in temperature." +" Collision rates of HCl with H» may differ from those with He, although it is difficult to quantify these differences."," Collision rates of HCl with $_2$ may differ from those with He, although it is difficult to quantify these differences." + The computed line profiles are plotted in Fig., The computed line profiles are plotted in Fig. + | for HF and in Fig.," \ref{fig-hf-line} + for HF and in Fig." + 2. for H?CI and H?'CI., \ref{fig-hcl-lines} for $^{35}$ Cl and $^{37}$ Cl. +" The agreement between observed and calculated line profiles is very good, except for the J=2—1 transition of H?CI and of H?""CI, which are predicted to be somewhat stronger than observed."," The agreement between observed and calculated line profiles is very good, except for the $J=2-1$ transition of $^{35}$ Cl and of $^{37}$ Cl, which are predicted to be somewhat stronger than observed." + The modest signal-to-noise ratio of these lines and the lack of collision rateconstants for HCl and H» could explain the discrepancies., The modest signal-to-noise ratio of these lines and the lack of collision rateconstants for HCl and $_2$ could explain the discrepancies. +" We derive an abundance relative to H» in the inner regions of the envelope of 8 x 107? for HF and 8 x 107? for H??CI, with a H?CI/H?CI abundance ratio of 3.3 + 0.3, consistent with that derived from previous observations of NaCl, KCl, and AICI in IRC 410216 (Cernicharoetal. 1987; Cernicharo 2000)."," We derive an abundance relative to $_2$ in the inner regions of the envelope of 8 $\times$ $^{-9}$ for HF and 8 $\times$ $^{-8}$ for $^{35}$ Cl, with a $^{35}$ $^{37}$ Cl abundance ratio of 3.3 $\pm$ 0.3, consistent with that derived from previous observations of NaCl, KCl, and AlCl in IRC +10216 \cite{cer87} + 1987; \cite{cer00} 2000)." + The abundances of HF and HCI (H**Cl + ΗΤΟΙ) are plotted in Fig., The abundances of HF and HCl $^{35}$ Cl + $^{37}$ Cl) are plotted in Fig. +" 3 as a function of radius, for a model in which the initial abundances is set by the observations, but its radial dependence is a model prediction."," \ref{fig-chemistry} as a function of radius, for a model in which the initial abundances is set by the observations, but its radial dependence is a model prediction." +" Both HF and HCl are predicted to show a decrease in abundance in the outer layers, owing to photodissociation by interstellar ultraviolet photons."," Both HF and HCl are predicted to show a decrease in abundance in the outer layers, owing to photodissociation by interstellar ultraviolet photons." +" However, most of the contribution to the observed line intensities (80 %)) comes from circumstellar regions inside ~2 x 1015 cm for HF, and 2-4 x 1015 cm for HCl, such that only the abundances in regions within these radii are properly sampled by the observed lines (see light shaded region in Fig. 3))."," However, most of the contribution to the observed line intensities $\sim$ 80 ) comes from circumstellar regions inside $\sim$ 2 $\times$ $^{15}$ cm for HF, and 2–4 $\times$ $^{15}$ cm for HCl, such that only the abundances in regions within these radii are properly sampled by the observed lines (see light shaded region in Fig. \ref{fig-chemistry}) )." +" The excitation of the levels involved in the observed HF and HCl lines is dominated by inelastic collisions with Ho, with the lines being subthermally excited beyond ~2 x 10!4 cm where the gas density is below 10? cm."," The excitation of the levels involved in the observed HF and HCl lines is dominated by inelastic collisions with $_2$, with the lines being subthermally excited beyond $\sim$ 2 $\times$ $^{14}$ cm where the gas density is below $^9$ $^{-3}$." +" Infrared pumping via the v=| vibrational state plays a non-negligible but minor role, enhancing the line intensities by 5 (HF) and 15 (HCI) with respect to the case where infrared pumping is neglected."," Infrared pumping via the $v=1$ vibrational state plays a non-negligible but minor role, enhancing the line intensities by 5 (HF) and 15 (HCl) with respect to the case where infrared pumping is neglected." +" Rotational lines within the v—1 state are predicted to be too weak to be detectable with HIFI, with predicted antenna temperatures of only ~0.025 K for the vy=1 J=3-2 transition of H?CI and less than 0.005 K for all other such transitions."," Rotational lines within the $v=1$ state are predicted to be too weak to be detectable with HIFI, with predicted antenna temperatures of only $\sim$ 0.025 K for the $v=1$ $J=3-2$ transition of $^{35}$ Cl and less than 0.005 K for all other such transitions." + The abundances derived here are estimated to be uncertain by a factor of two for both HF and HCl., The abundances derived here are estimated to be uncertain by a factor of two for both HF and HCl. +" The error of the observations being 10-20%,, 2-15 due to the noise in the spectra (see Table 1)) and 10 due to the calibration of HIFI, most of the uncertainty comes from the model."," The error of the observations being 10-20, 2-15 due to the noise in the spectra (see Table \ref{table-lineparameters}) ) and 10 due to the calibration of HIFI, most of the uncertainty comes from the model." +" For HCl, the error could be significantly larger if the collision rate constants with H» as collider are substantially different from those with He."," For HCl, the error could be significantly larger if the collision rate constants with $_2$ as collider are substantially different from those with He." + An increase in the collision rate constants would lower the abundance derived for HCl., An increase in the collision rate constants would lower the abundance derived for HCl. + The presence of both HF and HCl in the inner circumstellar regions of IRC +10216 is consistent with the thermochemical equilibrium (TE) calculations of the atmospheres of cool stars., The presence of both HF and HCl in the inner circumstellar regions of IRC +10216 is consistent with the thermochemical equilibrium (TE) calculations of the atmospheres of cool stars. +" In Fig. 3,,"," In Fig. \ref{fig-chemistry}," +" we compare the abundances derived for HF and HCl with those computed under the assumption of TE, adopting solar elemental abundances (Asplundetal. 2009)."," we compare the abundances derived for HF and HCl with those computed under the assumption of TE, adopting solar elemental abundances \cite{asp09} 2009)." +" The assumption of TE is only valid from the stellar photosphere out to a radius of ~3 R, (dark shaded region in Fig. 3)),"," The assumption of TE is only valid from the stellar photosphere out to a radius of $\sim$ 3 $_*$ (dark shaded region in Fig. \ref{fig-chemistry}) )," + beyond which the decrease in density and temperature causes the chemical reaction rates to drop rapidly and the molecular abundances to freeze out to the values of the TE region (Agündez&Cernicharo 2006)., beyond which the decrease in density and temperature causes the chemical reaction rates to drop rapidly and the molecular abundances to freeze out to the values of the TE region \cite{agu06} 2006). + Hydrogen fluoride and AIF (whose abundance relative to Ho is 7.5x 10-°; Agtindez 2009) are observed to be the main fluorine-bearing species in the inner envelope of IRC 10216., Hydrogen fluoride and AlF (whose abundance relative to $_2$ is $7.5 \times 10^{-9}$ ; \cite{agu09} 2009) are observed to be the main fluorine-bearing species in the inner envelope of IRC +10216. +" Thermochemical equilibrium calculations predict that HF is the major reservoir of fluorine in the TE region around both oxygen- and carbon-rich AGB stars, with the abundance of HF being essentially equal to the elemental abundance of"," Thermochemical equilibrium calculations predict that HF is the major reservoir of fluorine in the TE region around both oxygen- and carbon-rich AGB stars, with the abundance of HF being essentially equal to the elemental abundance of" +As the position was originally only known to c7 aremin. we used the l6aremün? imaging array on the Advanced CCD Imaging Spectrometer CACTS-IE: 2003)).,"As the position was originally only known to $\pm7\,$ arcmin, we used the $16\,$ $^2$ imaging array on the Advanced CCD Imaging Spectrometer (ACIS-I; )." + The data were reduced in a standard. way using the software package (version 4.1) and the 4.1 calibration files. restricting the energy range to kkeV. With the timing position of aavailable from. 573334002005. 43°1656S+οτα09. we were able to localise the source to the ACIS-L1 detector.," The data were reduced in a standard way using the software package (version 4.1) and the 4.1 calibration files, restricting the energy range to keV. With the timing position of available from 05, $-43\degr16\arcmin56\farcs8\pm0\farcs7$, we were able to localise the source to the ACIS-I1 detector." + The position is near a gap between CCDs of the ACIS-I detector. but is not in the gap: examination of the exposure map (which takes into account effective. areca maps olf each detector as well as the dither pattern of oon the skv) shows an clleetive area at. the position of ccomparable to the average of the ACIS-LL CCD.," The position is near a gap between CCDs of the ACIS-I detector, but is not in the gap: examination of the exposure map (which takes into account effective area maps of each detector as well as the dither pattern of on the sky) shows an effective area at the position of comparable to the average of the ACIS-I1 CCD." + However. we see no source at the position of4316.. and searches using did not find any —source closer than 1.5arcmin.," However, we see no source at the position of, and searches using did not find any source closer than $1.5\,$ arcmin." + We must &o out to a radius of -T aarcsec before there are any counts. and those counts appear consistent with the background. rate (0.0300.+0010countsarcsee 7).," We must go out to a radius of $>1$ arcsec before there are any counts, and those counts appear consistent with the background rate $0.0300\pm0.0010\,{\rm counts\,arcsec}^{-2}$ )." + We compare this with the raclio »osition uncertainty (2 O.Garesec). the aaspect uncertainty (0.Garesec at 90 per cent confidence. as his source is on-axis: there is no svsteniatic aspect offset isted for this observation). and the »point-spread. function (90 per cent encircled energy. radius of z laarcesec at l.5kkeV).," We compare this with the radio position uncertainty $\approx +0.6\,$ arcsec), the aspect uncertainty $0.6\,$ arcsec at 90 per cent confidence, as this source is on-axis; there is no systematic aspect offset listed for this observation), and the point-spread function (90 per cent encircled energy radius of $\approx 1$ arcsec at keV)." + Using a generous extraction radius of 2arcsec there are 2 counts with 0.4 expected from he background (see Figure 1)).," Using a generous extraction radius of $2\,$ arcsec there are 2 counts with 0.4 expected from the background (see Figure \ref{fig:image}) )." + Given Poisson fluctuations1986)... we can place a 30 upper limit of zz10 counts coming from 4316.. or à count-rate limit of =leountsks+.," Given Poisson fluctuations, we can place a $\sigma$ upper limit of $\approx +10$ counts coming from, or a count-rate limit of $\approx +1\,{\rm counts\,ks}^{-1}$." + Note that for aabout 10 per cent of the X-ray Εν is in an extended nebula &oing out to at least 132rcsec2009).. but. the contribution is small enough that our limits are not allected by the size of our extraction region.," Note that for about 10 per cent of the X-ray flux is in an extended nebula going out to at least $13\,$ arcsec, but the contribution is small enough that our limits are not affected by the size of our extraction region." + The Geld of (P=4477s. B=3. lot Gr= O4Myr and B=7107eres +) has been imaged by various X-ray instruments during observations targeting the probably unrelated: (see Section 3)) X-ray pulsar PSIUJISA46 0258 and its supernova remnant Wes 75 and references therein)," The field of $P=4.477\,$ s, $B=\expnt{3}{13}\,$ G, $\tau=0.4\,$ Myr, and $\dot E=\expnt{7}{31}\,\ergsec$ ) has been imaged by various X-ray instruments during observations targeting the probably unrelated (see Section \ref{sec:disc}) ) X-ray pulsar PSR $-$ 0258 and its supernova remnant Kes 75 and references therein)." +In this subsection we present a complete listing of the SC-SEC. and NEC* samples in a single table for ease of reference.,"In this subsection we present a complete listing of the 8C-NEC, and NEC* samples in a single table for ease of reference." + Object. classifications into low-excitation narrow-ine radio galaxy (LEG). high-excitation. narrow-line racio galaxy (σα). weak quasar (WO) and quasar (Q) follow a combination of Jackson Rawlings (1997) and Willott ct ((1998) criteria.," Object classifications into low-excitation narrow-line radio galaxy (LEG), high-excitation narrow-line radio galaxy (HEG), weak quasar (WQ) and quasar (Q) follow a combination of Jackson Rawlings (1997) and Willott et (1998) criteria." + For galaxies with O1]500.7 in the optical wid (2«0.7 for most spectra) we have split the racio ealaxies into LEG and LEC classes., For galaxies with ]500.7 in the optical band $z<0.7$ for most spectra) we have split the radio galaxies into LEG and HEG classes. + LECGs are defined to ave Olu]500.7 EW -23$, whereas Qs have at least one broad line and $M_{\rm B}<-23$ in unresolved flux." + To caleulate Adj we have assumed a power-law quasar spectrum with an optical spectral index. of 0.5 for consistency with Willott et (109085)., To calculate $M_{\rm B}$ we have assumed a power-law quasar spectrum with an optical spectral index of 0.5 for consistency with Willott et (1998). + A partial correlation analysis on the FRIL or probable ETUL sources from both the | LIL and the NEC* | 30% samples confirmed the same main dependences as those ound for the7€-1.11. 6€ and 3€ (LItL) samples. studied w Bluncdell et ((1999). namely that rest-frame spectral index at 1 Gllz correlates best with radio luminosity. aud hat source size correlates best with redshift. (also shown in Paper HD).," A partial correlation analysis on the FRII or probable FRII sources from both the + LRL and the NEC* + 3C* samples confirmed the same main dependences as those found for the, 6C and 3C (LRL) samples studied by Blundell et (1999), namely that rest-frame spectral index at 1 GHz correlates best with radio luminosity, and that source size correlates best with redshift (also shown in Paper II)." + Our trends are consistent with those seen by Blundell et al.," Our trends are consistent with those seen by Blundell et al.," + although as our 3€ sample is identical the results are not completely. independent., although as our 3C sample is identical the results are not completely independent. + One cüllerence between the LL samples and he NEC* | ος* samples is the lack of a strong spectral index size correlation in the latter SS)., One difference between the + LRL samples and the NEC* + 3C* samples is the lack of a strong spectral index – size correlation in the latter 8). + This seenis o be being driven mostly by the fattening of the spectra of he CSS sources., This seems to be being driven mostly by the flattening of the spectra of the CSS sources. + We show in 99 the redshift-size relation for FRILL sources from the |LRL and. NEC*|3€* samples in two cosmologies., We show in 9 the redshift-size relation for FRII sources from the +LRL and NEC*+3C* samples in two cosmologies. + As is conventional we have parameterised the redshift dependence of source size in terms of the inverse scale factor (1|2) as Dx(1]|:)3 and in Table 9 we eive the best-fitting exponents 5 for all redshifts and. in the case of the NEC* | 3C%* sample. for the grade a redshifts only.," As is conventional we have parameterised the redshift dependence of source size in terms of the inverse scale factor $(1+z)$ as $D\propto (1+z)^{-\eta}$, and in Table 9 we give the best-fitting exponents $\eta$ for all redshifts and, in the case of the NEC* + 3C* sample, for the grade $\alpha$ redshifts only." + We have also tried adding the three objects without spectroscopic redshifts in. with all redshifts set toeither 1.2 or 1.8. and find there is a small. but not significant reduction in g of « 0.1.," We have also tried adding the three objects without spectroscopic redshifts in, with all redshifts set toeither 1.2 or 1.8, and find there is a small, but not significant reduction in $\eta$ of $<0.1$ ." + The new selection criteria are. effective, The new selection criteria are effective + accuracy., accuracy. + Nevertheless. there retains an important goal bevoud such a statistical assessment of the Cosmic Microwave Backeround (CAIB) sla. namely to build an accurate nuage of the last-scattering surface which captures the detailed nature and morphology of our universe. aud iof simply some best-fit eusenible averaged view of it.," Nevertheless, there remains an important goal beyond such a statistical assessment of the Cosmic Microwave Background (CMB) sky, namely to build an accurate image of the last-scattering surface which captures the detailed nature and morphology of our universe, and not simply some best-fit ensemble averaged view of it." + hupediuneuts to this program include instrmucutal roise and svsteniatie artifacts. aud foreground enissiou youn local astrophysical objects.," Impediments to this program include instrumental noise and systematic artifacts, and foreground emission from local astrophysical objects." + On a fundamental level ron-cosiological foregrounds cau easily compronise aly conclusion regarding primordial physics unless properly accounted for. while ou a practical level they complicate voth algorithms and analyses.," On a fundamental level non-cosmological foregrounds can easily compromise any conclusion regarding primordial physics unless properly accounted for, while on a practical level they complicate both algorithms and analyses." + Alethods for cither removing. suppressing or at the very least coustraining," Methods for either removing, suppressing or at the very least constraining" +function of the Ha luminosity surface density in Figure 3.,function of the $\alpha$ luminosity surface density in Figure 3. +" Star formation rates can be estimated using SFR[Mo yyr7!]=7.9x 10-4? LL(Ha) ss] (Kennicutt 1998, see top x-axis in Fig."," Star formation rates can be estimated using $_\odot$ $^{-1}$ $\times$ $^{-42}$ $\alpha$ $^{-1}$ ] (Kennicutt 1998, see top x-axis in Fig." +" 3; choosing[erg a Kroupa IMF would decrease the SFRs by ~30%)) and the brightest region outside of 33077 (aperture #110) accounts for ~50% of the total SFR in the tidal complex (1.3x107? MMo ΥΥΙ1, or a SFR surface density for this aperture of 4x10 ΑΜΜΟ yyr! kkpc?)."," 3; choosing a Kroupa IMF would decrease the SFRs by $\sim$ ) and the brightest region outside of 3077 (aperture 10) accounts for $\sim$ of the total SFR in the tidal complex $\times$ $^{-3}$ $_\odot$ $^{-1}$, or a SFR surface density for this aperture of $\times$ $^{-4}$ $_\odot$ $^{-1}$ $^{-2}$ )." +" For reference, single massive stars create rregions with Ha luminosities of Lna,o7RI5x 10°%eergss~t and £5x 10?""eergss! (e.g., Devereux et 11997),Lyaos i.e. the total Ho flux in the tidal feature can in principle be created by a few massive stars."," For reference, single massive stars create regions with $\alpha$ luminosities of $_{\rm H\alpha, O7}\approx 5\times10^{36}$ $^{-1}$ and $_{\rm H\alpha, O5}\approx 5\times10^{37}$ $^{-1}$ (e.g., Devereux et 1997), i.e. the total $\alpha$ flux in the tidal feature can in principle be created by a few massive stars." + Figure 3 shows that the dust temperature does not change as a function of the star formation rate surface density over two orders of magnitude of the latter., Figure 3 shows that the dust temperature does not change as a function of the star formation rate surface density over two orders of magnitude of the latter. + This suggests that the currently observed star formation does not provide the main heating source for the dust on kpc scales and we speculate that other mechanisms may be responsible for the dust heating., This suggests that the currently observed star formation does not provide the main heating source for the dust on kpc scales and we speculate that other mechanisms may be responsible for the dust heating. +" Assuming Go ~4x107° for the intergalactic radiation field et 22002, note that Go=1 for the Galactic (Sternberginterstellar radiation field), that the temperature of dust goes as T~Gi!(48) and B—2, and scaling from the results by Li Draine (2001) for the Galactic interstellar radiation field KK for a silicate grain, 20KK for a graphite grain, Fig(16 3 in Li Draine 2001), we estimate that the dust in the tidal feature should have a temperature of KK in the intergalactic field."," Assuming $G_0\sim$ $\times$ $^{-3}$ for the intergalactic radiation field (Sternberg et 2002, note that $G_0$ =1 for the Galactic interstellar radiation field), that the temperature of dust goes as $T\sim G_0^{1/(4+\beta)}$ and $\beta$ =2, and scaling from the results by Li Draine (2001) for the Galactic interstellar radiation field K for a silicate grain, K for a graphite grain, Fig 3 in Li Draine 2001), we estimate that the dust in the tidal feature should have a temperature of K in the intergalactic field." +" This suggests that other heating sources (the radiation field of NGC 3077, an older stellar population in the feature as seen in the HST imaging by Weisz et 22008 must be partly responsible for heating the and/ordust to shocks)our derived temperature of 1242 K. The 250um/500um ratio does not change as a function of projected distance to 33077 within our uncertainties but we note that the measurements only span a small range in distances."," This suggests that other heating sources (the radiation field of NGC 3077, an older stellar population in the feature as seen in the HST imaging by Weisz et 2008 and/or shocks) must be partly responsible for heating the dust to our derived temperature of $\pm$ 2 K. The $\mu$ $\mu$ m ratio does not change as a function of projected distance to 3077 within our uncertainties but we note that the measurements only span a small range in distances." + From the SED fits discussed above we derive dust mass surface densities for each of our apertures , From the SED fits discussed above we derive dust mass surface densities for each of our apertures (Tab. +"1) with an average value of 7.4x10-? MM ppc? (Tab.(8=2, T=12.6KK)."," 1) with an average value of $\times$ $^{-2}$ $_\odot$ $^{-2}$ $\beta$ =2, K)." +" We derive a total dust mass in the tidal feature (excluding 33077 and upper limits) of —1.830.9x100 MM; (the large error bar includes uncertainties in dust properties, see below)."," We derive a total dust mass in the tidal feature (excluding 3077 and upper limits) of $\sim$ $\pm$ $\times$ $^6$ $_\odot$ (the large error bar includes uncertainties in dust properties, see below)." +" Our simple dust mass estimate is consistent with results from more detailed modeling using updated Draine Li (2007) models (Aniano et al,"," Our simple dust mass estimate is consistent with results from more detailed modeling using updated Draine Li (2007) models (Aniano et al.," + in prep.)., in prep.). +" The dust mass of 33077 is only 1.9x10? MM (8—2, KK), in reasonable agreement with the mass estimates by Price Gullixson (1989) of the absorbing central dust clouds based on NIR observations (they report a mass of 10? MM)."," The dust mass of 3077 is only $\times$ $^5$ $_\odot$ $\beta$ =2, K), in reasonable agreement with the mass estimates by Price Gullixson (1989) of the absorbing central dust clouds based on NIR observations (they report a mass of $\sim$ $^5$ $_\odot$ )." + Both mass estimates depend on the choice of 8 and the temperature., Both mass estimates depend on the choice of $\beta$ and the temperature. +" For example, if we chose 8—1.5 for the tidal feature, the dust mass would go down by a factor of ~2 (as the temperature would increase by ~3 KK, Sec."," For example, if we chose $\beta$ =1.5 for the tidal feature, the dust mass would go down by a factor of $\sim$ 2 (as the temperature would increase by $\sim$ K, Sec." + , 3.4). +"Likewise, lowering the dust temperature in 33077 3.4).by 5KK would increase its dust mass by a factor of ~2."," Likewise, lowering the dust temperature in 3077 by K would increase its dust mass by a factor of $\sim$ 2." + Given these large systematic uncertainties involved we assign a conservative error of to the dust mass of the tidal feature., Given these large systematic uncertainties involved we assign a conservative error of to the dust mass of the tidal feature. +" For the average ssurface mass densities of the apertures where dust emission was significantly detected, we derive an average value of 11.3MMg ppc? (Tab."," For the average surface mass densities of the apertures where dust emission was significantly detected, we derive an average value of $_\odot$ $^{-2}$ (Tab." +" 1), ie. more than two orders of magnitude larger than the dust surface densitites."," 1), i.e. more than two orders of magnitude larger than the dust surface densitites." +" The average ggas ratio is 6.5--3x10-?, and thet ratio does not vary within the errors between apertures and is not a function of"," The average gas ratio is $\pm$ $\times$ $^{-3}$, and the ratio does not vary within the errors between apertures and is not a function of" +explicitly triggered (?)..,explicitly triggered \citep{iwakami08}. + Very recently. ? have reported three-dimensional. parametric core-collapse simulations using Riemann solvers and covering the whole sphere.," Very recently, \citet{nordhaus10a} have reported three-dimensional, parametric core-collapse simulations using Riemann solvers and covering the whole sphere." + Their results are in line with previous studies in that they do not witness the development of large scale shock oscillations in the stalled phase. or spiral modes with. noticeable amplitudes.," Their results are in line with previous studies in that they do not witness the development of large scale shock oscillations in the stalled phase, or spiral modes with noticeable amplitudes." + Similarly. ? have presented full-sphere parametric explosions with a Riemann hydrodynamic solver. including the contraction of the protoneutron star and grey neutrino transport.," Similarly, \citet{wongwathanarat2010} + have presented full-sphere parametric explosions with a Riemann hydrodynamic solver, including the contraction of the protoneutron star and grey neutrino transport." + Their conclusions are similar to that of ? in that no coherent spiral modes are observed. with angular momenta saturating at a few times 107° & em? ο.," Their conclusions are similar to that of \citet{nordhaus10a} in that no coherent spiral modes are observed, with angular momenta saturating at a few times $10^{46}$ g $^2$ $^{-1}$." + ? observe specific angular momenta <10 em? s imparted stochastically to the protoneutron star by anisotropic accretion., \citet{fryer07} observe specific angular momenta $\lesssim 10^{13}$ $^2$ $^{-1}$ imparted stochastically to the protoneutron star by anisotropic accretion. +" These values. and those of are in agreement with the angular momentum fluctuations we observe in our fully saturated SASL which on average have a magnitude 10""?fanp/0.DMo300/150km?Mq em? st."," These values, and those of \citet{wongwathanarat2010}, are in agreement with the angular momentum fluctuations we observe in our fully saturated SASI, which on average have a magnitude $\sim 5\times 10^{12} (f_{\rm amp}/0.1)\dot{M}_{0.3}(\rs0/150~{\rm km})^2 M^{-1}_{1.3}$ $^2$ $^{-1}$." + | am grateful to Aristotle Socrates for discussions on angular momentum from linear modes. and to Thomas Janka for pointing out the cutout at the polar boundary as à fix to the numerical instability.," I am grateful to Aristotle Socrates for discussions on angular momentum from linear modes, and to Thomas Janka for pointing out the cutout at the polar boundary as a fix to the numerical instability." + I also thank Adam Burrows and Chris Thompson for constructive comments on the early manuscript., I also thank Adam Burrows and Chris Thompson for constructive comments on the early manuscript. + For useful discussions. I thank Tobias Heinemann. Shane Davis. Douglas Rudd. Jason Nordhaus. Manou Rantsiou. Brian Metzger. and Tim Brandt.," For useful discussions, I thank Tobias Heinemann, Shane Davis, Douglas Rudd, Jason Nordhaus, Manou Rantsiou, Brian Metzger, and Tim Brandt." + The anonymous referee made constructive comments. that have resulted in a significantly improved manuscript., The anonymous referee made constructive comments that have resulted in a significantly improved manuscript. + The author is supported by NASA through Einstein Postdoctoral Fellowship grant number PF-00062. awarded by the Chandra X-ray Center. which is operated by the Smithsonian Astrophysical Observatory for NASA under contract NAS8-03060.," The author is supported by NASA through Einstein Postdoctoral Fellowship grant number PF-00062, awarded by the Chandra X-ray Center, which is operated by the Smithsonian Astrophysical Observatory for NASA under contract NAS8-03060." + This research was supported in part by the National Science Foundation through TeraGrid resources (?).. provided by NCSA.," This research was supported in part by the National Science Foundation through TeraGrid resources \citep{catlett07}, provided by NCSA." + Computations were performed at the NCSA Abe and [AS Aurora clusters., Computations were performed at the NCSA Abe and IAS Aurora clusters. + I also thank CITA for access to their computational resources., I also thank CITA for access to their computational resources. + The steady accretion flow below the shock ts obtained by solving the time-independent Euler equations. using an ideal gas equation of state of adiabatic index 7 and the gravity of a point mass M. The boundary conditions at 72ry are given by the Rankine-Hugoniot jump conditions (e.g.. ?)).," The steady accretion flow below the shock is obtained by solving the time-independent Euler equations, using an ideal gas equation of state of adiabatic index $\gamma$ and the gravity of a point mass $M$, The boundary conditions at $r = \rs0$ are given by the Rankine-Hugoniot jump conditions (e.g., \citealt{landau}) )." +" The upstream flow is adiabatic and has Mach number .M, at ¢=ro.", The upstream flow is adiabatic and has Mach number $\mathcal{M}_1$ at $r=\rs0$. + For a given ratio rPoo. the normalization of the cooling function ts obtained by imposing Vr.)=OL," For a given ratio $r_*/\rs0$, the normalization of the cooling function is obtained by imposing $v_r(r_*) = 0$." + ? introduce Eulerian perturbations of the form shown in equation (1))., \citet{F07} introduce Eulerian perturbations of the form shown in equation \ref{eq:perturbation_form}) ). + To obtain à compact formulation of the system. the following perturbation variables are employed corresponding to the perturbed mass flux. energy flux. entropy. and an entropy-vortex combination. respectively.," To obtain a compact formulation of the system, the following perturbation variables are employed corresponding to the perturbed mass flux, energy flux, entropy, and an entropy-vortex combination, respectively." + The differential system for the radial profile of linear perturbations is obtained by perturbing the time-dependent fluid equations to first order. and rewriting the resulting equations in terms of (A4))-(A7)). obtaining (?) ," The differential system for the radial profile of linear perturbations is obtained by perturbing the time-dependent fluid equations to first order, and rewriting the resulting equations in terms of \ref{eq:h_def}) \ref{eq:K_def}) ), obtaining \citep{F07} + " +where we have used (4)) and (7) respectively (note that we also recover the following results if we use (6)) instead of (7))).,where we have used \ref{eq:sphcty}) ) and \ref{eq:Bevolsph2}) ) respectively (note that we also recover the following results if we use \ref{eq:Bevolsph1}) ) instead of \ref{eq:Bevolsph2}) )). +" Using (109). ΕΕ) and ¢5)) in (91) and rearranging. we find where 0,, refers to the Kronecker delta."," Using \ref{eq:deltarho}) ), \ref{eq:deltaBrho}) ) and \ref{eq:firstlawthermo}) ) in \ref{eq:deltaL}) ) and rearranging, we find where $\delta_{ab}$ refers to the Kronecker delta." +" Putting this back into (8). integrating the velocity term by parts and simplifying (using VaMusnmVSM so we obtain The SPH equations of motion are therefore given by where the stress tensor ο is detined as This form of the magnetic force term conserves linear momentum exactly (angular momentum is discussed in refsec:spmhdangmom)) but was shown by ? to be unstable in certain regimes (low magnetic .7),"," Putting this back into \ref{eq:varprin}) ), integrating the velocity term by parts and simplifying (using $\gwab = -\nabla_b W_{ba}$ ), we obtain The SPH equations of motion are therefore given by where the stress tensor $S^{ij}$ is defined as This form of the magnetic force term conserves linear momentum exactly (angular momentum is discussed in \\ref{sec:spmhdangmom}) ) but was shown by \citet{pm85} to be unstable in certain regimes (low magnetic $\beta$ )." + We resolve this instability by adding a short range repulsive force to prevent particles from clumping ?.. the implementation of which is described in paper I. We note that the conservative form of the momentum equation was derived using a non-conservative induction equation. which agrees with the treatment of Magnetic monopoles suggested by ? and 2..," We resolve this instability by adding a short range repulsive force to prevent particles from clumping \cite{monaghan00}, the implementation of which is described in paper I. We note that the conservative form of the momentum equation was derived using a non-conservative induction equation, which agrees with the treatment of magnetic monopoles suggested by \citet{janhunen00} and \citet{dellar01}." + Consistent sets of SPMHD equations may also be derived using alternative forms of the continuity and induction equations., Consistent sets of SPMHD equations may also be derived using alternative forms of the continuity and induction equations. + We give the example below since alternative forms of the pressure terms in the momentum equation are often explored in the context of SPH. without alteration of the other equations to make the formalisms self-consistent.," We give the example below since alternative forms of the pressure terms in the momentum equation are often explored in the context of SPH, without alteration of the other equations to make the formalisms self-consistent." + We expect that a lack of consistency in the discrete equations will inevitably lead to loss of accuracy in the resulting algorithm., We expect that a lack of consistency in the discrete equations will inevitably lead to loss of accuracy in the resulting algorithm. + For example. using the continuity equation and the induction equation results in the momentum equation This form of the SPMHD equations also conserves linear momentum exactly and in the hydrodynamic case has been found to give better performance in situations where there are large jumps in density (for example at a water-air interface).," For example, using the continuity equation and the induction equation results in the momentum equation This form of the SPMHD equations also conserves linear momentum exactly and in the hydrodynamic case has been found to give better performance in situations where there are large jumps in density (for example at a water-air interface)." + The consistent form of the energy equations are given in refsec:ultenergy.., The consistent form of the energy equations are given in \\ref{sec:altenergy}. . +mas.,mas. + Assume yg=0.35. so that the maximum magnification is “l=3. and the maximal brightness ratio of the images is 2=1/2.," Assume $\umin=0.35$, so that the maximum magnification is $A=3$, and the maximal brightness ratio of the images is $R=1/2$." + An interferometer with a 100m baseline operating at 2.2 yam (AN-band) has a resolution of 4.5 mas., An interferometer with a 100m baseline operating at 2.2 $\mu$ m $K$ -band) has a resolution of 4.5 mas. + If we have three such baselines arranged in an equilateral triangle. (μον would observe (he signals in astrometry. visibility. and closure phase shown in Fig. 3..," If we have three such baselines arranged in an equilateral triangle, they would observe the signals in astrometry, visibility, and closure phase shown in Fig. \ref{example}." + The astrometric signal has a maximal amplitude of ~0.3565. which in this example is about 0.15 mas.," The astrometric signal has a maximal amplitude of $\sim0.35\thetaE$, which in this example is about 0.15 mas." + The visibilitv. which is usually minimized at closest approach (uv= day). is here |V|= 0.85.," The visibility, which is usually minimized at closest approach $u=\umin$ ), is here $|V|=0.85$ ." + The closure phase has a maximum value of oy;=1.5., The closure phase has a maximum value of $\phi_{123}=1.5^\circ$. + With present technology. precisions of ~5% in |V| and ~1 in closure phase may be achieved. so al present such events should be studied by visibility.," With present technology, precisions of $\sim 5\%$ in $|V|$ and $\sim1^\circ$ in closure phase may be achieved, so at present such events should be studied by visibility." + However. aclvauces in nmeasurenient precision and observation al shorter wavelengths can sienilicantlv enhance (he sienal-to-noise.," However, advances in measurement precision and observation at shorter wavelengths can significantly enhance the signal-to-noise." + In the next subsection. we consider a reasonable range for the expected insirumental performance aud show how this affects (he prospects for determination of 6 using interlerometers.," In the next subsection, we consider a reasonable range for the expected instrumental performance and show how this affects the prospects for determination of $\thetaE$ using interferometers." + Except for highly resolved events. the astrometric signal scales as O6. while the visibility signal scales as ~62 and the closure phase as ~0.," Except for highly resolved events, the astrometric signal scales as $\sim\thetaE$, while the visibility signal scales as $\sim\thetaE^2$ and the closure phase as $\sim\thetaE^3$." +" These steep scalings improve ihe SNIQ in the derived Einstein radius: for example à SNR of 5 in visibility translates into a SATBλ of 10 in &,. while a closure phase SNI of 5 becomes a θ SNR of 15."," These steep scalings improve the SNR in the derived Einstein radius; for example a SNR of 5 in visibility translates into a SNR of 10 in $\thetaE$ , while a closure phase SNR of 5 becomes a $\thetaE$ SNR of 15." + Figure 4. plots the ONR3B in @ from astrometry. visibility and closure phase. assuming respectively optimistic errors (left panel) of LOjam in astrometry. in |V|. and 0.001 rad in closure phase. and (right panel) pessimistic errors of LOO san astrometry. visibility amplitude. and 1° closure phase.," Figure \ref{SNR} plots the SNR in $\thetaE$ from astrometry, visibility and closure phase, assuming respectively optimistic errors (left panel) of $10\mu$ m in astrometry, in $|V|$, and 0.001 rad in closure phase, and (right panel) pessimistic errors of 100 $\mu$ m astrometry, visibility amplitude, and $1^\circ$ closure phase." + If errors of 0.001 can be achieved in J band. then events with 6;20.1 mas can be measured with SNR=10.," If errors of 0.001 can be achieved in $J$ band, then events with $\thetaE\gtrsim0.1$ mas can be measured with $\gtrsim 10$." + The next step is to determine the brightnesses and. Einstein radii for (vpical events., The next step is to determine the brightnesses and Einstein radii for typical events. + Figure 5. illustrates (he properties of bulge events., Figure \ref{events} illustrates the properties of bulge events. + The first panel shows the distribution of peak / magnitudes (or in cases where the peak was not observed. the brightest observed magnitude) for events observed by the OGLE collaboration during the 1997-1999 seasons.," The first panel shows the distribution of peak $I$ magnitudes (or in cases where the peak was not observed, the brightest observed magnitude) for events observed by the OGLE collaboration during the 1997-1999 seasons." + Assuming that sources with A.«14 can be observed interferometricallv. and assuming that 1—N1.5. we estimate that roughly of events are bright enough to be followed up with interferometers.," Assuming that sources with $K<14$ can be observed interferometrically, and assuming that $I-K=1.5$, we estimate that roughly of events are bright enough to be followed up with interferometers." + ILowever. future surveys may eo deeper (han OGLE-II. returning a smaller fraction of bright events.," However, future surveys may go deeper than OGLE-II, returning a smaller fraction of bright events." + Next. we turn to the distribution of Einstein radii.," Next, we turn to the distribution of Einstein radii." + Since this has not been measured. we must estimate theoretically what the distribution will be.," Since this has not been measured, we must estimate theoretically what the distribution will be." + The rate of microlensing events depends upon the propertiesof the lenses ancl source stars., The rate of microlensing events depends upon the propertiesof the lenses and source stars. + We assume (wo typesof stars. bulge stars and disk stus.," We assume two typesof stars, bulge stars and disk stars." + For the disk stars. we use," For the disk stars, we use" +X-rays. al least in principle. present a powerful method of studying directly (he accretion processes of star formation.,"X-rays, at least in principle, present a powerful method of studying directly the accretion processes of star formation." + In the case of classical T Tauri stars (CTTS). (he magnetospheric accretion paradigm posits that material is fannelled by magnetic fields onto the star from a (runcated disk (e.g.Uchida&Shibata1984:Dertoutοἱal.1988).. rather than through direct. surface interaction with the disk itself.," In the case of classical T Tauri stars (CTTS), the magnetospheric accretion paradigm posits that material is funnelled by magnetic fields onto the star from a truncated disk \citep[e.g.\ +][]{Uchida.Shibata:84,Bertout.etal:88}, rather than through direct surface interaction with the disk itself." + Matter impacts the stellar surface at velocities of up to a lew hundred kms |[.., Matter impacts the stellar surface at free-fall velocities of up to a few hundred km $^{-1}$. +( The accreting material is then expected to form a shock at the stellar surface., The accreting material is then expected to form a shock at the stellar surface. + The resulting shocked plasma temperature is of order a few million Ix. and it will therefore radiate predominantly in A-ravs.," The resulting shocked plasma temperature is of order a few million K, and it will therefore radiate predominantly in X-rays." + For the ranges of mass accretion rates inferred for CTTS of LO-10. MAL. t (e.g.Hartiganetal.1995:Gullbringοἱal.1993:Johns-Ixrullet 2000).. the X-ray Iniminosities resulting [rom accretion should be >107. erg 7s 1 easily sulficient to be observed in nearby associations of T Tauri stars and regions of star formation.," For the ranges of mass accretion rates inferred for CTTS of $10^{-6}$ $10^{-10}M_\odot$ $^{-1}$ \citep[e.g.\ +][]{Hartigan.etal:95,Gullbring.etal:98,Johns-Krull.etal:00}, , the X-ray luminosities resulting from accretion should be $\ga +10^{31}$ erg $^{-2}$ $^{-1}$ —easily sufficient to be observed in nearby associations of T Tauri stars and regions of star formation." + The above scenario of copious accrelion-driven N-rays from CUTS contrasts sharply with what is observed., The above scenario of copious accretion-driven X-rays from CTTS contrasts sharply with what is observed. + While strong X-ray. emission appears (to be a ubiquitous characteristic of CTTS (e.g.Feigelson&Montinerle1999).. (he source plasma (temperatures are an order of magnitude higher (han can be produced in accretion shocks and heating can instead be attributed to magnetic processes analogous (o coronal activitv in late-tvpe main sequence and more evolved stars.," While strong X-ray emission appears to be a ubiquitous characteristic of CTTS \citep[e.g.\ +][]{Feigelson.Montmerle:99}, the source plasma temperatures are an order of magnitude higher than can be produced in accretion shocks and heating can instead be attributed to magnetic processes analogous to coronal activity in late-type main sequence and more evolved stars." + Accretion activity is largely revealed by strong UV-optical continuum enission. suggesting that accretion shocks are either formed (oo deep in the stellar atinosphere to be observed (Drake2005).. or that infall velocities are insullicient to attain X-ray temperatures in (he shock.," Accretion activity is largely revealed by strong UV-optical continuum emission, suggesting that accretion shocks are either formed too deep in the stellar atmosphere to be observed \citep{Drake:05}, or that infall velocities are insufficient to attain X-ray temperatures in the shock." + Nevertheless. (wo stars now stand out as probable exceptions and examples ol objects whose high resolution X-ray. spectra appear to be produced. at least in part. by accretion: TW Ilva (Ixastneretal.2002:Stelzer&Schmitt.2004) and BP Tau etal. 2005).," Nevertheless, two stars now stand out as probable exceptions and examples of objects whose high resolution X-ray spectra appear to be produced, at least in part, by accretion: TW Hya \citep{Kastner.etal:02,Stelzer.Schmitt:04} and BP Tau \citep{Schmitt.etal:05}." +. TW Iva has a dominant plasma temperature of 3x105 IX. as expected from an accretion shock resulting from free-fall of gas trom a truncated disk.," TW Hya has a dominant plasma temperature of $3\times 10^6$ K, as expected from an accretion shock resulting from free-fall of gas from a truncated disk." +" Dased on the densitv-sensitive ]Ile-like Ne and O lines. both TW να ancl BP Tau seem to be characterised by plasma with high electron densities 7,~ 101-10 at temperatures of 3x10 IN. (IKastner 2004).. in contrast to all other single and active binary stars studied in the survevs of Testaetal.(2004) ancl Nessοἱal.(2004).. where IHe-like O lines indicate n,c10! *"," Based on the density-sensitive He-like Ne and O lines, both TW Hya and BP Tau seem to be characterised by plasma with high electron densities $n_e\sim +10^{11}$ $10^{13}$ $^{-3}$ at temperatures of $\sim 3\times 10^6$ K \citep{Kastner.etal:02,Stelzer.Schmitt:04}, in contrast to all other single and active binary stars studied in the surveys of \citet{Testa.etal:04} and \citet{Ness.etal:04}, where He-like O lines indicate $n_e\sim 10^{10}$ $^{-3}$." + The X-ray spectra of both stars exhibit extremely weak lines of Mg. Si and Fe. and instead are dominated by O and Ne.," The X-ray spectra of both stars exhibit extremely weak lines of Mg, Si and Fe, and instead are dominated by O and Ne." + While this pattern is reminiscent of that seen in verv active RS CVn-tvpe binaries (e.g.IIuenemoerderetal.2001).. Stelzer&5climitt echoed the earlier suggestion of Herczegetal.(2002) that the metal depletion is instead a sienature of (he accretion of grain-depleted gas.," While this pattern is reminiscent of that seen in very active RS CVn-type binaries \citep[e.g.\ ][]{Huenemoerder.etal:01}, \cite{Stelzer.Schmitt:04} + echoed the earlier suggestion of \citet{Herczeg.etal:02} that the metal depletion is instead a signature of the accretion of grain-depleted gas." + Η the latter is indeed (he case.," If the latter is indeed the case," +or the jets of radio-Ioud active galactic nuclei (Laing 1980).,for the jets of radio-loud active galactic nuclei (Laing 1980). + Face-on observers would see a completely tangled magnetic ield. but. edge-on observers (in the comoving frame) would see an aligned field. and therefore would detect svnchrotron »olarised. radiation.," Face-on observers would see a completely tangled magnetic field, but edge-on observers (in the comoving frame) would see an aligned field, and therefore would detect synchrotron polarised radiation." + since the fireball is moving with a igh bulk Lorentz factor. the edge-on. comoving observer corresponds to an observer in the lab located at an angle ~L/L.," Since the fireball is moving with a high bulk Lorentz factor, the edge-on comoving observer corresponds to an observer in the lab located at an angle $\sim 1/\Gamma$." + Xecording to this idea. there is a tight link between he behaviour of the total and the polarised (lux as a function obl time.," According to this idea, there is a tight link between the behaviour of the total and the polarised flux as a function of time." + The light curve of the polarised [ux has two maxima (corresponding to the presence of the two edges of the jet) with a position angle switched by 907., The light curve of the polarised flux has two maxima (corresponding to the presence of the two edges of the jet) with a position angle switched by $90^\circ$. + The maxima occur just before and after the achromatic 7jet break in the light curve of the total lux., The maxima occur just before and after the achromatic “jet” break in the light curve of the total flux. + A main assumption of this moclel is that. at anv given. angle from the apex of the jet. the uminosity emitted. per unit solid angle along the jet axis and along the jet borders is the same.," A main assumption of this model is that, at any given angle from the apex of the jet, the luminosity emitted per unit solid angle along the jet axis and along the jet borders is the same." +" Let us call jets with his energy structure ""homogeneous"" jets (195) (see Fig.1)."," Let us call jets with this energy structure “homogeneous"" jets (HJs) (see Fig.1)." + Lt is possible. instead. that the radiated power (per unit solid angle) along the jet axis is larger than what is emitted along the “wings”.," It is possible, instead, that the radiated power (per unit solid angle) along the jet axis is larger than what is emitted along the “wings""." + If the wing energy distribution is a power-law. we refer to these configurations às “structured” jets (Ss) (sce Fig.1).," If the wing energy distribution is a power-law, we refer to these configurations as “structured"" jets (SJs) (see Fig.1)." +" As Rossi. Lazzati Rees (2002) (thereafter 1111092) and Zhang Mésszárros (2002) have demonstrated. if the luminosity per unit solid angle is L(0)x6 with e close to 2. then observers with a viewing angle 8, would see an achromatic jet break when E1/06,"," As Rossi, Lazzati Rees (2002) (thereafter RLR02) and Zhang Mésszárros (2002) have demonstrated, if the luminosity per unit solid angle is $L(\theta)\propto\theta^{-a}$ with $a$ close to 2, then observers with a viewing angle $\theta_{\rm o}$ would see an achromatic jet break when $\Gamma\sim 1/\theta_o$." + I is therefore possible that all GRB jets are intrinsically alike. having the same total intrinsic power and the same jet aperture angle: they appear different only. because they are. viewed: along dillerent orientations.," It is therefore possible that all GRB jets are intrinsically alike, having the same total intrinsic power and the same jet aperture angle: they appear different only because they are viewed along different orientations." + Lf the jet were uniform. instead. they should have a large variety of aperture angles. to account for the dilferent observed jet-break times (Erail et al.," If the jet were uniform, instead, they should have a large variety of aperture angles, to account for the different observed jet-break times (Frail et al." + 2001)., 2001). + As demonstrated analytically in RLRO2 and more recently numerically by Salmonson (2003) (thereafter 803). it ds dillicult. on the basis of the observed. light. curve. o discriminate between homogeneous and. structured jets (sce also Cranot Ixumar 2003).," As demonstrated analytically in RLR02 and more recently numerically by Salmonson (2003) (thereafter S03), it is difficult, on the basis of the observed light curve, to discriminate between homogeneous and structured jets (see also Granot Kumar 2003)." + However. as described in his paper. the two mocdels are markedly dillerent in the polarisation properties of the produced. afterglow flux.," However, as described in this paper, the two models are markedly different in the polarisation properties of the produced afterglow flux." + In xh models the polarisation is produced. because dilferent xwts of the emitting jet surfaces do not contribute equally to 16 observed Dux., In both models the polarisation is produced because different parts of the emitting jet surfaces do not contribute equally to the observed flux. +" In the homogeneous jet model this starts o occur when L/L becomes of the order of 6...6, (i.c. when 1e emitting surface available to the observer ""touches? the =wear border of the jet)."," In the homogeneous jet model this starts to occur when $1/\Gamma$ becomes of the order of $\theta_{\rm jet}-\thv$ (i.e. when the emitting surface available to the observer “touches"" the near border of the jet)." + In the structured jet model. instead. re required. asvmametry. is built-in in the assumption that 10 emission is a function of 8. so that the relevant emitting gsurface is never completely symmetric for oll-axis observers.," In the structured jet model, instead, the required asymmetry is built-in in the assumption that the emission is a function of $\theta$, so that the relevant emitting surface is never completely symmetric for off-axis observers." + Finally we consider a jet with a Gaussian. luminosity istribution (Zhang Aleszaros 2002)., Finally we consider a jet with a Gaussian luminosity distribution (Zhang Meszaros 2002). +" This can be regarded is a more realistic version of the sharp edged standard jet: 10 emission drops exponentially outside the typical angular size (6,1. within which it is roughly constant (see. Fig.1)."," This can be regarded as a more realistic version of the sharp edged standard jet: the emission drops exponentially outside the typical angular size $\theta_c$ ), within which it is roughly constant (see Fig.1)." + Let us call it the “Gaussian jet (GJ)., Let us call it the “Gaussian jet” (GJ). + It has been argued jw this configuration can accomocdate a unified. picture X GRBs ancl X-ray flashes., It has been argued that this configuration can accomodate a unified picture of GRBs and X-ray flashes. +" Phe underlving assumptions is 10 presence of an emission mechanism for which the peak energy ££, in the prompt. emission is a decreasing function of the angular distance from the jet axis.", The underlying assumptions is the presence of an emission mechanism for which the peak energy $E_p$ in the prompt emission is a decreasing function of the angular distance from the jet axis. + In this way rav. Lashes would be the result of observing a CtDs jet a large angles., In this way X-ray flashes would be the result of observing a GRBs jet at large angles. + According to Zhang et al. (, According to Zhang et al. ( +"2003) the GJ woulc reproduce the observed. correlation Ly,xETT (Amati ο al..","2003) the GJ would reproduce the observed correlation $E_p \propto E_{iso}^{1/2}$ (Amati et al.," + 2002). while under the same assumption the universa SJ and the stop hat jet would face severe problems.," 2002), while under the same assumption the universal SJ and the “top hat” jet would face severe problems." + We notice here. however. that the above correlation is still basec on à very small database in the X-ray Lashes regime (only two X-ray [lashes are included) and should be confirmed by future observations.," We notice here, however, that the above correlation is still based on a very small database in the X-ray flashes regime (only two X-ray flashes are included) and should be confirmed by future observations." + As regards afterglow properties. a Ci. seen within the core produces lighteurves that are similar (but with smoother breaks) to the 11 ones (Cranot ]|xumar 2003).," As regards afterglow properties, a GJ seen within the core produces lightcurves that are similar (but with smoother breaks) to the HJ's ones (Granot Kumar 2003)." + The luminosity variation with angle gives. as in the case of a SJ. a net polarisation without the need of edges and we show here that its temporal behaviour is indeed. dillerent from both the SJs and the LJs one.," The luminosity variation with angle gives, as in the case of a SJ, a net polarisation without the need of edges and we show here that its temporal behaviour is indeed different from both the SJ's and the HJ's one." + The detailed analysis of the polarisation characteristics and their connection with lighteurves in the homogeneous jet. universal structured. jet and in the Gaussian jet models is the main goal of this paper.," The detailed analysis of the polarisation characteristics and their connection with lightcurves in the homogeneous jet, universal structured jet and in the Gaussian jet models is the main goal of this paper." + In Section 2 we described he numerical code we have implemented. to study these models., In Section 2 we described the numerical code we have implemented to study these models. + Some analytical ancl semi-analytical results have en derived. by CGL99. and 899. for a non-spreading jet ancl for a sideway expanding jet respectively.," Some analytical and semi-analytical results have been derived by GL99 and S99, for a non-spreading jet and for a sideway expanding jet respectively." + The simplified »eserption assumed. by SOO for the lateral expansion led o prediction of a third peak in the light. curve of the »olarised. flux. for an observer close to the border of the jet., The simplified prescription assumed by S99 for the lateral expansion led to prediction of a third peak in the light curve of the polarised flux for an observer close to the border of the jet. + In addition. GL99 did not consider. for simplicity. the ellects of the dillerent travel times of photons produced in cillerent regions of the fireball. while SOO considered. this οσοι by representing the viewable region as a thin ring centred around the line of sight: the ring has an angular size of P. Land a constant width with respect to the ring radius.," In addition, GL99 did not consider, for simplicity, the effects of the different travel times of photons produced in different regions of the fireball, while S99 considered this effect by representing the viewable region as a thin ring centred around the line of sight: the ring has an angular size of $~\Gamma^{-1}$ and a constant width with respect to the ring radius." + Our numerical approach allows us to include the effects of the different photon travel time and to analyze and compare different prescriptions for the side expansion of the fireball., Our numerical approach allows us to include the effects of the different photon travel time and to analyze and compare different prescriptions for the side expansion of the fireball. +of various sizes and cdillerent selection criteria. it scems [air to sav that little light has so far been shed on the nature of quasars using these methods.,"of various sizes and different selection criteria, it seems fair to say that little light has so far been shed on the nature of quasars using these methods." + Phere appears to be two main reasons for this., There appears to be two main reasons for this. + Firstly. despite the ellorts which have been put into quasar monitoring programmes the data have on the whole proved inadequate for measuring useful parameters to characterise the variability.," Firstly, despite the efforts which have been put into quasar monitoring programmes the data have on the whole proved inadquate for measuring useful parameters to characterise the variability." + his is partly. because samples of quasars have been too small. and. partly because the run of data has been too short and inhomogeneous.," This is partly because samples of quasars have been too small, and partly because the run of data has been too short and inhomogeneous." + As a consequence it has not. proved. possible to unambiguously define the fundamental properties of the Hux variations of he quasars., As a consequence it has not proved possible to unambiguously define the fundamental properties of the flux variations of the quasars. + The second reason that quasar monitoring programmes rave not led to more progress in the understanding of ACGN concerns the lack of firm. predictions for variability. from he various competing AGN models., The second reason that quasar monitoring programmes have not led to more progress in the understanding of AGN concerns the lack of firm predictions for variability from the various competing AGN models. + A big step forward in this area has recently been made with the publication (IxcwaguchietaL.1998) of a detailed. model for ACN variability. from accretion dise instability., A big step forward in this area has recently been made with the publication \cite{k98} of a detailed model for AGN variability from accretion disc instability. + In. this. paper he authors make detailed: statistical predictions for the spectrum. of fluctuations for their model ancl also for the starburst model., In this paper the authors make detailed statistical predictions for the spectrum of fluctuations for their model and also for the starburst model. + These predictions are presented in a form hat enables meaningful comparison with observations of AGN variability., These predictions are presented in a form that enables meaningful comparison with observations of AGN variability. + Lt is the purpose of this paper to use the best available observational data of the variations of AGN to distinguish between the various models of variability., It is the purpose of this paper to use the best available observational data of the variations of AGN to distinguish between the various models of variability. + To this end. we describe a large scale monitoring programme of a sample containing some GOO quasars with regularly. sampled. light curves covering 24 vears., To this end we describe a large scale monitoring programme of a sample containing some 600 quasars with regularly sampled light curves covering 24 years. + We also use extensive monitoring data for Sevfert. galaxies taken from the recent literature., We also use extensive monitoring data for Seyfert galaxies taken from the recent literature. + Predictions of the models are published. in the form. of structure faunetions and we analyse the observational data in the same way to provide quantitative comparisons., Predictions of the models are published in the form of structure functions and we analyse the observational data in the same way to provide quantitative comparisons. + In order to extract information from observations of ACN variability it is necessary to find ways of quantitively characterising the nature of the variations., In order to extract information from observations of AGN variability it is necessary to find ways of quantitively characterising the nature of the variations. + “There is a vast literature on time series analysis. much of it concerned with extracting information from incomplete or inhomosgeneous datasets.," There is a vast literature on time series analysis, much of it concerned with extracting information from incomplete or inhomogeneous datasets." + There are several functions which iive been used for analvsing AGN variations. including he structure function. auto-correlation function and Fourier »ower spectrum.," There are several functions which have been used for analysing AGN variations, including the structure function, auto-correlation function and Fourier power spectrum." + Although all of these functions contain very similar information. in practice they each have advantages in xuwticular situations.," Although all of these functions contain very similar information, in practice they each have advantages in particular situations." + For example. although for an infinite and complete run of data the auto-correlation function and power spectrum are essentially equivalent to each other. or linite runs of data there are significant dillerences.," For example, although for an infinite and complete run of data the auto-correlation function and power spectrum are essentially equivalent to each other, for finite runs of data there are significant differences." + For ong runs of evenly spaced data the power spectrum is o be preferred. as i is on the whole easier to interpret and understand. the errors., For long runs of evenly spaced data the power spectrum is to be preferred as it is on the whole easier to interpret and understand the errors. + For short. or. inhomogeneous datasets the auto-correlation function. provides a more stable measurement. but as the individual points are not independent of cach other there can be cilliculties with interpretation.," For short or inhomogeneous datasets the auto-correlation function provides a more stable measurement, but as the individual points are not independent of each other there can be difficulties with interpretation." + Phe structure function is very similar to the auto-correlation function and has been widely used in the analysis of quasar light curves (Trevesectal...1994:Look and microlensing statistics (Wyithe&Turner2001).," The structure function is very similar to the auto-correlation function and has been widely used in the analysis of quasar light curves \cite{t94,h94,c96,a97a} and microlensing statistics \cite{w01}." +. Phe unction of choice will depend upon a number of factors. not cast of which is the form in which model predictions have oen mace.," The function of choice will depend upon a number of factors, not least of which is the form in which model predictions have been made." + The present paper has been largely prompted. by he publication (Ixawaguchietal..1998). of quantitative xedietions. for the statistics of AGN variability. and hese are presented in the [form of structure functions.," The present paper has been largely prompted by the publication \cite{k98} of quantitative predictions for the statistics of AGN variability, and these are presented in the form of structure functions." + Accordingly. we shall proceed. with the analysis of the observations in the same wav.," Accordingly, we shall proceed with the analysis of the observations in the same way." + The structure function 5 may xe defined by where m(f;) is the magnitude measure at epoch /;. and the sum runs over the Nr) epochs for which /;ἐν= 7.," The structure function $S$ may be defined by where $m(t_{i})$ is the magnitude measure at epoch $t_{i}$, and the sum runs over the $N(\tau)$ epochs for which $t_{j}-t_{i} = \tau$ ." + The interpretation of the structure function in the sense of identifving specilic characteristics of the variation is not usually feasible., The interpretation of the structure function in the sense of identifying specific characteristics of the variation is not usually feasible. + However. particular mocels of variability can be shown to produce structure functions with measurable parametric forms.," However, particular models of variability can be shown to produce structure functions with measurable parametric forms." + Although in. some cases ellorts have been made to precict the shape of the structure function (CidFernandesetal;1997).. it is perhaps more useful to generate structure functions from simulate data (Ixawaguchictal.1998)... and. this is the approach underlving the present. paper.," Although in some cases efforts have been made to predict the shape of the structure function \cite{c97}, it is perhaps more useful to generate structure functions from simulated data \cite{k98}, and this is the approach underlying the present paper." + In. addition to the stanclarc structure function defined above. we shall for the purpose of measuring asvnunetries also make use of two moclifie structure functions S and So.," In addition to the standard structure function defined above, we shall for the purpose of measuring asymmetries also make use of two modified structure functions $S_{+}$ and $S_{-}$." + These are defined as for S except that for δν the integration only includes. pairs of magnitudes for which the Hux becomes brighter. and for for which it becomes fainter.," These are defined as for $S$ except that for $S_{+}$ the integration only includes pairs of magnitudes for which the flux becomes brighter, and for $S_{-}$ for which it becomes fainter." + Vhe mechanism behind AGN variability has been the subject of much debate since their first. discovery., The mechanism behind AGN variability has been the subject of much debate since their first discovery. + At esent there are three broad approaches to explaining the observed: variations., At present there are three broad approaches to explaining the observed variations. + The most favoured model has invoked instabilities in the accretion disc surrounding the central lack hole. but à contending idea is that the variations are caused by some intermittent sequence of discrete events such as supernova bursts.," The most favoured model has invoked instabilities in the accretion disc surrounding the central black hole, but a contending idea is that the variations are caused by some intermittent sequence of discrete events such as supernova bursts." + A third possibility is that we are seeing he effects of gravitational microlensing by a population of small compact bodies along the line of sight., A third possibility is that we are seeing the effects of gravitational microlensing by a population of small compact bodies along the line of sight. + Each of hese models has good arguments in its [avour. but also ails to explain some aspects of AGN variability. and i seems likely that all three processes contribute at some leve o the observed light curves with perhaps one mechanism dominating in any particular regime.," Each of these models has good arguments in its favour, but also fails to explain some aspects of AGN variability, and it seems likely that all three processes contribute at some level to the observed light curves with perhaps one mechanism dominating in any particular regime." + Until recently. there ws been little attempt in the literature to make moce," Until recently, there has been little attempt in the literature to make model" +(Abdoetal.2009) is indicated by the arrow.,"\citep{Abd09} + is indicated by the arrow." +" We plot the results of cutoff power law fit to theSuzaku spectra in epochs 1 (black) and 2 (red) as well asthe time-averaged Swift/BAT data, correcting for both Galactic and intrinsic absorptions."," We plot the results of cutoff power law fit to the spectra in epochs 1 (black) and 2 (red) as well asthe time-averaged /BAT data, correcting for both Galactic and intrinsic absorptions." +" To examine the origin of the time variability, we analyze the difference spectrum of XIS-FIs between epochs 2 and 1."," To examine the origin of the time variability, we analyze the difference spectrum of XIS-FIs between epochs 2 and 1." +" Fitting with a single power law with the same double absorption as given in Table 1,, we find [z1.8."," Fitting with a single power law with the same double absorption as given in Table \ref{tab_s}, we find $\Gamma \approx +1.8$." + This result is also plotted in the figure , This result is also plotted in the figure (green curve). +"Assuming (greenthat the curve).global intrinsic SED of the jet emission in 4C 50.55 is similar to that of jet (Kuboetal.1998) with correction for an estimated beaming factor (6~1 for 4C 50.55 and 6~10 for blazars), the predicted X-ray emission is a factor of ~10!~4 less than the observed X-ray flux."," Assuming that the global intrinsic SED of the jet emission in 4C 50.55 is similar to that of jet \citep{Kub98} with correction for an estimated beaming factor $\delta \sim 1$ for 4C 50.55 and $\delta \sim 10$ for blazars), the predicted X-ray emission is a factor of $\sim 10^{1-4}$ less than the observed X-ray flux." + We thus conclude that X-ray emission due to a jet via synchrotron emission or inverse Compton should be very small in the total X-ray emission of this source., We thus conclude that X-ray emission due to a jet via synchrotron emission or inverse Compton should be very small in the total X-ray emission of this source. +" Based on the results, the ratio of the core luminosity at 5 GHz and that in the 2-10 keV band is estimated to be log Rx=—3.6."," Based on the results, the ratio of the core luminosity at 5 GHz and that in the 2–10 keV band is estimated to be log $R_{\rm X} = -3.6$." +" Thus, while 4C 50.55 should be classified as a radio loud object (Terashima&Wilson2003),, its radio to X-ray power ratio is much lower compared withtypical blazars and more powerful radio galaxies, like 3C 120 (log Rx= —2.1) (Kataokaetal. 2007).."," Thus, while 4C 50.55 should be classified as a radio loud object \citep{Ter03}, its radio to X-ray power ratio is much lower compared withtypical blazars and more powerful radio galaxies, like 3C 120 (log $R_{\rm X} = -2.1$ ) \citep{Kat07}. ." +" This confirms the conclusion by Molinaetal. (2007),, who"," This confirms the conclusion by \citet{Mol07}, , who" +"Coming back to the comparison of the rms scatters in Tab. 1,,","Coming back to the comparison of the $rms$ scatters in Tab. \ref{t:ferms}," + we now look at the rather surprising fact that the rms we derive for Fe abundances is higher from the high-resolution UVES spectra than from the intermediate-resolution GIRAFFE ones., we now look at the rather surprising fact that the $rms$ we derive for Fe abundances is higher from the high-resolution UVES spectra than from the intermediate-resolution GIRAFFE ones. +" This effect is particularly clear for clusters with metallicity —1.4 «[Fe/H]«-0.7 dex in our programme sample, which have data of higher quality."," This effect is particularly clear for clusters with metallicity $-1.4<$ $<-0.7$ dex in our programme sample, which have data of higher quality." +" More metal-rich clusters (e.g. NGC 6388 and NGC 6441) are quite distant, bulge clusters, severely affected by field contamination and required a series of long exposures which were not always completed in the ESO observing service queue (in particular for NGC 6441)."," More metal-rich clusters (e.g. NGC 6388 and NGC 6441) are quite distant, bulge clusters, severely affected by field contamination and required a series of long exposures which were not always completed in the ESO observing service queue (in particular for NGC 6441)." +" Analysis of more metal-poor clusters is somewhat hampered by the weakness of lines, increasing the difficulty of EW measurements."," Analysis of more metal-poor clusters is somewhat hampered by the weakness of lines, increasing the difficulty of $EW$ measurements." +" To explain the above mentioned effect, a possibility is that stars observed with UVES have intrinsically a larger scatter than those observed with GIRAFFE."," To explain the above mentioned effect, a possibility is that stars observed with UVES have intrinsically a larger scatter than those observed with GIRAFFE." +" This would happen if the intrinsic scatter is partly a function of the stellar luminosity, because we preferentially chose brighter stars as UVES targets (although the majority of the objects - about 170 out of 214 stars - are in common between the two data sets)."," This would happen if the intrinsic scatter is partly a function of the stellar luminosity, because we preferentially chose brighter stars as UVES targets (although the majority of the objects - about 170 out of 214 stars - are in common between the two data sets)." + To better understand this point we need to improve the estimate of the intrinsic scatter and in order to clarify the issue we proceeded as follows., To better understand this point we need to improve the estimate of the intrinsic scatter and in order to clarify the issue we proceeded as follows. + For each star observed with GIRAFFE or UVES (separately) we evaluated the difference between the [Fe/H] value for the individual stars and the average value [Fe/H] of the cluster., For each star observed with GIRAFFE or UVES (separately) we evaluated the difference between the [Fe/H] value for the individual stars and the average value [Fe/H] of the cluster. + These residuals were then plotted as a function of the absolute K magnitude Mt corrected for the apparent distance modulus and reddening in each cluster., These residuals were then plotted as a function of the absolute $K$ magnitude $M_K^0$ corrected for the apparent distance modulus and reddening in each cluster. + We chose the K band because (i) all near-IR magnitudes are from the 2MASS catalogue and they represent a very homogeneous dataset and (ii) this filter is much less sensitive to errors in the reddening estimate., We chose the $K$ band because (i) all near-IR magnitudes are from the 2MASS catalogue and they represent a very homogeneous dataset and (ii) this filter is much less sensitive to errors in the reddening estimate. +" Finally, all stars were binned in luminosity intervals and the average residual and rms scatter from the mean was computed for each bin."," Finally, all stars were binned in luminosity intervals and the average residual and $rms$ scatter from the mean was computed for each bin." + These averages are listed in Tab., These averages are listed in Tab. + 3 and plotted in Fig. 6.., \ref{t:diffe} and plotted in Fig. \ref{f:trend}. +" We restricted this exercise to the metallicity range [Fe/H] from -1.4 to -0.7 dex, where we have better quality data."," We restricted this exercise to the metallicity range [Fe/H] from -1.4 to -0.7 dex, where we have better quality data." +"We also study how the relative importance of synchrotron and SSC emission varies with the ratio (€,/€,), this ratio being the quantity which determines the relative importance of these two emission mechanisms (foradetailedanalysisoftheef-Galli&Piro 2007).","We also study how the relative importance of synchrotron and SSC emission varies with the ratio $(\epsilon_e/\epsilon_B)$, this ratio being the quantity which determines the relative importance of these two emission mechanisms \citep[for a detailed analysis of the effects of this ratio during early and late afterglow emission see][]{galli07}." +. We present our results in Fig., We present our results in Fig. + 9 for X-ray flare luminosity L=2x10?ergs~!., \ref{flarelum2e49z1Eb} for X-ray flare luminosity $L=2 \times 10^{49}~erg~s^{-1}$. +" As expected, the relative importance of the two processes increases with the ratio (€,/€g) thus favoring the detection of the high energy component even though the peak of SSC emission moves toward lower energies with smaller eg values."," As expected, the relative importance of the two processes increases with the ratio $(\epsilon_e/\epsilon_B)$ thus favoring the detection of the high energy component even though the peak of SSC emission moves toward lower energies with smaller $\epsilon_B$ values." +" We keep e,=0.54 and vary eg from 0.1 (red curves), to 0.01 (blue curves), and finally to 0.001 (purple curves)."," We keep $\epsilon_e=0.54$ and vary $\epsilon_B$ from 0.1 (red curves), to 0.01 (blue curves), and finally to $0.001$ (purple curves)." +" The predicted SSC emission can be detected by AGILE and GLAST up to ζωα~2.5 and ζω~2.7 for an integration time of 500 s, and up to ζω~1.2 and Zmax1.3 for an integration time of 500 s. For a luminosity L=10??ergs-! the high energy emission can be detected by AGILE and GLAST up to Zing,~5.2 and Zax~5.5 for an integration time of 500 s, and up to Zax~2.6 and Zax~2.8 for an integration time of 100 s. Falconeetal.(2007) have shown that X-ray flares spectra can be fitted both by a power law and/or by a Band model."," The predicted SSC emission can be detected by AGILE and GLAST up to $z_{max} \sim 2.5$ and $z_{max} \sim 2.7$ for an integration time of 500 s, and up to $z_{max} \sim 1.2$ and $z_{max} \sim 1.3$ for an integration time of 500 s. For a luminosity $L= 10^{50}~erg~s^{-1}$ the high energy emission can be detected by AGILE and GLAST up to $z_{max} \sim 5.2$ and $z_{max} \sim 5.5$ for an integration time of 500 s, and up to $z_{max} \sim 2.6$ and $z_{max} \sim 2.8$ for an integration time of 100 s. \citet{falcone07} have shown that X-ray flares spectra can be fitted both by a power law and/or by a Band model." +" However, due to the incomplete spectral coverage they could constrain the flare peak energy only in some cases, and suggested that typically this peak energy should be in the soft X-ray band, or between the optical and X-ray bands."," However, due to the incomplete spectral coverage they could constrain the flare peak energy only in some cases, and suggested that typically this peak energy should be in the soft X-ray band, or between the optical and X-ray bands." +" Figures 7,, 8 and 9 show that if we assume f,~100 ms and Γ~100, the peak energy of the X-ray flare emission falls in, or just below, the XRT band consistent with the findings of the flare spectral analysis performed by Falconeetal.(2007)."," Figures \ref{flarelum2e49z1}, \ref{flarelum2e50z1} and \ref{flarelum2e49z1Eb} show that if we assume $t_v\sim 100$ ms and $\Gamma \sim 100$, the peak energy of the X-ray flare emission falls in, or just below, the XRT band consistent with the findings of the flare spectral analysis performed by \citet{falcone07}." +. In Fig., In Fig. +" 10 we show the predicted synchrotron and SSC flare emission for a range of t, values similar to that typically observed during the prompt emission, i.e. 4,~ 10 ms - 1 s, with Il=100 and L-22x109ergcm?."," \ref{flarelum2e49z1tv} we show the predicted synchrotron and SSC flare emission for a range of $t_v$ values similar to that typically observed during the prompt emission, i.e. $t_v \sim$ 10 ms - 1 s, with $\Gamma=100$ and $L=2 \times 10^{49}~erg~cm^{-2}$." +" As we can see from this figure, when one assumes a Lorentz factor of the order of one hundred for this range of {ν the peak energy of the X-ray flare is always inside or just below the XRT band."," As we can see from this figure, when one assumes a Lorentz factor of the order of one hundred for this range of $t_v$ the peak energy of the X-ray flare is always inside or just below the XRT band." +" The detection of the SSC component related to the X-ray flare depends strongly on the flare temporal variability: for 4,< 10 ms the spectral cutoff due to pair production is shifted to lower energies (Eq.19ofGuetta&Granot2003), i.e. in the AGILE and GLAST bands, making the SSC emission more difficult to detect."," The detection of the SSC component related to the X-ray flare depends strongly on the flare temporal variability: for $t_v <$ 10 ms the spectral cutoff due to pair production is shifted to lower energies \citep[Eq. 19 of][]{guetta03}, i.e. in the AGILE and GLAST bands, making the SSC emission more difficult to detect." +" In the same way, a larger temporal variability 4,z 1 s shifts the peak energy of the SSC component below the AGILE and GLAST energy bands, and this again makes the high energy flare more difficult to detect."," In the same way, a larger temporal variability $t_v \gtrsim$ 1 s shifts the peak energy of the SSC component below the AGILE and GLAST energy bands, and this again makes the high energy flare more difficult to detect." +" In order to have both the X-ray peak energy in the XRT band and a detectable high energy emission for I ~100, we need {ν~50—100 ms."," In order to have both the X-ray peak energy in the XRT band and a detectable high energy emission for $\Gamma \sim$ 100, we need $t_v\sim 50-100$ ms." +" This implies that the flux of the X-ray flares should vary on a time scale much smaller than the flare duration, i.e f,<$ 75 counts) and arcsec for the fainter ones $<$ 75 counts). + In Table 2. the olfset between the optical aud X-ray coordinates for our 28 galaxies is E Saaresec. within the 20 positional uncertainty for faint sources derived above.," In Table \ref{sample} the offset between the optical and X-ray coordinates for our 28 galaxies is $\la 5$ arcsec, within the $2\sigma$ positional uncertainty for faint sources derived above." + ‘The luminosity-redshift relation or our sample is compared in Fig., The luminosity-redshift relation for our sample is compared in Fig. + 2 with the ‘normal’ gal:uxies from the CDE-North and South., \ref{lxz} with the `normal' galaxies from the CDF-North and South. + For the CDE-North we use the spectroscopic sample of Llornschemeicr et. al. (, For the CDF-North we use the spectroscopic sample of Hornschemeier et al. ( +2003) while for the CDE-South we select oefieff.)τς2 sources [rom the kkeV catalogue of Ciaconni et al. (,"2003) while for the CDF-South we select $\log +(f_x /f_o)<-2$ sources from the keV catalogue of Giaconni et al. (" +οί102) with spectroscopic or photometric recshifts obtained rom Szokolv et al. (,2002) with spectroscopic or photometric redshifts obtained from Szokoly et al. ( +2004) and Zheng et al. (,2004) and Zheng et al. ( +2004).,2004). + From Lig., From Fig. + 2 it can be seen that our sample is complementary to the CDE. covering the low redshift and. hie 1luminosity par of the Luminosity-recdshilt jane.," \ref{lxz} it can be seen that our sample is complementary to the CDF, covering the low redshift and high luminosity part of the luminosity-redshift plane." +" We derive tie binned ""norm:Wo galaxy X-ray luminosity ""unction using he method. desπρος by Page Carrera (2000).", We derive the binned `normal' galaxy X-ray luminosity function using the method described by Page Carrera (2000). +" This ds variant of the* classical non-paranictric 1/1, method (Schmidt LOGS) and has the advantage that it is least allected by systematic errors for objects close to he [lux limit of the survey.", This is variant of the classical non-parametric $1/V_{max}$ method (Schmidt 1968) and has the advantage that it is least affected by systematic errors for objects close to the flux limit of the survey. +" For a given redshift and. X- luminosity interval the binned Luminosity function. is estimated from the relation: where AN is the number of sources with luminosity in the range L,,5, and L,,;4 and dVdz is the volume clement vcr redshift interval dz.", For a given redshift and X-ray luminosity interval the binned luminosity function is estimated from the relation: where $N$ is the number of sources with luminosity in the range $L_{min}$ and $L_{max}$ and $dV/dz$ is the volume element per redshift interval $dz$. +" For a given luminosity £L. zí;,L) and z,,,:CL) are the minimum and the maximum redshifts »ossiblefor a source of that luminosity to remain within the lux limits of the survey and to lie within the redshift bin."," For a given luminosity $L$, $z_{min}(L)$ and $z_{max}(L)$ are the minimum and the maximum redshifts possiblefor a source of that luminosity to remain within the flux limits of the survey and to lie within the redshift bin." + O(L.z) is the solid angle of the N-rav survey available to a source with Luminosity £ at a redshift z (corresponding o a given flux in the N-rav area curve).," $\Omega(L,z)$ is the solid angle of the X-ray survey available to a source with luminosity $L$ at a redshift $z$ (corresponding to a given flux in the X-ray area curve)." + The logarithmic xn size of the luminosity function. varies so that cach bin comprises approximately equal number of sources IN., The logarithmic bin size of the luminosity function varies so that each bin comprises approximately equal number of sources $N$. + The uncertainty of a given luminosity bin is estimated assuming Poisson statistics from the relation: We also derive the luminosity. function using he parametric Maximum Likelihood Method (ALL: ‘Tammann.Yahil Sandage 19079).," The uncertainty of a given luminosity bin is estimated assuming Poisson statistics from the relation: We also derive the luminosity function using the parametric Maximum Likelihood Method (ML; Tammann,Yahil Sandage 1979)." + We use a Schechter (1976) form for the luminosity function as this clescribes very well the Luminosity function in e.g. optical wavelengths (Dingclli. Sandage ‘Tammann 1988).," We use a Schechter (1976) form for the luminosity function as this describes very well the luminosity function in e.g. optical wavelengths (Bingelli, Sandage Tammann 1988)." + Moreover. it has a strong theoretical ooling as itis derived from self-similar gravitational collaSC models (Press Schechter 1974).," Moreover, it has a strong theoretical footing as it is derived from self-similar gravitational collapse models (Press Schechter 1974)." +" The Schechter function is expressed. as: In the above expression £, denotes the characteristic luminosity where the function above changes from a power-law with slope a at the faint-end to an exponential drop at brighter luminosities.", The Schechter function is expressed as: In the above expression $L_\star$ denotes the characteristic luminosity where the function above changes from a power-law with slope $\alpha$ at the faint-end to an exponential drop at brighter luminosities. + A likelihood. function is constructed as the product of probabilities 2that a galaxy at redshift > is detected with a luminosity £., A likelihood function is constructed as the product of probabilities $P_i$that a galaxy at redshift $z$ is detected with a luminosity $L$. + Thus 2 is defined as the ratio of the number of galaxies. with luminosity. between L and L|dL over the total number observed. P=oL)he b(L£)yd£.," Thus $P_i$ is defined as the ratio of the number of galaxies with luminosity between $L$ and $L+dL$ over the total number observed, $P_i=\Phi(L)/\int^{\infty}_{L_{min(z)}} \Phi(L) dL $ ." +" Vhen we maximise the sum In;nf by varvineving LL, andl o.", Then we maximise the sum $\displaystyle \sum^{n} ln P_i$ by varying $L_\star$ and $\alpha$ . +" TheTl errors on L£, andl a are estimated [rom the 6£=0.5 regions around the maxiniun", The errors on $L_\star$ and $\alpha$ are estimated from the $\delta L=0.5 $ regions around the maximum +veiling and the radial velocity fluctuations.,veiling and the radial velocity fluctuations. + We will illustrate this iu the present paper bv complementing our analvsis with stars hat show similar spectral line variations. namely RW Aw A. DI Cop. RU Lup. and S CrA SE.," We will illustrate this in the present paper by complementing our analysis with stars that show similar spectral line variations, namely RW Aur A, DI Cep, RU Lup, and S CrA SE." +" DR Tau was for a long period a relatively faint star until in 1976 it rather suddenly brehteue bv several magnitudes in the blue (Clhavarria-k. 1979)). aud the star ds ποnetimes classified as an ENor star (sec ιο, Lorenzetti et al. 20093)."," DR Tau was for a long period a relatively faint star until in 1976 it rather suddenly brightened by several magnitudes in the blue (Chavarria-K. \cite{chavarria79}) ), and the star is sometimes classified as an EXor star (see e.g. Lorenzetti et al. \cite{lorenzetti09}) )." + Towever. siico. that time it has stavec at this bright level bu with cramatic and fairly mregulhuw light variations (Artem nkoe al. 2010)).," However, since that time it has stayed at this bright level but with dramatic and fairly irregular light variations (Artemenko et al. \cite{artemenko10}) )." + Teoutative photometric periods propeISOC by Riciter et al. (1992)).," Tentative photometric periods proposed by Richter et al. \cite{richter92}) )," + Bouvier et al. (1993)).," Bouvier et al. \cite{bouvier93}) )," + and Douvier e al. (1995)), and Bouvier et al. \cite{bouvier95}) ) + differ bv several dave. and are differeit from a more recent determiuaion by Percy et al. (2010)).," differ by several days, and are different from a more recent determination by Percy et al. \cite{percy10}) )," + w10 assign a period of 5.0 davs., who assign a period of 5.0 days. + This is also iu the sale range of possible periods found froi near-infrared CNIR) photometry by Ixeuvon et al. (1 9911).," This is also in the same range of possible periods found from near-infrared (NIR) photometry by Kenyon et al. \cite{kenyon94}) )," + who relate the periodicity of DR Tau to a hot spot ou a rotating star with a naeuetic axis inclined to the stella rotation axis., who relate the periodicity of DR Tau to a hot spot on a rotating star with a magnetic axis inclined to the stellar rotation axis. + Pronounced spectral variability iu DR Tau Was recognized carly (Bertout et al. 1977: , Pronounced spectral variability in DR Tau was recognized early (Bertout et al. \cite {bertout77}; ; +Irautter Bastian 1980: Muxdt 198S Ajad ct al. 1981:, Krautter Bastian \cite{krautter80}; ; Mundt \cite{mundt84}; Aiad et al. \cite{aiad84}; + Appenzeller et al. 19558)., Appenzeller et al. \cite{appenzeller88}) ). +" Tje strong emission lines oi occasion show inverse P Cveni structures, which appear arc disappear on scales assrort as a few hours (Snütlhi et al. 1997.. 1999))."," The strong emission lines on occasion show inverse P Cygni structures, which appear and disappear on time-scales as short as a few hours (Smith et al. \cite{smith97}, \cite{smith99}) )." + Dax Batalha (1990)) demonstrated that the veiling is huge axd varlable. and subsequeit investigations of rolatious betweolj variations in emissionlinesaud veiling ed Cueuther Tessinan," Basri Batalha \cite{basri90}) ) demonstrated that the veiling is large and variable, and subsequent investigations of relations between variations in emissionlinesand veiling led Guenther Hessman" + , + isa blue hypergiaut (de Jager L998) or a Luuinous Blue Variable (LBY. Thunphrervs Davidson 1991) whose observed characteristics male the star zione the most peculiar ones in the Galaxy.,"is a blue hypergiant (de Jager 1998) or a Luminous Blue Variable (LBV, Humphreys Davidson 1994) whose observed characteristics make the star among the most peculiar ones in the Galaxy." + The properties of aud its wind have heen reviewed by Israchan aud de Croot (1999)., The properties of and its wind have been reviewed by Israelian and de Groot (1999). + Niurow absorption line components called DACs were discovered in Baliner line profiles of by de Groot (1969)., Narrow absorption line components called DACs were discovered in Balmer line profiles of by de Groot (1969). + Te also found them iu lines of Ic. Fe aud many other elemieuts.," He also found them in lines of He, Fe and many other elements." + Ideutificatious of other lunes were published bx others., Identifications of other lines were published by others. + Cassatella et al. (, Cassatella et al. ( +1979) and Laid and Sapar (1980) detected DACs in UV lines of various ious. such asCrib.Nill. aud others.,"1979) and Luud and Sapar (1980) detected DACs in UV lines of various ions, such as, and others." + Lamers et al. (, Lamers et al. ( +1985) found them in lines.,1985) found them in lines. +of the slaw which are necessary to trace the large-scale structure of the Universe at the redshifts where the NRB was produced.,of the sky which are necessary to trace the large-scale structure of the Universe at the redshifts where the XRB was produced. + The obvious way to eo would be to survey very large areas of the sky (the whole sky even better) Or N-rav sources. 1 order to have a 1iost complete picture.," The obvious way to go would be to survey very large areas of the sky (the whole sky even better) for X-ray sources, in order to have a most complete picture." + Unless hard N-ravs are produced at significantly lower redshifts than soft N-ravs (Gvlüchl is doubtful iu vicav of the ASCA audBeppoSAN surveys). to reach 2~1 where a significant fracion of the N-rav οwissivity in the Universe resides. these surveys will have to go at least down to ~1üHlerecniS ," Unless hard X-rays are produced at significantly lower redshifts than soft X-rays (which is doubtful in view of the $ASCA$ and surveys), to reach $z\sim 1$ where a significant fraction of the X-ray emissivity in the Universe resides, these surveys will have to go at least down to $\sim 10^{-14}\, {\rm +erg}\, {\rm cm}^{-2}\, {\rm s}^{-1}$." +There is anaternative which is to perform higL sensitivity Observetious of the NRB witha bean1 COLTCSPOxdiue to the linear scale o be probed (Barcois. Favan Carrera 1998).," There is an alternative which is to perform high sensitivity observations of the XRB with a beam corresponding to the linear scale to be probed (Barcons, Fabian Carrera 1998)." +" Ast1ο peal of the power spectrum o‘the deusitv field of he UUVCTSC occurs af comoviig Wwaventiibers ~0.01.0.15METος+. for a staudax ecolctry a 1"" resolution is well matche dtothisat:~1 3."," As the peak of the power spectrum of the density field of the Universe occurs at comoving wavenumbers $\sim 0.01-0.1\, h \, {\rm Mpc}^{-1}$, for a standard geometry a $1^{\circ}$ resolution is well matched to this at $z\sim +1-3$." +À ]-skv measurclients of the NRB intensity on that aieular scale with a precision of a few colId theji be 1sed to detect the excess fhctuatiois due to source clusteric which are expected to )o just below in amplitude., All-sky measurements of the XRB intensity on that angular scale with a precision of a few could then be used to detect the excess fluctuations due to source clustering which are expected to be just below in amplitude. + Cotrolling all other possile sources of excess fluctiatious well below that leve requires a stable laree-area detector (to redice photon counutiug noise) and probably an N-ray monitor which images simultaneously the brightest sources in the field., Controlling all other possible sources of excess fluctuations well below that level requires a stable large-area detector (to reduce photon counting noise) and probably an X-ray monitor which images simultaneously the brightest sources in the field. +"Inside the forward-elimination scheme for the RT process we must propagate not onlv the upgoing and downgoing specific intensities (which brings about the propagation of the source [unction as defined by eq.s (2) and (3)). but also the second derivative S""(7) of the source function in the cubic spline scheme.","Inside the forward-elimination scheme for the RT process we must propagate not only the upgoing and downgoing specific intensities (which brings about the propagation of the source function as defined by eq.s (2) and (3)), but also the second derivative $S^{\prime\prime}(\tau)$ of the source function in the cubic spline scheme." +" As already said. we assume that in the first laver (75.74) thesource function S(7) ean be approximated by an are of parabola. which implies that 5""(7,)=$""(7,)."," As already said, we assume that in the first layer $(\tau_{0},\tau_{1})$ thesource function $S(\tau)$ can be approximated by an arc of parabola, which implies that $S^{\prime\prime}(\tau_{0}) = S^{\prime\prime}(\tau_{1})$." +" This condition will be included in the coefficients of the relation Qem where the values of 5(75).5(74).9""(74).9""(7,) and the set (4.(79.40).J=1..ND] are unknown."," This condition will be included in the coefficients of the relation 0em where the values of $S(\tau_{0}), S(\tau_{1}), S^{\prime\prime}(\tau_{0}), +S^{\prime\prime}(\tau_{1})$ and the set $\lbrace I^{+}(\tau_{0},\mu_{J}), J = 1,ND\rbrace$ are unknown." + In order to fulfill the above boundary condition. all the coefficients in eq. (," In order to fulfill the above boundary condition, all the coefficients in eq. (" +26)mist be equal to zero. excepted cdss2 that must be set equal to one.,"26)must be equal to zero, excepted ${\bf{cdss2}}$ that must be set equal to one." + To express here οἔτι) as a function of οτη). οτι). οτη) itself. ο(τι) and the set (4.(79.40).J=1.NDI is just for algorithmical ease.," To express here $S^{\prime\prime}(\tau_{0})$ as a function of $S(\tau_{0})$, $S(\tau_{1})$, $S^{\prime\prime}(\tau_{0})$ itself, $S^{\prime\prime}(\tau_{1})$ and the set $\lbrace I^{+}(\tau_{0},\mu_{J}), J = 1,ND\rbrace$ is just for algorithmical ease." + When convenient. we will solve for τη) - and for οέτη) - in terms of οτι) οτι) and (4.(74.poy)}.," When convenient, we will solve for $S(\tau_{0})$ - and for $S^{\prime\prime}(\tau_{0})$ - in terms of $S(\tau_{1})$ , $S^{\prime\prime}(\tau_{1})$ and $\lbrace I^{+}(\tau_{1},\mu_{J})\rbrace$." + We are going to show here how the treatment of the first laver (75. τι). labelled by £L= 1. will vield the coefficients of the relation Qem and those of therelation," We are going to show here how the treatment of the first layer $(\tau_{0},\tau_{1})$ , labelled by $L = 1$ , will yield the coefficients of the relation 0em and those of therelation" +totality) must. display au afterglow etission superimposed on the burst itself and uo break of coutiuitv.,"totality) must display an afterglow emission superimposed on the burst itself, and no break of continuity." + The relevance of the above arguments to the problem of the identification of the bursts’ orogeuitors is clear., The relevance of the above arguments to the problem of the identification of the bursts' progenitors is clear. + Bloom. Sigurdsson auc Pols (1999) have shown that there is a well-defined distribution of expected distauces of GRBs from their parent. galaxies. if they originate from the uerger of neutron stars.," Bloom, Sigurdsson and Pols (1999) have shown that there is a well–defined distribution of expected distances of GRBs from their parent galaxies, if they originate from the merger of neutron stars." + lu. particular. hey showed that zz15% of all burst progenitors may be able to escape [rom their parent galaxy altogether. aud that about 50% of all bursts will be located uore than 5Ape from their site of origiu. nearly in the galactic halo.," In particular, they showed that $\approx 15\%$ of all burst progenitors may be able to escape from their parent galaxy altogether, and that about $50\%$ of all bursts will be located more than $8\; kpc$ from their site of origin, nearly in the galactic halo." + This feature is potentially verifiable also with optical investigations. but we know that even the most powerful ground-based elescopes are ofteu inadequate to [ind tie host galaxy. while HST searches. which up to now have scored a remarkable 5/6 success rate (Fruchter 2000). are slow. cum)ersome. and. for some of the vost clistaut bursts. caunuot £o deep euoteh in the luminosity αποτοι.," This feature is potentially verifiable also with optical investigations, but we know that even the most powerful ground–based telescopes are often inadequate to find the host galaxy, while HST searches, which up to now have scored a remarkable $5/6$ success rate (Fruchter 2000), are slow, cumbersome, and, for some of the most distant bursts, cannot go deep enough in the luminosity function." + The test I propose is iusteacl simple. aud a statistically meaninelil database will be secured in the 1ear [uture. since several space nissions CANAF. Hete IL. Integral. NMA. SWIFT) will observe huncdreds of bursts lor several hours alter the burst.," The test I propose is instead simple, and a statistically meaningful database will be secured in the near future, since several space missions (AXAF, Hete II, Integral, XMM, SWIFT) will observe hundreds of bursts for several hours after the burst." + Especially important aiioug them is SWIFT. whicl will be responsible for most of these observations. aud will provide continuous coverage of each ¢etected bursts in both X-ray and UV/optical wavebands.," Especially important among them is SWIFT, which will be responsible for most of these observations, and will provide continuous coverage of each detected bursts in both X–ray and UV/optical wavebands." + From this database of perhaps 300 burss observed continuously over several hours after the burst. we may expect 2z50 bursts located iu tre ICM inediuin. and another zzLOO located in the haloes of their parent. galaxies.," From this database of perhaps $300$ bursts observed continuously over several hours after the burst, we may expect $\approx 50$ bursts located in the IGM medium, and another $\approx +100$ located in the haloes of their parent galaxies." + Thus. within this scenario we expect about a third of all bursts to have delays of several ninutes. and a few teus o have delays of a few hours.," Thus, within this scenario we expect about a third of all bursts to have delays of several minutes, and a few tens to have delays of a few hours." + The flux should then peak again to a factor zzἐν below that of tje burst. proper., The flux should then peak again to a factor $\approx t_{b}/\xi t_d$ below that of the burst proper. + The very same test cau also be used to check whether bursts are surrounded by the —jassive winds expected iu all scenarios iuvolviug massive stars., The very same test can also be used to check whether bursts are surrounded by the massive winds expected in all scenarios involving massive stars. + In. particular. it is expected tha uo time-delay will ever be observed. except perhaps for the slortes bursts. fp<0.03+)s.," In particular, it is expected that no time–delay will ever be observed, except perhaps for the shortest bursts, $t_{b} \ll 0.03\;s$." +" One may wonder what happens when only incomplete data are available.νο, when tle burs disappears shortly after {ραxcd is re-observecl when already in the afterglow regune."," One may wonder what happens when only incomplete data are available, when the burst disappears shortly after $t_b$ and is re–observed when already in the afterglow regime." + This is tlie case of BeppoSAX which. because of iustrumentational limitations. is incapable of providing significan iulormation ou the key sileu period described here.," This is the case of BeppoSAX which, because of instrumentational limitations, is incapable of providing significant information on the key silent period described here." + It should be notice that the above estimates lor the luminosity (Lj at /5. aux Lyla/Elg at 214) fall precisely onal+ slope.," It should be notice that the above estimates for the luminosity $L_b$ at $t_b$, and $L_b t_d/\xi t_d$ at $2 t_d$ ) fall precisely on a $t^{-1}$ slope." + So. if further observations ol the afterglow find au alterelow slope close to —1. extrapolation ofthe afterglow luminosity to early time will match closely witi the burst Iuminosity. regzuclless of the existence of the silent perio.," So, if further observations of the afterglow find an afterglow slope close to $-1$, extrapolation of the afterglow luminosity to early time will match closely with the burst luminosity, regardless of the existence of the silent period." + Thus. when ouly iucoimplete data are available. only. bursts with slopes significautly different frou —] can be helpful iu decidiug whether a silent period exists.," Thus, when only incomplete data are available, only bursts with slopes significantly different from $-1$ can be helpful in deciding whether a silent period exists." + A corollary of the above tests comes from the observations of flares in the racio lighteurves., A corollary of the above tests comes from the observations of flares in the radio lightcurves. + In fact. these flares are expected only from afterglow sources with radii smaller than 2. (Coodiuau," In fact, these flares are expected only from afterglow sources with radii smaller than $R_c$ (Goodman" +where the boost factor {2 varies between 100 and 5000 (depending on the particle physics model).,where the boost factor $B$ varies between $100$ and $5000$ (depending on the particle physics model). +" The corresponding WIMP mass is taken from the models in ? described above and ranges from 100 GeV-4 TeV. A key question for DS is the final mass, as the DS accretes more and more material."," The corresponding WIMP mass is taken from the models in \citet{DMinterpdata} described above and ranges from $100$ $4$ TeV. A key question for DS is the final mass, as the DS accretes more and more material." +" As long as there is a reservoir of DM to heat the DS, the star continues to grow."," As long as there is a reservoir of DM to heat the DS, the star continues to grow." +" In the original work of ?., the assumption was made that the initial DM inside the DS annihilates away in ~500.000 years for a spherical DM halo; here theDS grow to ~1000.V.."," In the original work of \citet{DSnl}, the assumption was made that the initial DM inside the DS annihilates away in $\sim 500,000$ years for a spherical DM halo; here theDS grow to $\sim 1000 \msun$." +" In later work of ?., this assumption was questioned due to the fact that DM haloes are instead triaxial, so that a variety of DM orbits can keep the central DM density higher for longer periods of time and the DS can grow supermassive >10?."," In later work of \citet{SMDS}, this assumption was questioned due to the fact that DM haloes are instead triaxial, so that a variety of DM orbits can keep the central DM density higher for longer periods of time and the DS can grow supermassive $>10^5 \msun$." + In reality dark stars will form in a variety of dark matter environments and will grow to a variety of masses., In reality dark stars will form in a variety of dark matter environments and will grow to a variety of masses. +" For the purpose of illustrating how DS vary due to differences in the halo concentration parameter and also due to enhanced annihilation rates, we will restrict ourselves to the first option for adiabatie contraction. in which the DM originally in the star (due to adiabatic contraction) is the only DM available to the DS: i.c. the DS can grow to ~10003.."," For the purpose of illustrating how DS vary due to differences in the halo concentration parameter and also due to enhanced annihilation rates, we will restrict ourselves to the first option for adiabatic contraction, in which the DM originally in the star (due to adiabatic contraction) is the only DM available to the DS; i.e. the DS can grow to $\sim 1000 \msun$." +" In addition to this simple adiabatic contraction, we will also consider the effect of captured DM on the first stars (Iocco 2008; Freese, Spolyar, and Aguirre 2008)."," In addition to this simple adiabatic contraction, we will also consider the effect of captured DM on the first stars (Iocco 2008; Freese, Spolyar, and Aguirre 2008)." +" In this case, DM passing through the first stars can scatter off the baryons multiple times, lose energy, and become bound to the star (direct detection experiments are based on the same physics: scattering of DM particles off of nuclei)."," In this case, DM passing through the first stars can scatter off the baryons multiple times, lose energy, and become bound to the star (direct detection experiments are based on the same physics: scattering of DM particles off of nuclei)." +" Subsequently, the star builds up a reservoir made up of captured DM, which can power stars."," Subsequently, the star builds up a reservoir made up of captured DM, which can power stars." + In the 'minimal capture case; DM heating from captured DM and fusion powers the star in equal measure once it reaches the main sequence.," In the 'minimal capture case,' DM heating from captured DM and fusion powers the star in equal measure once it reaches the main sequence." + In section 2. we describe the elements necessary to study the stellar structure of the DS., In section \ref{sec:setup} we describe the elements necessary to study the stellar structure of the DS. + In Section ?? we present results for the influence of varying the concentration parameter and the boost factor on the formation and evolution of Dark Stars and their properties., In Section \ref{sec:results} we present results for the influence of varying the concentration parameter and the boost factor on the formation and evolution of Dark Stars and their properties. + We summarize in Section 4.., We summarize in Section \ref{sec:summary}. . +panels A and D in Figure 1..,panels A and B in Figure \ref{fig:ISM:lightcurves}. + Note that since Sari et al. (, Note that since Sari et al. ( +L998) did not discuss 16 cooling. there is no related segment in their e=0 light curves.w,"1998) did not discuss IC cooling, there is no related segment in their $\epsilon=0$ light curves.," +"ind. (he orders of the crossing times are (A) ty«£y,lu,\nu_{cm}$; (B) $t_{a}t_{c}$ ); (B) $F_{\nu}\propto +t^{(7-5\epsilon)/2(2-\epsilon)}\nu^{5/2}$ $tt_{m}$ ); (C) $F_{\nu}\propto +t^{(7-5\epsilon)/2(2-\epsilon)}\nu^{5/2}$ $tt_{m}$ ); (D) $F_{\nu}\propto +t^{(7-5\epsilon)/2(2-\epsilon)}\nu^{5/2}$ $tt_{m}$ )." +The light curves in the stellar wind case are illustrated in Figure 3.., The light curves in the stellar wind case are illustrated in Figure \ref{fig:wind:lightcurves}. +" The crossing; tme /. in cases C and D occurs very early al low observing frequency. while /,, in case D occurs very late."," The crossing time $t_{c}$ in cases C and D occurs very early at low observing frequency, while $t_{m}$ in case D occurs very late." + We neglect these crossing (nes in {his figure., We neglect these crossing times in this figure. + The radiation efficiency has a significant effect on the light curves in the wind case., The radiation efficiency has a significant effect on the light curves in the wind case. +" The flux density in the optical/infrared light curve decays initially with /(bo072202404, rather (han /Lil in the adiabatie case. which is shown in case A. For the N-rav alterglow (he crossing time /,, when Che twpical frequency v,, crosses the observing Irequency is much earlier.B the lightB curve behaves as ¢P?E>2(007241/202OD0«4-5063 dune. the whole fast-cooling. phase. which is more consistent with observations than (the adiabatic light. curve (Berger. ]vulkarni. Frail 2003)."," The flux density in the optical/infrared light curve decays initially with $t^{-(1+\epsilon)/2(2-\epsilon)}\sim t^{-0.4}$, rather than $t^{-1/4}$ in the adiabatic case, which is shown in case A. For the X-ray afterglow the crossing time $t_{m}$ when the typical frequency $\nu_{m}$ crosses the observing frequency is much earlier, the light curve behaves as $t^{-[3p-2-(p-2)\epsilon]/2(2-\epsilon)}\sim t^{-1.36}$ during the whole fast-cooling phase, which is more consistent with observations than the adiabatic light curve (Berger, Kulkarni, Frail 2003)." + The light curve at high. frequency. flattens when the alterglow transits to the slow-cooling phase., The light curve at high frequency flattens when the afterglow transits to the slow-cooling phase. +" Dy (he same wav as in the ISM case. [rom equation (54)) for Y aud adopting =2. the change of the temporal index aroundf,,,,Hag is Aa=(p—2)/(1—p) in the wind case."," By the same way as in the ISM case, from equation \ref{eqn:sc:spectrum}) ) for $Y$ and adopting $k=2$, the change of the temporal index around $t_{cm}$ is $\Delta\alpha=(p-2)/(4-p)$ in the wind case." + Since Chevalier Li (2000) did not include IC cooling. there is no relevant [Iattening segment in their e=0 lighteurves.," Since Chevalier Li (2000) did not include IC cooling, there is no relevant flattening segment in their $\epsilon=0$ lightcurves." + Although the llattening of the optical/X-rav lightcurve around {ων predicted in (he inverse Compton dominated cooling regime in the stellar wind case is more obvious than in theISAT case. the change of the temporaldecaving index is only Aa~0.1 lor the formercase.," Although the flattening of the optical/X-ray lightcurve around $t_{cm}$ predicted in the inverse Compton dominated cooling regime in the stellar wind case is more obvious than in theISM case, the change of the temporaldecaying index is only $\Delta\alpha\sim 0.1$ for the formercase." + The detailed theoretical optical light curves taking into account the equal arrival time surface effect. ancl (he large error bars in X-ray afterglow observations prevent us [rom the identifications of such flattening., The detailed theoretical optical light curves taking into account the equal arrival time surface effect and the large error bars in X-ray afterglow observations prevent us from the identifications of such flattening. +medium forms radio loES ALL hot spots’.,medium forms radio lobes and `hot spots'. + Of special interest are tjo lost powerful ACNsS where sLocks Ceur accelerate particles to energies well above a LeV via the first-order Ferni luec.iuis., Of special interest are the most powerful AGNs where shocks can accelerate particles to energies well above an EeV via the first-order Fermi mechanism. +" These sources lay ο responsible for the dux of UIIECTs up to he GZK απο A nearby specially OWExf] sorwee may be able to reach energies vast the cutoff,"," These sources may be responsible for the flux of UHECRs up to the GZK \cite{RB93} + A nearby specially powerful source may be able to reach energies past the cutoff." + However. extreuely ower] ACNS with radio lobes aux hot spots are rare and far apart.," However, extremely powerful AGNs with radio lobes and hot spots are rare and far apart." +" The closest kikwh object is M""NT in the Vireo chster (~ Ls Mpc away) and could ]0 a lnain source of UMECRs.", The closest known object is M87 in the Virgo cluster $\sim$ 18 Mpc away) and could be a main source of UHECRs. + Although a sinele nearby source with cspeciav hare spectra may fit the spectrum for a eiven streneth and structuirc oftjo inter'ealactic 1iagneic ficld7 it is unlikely to match the observed arriva (irectio1 distribution., Although a single nearby source with especially hard spectra may fit the spectrum for a given strength and structure of the intergalactic magnetic \cite{BO99} it is unlikely to match the observed arrival direction distribution. + I AIST is the primary source of VITECRs a couceutratio1 of events iu the direction of ALS? or the Vireo cluster should be seen in arrival cdi‘ectious., If M87 is the primary source of UHECRs a concentration of events in the direction of M87 or the Virgo cluster should be seen in arrival directions. + No suc1 hot spot is observedspot in Table 13., No such hot spot is observed in Table 1). + The nest known jicnrby source ator MIST is NGC315 which is already too far at a distiuice of ~ SO AIpe., The next known nearby source after M87 is NGC315 which is already too far at a distance of $\sim $ 80 Mpc. + Any unknown source between AIST and NCC315 would likely coutribute a seco hot spot. not au isotropic distribution.," Any unknown source between M87 and NGC315 would likely contribute a second hot spot, not an isotropic distribution." + The very disiit radio lobes will coutribute a GZIN cut spectiuu which is not observed., The very distant radio lobes will contribute a GZK cut spectrum which is not observed. + The lack of a clear hot spot in the direction of M87 has eucouraged t1C idea that a strong Galactic maguetic wind may exist that could help isotropiZe he arrival directions of UIIECTs., The lack of a clear hot spot in the direction of M87 has encouraged the idea that a strong Galactic magnetic wind may exist that could help isotropize the arrival directions of UHECRs. + A Galactic wind with a strongly maguctized azimuthal component (GalactieWind in Table 1) can siguificantly alter t1C oaths of UIIEC'Rs such that the observed arrival direcions of events above 20 eV would trace back to the North Galactic Pole which is close to the Vireo where ALS? resides., A Galactic wind with a strongly magnetized azimuthal \cite{ABMS99} $Galactic Wind$ in Table 1) can significantly alter the paths of UHECRs such that the observed arrival directions of events above $^{20}$ eV would trace back to the North Galactic Pole which is close to the Virgo where M87 resides. + If our Galaxy has such a wind is vet to be deteruined., If our Galaxy has such a wind is yet to be determined. + T1ο xoposed wind would focus most observed events ia) 1ο northern Calactic role aud reider point source identification fruitless:*! Future observatious of UIIECTRs frou the Southern Uemisphere bx the Souther1 Auger Observatory will provide ]xecious data ou previously uuobserved outs of the sky and help distinguish pausible proposals for the effect of local uaenetic fields on arriva directions., The proposed wind would focus most observed events into the northern Galactic pole and render point source identification \cite{BLS00} Future observations of UHECRs from the Southern Hemisphere by the Southern Auger Observatory will provide precious data on previously unobserved parts of the sky and help distinguish plausible proposals for the effect of local magnetic fields on arrival directions. + FiIl «kv coverage is a key discriminator of such proposals., Full sky coverage is a key discriminator of such proposals. +Regions: The powerful cugines that eive rise to the observe jets and rack| lobes are located iu the ceutral regious o active ealaxies ac are powered bv the accretioi of matter outo supermassive black holes., The powerful engines that give rise to the observed jets and radio lobes are located in the central regions of active galaxies and are powered by the accretion of matter onto supermassive black holes. + It is reasonable to consider the central cugines thoiiselves as the likely Tn principle. the nuclei of eeneric active galaxies (not only the ones with radio lobes) can accelerate articles via a unipolar inductor not uulike the one operating iu pulsars.," It is reasonable to consider the central engines themselves as the likely \cite{T86} In principle, the nuclei of generic active galaxies (not only the ones with radio lobes) can accelerate particles via a unipolar inductor not unlike the one operating in pulsars." + Iu the case of ACNs. the magnetic field may be provided by the iufalliug mater and the spinning black hole horizon provides the imperfect conductor for he unipolar induction.," In the case of AGNs, the magnetic field may be provided by the infalling matter and the spinning black hole horizon provides the imperfect conductor for the unipolar induction." +"5, 7, and 10 K, and a cosmic ray ionization rate of 5x10717 s71,","5, 7, and 10 K, and a cosmic ray ionization rate of $5\times10^{-17}$ $^{-1}$." +" The elemental rratio in each model is generally assumed to be 1/400, although the effects of using other values were also investigated."," The elemental ratio in each model is generally assumed to be 1/400, although the effects of using other values were also investigated." +" A key parameter is the branching ratio for the dissociative recombination ofNoH?:: We consideredvalues for f=0.0, 0.02, and 0.05, based on the experimental results of Molek et ((2007)."," A key parameter is the branching ratio for the dissociative recombination of: We consideredvalues for $f = 0.0$, 0.02, and 0.05, based on the experimental results of Molek et (2007)." +" We use elemental abundances for C, O, and N of 140, 290, and 80 parts per million respectively, relative to hydrogen (Savage Sembach 1996), and assume complete depletion of metals."," We use elemental abundances for C, O, and N of 140, 290, and 80 parts per million respectively, relative to hydrogen (Savage Sembach 1996), and assume complete depletion of metals." +" All the carbon is initially in the form of CO, and the remaining oxygen is atomic."," All the carbon is initially in the form of CO, and the remaining oxygen is atomic." +" As before, we assume that CO freezes out onto grains with a sticking coefficient of unity, whereas N and Νο remain in the gas."," As before, we assume that CO freezes out onto grains with a sticking coefficient of unity, whereas N and $_2$ remain in the gas." +" The reason for this selective depletion of CO versus No is controversial, as laboratory experiments reveal that the two species have similar binding energies (Obberg et 22005)."," The reason for this selective depletion of CO versus $_2$ is controversial, as laboratory experiments reveal that the two species have similar binding energies (Öbberg et 2005)." +" Nevertheless, observations of pre-stellar cores show ample evidence for the presence of Na-rich, CO-poor regions toward the centers of these objects (Bergin Tafalla 2007)."," Nevertheless, observations of pre-stellar cores show ample evidence for the presence of $_2$ -rich, CO-poor regions toward the centers of these objects (Bergin Tafalla 2007)." +" Due to their low polarizabilities, atoms should have the lowest binding energies for physisorption to icy dust grains."," Due to their low polarizabilities, atoms should have the lowest binding energies for physisorption to icy dust grains." + Reaction with an H atom forms a simple hydride that can stick more effectively due to hydrogen bonding with the substrate., Reaction with an H atom forms a simple hydride that can stick more effectively due to hydrogen bonding with the substrate. +" Thus, we assume that O atoms are hydrogenated on the grains to form water ice."," Thus, we assume that O atoms are hydrogenated on the grains to form water ice." +" Conversely, recent laboratory experiments indicate a very low efficiency for the reaction of N° and H on ice surfaces (T Hiraoka, private communication), which supports our assumption that N atoms do not stick."," Conversely, recent laboratory experiments indicate a very low efficiency for the reaction of $^0$ and H on ice surfaces (T Hiraoka, private communication), which supports our assumption that N atoms do not stick." + We have adapted our model to track the rratios as successive monolayers (ML) of ammonia ice are accreted., We have adapted our model to track the ratios as successive monolayers (ML) of ammonia ice are accreted. +" ‘typical’ interstellar grain of size 0.1 jum has ~10 surface sites, Aand an abundance relative to hydrogen of ~10~'?."," A `typical' interstellar grain of size 0.1 $\mu$ m has $\sim 10^6$ surface sites, and an abundance relative to hydrogen of $\sim 10^{-12}$." +" Hence, one ML corresponds to total solid phase abundance of 109, and our elemental N abundancea corresponds to a maximum of 80 ML of ice, assuming that all the nitrogen freezes out as NH3 (or ΝΗ2)."," Hence, one ML corresponds to a total solid phase abundance of $10^{-6}$, and our elemental N abundance corresponds to a maximum of 80 ML of ice, assuming that all the nitrogen freezes out as $_3$ (or $_2$." +". In fact, a large fraction of the nitrogen remains in the gas phase in the form of N°, and we typically find that we form ~30 ML of ammonia ice."," In fact, a large fraction of the nitrogen remains in the gas phase in the form of $^0$, and we typically find that we form $\sim 30$ ML of ammonia ice." +" We began by investigating the importance of the branching ratio, f', in the recombination of@."," We began by investigating the importance of the branching ratio, $f$, in the recombination of." +". We found only very small differences in the results of models with f equal to 5, 2, and 0 per cent, and conclude that, as long as f€0.05, the presence of channel (4)) does not significantly affect the cchemistry."," We found only very small differences in the results of models with $f$ equal to 5, 2, and 0 per cent, and conclude that, as long as $f \leq 0.05$, the presence of channel \ref{BR2}) ) does not significantly affect the chemistry." +" We then varied the elemental nitrogen isotope ratio, using values for oof 800, 400, and 100."," We then varied the elemental nitrogen isotope ratio, using values for of 800, 400, and 100." +" In every case, the eenhancements are identical, relative to the underlying ratio."," In every case, the enhancements are identical, relative to the underlying ratio." +" Henceforth, we discuss models with f=0.02 and 400.."," Henceforth, we discuss models with $f = 0.02$ and $\nfo/\nf = 400$ ." +" Figure 2 shows the abundances of the three main repositories of nitrogen — gaseous N° and No, and solid NHs — as a function of time, assuming that all of the nitrogen is initially present as No.."," Figure \ref{fig:NN2} shows the abundances of the three main repositories of nitrogen – gaseous $^0$ and $_2$, and solid $_3$ – as a function of time, assuming that all of the nitrogen is initially present as $_2$." + The overall nitrogen chemistry is the same at 10 K and 7 K: No is degraded on a time-scale ~ Myr., The overall nitrogen chemistry is the same at 10 K and 7 K: $_2$ is degraded on a time-scale $\sim$ Myr. +" At late times just over half of the total nitrogen is in the gas phase as atoms, and just under half has frozen out as ammonia ice."," At late times just over half of the total nitrogen is in the gas phase as atoms, and just under half has frozen out as ammonia ice." +" At 5 K, however, very little ice is formed, due to the endo-ergocity of the reaction We have assumed an activation energy barrier of 85 K for this reaction, based on the value in the UMIST reactionrate database (Woodall et 22007)."," At 5 K, however, very little ice is formed, due to the endo-ergocity of the reaction We have assumed an activation energy barrier of 85 K for this reaction, based on the value in the UMIST reactionrate database (Woodall et 2007)." +" At 5 K, the reaction becomes so slow that radiative recombination becomes the dominant loss route for N* ions, and only small amounts of gas-phase NH» and NH3 are produced."," At 5 K, the reaction becomes so slow that radiative recombination becomes the dominant loss route for $^+$ ions, and only small amounts of gas-phase $_2$ and $_3$ are produced." +" In effect, the barrier for reaction (5)) sets a limit on the nitrogen chemistry in that, as the temperature drops, it eventually becomes too cold to produce ammonia."," In effect, the barrier for reaction \ref{eqn:n+h2}) ) sets a limit on the nitrogen chemistry in that, as the temperature drops, it eventually becomes too cold to produce ammonia." + In extremely cold cores the chemistry simply transforms the initial gas-phase N» into gas-phase N?.., In extremely cold cores the chemistry simply transforms the initial gas-phase $_2$ into gas-phase $^0$. +" In the following, we therefore look at the fractionation in 7 K and 10 K gas."," In the following, we therefore look at the fractionation in 7 K and 10 K gas." + Figure 3aa shows the fractionation in the most important molecules., Figure \ref{fig:tfrac}a a shows the fractionation in the most important molecules. +" The results for 10 K gas are similar to those shown in Paper I, whereas at 7 significantly larger peak rratios are found in gas-phaseK NHs and N».."," The results for 10 K gas are similar to those shown in Paper I, whereas at 7 K significantly larger peak ratios are found in gas-phase $_3$ and $_2$." +" At early times, the ammonia formed at 7 K is actuallydepleted in@."," At early times, the gas-phase ammonia formed at 7 K is actually in." +. This is due to the reduced rate of reaction (5)) which leads to a much larger Nt abundance than at 10K., This is due to the reduced rate of reaction \ref{eqn:n+h2}) ) which leads to a much larger $^+$ abundance than at 10. +. These N* ions undergo isotope-exchange reactions with Nz (Freysinger et 11994): where AF3=28.3 K (Terzieva Herbst 2000)., These $^+$ ions undergo isotope-exchange reactions with $_2$ (Freysinger et 1994): where $\Delta E_3 = 28.3$ K (Terzieva Herbst 2000). +" This reaction shuffles bback into Ne, reducing the 15N.-fractionation in N* and thus ammonia."," This reaction shuffles back into $_2$, reducing the -fractionation in $^+$ and thus ammonia." +" At late times, this effect is still suppressing the N* fractionation relative to No, but the enormous !°N--enhancements in No ensures that N* and NHs are more fractionated than at 10 K."," At late times, this effect is still suppressing the $^+$ fractionation relative to $_2$, but the enormous -enhancements in $_2$ ensures that $^+$ and $_3$ are more fractionated than at 10 ." +". In terms of the bulk rratio in the ammonia ice, both the 10 K and 7 K models predict similar enhancements of zz 1.8.."," In terms of the bulk ratio in the ammonia ice, both the 10 K and 7 K models predict similar enhancements of $\approx 1.8$ ." +" However, as discussed earlier, the time evolution of the isotope ratios will be preserved in the layered structure of the ices."," However, as discussed earlier, the time evolution of the isotope ratios will be preserved in the layered structure of the ices." + Even though the overall icy, Even though the overall icy + (Phillipsetal.1999). (Kasen&Woosley2007: (Mazzalietal.2007)... 2003).. (Hillebrandt&Niemeyer2000.andreferences (Nomotoetal.1984;Woosley1956). (Paczynski2006).. (Lesaffreetal.," \citep{phi99} \citep{kw07,woo07} + \citep{maz07}. \citep{tbt03}. \citep[][and references therein]{hn00}. \citep{nom84,ww86}. \citep{pac72,bru73,ca75,ibe78a,ibe78b,ibe82,bw90,moc96,ste99,bk01,les05,sw06}. \citep{les05}." +2005).. ~(5-6)«I0?K ~10°s electron captures on “Na (Piro&Bildsten2007).. and the convective Urea process will cease.," $\approx(5-6)\times10^8\ {\rm K}$ $\sim10^5\ {\rm s}$ electron captures on $^{23}$ Na \citep{pb07}, and the convective Urca process will cease." + During the last ~10°s any compositional gradients are mixed homogeneously by subsequent convection., During the last $\sim10^5\ {\rm s}$ any compositional gradients are mixed homogeneously by subsequent convection. + An additional place where simmering is important 1s for understanding the conditions within the WD immediately prior to the explosion (García-Senz&Woosley1995;Hóflich 2004).," An additional place where simmering is important is for understanding the conditions within the WD immediately prior to the explosion \citep{gw95,hs02,woo04,ww04}." +. The properties of the temperature fluctuations present in the convection set the size and distribution of the ignition points. which are crucial for determining the success of the subsequent burning wave (seeRópkeetal.2006.andrefer-ences therein)..," The properties of the temperature fluctuations present in the convection set the size and distribution of the ignition points, which are crucial for determining the success of the subsequent burning wave \citep[see][and references therein]{rop06}." + The interaction of convection with rotation sets the morphology of convective motions (Kuhlen2006) as well as the overall rotation profile of the WD (Piro 2008)., The interaction of convection with rotation sets the morphology of convective motions \citep{kwg06} as well as the overall rotation profile of the WD \citep{pir08}. +. The last way simmering has gained attention is 1n its ability to enhance the neutron abundance in the WD core (Piro&Bildsten2007:Chamulaketal.2007).," The last way simmering has gained attention is in its ability to enhance the neutron abundance in the WD core \citep{pb07,cha07}." +". This happens primarily via the reaction chain. ""Ctp.5) Νις1)! C. where the protons are leftover from ""C burning."," This happens primarily via the reaction chain $^{12}$ $(p,\gamma)^{13}$ $(e^-,\nu_e)^{13}$ C, where the protons are leftover from $^{12}$ C burning." + Depending on the amount of carbon that is consumed before burning becomes dynamical. as well as the density at which it takes place. this neutronization enhancement could very well be large enough to mask any trend expected with metallicity in environments that have roughly sub-solar metallicity.," Depending on the amount of carbon that is consumed before burning becomes dynamical, as well as the density at which it takes place, this neutronization enhancement could very well be large enough to mask any trend expected with metallicity in environments that have roughly sub-solar metallicity." + In this present work we focus on the general properties of the simmering convection. with the aim of identifying characteristics that may introduce diversity to the SN la progenitors.," In this present work we focus on the general properties of the simmering convection, with the aim of identifying characteristics that may introduce diversity to the SN Ia progenitors." + We begin in 82. by presenting the main features of our models., We begin in \ref{sec:models} by presenting the main features of our models. + We illustrate how time-dependent convection in the simmering phase differs from the familiar case of steady-state convection., We illustrate how time-dependent convection in the simmering phase differs from the familiar case of steady-state convection. + In this new picture. the convective flux decreases outside the central heating zone due to both the heating of new material as the convective region grows and the inability to transfer significant energy to the conductive exterior.," In this new picture, the convective flux decreases outside the central heating zone due to both the heating of new material as the convective region grows and the inability to transfer significant energy to the conductive exterior." + In $3.) we explore the location ofthe topof the convective zone., In \ref{sec:boundary} we explore the location ofthe topof the convective zone. + We point out that degeneracyeffects enhance the response of the boundary location to changes in composition., We point out that degeneracyeffects enhance the response of the boundary location to changes in composition. + We conclude with a summary of our results and, We conclude with a summary of our results and +responsible for the impression that old clusters have a steep gradient al Re;< 10-12 kpe.,responsible for the impression that old clusters have a steep gradient at $_{\rm G}<$ 10-12 kpc. + Once NGC 6791 is removed [rom the selection of old clusters. Fig.," Once NGC 6791 is removed from the selection of old clusters, Fig." + 9 illustrates that (his population has a shallower eradient than usually invoked., 9 illustrates that this population has a shallower gradient than usually invoked. + It is worth noting that cluster Collinder 261. with [Fe/II]|-0.13 (Sestito et al.," It is worth noting that cluster Collinder 261, with [Fe/H]=0.13 (Sestito et al." + 2008). could also be an intruder.," 2008), could also be an intruder." + However. its iron abundance is controversial (Friel et al.," However, its iron abundance is controversial (Friel et al." + 2003 and. Carretta et al., 2003 and Carretta et al. + 2005 found. |Fe/11] respectively -0.02 and -0.03 dex: we adopt the latter value in Figure 9)., 2005 found [Fe/H] respectively -0.02 and -0.03 dex; we adopt the latter value in Figure 9). + The clichotomy between old ancl voung clusters is (hen becoming more apparent. and suggests that the gradient slope change noted at Re10 kpe by several authors could result [rom the superposition of two different gradients for voung ancl old clusters.," The dichotomy between old and young clusters is then becoming more apparent, and suggests that the gradient slope change noted at $_{\rm G}\sim$ 10 kpc by several authors could result from the superposition of two different gradients for young and old clusters." + The distribution of intermediate age clusters shows (expectedlv) a combination of the two behaviors., The distribution of intermediate age clusters shows (expectedly) a combination of the two behaviors. + We have not tried (to make a fit to quantily the gradients within the groups of clusters: the iumnber of objects in each group is small. aud some of them are still being affected by large errors. making it diffieult to choose the correct values of metallicities ancl ealactocentrie distances.," We have not tried to make a fit to quantify the gradients within the groups of clusters: the number of objects in each group is small, and some of them are still being affected by large errors, making it difficult to choose the correct values of metallicities and galactocentric distances." + Moreover. due to the lack of accurate information on the possible orbits of each cluster. it would be difficult not to make an arbitrary. selection of which Clusters should be included or not in the old sample.," Moreover, due to the lack of accurate information on the possible orbits of each cluster, it would be difficult not to make an arbitrary selection of which clusters should be included or not in the old sample." + llowever. for illustrative purpose. we plotted different gradients on Figure 9 to see how PN 5gradients are compatible with the above description.," However, for illustrative purpose, we plotted different gradients on Figure 9 to see how PN gradients are compatible with the above description." + The oxvgenA5 5gradient derived for PNe with progenitor vounger than 1 Gyr is -0.035 dex +t., The oxygen gradient derived for PNe with progenitor younger than $\sim$ 1 Gyr is -0.035 dex $^{-1}$. +" The old PN population. with progenitors older than 5 (ντ, have flat metallicity gradient (-0.011 dex +)."," The old PN population, with progenitors older than $\sim$ 5 Gyr, have flat metallicity gradient (-0.011 dex $^{-1}$ )." + Allowing5 for the factor 2 that has been evoked when convertingὃ oxvgenUSNS to iron abundances. we estimate an iron gradient of the order of -0.07 dex ! [or the voung population. and a slope of ~-0.02 dex ! [or the old population.," Allowing for the factor 2 that has been evoked when converting oxygen to iron abundances, we estimate an iron gradient of the order of -0.07 dex $^{-1}$ for the young population, and a slope of $\sim$ -0.02 dex $^{-1}$ for the old population." + These are plotted as continuous lines on Fig., These are plotted as continuous lines on Fig. + 9., 9. + Concerning the voung population. we note good consistency between (he gradients," Concerning the young population, we note good consistency between the gradients" +The vector harmonic decomposition of the proper motion field delined by Eq. (5)),The vector harmonic decomposition of the proper motion field defined by Eq. \ref{2a}) ) + can be given now in the following form(34) which elucidates that the proper motion field caused by (he secular aberration is represented bv the three low-order electric dipole harmonics of first order (η=1) ancl it is independent of the magnetic-tvpe harmonies.," can be given now in the following form, which elucidates that the proper motion field caused by the secular aberration is represented by the three low-order electric dipole harmonics of first order $n=1$ ) and it is independent of the magnetic-type harmonics." + This svstematic vector field affects all observable directions and can be extracted from the randomly distributed vector field of stellar proper motions., This systematic vector field affects all observable directions and can be extracted from the randomly distributed vector field of stellar proper motions. + llowever. (his subtle effect is submerged in the pattern of the physical proper motion field of ealactie stars. which is roughly three orders of magnitude larger than (he secular aberration effect (Olling&Dehnen2003).," However, this subtle effect is submerged in the pattern of the physical proper motion field of galactic stars, which is roughly three orders of magnitude larger than the secular aberration effect \citep{olde}." +. For quasars. because of their negligible physical proper motions. the svstematic pattern of secular aberration stands out clearly. and is a dominant component of the quasar proper motions.," For quasars, because of their negligible physical proper motions, the systematic pattern of secular aberration stands out clearly, and is a dominant component of the quasar proper motions." + Fig., Fig. + d shows the sky. distribution of the proper motion pattern caused by the acceleration of (he solar svstem barvcenter., \ref{pmfield.fig} shows the sky distribution of the proper motion pattern caused by the acceleration of the solar system barycenter. + SIM PlanetQuest is a NASA Origins project dedicated mostly to the search of planets around nearby stars by astrometric interferometry., SIM PlanetQuest is a NASA Origins project dedicated mostly to the search of planets around nearby stars by astrometric interferometry. + As a necessary condition of achieving this eoal. SIMI will create a global astrometric relerence frame over all (he skv to an unprecedented accuracy of 4-5 in position. based on wide-angle measurements of about 1300 reference erid stars.," As a necessary condition of achieving this goal, SIM will create a global astrometric reference frame over all the sky to an unprecedented accuracy of 4-5 in position, based on wide-angle measurements of about 1300 reference grid stars." + His crucial lor the astrometric coordinate grid to include a sufficient number of oplically bright quasars. which constrain (he parallax solution of the astrophysical targets in such a wav (hat the large-scale random distortions of the parallax error distribution are drastically reduced (Malsirov&Milman2005).," It is crucial for the astrometric coordinate grid to include a sufficient number of optically bright quasars, which constrain the parallax solution of the astrophysical targets in such a way that the large-scale random distortions of the parallax error distribution are drastically reduced \citep{mami}." +. The same grid quasars can be directly used to determine the secular acceleration of the Sun from measuring the secular aberration effect as explained in the previous sections of (liis paper., The same grid quasars can be directly used to determine the secular acceleration of the Sun from measuring the secular aberration effect as explained in the previous sections of this paper. + To estimate (he measurement accuracy of the secular aberration effect lor SIM DPlIanetQuest we make use of full-scale numerical simulations of SIM observations and the astrometric grid reduction model (Alakarov&Milman2005)., To estimate the measurement accuracy of the secular aberration effect for SIM PlanetQuest we make use of full-scale numerical simulations of SIM observations and the astrometric grid reduction model \citep{mami}. +. The simulation model is rather sophisticated and realistic in that it includes the SIM. instrument model ancl incorporates the specific technology of SIM astrometric measurements., The simulation model is rather sophisticated and realistic in that it includes the SIM instrument model and incorporates the specific technology of SIM astrometric measurements. + The grid reduction model has about 160.000," The grid reduction model has about 160,000" +central 5 h.+ kpe ave found within the 3D central region in ealaxv-sized haloes at 2=0 (for groups this decreases to )).,central 5 $h^{-1}$ kpc are found within the 3D central region in galaxy-sized haloes at $z = 0$ (for groups this decreases to $\sim $ ). + At:=1 this fraction isΕλ... dropping to ~ in eroup-sized haloes (see Table 2)).," At $z = 1$ this fraction is, dropping to $\sim$ in group-sized haloes (see Table \ref{3d}) )." + All of the satellites within the 3D central region are ‘orphan’ galaxies (see Section 3.3))., All of the satellites within the 3D central region are `orphan' galaxies (see Section \ref{discussion}) ). + We use the CLASS survey as the primary observational data., We use the CLASS survey as the primary observational data. + This survey discovered. 22 new gravitational lenses in the radio (2: 7))., This survey discovered 22 new gravitational lenses in the radio \citealt{bib:Browne03}; \citealt{bib:Myers03}) ). + ακο 6 lenses from this survey to study the amount of substructure in lensing galaxies., \citet{bib:Kochanek04} used 6 lenses from this survey to study the amount of substructure in lensing galaxies. + In this work. we have used the whole survey to gather statistics: 5 of the 22 CLASS lenses have luminous satcllite galaxies within of the main lensing galaxy: BIGOS|656. B2045|265. 00414|0534. DI127|385 and D1359|154.," In this work, we have used the whole survey to gather statistics; 5 of the 22 CLASS lenses have luminous satellite galaxies within of the main lensing galaxy: B1608+656, B2045+265, 0414+0534, B1127+385 and B1359+154." +" For B1608]656. the main lensing galaxy (1) is at redshift, z;:=0.6363."," For B1608+656, the main lensing galaxy (G1) is at redshift $z_l=0.63$." + In addition. there is a faint galaxy. G2. about 0.73 aresee away. which is 1.5 magnitudes fainter than GI both in the LIST FIGOW and ESIAW. (?)) filters.," In addition, there is a faint galaxy, G2, about 0.73 arcsec away, which is 1.8 magnitudes fainter than G1 both in the HST F160W and F814W \citealt{bib:Koopmans03}) ) filters." + Phere are also four groups along the line of sight. including one at the redshift of the lensing galaxy Gl (2)).," There are also four groups along the line of sight, including one at the redshift of the lensing galaxy G1 \citealt{bib:Fassnacht06}) )." + Lf G2 is at the same redshift as G1. then the projected: separation iskpe.," If G2 is at the same redshift as G1, then the projected separation is." +. For B2045|265. 7? found a galaxy. G2. about 0.66 arcsec away [rom the main lensing galaxy Gl (at reclshilt ).S67). which is between 3.6 and 4.5 magnitudes fainter than he main lensing galaxy Gl in FSI4W and E160W. The ποιοιτίς redshift of 5 is consistent with that of Gil. although it is also consistent with being at recshilt ~ 45.," For B2045+265, \cite{bib:McKean07} found a galaxy, G2, about 0.66 arcsec away from the main lensing galaxy G1 (at redshift 0.867), which is between 3.6 and 4.5 magnitudes fainter than the main lensing galaxy G1 in F814W and F160W. The photometric redshift of G2 is consistent with that of G1, although it is also consistent with being at redshift $\sim 4-5$." +10 he redshifts of GI and G2 are the same. then the projected separation is 3.5 fh.! kpe.," If the redshifts of G1 and G2 are the same, then the projected separation is 3.5 $ h^{-1}$ kpc." + For the quadrupole lens 0041410534. 2 found a aunter companion that is about 1 aresec away from the main ensing galaxy (which is at redshift 0.96).," For the quadrupole lens 0414+0534, \cite{bib:Schechter93} found a fainter companion that is about 1 arcsec away from the main lensing galaxy (which is at redshift 0.96)." + The object “Xo is about 2.62.44 magnitudes fainter than the main lensing ealaxy in the HST images of FIGOW and PSI4W. Lf the object N. is at redshift 0.96. then the projected separation is 5.5 h1 kpe.," The object `X' is about $2.6 - 2.44$ magnitudes fainter than the main lensing galaxy in the HST images of F160W and F814W. If the object `X' is at redshift 0.96, then the projected separation is 5.5 $ h^{-1}$ kpc." + For D1127|385. there are also two lensing galaxies. G1 and G2 (?)).," For B1127+385, there are also two lensing galaxies, G1 and G2 \citealt{bib:Koopmans99}) )." + The fainter one. G2. is about. 1. magnitude fainter than Gl in both ESI4 (7=22.5 for G1) and E555 (V—244 for G1).," The fainter one, G2, is about 1 magnitude fainter than G1 in both F814 $I=22.5$ for G1) and F555 $V=24.4$ for G1)." + The separation between these two ealaxies is about 0.6 arcsec., The separation between these two galaxies is about 0.6 arcsec. + If the lensing galaxys recshift is between 0.5 and 1. then the projected separation is about 2533h * kpe.," If the lensing galaxy's redshift is between 0.5 and 1, then the projected separation is about $2.5 - 3.3$ $ h^{-1}$ kpc." + 131359|154 is a six image svstem. produced by a small eroup of galaxies., B1359+154 is a six image system produced by a small group of galaxies. + Three primary lens galaxies lic on the vertices of a triangle separated by O.7 aresec at z 1 (corresponding to a projected separation of ~ 3.9 h+ κρυο. with magnitudes in £ of 22.68c0.28 ancl 23.69+0.24 and 23.70+0.33 (23).," Three primary lens galaxies lie on the vertices of a triangle separated by 0.7 arcsec at z $\sim 1$ (corresponding to a projected separation of $\sim$ 3.9 $ h^{-1}$ kpc), with magnitudes in $I$ of $22.68\pm 0.28$ and $23.69\pm 0.24$ and $23.70\pm 0.33$ \citealt{bib:Rusin01}) )." + In the left panel of Fig., In the left panel of Fig. + 3. we show the Iuminosities of the observed. lenses. found. by the CLASS survey., \ref{obs} we show the luminosities of the observed lenses found by the CLASS survey. + The patterned histogram shows 16 of the CLASS lenses for which we have redshifts and. I-band magnitudes (taken from the CASTLES website?))., The patterned histogram shows 16 of the CLASS lenses for which we have redshifts and I-band magnitudes (taken from the CASTLES ). + Over-plotted (solid. histogram) are the 4 CLASS lenses which have been shown to host luminous satellites: for DII27|385. its luminosity is unknown due to the uncertain lens redshift.," Over-plotted (solid histogram) are the 4 CLASS lenses which have been shown to host luminous satellites; for B1127+385, its luminosity is unknown due to the uncertain lens redshift." + The right panel of Fig., The right panel of Fig. + 3. shows the redshift distribution of the CLASS lenses., \ref{obs} shows the redshift distribution of the CLASS lenses. + All of the lenses with luminous satellites have redshifts higher than the median. value. of About of the lenses with z z 0.8 have luminous satellites., All of the lenses with luminous satellites have redshifts higher than the median value of About of the lenses with z $>$ 0.8 have luminous satellites. + We caution that the six remaining lenses of he CLASS sample (with unknown redshifts) may be. on average. at higher z. By ignoring these lenses. the redshift distribution may be somewhat skewed.," We caution that the six remaining lenses of the CLASS sample (with unknown redshifts) may be, on average, at higher z. By ignoring these lenses, the redshift distribution may be somewhat skewed." + This could mean that he probability of a high redshift lens hosting a luminous satcllite may not be as high as implied., This could mean that the probability of a high redshift lens hosting a luminous satellite may not be as high as implied. + Fie., Fig. + 4 shows the dilference in magnitude between the vost and satellite galaxy versus the projected: separation of the satellite galaxy. from the host., \ref{deltam} shows the difference in magnitude between the host and satellite galaxy versus the projected separation of the satellite galaxy from the host. + We show a random selection of our group-sized haloes with ‘dark’ substructure (crosses) anc bright substructure (circles) from our 2=1 sample., We show a random selection of our group-sized haloes with `dark' substructure (crosses) and bright substructure (circles) from our $z = 1$ sample. + The 5 CLASS lenses found to have luminous satellite galaxies are plotted with solic circles: for B1127|385. the rorizontal bar shows the range of separations when the lens redshift is varied. from 0.5 to 1.," The 5 CLASS lenses found to have luminous satellite galaxies are plotted with solid circles; for B1127+385, the horizontal bar shows the range of separations when the lens redshift is varied from 0.5 to 1." + Selection ellects may be complicated and have not been taken into account in this study., Selection effects may be complicated and have not been taken into account in this study. + While it will be dillicult to observe satellites with laree magnitude differences at. small separations. we find that there are also few simulated: satellites at very small separations. (," While it will be difficult to observe satellites with large magnitude differences at small separations, we find that there are also few simulated satellites at very small separations. (" +Lhe increase in number with separation is due to the [arger area considered).,The increase in number with separation is due to the larger area considered). + As illustrated with the histograms in Fig., As illustrated with the histograms in Fig. + 4. we find that our sample of host galaxies and their luminous satellites is comparable to the observed ealaxies in the (small) CLASS sample., \ref{deltam} we find that our sample of host galaxies and their luminous satellites is comparable to the observed galaxies in the (small) CLASS sample. + As haloes fall into a larger system. they are exposed to tidal forces ancl are stripped as they orbit. the host system.," As haloes fall into a larger system, they are exposed to tidal forces and are stripped as they orbit the host system." + The extent to which a halo is stripped depends on resolution and the inner density profile of the halo (22)., The extent to which a halo is stripped depends on resolution and the inner density profile of the halo \citealt{bib:Moore96}) ). + The, The +lens model from the previous section in which o?=150 km ! and s*=1005.! kpe. and sources will be placed in single planes in redshift (1.e.. all sources will be assigned identical redshifts).,"lens model from the previous section in which $\sigma_v^\ast = 150$ km $^{-1}$ and $s^\ast = 100h^{-1}$ kpc, and sources will be placed in single planes in redshift (i.e., all sources will be assigned identical redshifts)." +" Figures 2. 3. and 4. then. show the probabilitv. (Νε). (hat a given source wilh redshift z; will be leused bv NV, foreground galaxies. where each gives rise to a shear of 5>0.0025. 5>0.005. and 5>001. respectively (ie.. the minimum shear in (hese figures corresponds to half the baseline value. tlie baseline value. and (ice the baseline value. respectively)."," Figures 2, 3, and 4, then, show the probability, $P(N_L)$, that a given source with redshift $z_s$ will be lensed by $N_L$ foreground galaxies, where each gives rise to a shear of $\gamma > 0.0025$, $\gamma > 0.005$, and $\gamma > 0.01$, respectively (i.e., the minimum shear in these figures corresponds to half the baseline value, the baseline value, and twice the baseline value, respectively)." +" Here PON),=2) is the probability (hat a given source will be lensed by two individual foreground galaxies. each of which lensed the source galaxy. at a level that is comparable to or greater (han the minimum shear value."," Here $P(N_D = 2)$ is the probability that a given source will be lensed by two individual foreground galaxies, each of which lensed the source galaxy at a level that is comparable to or greater than the minimum shear value." + Since the minimun values adopted in Figures 2. 3.2 and 4 are “substantial” values of the galaxv-galaxy lensing shear. the results shown in these figures are conservative estimates of the frequency. of multiple dellections.," Since the minimum values adopted in Figures 2, 3, and 4 are “substantial” values of the galaxy-galaxy lensing shear, the results shown in these figures are conservative estimates of the frequency of multiple deflections." + The line tvpes in Figures 2. 3. and 4 correspond to different values of the cosmological parameters.," The line types in Figures 2, 3, and 4 correspond to different values of the cosmological parameters." + In all cases Lf)=70 km ! ! is adopted., In all cases $H_0 = 70$ km $^{-1}$ $^{-1}$ is adopted. +" Solid lines show results for a flat A-clominated universe with O,,4=0.3 and Q4,=0.7. dashed lines show results lor an open universe wilh μι=0.3 and O49=0.0. and dotted lines show results for an Einstein-de Sitter universe."," Solid lines show results for a flat $\Lambda$ -dominated universe with $\Omega_{m0} = 0.3$ and $\Omega_{\Lambda 0} = 0.7$, dashed lines show results for an open universe with $\Omega_{m0} = 0.3$ and $\Omega_{\Lambda 0} = 0.0$, and dotted lines show results for an Einstein-de Sitter universe." + Figures 2. 3. and 4 demonstrate two fully expected results.," Figures 2, 3, and 4 demonstrate two fully expected results." + First. the frequency οἱ multiple deflections in galaxv-galaxy lensing is a function of the source redshilt: the higher the redshift. the more likely multiple deflections are to occur.," First, the frequency of multiple deflections in galaxy-galaxy lensing is a function of the source redshift: the higher the redshift, the more likely multiple deflections are to occur." + Second. (he frequency οἱ multiple deflections in galaxy-galaxy lensine depends upon (he minimum shear value (hat is adopted: the lower the value of the minimum shear. the more likely that multiple deflections of at least the minimum value will occur.," Second, the frequency of multiple deflections in galaxy-galaxy lensing depends upon the minimum shear value that is adopted: the lower the value of the minimum shear, the more likely that multiple deflections of at least the minimum value will occur." + Figure 2 shows that multiple deflections in which each individual deflection results in a shear ol>0.0025 are highly probable., Figure 2 shows that multiple deflections in which each individual deflection results in a shear of $\gamma > 0.0025$ are highly probable. +" The probability ranges [rom [or sources with ο,=0.75 to for sources wilh ος=2.0.", The probability ranges from for sources with $z_s = 0.75$ to for sources with $z_s = 2.0$. + Similarly. Figure 3 shows that multiple deflections in which each individual deflection results in a shear of 5>0.005 are highly probable.," Similarly, Figure 3 shows that multiple deflections in which each individual deflection results in a shear of $\gamma > 0.005$ are highly probable." +" In this case. the probability ranges from for sources with z,=0.75to [or sources with ος=2.0."," In this case, the probability ranges from for sources with $z_s = 0.75$to for sources with $z_s = 2.0$." + Multiple deflections in which each individual deflection results in a shear of 5>0.01 are relatively rare for sources with 2.<1.0. but the probability of such very large multiple deflections increases to [or sources with 2.=2.0 (Figure 4).," Multiple deflections in which each individual deflection results in a shear of $\gamma > 0.01$ are relatively rare for sources with $z_s \le 1.0$, but the probability of such very large multiple deflections increases to for sources with $z_s = 2.0$ (Figure 4)." + In addition to the frequency of multiple deflections. Figures 2. 3. and 4 make an important point about the role of the cosmological parameters in galaxv-galaxy lensing.," In addition to the frequency of multiple deflections, Figures 2, 3, and 4 make an important point about the role of the cosmological parameters in galaxy-galaxy lensing." + By and large. (he number and magnitude of individual weak lensing delflections is unaffected by the choice of the cosmological parameters.," By and large, the number and magnitude of individual weak lensing deflections is unaffected by the choice of the cosmological parameters." + That is. galaxv-galaxy lensingprimarily provides intormation about the potentials of the lens galaxies. not the cosmology per se (see also BBS).," That is, galaxy-galaxy lensingprimarily provides information about the potentials of the lens galaxies, not the cosmology per se (see also BBS)." +" Therefore. for the remainder of the manuscript a flat. A-dominatecl universe with ll,—το km ! |. Q,,= 0.3. and Q4=0.7 will be adopted."," Therefore, for the remainder of the manuscript a flat $\Lambda$ -dominated universe with $H_0 = 70$ km $^{-1}$ $^{-1}$ , $\Omega_{m0} = 0.3$ , and $\Omega_{\Lambda 0} = 0.7$ will be adopted." +it is clear that once the shock fronts have now passed well bevond the emission. line regions. the contribution of ionising photons produced. by the shocks will decrease rapidly: this is in complete accord with the larger sources having photoionisation dominated emission line regions.,"it is clear that once the shock fronts have now passed well beyond the emission line regions, the contribution of ionising photons produced by the shocks will decrease rapidly; this is in complete accord with the larger sources having photoionisation dominated emission line regions." + The physical extent of the emission. line region of each galaxy along the slit cirection was provided in Table 1.., The physical extent of the emission line region of each galaxy along the slit direction was provided in Table \ref{props}. +" For comparison. the extent of the aligned. optical (rest.frame ultraviolet) emission has also been determined from the LIST observations of Best shorteitebesO7e:; using the HIST. image taken through the filter at à restframe wavelength of about4000... the angular distance over which optical emission was observed at ereater than three times the rms sky. noise level of the image was measured for cach galaxy. and the corresponding ""optical sizes” are given in Table 1.."," For comparison, the extent of the aligned optical (rest–frame ultraviolet) emission has also been determined from the HST observations of Best \\shortcite{bes97c}; using the HST image taken through the filter at a rest–frame wavelength of about, the angular distance over which optical emission was observed at greater than three times the rms sky noise level of the image was measured for each galaxy, and the corresponding `optical sizes' are given in Table \ref{props}." + Phese values can further be compared with these results of Best shorteitebesOSd.. who showed. from nearinfrared. imaging that. underlving the aligned emission. the radio sources are hosted by giant. elliptical galaxies with characteristic radii of typically 10 to kkpe.," These values can further be compared with these results of Best \\shortcite{bes98d}, who showed from near–infrared imaging that, underlying the aligned emission, the radio sources are hosted by giant elliptical galaxies with characteristic radii of typically 10 to kpc." + The extent of the optical aligned emission. does. not exceed kkpe except in three cases: 3C247. 8C265 and 3€368.," The extent of the optical aligned emission does not exceed kpc except in three cases: 3C247, 3C265 and 3C368." +" For 3€368. the LIST ""continuum image is actually dominated. by a combination of line emission. and. the correspondingly luminous nebular continuum emission (see cliscussion in Section 4.5))."," For 3C368, the HST `continuum' image is actually dominated by a combination of line emission and the correspondingly luminous nebular continuum emission (see discussion in Section \ref{contal}) )." + Phe large extent of 3C'2AT is also likely to be predominantly line emission. since it arises from a dilfuse halo of emission exactly tracking that seen in a narrowband. ΟΙ] 37 image hy AleCarthy shortcitemecd5..," The large extent of 3C247 is also likely to be predominantly line emission, since it arises from a diffuse halo of emission exactly tracking that seen in a narrow–band [OII] 3727 image by McCarthy \\shortcite{mcc95}." + With the exception of 3€265 (which. as discussed. in Paper 1. is an unusual source in many ways). it is therefore reasonable to sav that the aligned. continuum emission has an extent of only a couple of eharacteristic radii. and so lies within the body of the host galaxy.," With the exception of 3C265 (which, as discussed in Paper 1, is an unusual source in many ways), it is therefore reasonable to say that the aligned continuum emission has an extent of only a couple of characteristic radii, and so lies within the body of the host galaxy." + The situation with the emission line gas is very dilferent: this has a physical extent which can exceed 100kkpce. with a mean extent of over kkpc.," The situation with the emission line gas is very different: this has a physical extent which can exceed kpc, with a mean extent of over kpc." + The emission line gas clearly extends well bevond he confines of the host galaxy., The emission line gas clearly extends well beyond the confines of the host galaxy. + As was shown in Figure 7.. here is also a dillerence in the physical extent of the line emitting regions between large and small radio sources. with ine emission at radii of 30 to kkpe generally only seen in small racio sources.," As was shown in Figure \ref{emissize}, there is also a difference in the physical extent of the line emitting regions between large and small radio sources, with line emission at radii of 30 to kpc generally only seen in small radio sources." + Unless there is an intrinsic dillerence ovtween the environments of the small and large. racio sources. which seems unlikely eiven all of the correlations ound. the emission line gas clouds must also be present out o radii zz30 kkpe in large radio sources. but is not visible.," Unless there is an intrinsic difference between the environments of the small and large radio sources, which seems unlikely given all of the correlations found, the emission line gas clouds must also be present out to radii $\gta 30$ kpc in large radio sources, but is not visible." + Again. the role of shocks can be considered to explain his.," Again, the role of shocks can be considered to explain this." + At these radii. the Dux of ionising photons from the active nucleus may be insullicient to produce an observable emission line luminosity.," At these radii, the flux of ionising photons from the active nucleus may be insufficient to produce an observable emission line luminosity." + As the radio source shocks pass through these regions. however. the eas density will be increased and. as discussed. above. a larec source of local ionising photons will become available. pushing up the emission. line. luminosity.," As the radio source shocks pass through these regions, however, the gas density will be increased and, as discussed above, a large source of local ionising photons will become available, pushing up the emission line luminosity." + Following the passage of the radio shocks and the consequent. removal of the associated ionising photons. this enhanced line emission. will [ade over inmescales much shorter than the radio source lifetime.," Following the passage of the radio shocks and the consequent removal of the associated ionising photons, this enhanced line emission will fade over timescales much shorter than the radio source lifetime." + Thus. uminous line emission is only seen from the clouds at. raclii 30 to kkpe at the time that the radio source shocks are »wsing through these regions.," Thus, luminous line emission is only seen from the clouds at radii 30 to kpc at the time that the radio source shocks are passing through these regions." + A direct consequence of this model is that for radio sources smaller than about kkpc a positive correlation between radio source size and emission ine region size should be observed. since line emission from he clouds at radii 30 to kkpe will not be seen until the radio source has advanced that far.," A direct consequence of this model is that for radio sources smaller than about kpc a positive correlation between radio source size and emission line region size should be observed, since line emission from the clouds at radii 30 to kpc will not be seen until the radio source has advanced that far." + Such a correlation has indeed. been observed in the [ντα emission of radio galaxies with zz2 (7).," Such a correlation has indeed been observed in the $\alpha$ emission of radio galaxies with $z +\ga 2$ \cite{oji97}." + An interesting test of the model presented: here. could be carried. out by. taking high spatial resolution longslit spectra of a sample of radio galaxies with radio sizes smaller than the size of the emission line regions., An interesting test of the model presented here could be carried out by taking high spatial resolution long–slit spectra of a sample of radio galaxies with radio sizes smaller than the size of the emission line regions. + The prediction 1s that within the region of the host galaxy. occupied. by the radio source. the radio source shocks will be important: the emission line ratios will be consistent with shock ionisation. and the eas kinematies will be distorted with broad. velocity dispersions.," The prediction is that within the region of the host galaxy occupied by the radio source, the radio source shocks will be important; the emission line ratios will be consistent with shock ionisation, and the gas kinematics will be distorted with broad velocity dispersions." + Outside of this region. however. the gas clouds will not vet have been inlluenced by the radio source shocks and photoionisation should dominate.," Outside of this region, however, the gas clouds will not yet have been influenced by the radio source shocks and photoionisation should dominate." + X study with a similar principle has been carried out on the radio source 1243|036. a radio galaxy of radio size about kkpe at a redshift z= 3.6.," A study with a similar principle has been carried out on the radio source 1243+036, a radio galaxy of radio size about kpc at a redshift $z = +3.6$ ." + Distorted Ly-a velocity structures with large velocity INLLM are seen within the radio source structure. but Ly-a emission also extends beyond that to at least kkpe radius in an apparently rotating halo (7)..," Distorted $\alpha$ velocity structures with large velocity FWHM are seen within the radio source structure, but $\alpha$ emission also extends beyond that to at least kpc radius in an apparently rotating halo \cite{oji96a}." + VillarMart£nn shorteitevilóOa— have. also found that. the. line. emission of 22250 41 (2:= 0.308) is composed of. distinct kinematic components: à low ionisation component. with οσα. velocity. width in the region of the radio source structure. and a narrower high ionisation component which extends beyond the radio lobe.," Villar–Martínn \\shortcite{vil99a} have also found that the line emission of $-$ 41 $z=0.308$ ) is composed of distinct kinematic components: a low ionisation component with broad velocity width in the region of the radio source structure, and a narrower high ionisation component which extends beyond the radio lobe." + Carrying out studies such as 1ese for a large sample of radio sources is important because 16 velocity structures of the line emission in regions outside 10 radio shocks will directly show the initial motions of ie emission line clouds ancl can be used to determine whether these clouds are simply material associated with 10 formation of the galaxy which has been expelled. into 16 LGAL or whether they have an external origin. brought in either by a galaxy merger or a cooling How.," Carrying out studies such as these for a large sample of radio sources is important because the velocity structures of the line emission in regions outside the radio shocks will directly show the initial motions of the emission line clouds and can be used to determine whether these clouds are simply material associated with the formation of the galaxy which has been expelled into the IGM, or whether they have an external origin, brought in either by a galaxy merger or a cooling flow." + Lt is cillicult o clistineuish between such scenarios in larger radio sources since information on the initial cloud velocitieshas been destroved by the bow shock acceleration., It is difficult to distinguish between such scenarios in larger radio sources since information on the initial cloud velocitieshas been destroyed by the bow shock acceleration. + One significant issue remains to be explained in this picture.," One significant issue remains to be explained in this picture," +belund the compact object.,behind the compact object. + Such increases are not secu iu USSco., Such increases are not seen in Sco. + Furthermore. achromatic Thompson scattering would also leave its footpriuts in the UV and optical helt curves. and plotoclectric absorption by NV plasma in a low state of ionization appears more likely for USSco.," Furthermore, achromatic Thompson scattering would also leave its footprints in the UV and optical light curves, and photoelectric absorption by $N_{\rm H}$ plasma in a low state of ionization appears more likely for Sco." + From the simultancous ANaav UV. and optical observations of the Loth recorded outburst of the recurrent. eclipsing nova SSco. we have deduced new iusights iuto time variability. spectral properties. aud spatial structure:," From the simultaneous X-ray, UV, and optical observations of the 10th recorded outburst of the recurrent, eclipsing nova Sco, we have deduced new insights into time variability, spectral properties, and spatial structure:" +have gas fractions above to account for the stellar mass produced during the merger.,have gas fractions above to account for the stellar mass produced during the merger. + Therefore most starbursts at Zmedian=0.65 — those with anomalous morphologies and kinematics — are consistent with gas-rich merger phases leading to rebuilt disks., Therefore most starbursts at $z_{median}$ =0.65 – those with anomalous morphologies and kinematics – are consistent with gas-rich merger phases leading to rebuilt disks. +" Our interpretation of the morpho-kinematic evolution (see Table 1) is then straightforward: ~ 6 Gyrs ago, of the galaxy population was involved in major mergers and most of them x 46%== 35%)) were sufficiently gas rich to rebuild a disk."," Our interpretation of the morpho-kinematic evolution (see Table 1) is then straightforward: $\sim$ 6 Gyrs ago, of the galaxy population was involved in major mergers and most of them $\times$ = ) were sufficiently gas rich to rebuild a disk." +" Those can be considered as progenitors of the present-day numerous spirals — although this deserves a careful analysis of the exchanges of angular momenta — while the others could be progenitors of E/SO and of the scarce population of massive irregulars at the present-epoch (~10%,seeDelgado-Serranoetal. 2009)."," Those can be considered as progenitors of the present-day numerous spirals – although this deserves a careful analysis of the exchanges of angular momenta – while the others could be progenitors of E/S0 and of the scarce population of massive irregulars at the present-epoch \citep[$\sim$ 10\%, see ][]{Delgado09}." +". Thus as much as half of the present-day spirals are coming from disk rebuilding from recent mergers, the other half being already assembled into quiescent or warm disks at Zmedian=0.65 (Table 1)."," Thus as much as half of the present-day spirals are coming from disk rebuilding from recent mergers, the other half being already assembled into quiescent or warm disks at $z_{median}$ =0.65 (Table 1)." + More statistics are certainly needed to obtain a more precise estimate of the amount of gas that has been consumed during the different merger phases., More statistics are certainly needed to obtain a more precise estimate of the amount of gas that has been consumed during the different merger phases. + The median time spent in each merger phase ranges from 0.5 to 1.4 Gyr (see Fig., The median time spent in each merger phase ranges from 0.5 to 1.4 Gyr (see Fig. +" 8 and also Table 3): the scenario naturally explains why distant starbursts show a so important contribution of intermediate-age stars revealed by their very large Balmer absorption lines in their spectra (e.g. Hammeretal.1997;Marcillac 2006., see also Poggiantietal.1999 for another perspective in galaxy-cluster environments)."," 8 and also Table 3): the scenario naturally explains why distant starbursts show a so important contribution of intermediate-age stars revealed by their very large Balmer absorption lines in their spectra (e.g. \citealt{Hammer97,Marcillac06}, see also \citealt{Poggianti99} for another perspective in galaxy-cluster environments)." + The median baryonic mass of the sample is 0.75 times that of the Milky Way., The median baryonic mass of the sample is 0.75 times that of the Milky Way. +" Their progenitors should be galaxies at larger redshifts, approximately 1 Gyr earlier, i.e. at z~ 0.83."," Their progenitors should be galaxies at larger redshifts, approximately 1 Gyr earlier, i.e. at $\sim$ 0.83." + At such redshifts the large gas fractions in progenitors is not exceptional., At such redshifts the large gas fractions in progenitors is not exceptional. +" Accounting for the gas consumed during the merger, the median stellar mass and gas fraction of their progenitors are 7.5 10? Mo and 50%,, respectively."," Accounting for the gas consumed during the merger, the median stellar mass and gas fraction of their progenitors are 7.5 $10^{9}$ $M_{\odot}$ and , respectively." +" In present-day galaxies within this mass range, the gas fraction averages to ~26% for local galaxies (fromSchimi-novich 2008),, and it could be not exceptional that 7 Gyrs ago such galaxies had twice their present gas content."," In present-day galaxies within this mass range, the gas fraction averages to $\sim$ for local galaxies \citep[from][]{Schiminovich08}, and it could be not exceptional that 7 Gyrs ago such galaxies had twice their present gas content." + Improvements are also required to estimate the stellar masses since a proxy (absolute J-band magnitude) of the stellar mass has been used in this study to select our sample., Improvements are also required to estimate the stellar masses since a proxy (absolute J-band magnitude) of the stellar mass has been used in this study to select our sample. + Combination of realistic stellar population with different ages and metal content has to be performed on both the whole spectral energy distribution (from UV to near-IR) and the spectroscopic absorption lines (Lick indices)., Combination of realistic stellar population with different ages and metal content has to be performed on both the whole spectral energy distribution (from UV to near-IR) and the spectroscopic absorption lines (Lick indices). +" Nevertheless, we dofind that all distant starbursts are consistent with major"," Nevertheless, we dofind that all distant starbursts are consistent with major" +results considerablv.,results considerably. + The largest differences occur just after a burst: the C/O. AY/7AO. and Z/O values decrease. diminishing the differences of C/O aud Z/O with the observed values but increasing the ciffercuces of the AY/AO with observed value.," The largest differences occur just after a burst: the C/O, $\Delta Y/\Delta {\rm O}$, and $Z$ /O values decrease, diminishing the differences of C/O and $Z$ /O with the observed values but increasing the differences of the $\Delta Y/\Delta {\rm O}$ with observed value." + Manuel Penubert acknowledges several ilhuninating discussions with Evan Skilhuan aud Gerry Cilnore during the Syiuposiuii ou Cosinie Chemical Evolution held iu NORDITA to honor Professor Bernard Pagel., Manuel Peimbert acknowledges several illuminating discussions with Evan Skillman and Gerry Gilmore during the Symposium on Cosmic Chemical Evolution held in NORDITA to honor Professor Bernard Pagel. + We also acknowledge a thorough reading of au eulier version of this paper aud several excellent sugecstious by the referee Mario Mateo., We also acknowledge a thorough reading of an earlier version of this paper and several excellent suggestions by the referee Mario Mateo. + We made use of the NASA/TPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory. California Institute of Technology. under contract with the National Aeronautics and Space Adininistration.," We made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration." + This work was partially supported by DGAPA/UNAM through project IN-10099L., This work was partially supported by DGAPA/UNAM through project IN-100994. +containing stellar-mass black holes lie close to the first group. but have larger Γρη values.,"containing stellar-mass black holes lie close to the first group, but have larger $r_b/r_h$ values." + The two core-collapsed cases are placed at 75/7;=0. since we cannot formally measure a break radius for them.," The two core-collapsed cases are placed at $r_b/r_h=0$, since we cannot formally measure a break radius for them." + For the 74/7; case. the actual values change. but the behavior is similar.," For the $r_{ck}/r_h$ case, the actual values change, but the behavior is similar." + The only group of models that clearly separates from the rest in both plots are those with very steep central slopes and non-detectable turnover radius. which correspond to clusters that do not contain IMBHs and have undergone core-collapse.," The only group of models that clearly separates from the rest in both plots are those with very steep central slopes and non-detectable turnover radius, which correspond to clusters that do not contain IMBHs and have undergone core-collapse." + We overlay on both planes all the Galactic clusters in NGOG. plus omega Centauri and GI.," We overlay on both planes all the Galactic clusters in NG06, plus omega Centauri and G1." +" For Gl we measure the central slope using the profile in Gebhardtetal.(2005).. while ο, and ry, values come from the analysis of Maetal.(2007)."," For G1 we measure the central slope using the profile in \citet{geb05}, while $r_c$ and $r_h$ values come from the analysis of \citet{ma07}." +. The first thing to notice is that the Galactic clusters occupy a larger area in the plane thàn the modeled ones., The first thing to notice is that the Galactic clusters occupy a larger area in the plane than the modeled ones. +" The two clusters for which there are kinematical indications of hosting an IMBH. GI and omega Centauri have central density slopes shallower than -0.1. and their r,./rj values are different."," The two clusters for which there are kinematical indications of hosting an IMBH, G1 and omega Centauri have central density slopes shallower than -0.1, and their $r_c/r_h$ values are different." +" Omega Centauri and GI sit near the locus of our models. but both of them have more extreme values of 7./r, than the models with IMBHs."," Omega Centauri and G1 sit near the locus of our models, but both of them have more extreme values of $r_c/r_h$ than the models with IMBHs." + Very concentrated clusters. like MI5. which are assumed to have undergone core-collapse. do lie very close to the models without IMBHs and long evolutionary times.," Very concentrated clusters, like M15, which are assumed to have undergone core-collapse, do lie very close to the models without IMBHs and long evolutionary times." + It should be noticed that some individual Galactic clusters change location from one plane to the other MIS was the first cluster for which the presence of a central massive black hole was kinematically investigated. mainly due to its concentrated central profile.," It should be noticed that some individual Galactic clusters change location from one plane to the other M15 was the first cluster for which the presence of a central massive black hole was kinematically investigated, mainly due to its concentrated central profile." + It was only later when it became clear that à projected steep central cusp is not the expected behavior for a star cluster containing a black hole., It was only later when it became clear that a projected steep central cusp is not the expected behavior for a star cluster containing a black hole. + This stresses the need to develop better diagnostics to diseriminate suitable candidates for detailed kinematical measurements when looking for IMBHs., This stresses the need to develop better diagnostics to discriminate suitable candidates for detailed kinematical measurements when looking for IMBHs. + In this paper we have created realistic synthetic images from N-body models of star clusters with and without intermediate-mass black holes., In this paper we have created realistic synthetic images from N-body models of star clusters with and without intermediate-mass black holes. + We have analyzed these images in the same way we analyze data for a sample of Galactic globular clusters and we compare both datasets., We have analyzed these images in the same way we analyze data for a sample of Galactic globular clusters and we compare both datasets. + We explore two quantities as possible diagnostic tools for the presence of black holes: the central logarithmic slope of the surface brightness profile. and the ratio of core radius to half light radius.," We explore two quantities as possible diagnostic tools for the presence of black holes: the central logarithmic slope of the surface brightness profile, and the ratio of core radius to half light radius." + We find that the πρ ratio cannot discriminate between models with and without black holes. as Hurley(2007) already found. but that the central logarithmic slope can.," We find that the $r_c/r_h$ ratio cannot discriminate between models with and without black holes, as \citet{hur07} already found, but that the central logarithmic slope can." + N-body clusters without IMBHs show either flat central cores. or steep cusps if they have undergone core-collapse. while clusters containing IMBHs show shallow central cusp for all except two cases.," N-body clusters without IMBHs show either flat central cores, or steep cusps if they have undergone core-collapse, while clusters containing IMBHs show shallow central cusp for all except two cases." + We want to emphasize that when dealing with density profiles of star clusters. saying ‘core radius? alone is not enough. one has to specify how that radius is measured in order to compare its value to models or other observations.," We want to emphasize that when dealing with density profiles of star clusters, saying 'core radius' alone is not enough, one has to specify how that radius is measured in order to compare its value to models or other observations." + Historically. the definition that we call 7; 1s the most popular one. but we show here that this definition is only useful for clusters whose profiles have a flat central core.," Historically, the definition that we call $r_{ch}$ is the most popular one, but we show here that this definition is only useful for clusters whose profiles have a flat central core." + When the profiles have central slopes different from zero. rj or rj appear to be more suitable. although they can differ by up to a factor of two for the same cluster.," When the profiles have central slopes different from zero, $r_{ck}$ or $r_b$ appear to be more suitable, although they can differ by up to a factor of two for the same cluster." + For density profiles with a flat central core and clear turnovers. all three definitions mark practically the same radius.," For density profiles with a flat central core and clear turnovers, all three definitions mark practically the same radius." + There are various ways m which our N-body simulations are idealized compared to Galactic globular clusters., There are various ways in which our N-body simulations are idealized compared to Galactic globular clusters. + First.," First," +evolution.,evolution. +" The first measurements of velocity dispersion of a few of ""normal-size"" high-z ETGs confirmed that they are similar to typical local ones also from the dynamic point of view (Cenarro et al."," The first measurements of velocity dispersion of a few of ""normal-size"" high-z ETGs confirmed that they are similar to typical local ones also from the dynamic point of view (Cenarro et al." + 2009: Cappellari et al., 2009; Cappellari et al. + 2009: Onodera et al., 2009; Onodera et al. + 2010)., 2010). + Concurrently. evidence of the presence of a significant fraction of compact ETGs in the local Universe similar to the high-z ones came out (e.g. Trujillo et al.," Concurrently, evidence of the presence of a significant fraction of compact ETGs in the local Universe similar to the high-z ones came out (e.g. Trujillo et al." + 2009: Valentinuzzi et al., 2009; Valentinuzzi et al. + 2010a: 2010b) casting the first doubts about the size evolution scenario., 2010a; 2010b) casting the first doubts about the size evolution scenario. + The question naturally arising from these new pieces of evidence is whether compact ETGs were so much more numerous at earlier epochs to require their effective radius evolution., The question naturally arising from these new pieces of evidence is whether compact ETGs were so much more numerous at earlier epochs to require their effective radius evolution. + Recently. evidence that the number density of compact ETGs at «z>=1 was not significantly higher than the number density of compact ETGs seen in local cluster of galaxies has come out (Saraeco. Longhetti Gargiulo 2010).," Recently, evidence that the number density of compact ETGs at $\simeq1.5$ was not significantly higher than the number density of compact ETGs seen in local cluster of galaxies has come out (Saracco, Longhetti Gargiulo 2010)." + This evidence conflicts with the hypothesized effective radius evolution of high-z ETGs while shows that among them there are the progenitors of the compact ETGs seen in local clusters of galaxies and that they were as we see them today already 9-10 Gyr ago as contirmed by recent studies on high-z cluster galaxies (e.g. Strazzullo et al., This evidence conflicts with the hypothesized effective radius evolution of high-z ETGs while shows that among them there are the progenitors of the compact ETGs seen in local clusters of galaxies and that they were as we see them today already 9-10 Gyr ago as confirmed by recent studies on high-z cluster galaxies (e.g. Strazzullo et al. + 2010)., 2010). + Moreover. at z~1.5 a majority of normal ETGs co-exist with compact early-types from ~2 to ~6 times smaller in spite of the same mass and redshift.," Moreover, at $z\sim1.5$ a majority of normal ETGs co-exist with compact early-types from $\sim2$ to $\sim6$ times smaller in spite of the same mass and redshift." + Actually. this picture is not ditferent at least qualitatively from what is observed in the local universe: most of the ETGs lie on a well defined sealing relation and a minor fraction of them (e.g. ~20-40 per cent in cluster of galaxies. Valentinuzzi e al.," Actually, this picture is not different at least qualitatively from what is observed in the local universe: most of the ETGs lie on a well defined scaling relation and a minor fraction of them (e.g. $\sim$ 20-40 per cent in cluster of galaxies, Valentinuzzi et al." + 2010a: 2010b) are significantly denser than the others., 2010a; 2010b) are significantly denser than the others. + Thus. ETGs appear a composite population from z=0 up to at leas zc1.8—3.," Thus, ETGs appear a composite population from $z=0$ up to at least $z\sim1.5-2$." + To corroborate this view is the recent study conducted by Gargiulo et al. (, To corroborate this view is the recent study conducted by Gargiulo et al. ( +2010) who show that at |«z2 ETGs with negative color gradient (redder toward the center) co-exis with ETGs characterized by positive color gradient (bluer toward the center).,2010) who show that at $1 2) when they have been assembled.," Consequently, this non homogeneity of the population of ETGs must originate at an earlier epoch $z>2$ ) when they have been assembled." +" The relevant question is which formation scenario and early physical conditions can account for the observed ""itferent properties of ETGs.", The relevant question is which formation scenario and early physical conditions can account for the observed different properties of ETGs. + In this paper we try to constrain these issues by probing the past history of a large number of ETGs at 0.9 5). te. their old age.," We are rather inclined to ascribe this difference to the fact that the NICMOS sample collects ETGs pre-selected on the basis of their red colors (e.g. $>5$ ), i.e. their old age." + Since old ETGs are smaller for fixed mass and more massive for fixed radius (e.g. Bernardi et al., Since old ETGs are smaller for fixed mass and more massive for fixed radius (e.g. Bernardi et al. + 2008: Valentinuzzi et al 2010) NICMOS sample is consequently biased toward compact ETOs., 2008; Valentinuzzi et al 2010) NICMOS sample is consequently biased toward compact ETGs. + We verified this by using the complete ACS sample. unbiased with respect to any color selection.," We verified this by using the complete ACS sample, unbiased with respect to any color selection." + We have selected galaxies from this sample at different Fo06W-K colors (close to R-K color) and we have count the fraction of compact ETGs. which we define as those falling more than one sigma below the local size-mass relation. at different color cuts.," We have selected galaxies from this sample at different F606W-K colors (close to R-K color) and we have count the fraction of compact ETGs, which we define as those falling more than one sigma below the local size-mass relation, at different color cuts." + The result is shown in Fig., The result is shown in Fig. + 2 where the fraction of compact ETGs is shown as a function of F606W- color cuts., 2 where the fraction of compact ETGs is shown as a function of F606W-K color cuts. + It is evident that the fraction of compact ETGs increases systematically toward redder color cuts showing the strong selection effect attecting the NICMOS sample and all those, It is evident that the fraction of compact ETGs increases systematically toward redder color cuts showing the strong selection effect affecting the NICMOS sample and all those +bright calibration objects. such as the Moon. Tau Alpha and RCW38.,"bright calibration objects, such as the Moon, Tau Alpha and RCW38." + These sources are brieht cuough to be seen visually in each detector time stream. and they can therefore bias auv noise estimates unless properly accounted for.," These sources are bright enough to be seen visually in each detector time stream, and they can therefore bias any noise estimates unless properly accounted for." +" Such objects also complicate automated data selection processes, since it is difficult to distiuguisli between an astroplivsical object aud an instrmucutal elitch."," Such objects also complicate automated data selection processes, since it is difficult to distinguish between an astrophysical object and an instrumental glitch." + Iu this section we show how the algoritlin developed iu Section { may be applied to such situations., In this section we show how the algorithm developed in Section \ref{sec:algorithm} may be applied to such situations. + Specials: we consider a observing session lasting for about 10 minutes of a field inchiding a bright source with known location. aud asstune that the data may be modeled as dn!Ta| xu.," Specifically, we consider a observing session lasting for about 40 minutes of a field including a bright source with known location, and assume that the data may be modeled as $\d = \n + \T\a ++ \m$ ." + Here T is a single template describing possible sidelobe pick-up from the ground. constructed from the full observing season as described bx QUIET (2011).. and xn ds a time-domain mask that removes auv siuuples that happen to fall closer than 17 from the source center.," Here $\T$ is a single template describing possible sidelobe pick-up from the ground, constructed from the full observing season as described by \citet{quiet:2011}, and $\m$ is a time-domain mask that removes any samples that happen to fall closer than $1^{\circ}$ from the source center." + The total nuuber of samples in the data stream is 609919. and the total nuniber of masked samples is 651.," The total number of samples in the data stream is 949, and the total number of masked samples is 651." + The simulations used in this section are coustructed as follows., The simulations used in this section are constructed as follows. + We set up an cuscurble of 105 time streams containing emtd Gaussian random noise with a=10 ?V. vetaiudexLe clateaud fi=Oz: the white noise aud E are represcutative for a QUIET detector. while the knee frequeney is grossly exaggerated to push the aleorithin iuto a difficult region of parameter space. as well as to more clearly visualize the outputs of the aleorithiu.," We set up an ensemble of $10^4$ time streams containing correlated Gaussian random noise with $\sigma_0 = 10^{-5}\textrm{V}$ , $\alpha=-1.8$ and $f_{\textrm{k}} = 0.1\textrm{Hz}$; the white noise and spectral index are representative for a QUIET detector, while the knee frequency is grossly exaggerated to push the algorithm into a difficult region of parameter space, as well as to more clearly visualize the outputs of the algorithm." + A far more reasonable value for QUIET is fi=lulz. aud we have of course verified that the algoritlian also works for such cases.," A far more reasonable value for QUIET is $f_{\textrm{k}} = 10\textrm{mHz}$, and we have of course verified that the algorithm also works for such cases." + Further. it reaches convergence faster in that case than with the extreme value of fi used in the present simulations.," Further, it reaches convergence faster in that case than with the extreme value of $f_{\textrm{k}}$ used in the present simulations." + Before considering the statistical properties of the resulting posterior distributions. it is useful to look visually at a few constrained realizations in order to build up intuition about the aleorithin.," Before considering the statistical properties of the resulting posterior distributions, it is useful to look visually at a few constrained realizations in order to build up intuition about the algorithm." +" In order to highlieht the behavior of the coustrained realizations. we male two adjustineuts to the above simulation procedure for this case alone: First. we replace the tuned mask with a wide 6000-uple mask. covering the entire time rauge in which the source is visible. aud second. we male the correlated noise component stronger by setting LO OW fü,=Uz anda =Fieure2.3."," In order to highlight the behavior of the constrained realizations, we make two adjustments to the above simulation procedure for this case alone: First, we replace the tuned mask with a wide 6000-sample mask, covering the entire time range in which the source is visible, and second, we make the correlated noise component stronger by setting $\sigma_0=10^{-6}\textrm{V}$ , $\fknee = 1\textrm{Hz}$ and $\alpha=-2.3$." + The results are shown iu 2.., The results are shown in Figure \ref{fig:constrained_realizations}. + The raw data are shown in the solid black line. aud the vertical daslied lines indicate the exteut of the gap.," The raw data are shown in the solid black line, and the vertical dashed lines indicate the extent of the gap." + The colored curves within 1e eap shows 5 difference constrained realizations: note iat together with the black solid curve outside the nask. any of these form a valid noise realization with ie appropriate nolse power spectrum as defined by 0. a and Proce," The colored curves within the gap shows 5 difference constrained realizations; note that together with the black solid curve outside the mask, any of these form a valid noise realization with the appropriate noise power spectrum as defined by $\sigma_0$, $\alpha$ and $\fknee$." + They are cach a valid. sample drawn from P(n.an|d).," They are each a valid sample drawn from $P(\n, \m|\d)$." + Ilowever. if one had tried to estiuate the i0lse spectriii also usine the data inside the eap. the source signal (seen as sharp spikes iu Figure 2)) would das the resulting uoise paraieters.," However, if one had tried to estimate the noise spectrum also using the data inside the gap, the source signal (seen as sharp spikes in Figure \ref{fig:constrained_realizations}) ) would bias the resulting noise parameters." + Iu this paper. we consider the coustrained realizatious oxiuariv to be a useful tool that allows for fast loise covariance matrix nultiplicatious iu Fourier space.," In this paper, we consider the constrained realizations primarily to be a useful tool that allows for fast noise covariance matrix multiplications in Fourier space." + However. these constrained realizations can of course also ve useful iu their own right. for instance for deelitching a time stream before map making," However, these constrained realizations can of course also be useful in their own right, for instance for deglitching a time stream before map making." + We now seek to statistically validate our algorithniuus and codes., We now seek to statistically validate our algorithms and codes. + Both the posterior maxiuization and the (ας sampling algorithius are considered., Both the posterior maximization and the Gibbs sampling algorithms are considered. + The number of simulations are 0000 for posterior maximization aud 5000. for Cabbs sampling. with properties as described above.," The number of simulations are 000 for posterior maximization and 5000 for Gibbs sampling, with properties as described above." + In cach case. we cousider four different models.," In each case, we consider four different models." + Fist. we analvze simulations mceludius only noise aud eaps.," First, we analyze simulations including only noise and gaps." + Second. we add a CAB signal to cach realization. but do not attempt to correct for it.," Second, we add a CMB signal to each realization, but do not attempt to correct for it." + Third. we add a strong eround template to cach realization. aud do also not attempt to correct for it.," Third, we add a strong ground template to each realization, and do also not attempt to correct for it." + Fourth. we analyze the same eround-coutamunated simulations as above. but this tine do mareinalize over au appropriate template.," Fourth, we analyze the same ground-contaminated simulations as above, but this time do marginalize over an appropriate template." + The same random seeds were used iu each of the four simulationaud analysis results. iu order to allow for direct comparison of results between runs.," The same random seeds were used in each of the four simulationand analysis results, in order to allow for direct comparison of results between runs." + The results from this exercise are sunuuarized iu, The results from this exercise are summarized in +and where A; is an abbreviation for 27wd;.,and where $\Delta_i$ is an abbreviation for $2\pi\omega\delta_i$. +" This minimum is achieved by setting the partial differentials.B ofB Q7L7 withn respect to the [ourB unknowns a. αμ. p,. and p, equal to zero."," This minimum is achieved by setting the partial differentials of $Q^2$ with respect to the four unknowns $a_x$ , $a_y$, $p_x$ , and $p_y$ equal to zero." + IfB uto)n represents a vector of (hese respective unknowns al each vw. we must solve a system of 4 linear equations where the coefficients of Cj; of the matrix and 4; of the vector are listed in Table 4..," If ${\bf u}(\omega)$ represents a vector of these respective unknowns at each $\omega$, we must solve a system of 4 linear equations where the coefficients of $C_{i,j}$ of the matrix and $b_i$ of the vector are listed in Table \ref{linear_eq_coeffs}." +" After solving for each vector ule) over all ω, one simply evaluates the inverse Fourier transforms of the two pairs of terms. πω}+usto) and use)+fuyl) lo recover (he best representations of ACA) ancl P(A). respectively."," After solving for each vector ${\bf u}(\omega)$ over all $\omega$ , one simply evaluates the inverse Fourier transforms of the two pairs of terms, $u_1(\omega)+iu_2(\omega)$ and $u_3(\omega)+iu_4(\omega)$ to recover the best representations of $A(\lambda)$ and $P(\lambda)$, respectively." + Large increases in the magnitudes of terms in the error matrices πο”| at certain frequencies indicate places where the solutions are ill-defined.," Large increases in the magnitudes of terms in the error matrices $[{\bf +C}(\omega)]^{-1}$ at certain frequencies indicate places where the solutions are ill-defined." + As one would expect. the outcomes for frequencies whose inverses are much larger than the total span of the 6; are nol well determined.," As one would expect, the outcomes for frequencies whose inverses are much larger than the total span of the $\delta_i$ are not well determined." + The solutions for fA) and (A) can exhibit very broad. spurious undulations (of opposite sign). as an outcome of the analvsis program's attempt to reconcile small differences in the low-Irequency. components in the observed spectra. arising; simply [rom noise and subtle svstematic errors.," The solutions for $A(\lambda)$ and $P(\lambda)$ can exhibit very broad, spurious undulations (of opposite sign), as an outcome of the analysis program's attempt to reconcile small differences in the low-frequency components in the observed spectra arising simply from noise and subtle systematic errors." + As a practical matter. it is reasonable to assign artificially a condition (hat any low-frequency components of the observed spectra must arise [rom either (he source spectrum (A) or the detector response P(A).," As a practical matter, it is reasonable to assign artificially a condition that any low-frequency components of the observed spectra must arise from either the source spectrum $A(\lambda)$ or the detector response $P(\lambda)$." + A similar quandary arises [or certain [requencies where integral numbers of sinusoidal variations in the spectrum can exactly match the spacings between all of the 0;., A similar quandary arises for certain frequencies where integral numbers of sinusoidal variations in the spectrum can exactly match the spacings between all of the $\delta_i$. + One consequence of this phenomenon is (hat the programmed intent of having equal step sizes the EP-SPLIT routine for GIRS was a misguided Fortunately. in practice thestepsizes usually turn outto benot quite equal. aud (his removes the degeneracies of the solutions.," One consequence of this phenomenon is that the programmed intent of having equal step sizes the FP-SPLIT routine for GHRS was a misguided Fortunately, in practice thestepsizes usually turn outto benot quite equal, and this removes the degeneracies of the solutions." +Current A-rav observations. are limited {ο spectral characteristics anc timing variability over à relatively narrow electromagnetic window (~0.150 keV).,Current X-ray observations are limited to spectral characteristics and timing variability over a relatively narrow electromagnetic window $\sim 0.1 - 50$ keV). + This often leads to ambiguities in the interpretation of the data. where two or more dillerent models can explain. the same observations with equal success.," This often leads to ambiguities in the interpretation of the data, where two or more different models can explain the same observations with equal success." + This degeneracy may be resolved if polarization measurements are available., This degeneracy may be resolved if polarization measurements are available. + X-rav Polarization observations may provide more precise diagnostic information about the emission. processes and the geometries of the emission. regions (seec.g.Sunvaev&Vitarchuk1985:Lapidus.SvunvaevVitarehuk 1985).," X-ray Polarization observations may provide more precise diagnostic information about the emission processes and the geometries of the emission regions \citep[see e.g.][]{ST85,Lapidus85}." +. Considerable effort is currently underway to develop the X-rav instruments capable of measuring polarization ofat least a lew percent (Costaetal.2001.2008).," Considerable effort is currently underway to develop the X-ray instruments capable of measuring polarization of at least a few percent \citep{Costa01,Costa08}." +. The last dedicated. experiment to measure X-ray polarization of astronomical sources bevond the solar svstenm was conducted over thirty vears agodetails)., The last dedicated experiment to measure X-ray polarization of astronomical sources beyond the solar system was conducted over thirty years ago. +. Since that first successful measurcment.et several high-energy missions. were planned o include X-ray. polarimeters (c.g. Observatory. Spectrum-X).," Since that first successful measurement, several high-energy missions were planned to include X-ray polarimeters (e.g. Observatory, Spectrum-X)." +. However. none of these polarimeters were aunched.," However, none of these polarimeters were launched." + Developing a polarimeter capable of measuring inear polarization of astronomical sources in the range L1.50 keV has many challenges and two different: types of polarimeters have been proposed: scattering polarimicters ancl photoclectron polarimeters (seeWeisskopfetal.2006.oradetailed cleseription).., Developing a polarimeter capable of measuring linear polarization of astronomical sources in the range $0.1 - 50$ keV has many challenges and two different types of polarimeters have been proposed: scattering polarimeters and photoelectron polarimeters \citep[see][for a detailed description]{Weisskopf06}. + Each tvpe of detector has its own limitations. although photoelectrie X-ray polarimicters with gas detectors have recently reached a mature level of development ancl variations of this model have. been proposed for a number of future missions (fore.g.seeCostaal.2007:AXrimotoet 2008).," Each type of detector has its own limitations, although photoelectric X-ray polarimeters with gas detectors have recently reached a mature level of development and variations of this model have been proposed for a number of future missions \citep[for e.g. see][]{Costa01, Bellazzini07, Gunji04, Jahoda07, Arimoto08}." +. To date. however. very Little theoretical work has been done on this subject.," To date, however, very little theoretical work has been done on this subject." + Indeed. the discriminating polarization signatures of the most. powerful cosmic X-ray sources has not vet been determined.," Indeed, the discriminating polarization signatures of the most powerful cosmic X-ray sources has not yet been determined." + We have developed. a Monte. Carlo algorithm to model polarized. photon transport resulting from Compton, We have developed a Monte Carlo algorithm to model polarized photon transport resulting from Compton +Alternatively. large-amplitude breathing modes may simply be uncommon in starless cores.,"Alternatively, large-amplitude breathing modes may simply be uncommon in starless cores." + If the pulsations are driven by the turbulence from the parent molecular cloud. it may be difficult to excite monopole oscillations.," If the pulsations are driven by the turbulence from the parent molecular cloud, it may be difficult to excite monopole oscillations." + The intra-core motions are typically subsonic. and at the core scale. the turbulence is therefore nearly incompressible.," The intra-core motions are typically subsonic, and at the core scale, the turbulence is therefore nearly incompressible." + However. the monopole modes generally. and the breathing mode specifically. are primarily oscillations.," However, the monopole modes generally, and the breathing mode specifically, are primarily compressive oscillations." + Thus. the molecular cloud turbulencecompressive can only weakly couple to these oscillations. either through a small failure of the incompressible condition or through non-linear mode coupling.," Thus, the molecular cloud turbulence can only weakly couple to these oscillations, either through a small failure of the incompressible condition or through non-linear mode coupling." + Por these reasons we will not consider pulsations further. restricting our attention henceforth monopoleto oscillations with Ll.," For these reasons we will not consider monopole pulsations further, restricting our attention henceforth to oscillations with $l\ge1$." + Higher-order pulsations are nearly always stabilizing. Le. they increase the allowed surface pressure at which stable isothermal cores exist. or alternatively increase the mass that a core can support.," Higher-order pulsations are nearly always stabilizing, i.e., they increase the allowed surface pressure at which stable isothermal cores exist, or alternatively increase the mass that a core can support." + The exception being the 7= 1./=| oscillation which produces a small negative pressure near Coat.," The exception being the $n=1$, $l=1$ oscillation which produces a small negative pressure near $\zc$." +" From Equation (4)) and the asymptotic behaviors of the 5, for the non-radial oscillations. it is straightforward to estimate the contribution to the surface pressure from the oscillations: where P, is the surface pressure of the unperturbed configuration."," From Equation \ref{eq:P}) ) and the asymptotic behaviors of the $\omega_{nlm}$ for the non-radial oscillations, it is straightforward to estimate the contribution to the surface pressure from the oscillations: where $P_0$ is the surface pressure of the unperturbed configuration." + The precise constant of proportionality depends upon ¢ and weakly on the energy spectrum., The precise constant of proportionality depends upon $\zeta$ and weakly on the energy spectrum. +" Because for />0 the form of ομΝ) 1s well approximated by either R7! (1> I) or R77 (i= 0). in practice it is not necessary to fully specify the £,,,."," Because for $l>0$ the form of $\omega_{nlm}(R)$ is well approximated by either $R^{-1}$ $n>1$ ) or $R^{-3/2}$ $n=0$ ), in practice it is not necessary to fully specify the $E_{nlm}$." +" Rather. it is sufficient to define E"",ose=SZ5n0.0mEnim and EZ?ose—M7neldsOmΕμ. to the m fundamental oscillations and the p-modes. correspondingrespectively."," Rather, it is sufficient to define $\Eo^0=\sum_{n=0,l>0,m} E_{nlm}$ and $\Eo^{>0}\equiv\sum_{n\ge1,l>0,m} E_{nlm}$, corresponding to the energy in fundamental oscillations and the p-modes, respectively." +" The energyresulting excess pressure due to the pulsations is then where V=4zR/3 and the difference between the denominators arises from the different asymptotic behaviors of the :c,/,€R).", The resulting excess pressure due to the pulsations is then where $V=4\pi R^3/3$ and the difference between the denominators arises from the different asymptotic behaviors of the $\omega_{nlm}(R)$. +" Note that this is confined to the somewhat narrow from E4,,/3VxP4,0}$." +The particular form of the £0.energy spectrum reflects both the mechanism by which the pulsations are excited and their subsequent evolution within the core., The particular form of the energy spectrum reflects both the mechanism by which the pulsations are excited and their subsequent evolution within the core. + Here we consider three different forms for the turbulent energy spectrum. seeking to bracket the possible consequences.," Here we consider three different forms for the turbulent energy spectrum, seeking to bracket the possible consequences." +" A natural place to begin is to assume a Kolmogorov spectrum for the oscillations. Le.. where so that E;=dirk)EX,ο"," A natural place to begin is to assume a Kolmogorov spectrum for the oscillations, i.e., where so that $E_k = 4\pi k_{nlm}^2 E_{nlm}^K \propto k^{-5/3}$." + Despite the heavy weight upon long-wavelengths. this is dominated by #>0 modes. primarily due to the dipole and quadrupole oscillations. such that we have E20/E?~3.5.," Despite the heavy weight upon long-wavelengths, this is dominated by $n>0$ modes, primarily due to the dipole and quadrupole oscillations, such that we have $\Eo^{>0}/\Eo^0\simeq3.5$." +" For concreteness. in Figure the resulting surface pressure is shown by the red line for Ey.=0.58. though this scales linearly with E,/Ep."," For concreteness, in Figure \ref{fig:PvR} the resulting surface pressure is shown by the red line for $\Eo=0.3\Eb$, though this scales linearly with $\Eo/\Eb$." + While not motivated by any particular turbulence model. a flat energy spectrum does have the virtue that all realistic choices. for the turbulent spectra lie. between it and the Kolmogorov distributions.," While not motivated by any particular turbulence model, a flat energy spectrum does have the virtue that all realistic choices for the turbulent spectra lie between it and the Kolmogorov distributions." + Therefore. we also consider. which is flat for 5.7<5 and vanishing otherwise.," Therefore, we also consider, which is flat for $n,l\le5$ and vanishing otherwise." + The truncation is arbitrary. here set by numerical convenience.," The truncation is arbitrary, here set by numerical convenience." + However. as argued above. the particulars of the cut-off are not important in practice since 1t is primarily the relative values of EO. and Ej! that matter.," However, as argued above, the particulars of the cut-off are not important in practice since it is primarily the relative values of $\Eo^0$ and $\Eo^{>0}$ that matter." + As with the Kolmogorov spectrum the latter dominates with /E.-3.9 implying that the resulting perturbation to theE; surface pressure will be similar., As with the Kolmogorov spectrum the latter dominates with $\Eo^{>0}/\Eo^0\simeq 3.9$ implying that the resulting perturbation to the surface pressure will be similar. + Indeed. despite the considerable difference in their particulars. since EUΕως are similar for both spectra the resulting surface pressures are nearly indistinguishable.," Indeed, despite the considerable difference in their particulars, since $\Eo^{>0}/\Eo^0$ are similar for both spectra the resulting surface pressures are nearly indistinguishable." +" The surface pressure for the Flat energy spectrum is shown in Figure |]. by the blue line (when £,.=0.3£)).", The surface pressure for the Flat energy spectrum is shown in Figure \ref{fig:PvR} by the blue line (when $\Eo=0.3\Eb$ ). + For both cases we find PoiPy=OSEoΕν]. implying that the fractional change in the maximum stable mass of an oscillating isothermal core is approximately 0.25[Ey/Ej].," For both cases we find $\Po/P_0\simeq 0.5 +\left|\Eo/\Eb\right|$, implying that the fractional change in the maximum stable mass of an oscillating isothermal core is approximately $0.25\left|\Eo/\Eb\right|$." + Finally. we consider à. fundamental-dominated energy spectrum. ie.. one in which only the 7=0 modes are excited. with an otherwise Kolmogorov spectrum. as described for Enim," Finally, we consider a fundamental-dominated energy spectrum, i.e., one in which only the $n=0$ modes are excited, with an otherwise Kolmogorov spectrum, as described for $E_{nlm}^K$." + That is. Aside from presenting an extreme alternative. such an energy spectrum will be motivated in Section ??.. where we discuss the evolution of the energy spectrum during core formation.," That is, Aside from presenting an extreme alternative, such an energy spectrum will be motivated in Section \ref{sec:EoaMSSC}, where we discuss the evolution of the energy spectrum during core formation." +" In this case Ej,=EO, explicitly. and the resulting surface pressure. shown by the green line in Figure | (again for Ey.= 0.3EU). is substantially larger than those produced by the previous two spectra."," In this case $\Eo=\Eo^0$ explicitly, and the resulting surface pressure, shown by the green line in Figure \ref{fig:PvR} (again for $\Eo=0.3\Eb$ ), is substantially larger than those produced by the previous two spectra." +" This is a result of both the dependence of P, upon the division of energy between E? and E;"" as well as the departure from the asymptotic expressions of the nim Dear Qua for n>0.", This is a result of both the dependence of $\Po$ upon the division of energy between $\Eo^0$ and $\Eo^{>0}$ as well as the departure from the asymptotic expressions of the $\omega_{nlm}$ near $\zc$ for $n>0$. + As a consequence. in this case we find PaciPy~LOEncΕν]. corresponding to a fractional increase in the maximum stable mass of approximately 0.5[EEy.," As a consequence, in this case we find $\Po/P_0\simeq 1.0 \left|\Eo/\Eb\right|$, corresponding to a fractional increase in the maximum stable mass of approximately $0.5\left|\Eo/\Eb\right|$." +" In summary. we have found that the non-radial oscillations/ generally produce an increase in the surface pressure of the isothermal cores. with magnitude linearly related to the total energy in the pulsations and bounded near Cui, by for an extraordinarily broad class of energy spectra."," In summary, we have found that the non-radial oscillations generally produce an increase in the surface pressure of the isothermal cores, with magnitude linearly related to the total energy in the pulsations and bounded near $\zc$ by for an extraordinarily broad class of energy spectra." + This corresponds to an increase in the maximum mass of stable cores of approximately, This corresponds to an increase in the maximum mass of stable cores of approximately +"In this Coulomb system, nearby plasma is polarized by cach ion.","In this Coulomb system, nearby plasma is polarized by each ion." +" When two ions approach with the possibility of engaging in a nuclear reaction, each ion is surrounded by a sereening cloud."," When two ions approach with the possibility of engaging in a nuclear reaction, each ion is surrounded by a screening cloud." + Thus each ion is attracted by the electrons and repelled by the protons in its partner's cloud., Thus each ion is attracted by the electrons and repelled by the protons in its partner's cloud. + The combined effect of the particles in the screening clouds on the potential energy of the pair of ions is referred to as screening., The combined effect of the particles in the screening clouds on the potential energy of the pair of ions is referred to as screening. + This screening effect reduces the standard Coulomb potential between approaching ions in a plasma to a sereened potential which includes the contribution to the potential from the surrounding plasma., This screening effect reduces the standard Coulomb potential between approaching ions in a plasma to a screened potential which includes the contribution to the potential from the surrounding plasma. +" The reduced potential enables the ions to tunnel through the potential barrier more easily, thus enhancing fusion rates."," The reduced potential enables the ions to tunnel through the potential barrier more easily, thus enhancing fusion rates." + Salpeter(1954) derived an expression for the enhancement of nuclear reaction rates due to electron screening., \citet{Salpeter_1954} derived an expression for the enhancement of nuclear reaction rates due to electron screening. +" By solving the Poisson-Boltzmann equation for electrons and ions in a plasma under the condition of weak screening (dincnuion<< Kg7). Salpeter arrived at an expression for the screening energy that is equivalent to that of the Debye-Hücckel theory of dilute solutions of electrolytes (Debye&Hückel1923).. where the Debye length, Up, is the characteristic screening length of a plasma at temperature T with number density η. Although Salpeter's approximation for screening is widely accepted, several papers over the last few decades (e.g.Shaviv&1996;Carraroetal.1988:Weiss2001) have questioned either the derivation itself or the validity of applying the approximation to hot, dense, Coulomb systems like the plasma of the solar core."," By solving the Poisson-Boltzmann equation for electrons and ions in a plasma under the condition of weak screening $\phi_{\rm{interaction}}<< k_BT$ ), Salpeter arrived at an expression for the screening energy that is equivalent to that of the Debye-Hücckel theory of dilute solutions of electrolytes \citep{Debye_1923}, where the Debye length, $\lambda_D$, is the characteristic screening length of a plasma at temperature $T$ with number density $n$, Although Salpeter's approximation for screening is widely accepted, several papers over the last few decades \citep[e.g.][]{Shaviv_1996, +Carraro_1988, Weiss_2001} have questioned either the derivation itself or the validity of applying the approximation to hot, dense, Coulomb systems like the plasma of the solar core." +" Various work deriving alternative formulae for screening (Carraroetal...1988:Opher&2000:Shaviv1996:1999:Lavagno&Quarati2000:Tsytovich2000) were refuted in subsequent papers (seeBahcalletal.2002,forasummaryofargumentsinSalpeter’sdefense).."," Various work deriving alternative formulae for screening \citep{Carraro_1988, Opher_2000, Shaviv_1996, Savchenko_1999, Lavagno_2000, +Tsytovich_2000} were refuted in subsequent papers \citep[see][for a summary of +arguments in Salpeter's defense]{Bahcall_2002}." +" However, the question of screening remains open."," However, the question of screening remains open." + Dynamic screening arises because the protons in a plasma are much slower than the electrons., Dynamic screening arises because the protons in a plasma are much slower than the electrons. + They are therefore not able to rearrange themselves as quickly around individual faster moving ions., They are therefore not able to rearrange themselves as quickly around individual faster moving ions. +" Since nuclear reactions require energies several times the average thermal energy, the ions that are able to engage in nuclear reactions in the Sun are such faster moving ions, which therefore may not be accompanied by their full screening cloud."," Since nuclear reactions require energies several times the average thermal energy, the ions that are able to engage in nuclear reactions in the Sun are such faster moving ions, which therefore may not be accompanied by their full screening cloud." + Salpeter uses the mean-field approach in which the many-body interactions are reduced to an average interaction that simplifies calculations., Salpeter uses the mean-field approach in which the many-body interactions are reduced to an average interaction that simplifies calculations. + This technique is quite useful in thermodynamical calculations that rely on the average behavior of the plasma., This technique is quite useful in thermodynamical calculations that rely on the average behavior of the plasma. +" However, dynamic effects for the fast-moving, interacting ions lead to a screened potential that deviates from the average value."," However, dynamic effects for the fast-moving, interacting ions lead to a screened potential that deviates from the average value." + The nuclear reaction rates therefore differ from those computed with the mean-field approximation., The nuclear reaction rates therefore differ from those computed with the mean-field approximation. +" Shaviv&(1996,1997,2000,2001) used the method of molecular dynamics to model"," \citet{Shaviv_1996, Shaviv_1997, Shaviv_2000, Shaviv_2001} + used the method of molecular dynamics to model" +where in the first line on the right hand side the factor 2 accounts for the fact that a disk has (wo surfaces. in the third line we have used the boundary conditions £(r—o)=1. gQpí(r—x)0. and gQp(r=r4)0.,"where in the first line on the right hand side the factor $2$ accounts for the fact that a disk has two surfaces, in the third line we have used the boundary conditions $E^+(r\rightarrow \infty) = 1$, $g\Omega_D (r\rightarrow \infty) = 0$, and $g\Omega_D (r=r_{ms}) = 0$." + The power of the black hole. which is the energy transferecl [rom the black hole to the disk per unit time as measured by an observer αἱ infinity. is so equation (18)) can be written as where is the efficiency. of accretion. ie.. the effidency of the disk when (he magnetic coupling between the black hole and the disk does not exist.," The power of the black hole, which is the energy transfered from the black hole to the disk per unit time as measured by an observer at infinity, is so equation \ref{int_p}) ) can be written as where is the efficiency of accretion, i.e., the efficiency of the disk when the magnetic coupling between the black hole and the disk does not exist." +" For a Schwarzschilel black hole. ειz0.06: for a ον black hole of s=«fM;0.998. ει2 0.32: for an extreme Ixeir black hole of 5— lee,&0.42 (Thorne 1974).."," For a Schwarzschild black hole, $\epsilon_0 \approx 0.06$; for a Kerr black hole of $s \equiv a/M_H = +0.998$, $\epsilon_0 \approx 0.32$ ; for an extreme Kerr black hole of $s = 1$, $\epsilon_0\approx 0.42$ \citep{tho74}. ." + For any thin Ixeplerian disk around a Ixerr black hole. eg«0.42 always.," For any thin Keplerian disk around a Kerr black hole, $\epsilon_0 < 0.42$ always." + Equation (20)) describes the global balance of enerev lor a quasi-steady accretion disk magnetically coupled to a Kerr black hole., Equation \ref{bal}) ) describes the global balance of energy for a quasi-steady accretion disk magnetically coupled to a Kerr black hole. + £ is the total power of the disk., ${\cal L}$ is the total power of the disk. + Mpey represents the rate of change in the gravitational energv of the disk. as in the standard theory of an accretion disk.," $\dot{M}_D\,\epsilon_0$ represents the rate of change in the gravitational energy of the disk, as in the standard theory of an accretion disk." + μυ represents the rate of energy transfered [rom Cie black hole to the disk. which is absent in the standard theory of an aceretion disk.," ${\cal L}_{HD}$ represents the rate of energy transfered from the black hole to the disk, which is absent in the standard theory of an accretion disk." + From equation (20)). the total efficiency of the disk is Lay =0.re. there is no energy transfer between the black hole and the disk by the magnetic coupling as the case in the standard theory of an accretion disk. e=ej aud the power of (he disk purely comes from (he gravitational enerev of the disk.," From equation \ref{bal}) ), the total efficiency of the disk is If ${\cal L}_{HD} = 0$, i.e. there is no energy transfer between the black hole and the disk by the magnetic coupling – as the case in the standard theory of an accretion disk, $\epsilon = \epsilon_0$ and the power of the disk purely comes from the gravitational energy of the disk." + I μυ>0. which is the case when the black hole rotates faster than the disk. energy is transfered from the black hole to the disk.," If ${\cal L}_{HD}>0$, which is the case when the black hole rotates faster than the disk, energy is transfered from the black hole to the disk." + Then there are (wo sources for the power of the disk: one is the eravitational energy ofthe disk(represented by M peo). the other is the rotational energy of," Then there are two sources for the power of the disk: one is the gravitational energy ofthe disk(represented by $\dot{M}_D\,\epsilon_0$ ), the other is the rotational energy of" +2007).,2007). + For a passively aging stellar population there would be a blueward shift of the CMIC with increasing lookback time (recshift): Holden et al. (, For a passively aging stellar population there would be a blueward shift of the CMR with increasing lookback time (redshift); Holden et al. ( +2004) and Taylor et al. (,2004) and Taylor et al. ( +2008) find some evidence of this colour evolution.,2008) find some evidence of this colour evolution. + In this paper we aim to obtain an accurate measurement of the evolution of the CMIU to 2=0.36., In this paper we aim to obtain an accurate measurement of the evolution of the CMR to $z=0.36$. + However. to determine the CMIR over à wide redshift range. but in a fixed rest-frame colour (e.g. gr). we need to apply accurate é- to convert the observed photometric magnitudes back to the galaxy rest-[rames.," However, to determine the CMR over a wide redshift range, but in a fixed rest-frame colour (e.g. $g-r$ ), we need to apply accurate $k$ -corrections to convert the observed photometric magnitudes back to the galaxy rest-frames." +" Galaxy Á-corrections. are commonly derived. from modelled: spectra. but. in. reality each galaxy has its own individual A-correction. and the uncertainties in modelled A-corrections (even a [ων 0.01 mag) may well be comparable to the small evolution that we aim to study in the οδι,"," Galaxy $k$ -corrections are commonly derived from modelled spectra, but in reality each galaxy has its own individual $k$ -correction, and the uncertainties in modelled $k$ -corrections (even a few 0.01 mag) may well be comparable to the small evolution that we aim to study in the CMR." + Thus. it would be much preferable to derive either A-corrections. or rest-frame colours. directly from the galaxy spectra. but for good statistics on the CAL a database of many thousand high quality. Lux calibrated spectra are recuired.," Thus, it would be much preferable to derive either $k$ -corrections, or rest-frame colours, directly from the galaxy spectra, but for good statistics on the CMR a database of many thousand high quality, flux calibrated spectra are required." + The Sloan Digital Sky Survey (SDSS. Stoughton et al.," The Sloan Digital Sky Survey (SDSS, Stoughton et al." + 2002) had as one of its stated aims to revolutionize the stucly of galaxies at moclerate redshifts. by obtaining hundreds of thousands of spectra. together with five-hancl (θές) photometry.," 2002) had as one of its stated aims to revolutionize the study of galaxies at moderate redshifts, by obtaining hundreds of thousands of spectra together with five-band $ugriz$ ) photometry." + Bernardi ct al. (, Bernardi et al. ( +2003a). carried. out an initial study of the early-type galaxies in the SDSS. selecting 9000 I2/S0s (from the 65000 ealaxy spectra available at that time) using a combination of morphological ancl spectral criteria.,"2003a) carried out an initial study of the early-type galaxies in the SDSS, selecting 9000 E/S0s (from the $\sim 65000$ galaxy spectra available at that time) using a combination of morphological and spectral criteria." + Rest-frame colours and magnitudes were estimated. using A-corrections based on (i) an evolving Bruzual Charlot (2003. hereafter DCO3) model with a single burst of star-formation 9 Cyr ago. with solar abundances and a Ixroupa (2001) LAIR. (ii) an observed elliptical template spectrum from Coleman. Wu and Weedman (1980. hereafter CWWMD," Rest-frame colours and magnitudes were estimated, using $k$ -corrections based on (i) an evolving Bruzual Charlot (2003, hereafter BC03) model with a single burst of star-formation 9 Gyr ago, with solar abundances and a Kroupa (2001) IMF, (ii) an observed elliptical template spectrum from Coleman, Wu and Weedman (1980, hereafter CWW)." + For these L/80 salaxies Bernardi et al. (, For these E/S0 galaxies Bernardi et al. ( +"2003b) estimated. evolution rates of A(AL,)l.15z. ACAL,)=O.S5s anc ACAL;)=0.75.","2003b) estimated evolution rates of $\Delta(M_g)=-1.15z$, $\Delta(M_r)=-0.85z$ and $\Delta(M_i)=-0.75z$." + Dernardi et al. (, Bernardi et al. ( +00020) derived a CAIR using a k-correction from a compositeof the above two models. A4)9AeGL,"2003c) derived a CMR using a k-correction from a compositeof the above two models, $K_{CWW}^{evol}(z)=K^{no-ev}_{CWW}(z)+K^{evol}_{BC}-K^{no-ev}_{BC}$." +" The rest-[rame colour (gr)er correlated with luminosityIN and velocity. dispersion. as 0.025+0.003)AZ,. and o7£977, ", The rest-frame colour $(g-r)_{rf}$ correlated with luminosity and velocity dispersion as $(-0.025\pm 0.003)M_r$ and $\sigma^{0.26\pm 0.02}$. +Metal abundances in the [E/S0s correlated. with velocity dispersion1 e.g. as Alesx077οουσ— and {hey5oxgHοΕυ0 and the mean stellar age was estimated as 9 Civr.," Metal abundances in the E/S0s correlated with velocity dispersion e.g. as ${\rm Mg_2}\propto \sigma^{0.20\pm 0.02}$ and $\langle \rm Fe \rangle \propto \sigma^{0.11\pm 0.02}$, and the mean stellar age was estimated as 9 Gyr." + Bernardi et al. (, Bernardi et al. ( +2005) re-examined the CAL. using 39320 earlv-tvpe. galaxies. from the SDSS. and. showed that it was the result. of more fundamental correlations between colour ancl velocity dispersion o. ancl between e and. Luminosity.,"2005) re-examined the CMR, using 39320 early-type galaxies from the SDSS, and showed that it was the result of more fundamental correlations between colour and velocity dispersion $\sigma$, and between $\sigma$ and luminosity." + CGallazzi ct al (2006). using a similar sample of SDSS I5/SOs. found a steep correlation of both metallicity and Alefhe ratio with stellar mass. as traced by either luminosity or velocity. dispersion. (e.g. Algaex.o 7735 ," Gallazzi et al (2006), using a similar sample of SDSS E/S0s, found a steep correlation of both metallicity and Mg/Fe ratio with stellar mass, as traced by either luminosity or velocity dispersion (e.g. ${\rm Mg_2}\propto \sigma^{0.25\pm0.02}$ )." +"""Phey explained the CALR as a sequence in stellar mass. with some increase in mean age."," They explained the CMR as a sequence in stellar mass, with some increase in mean age." + Phe CMI exhibited. only a minimal rechward shift (0.00640.003 maging or) between less and more dense clustering environments., Their CMR exhibited only a minimal redward shift $0.006\pm0.003$ mag in $g-r$ ) between less and more dense clustering environments. + Jimenez et al. (, Jimenez et al. ( +2007) concluded: from the small scatter in the CATR that the E/S0s formed. most of their stars at 2=2. and from the super-solar Mg/Ee abundance ratios Ca-cnohancement’) of the more massive LE/SOs that their star-formation took place in a short burst (~1 Civr).,"2007) concluded from the small scatter in the CMR that the E/S0s formed most of their stars at $z>2$, and from the super-solar Mg/Fe abundance ratios $\alpha$ -enhancement') of the more massive E/S0s that their star-formation took place in a short burst $\sim 1$ Gyr)." + Continued aad ongoing SDSS observations have greatly enlarged. the database of spectra. enabling us to analyse the CATR of a Larger sample of I2/S0s than previously.," Continued and ongoing SDSS observations have greatly enlarged the database of spectra, enabling us to analyse the CMR of a larger sample of E/S0s than previously." + In Section 2 we describe the data ancl sample selection. and in Section 3. the derivation of the AÁ-corrections from the spectra.," In Section 2 we describe the data and sample selection, and in Section 3, the derivation of the $k$ -corrections from the spectra." + In Section 4 we present our CMIU ancl compare it with CALRs obtained using other apertures and A-correct ion prescriptions., In Section 4 we present our CMR and compare it with CMRs obtained using other apertures and $k$ -correction prescriptions. + We present a similar analysis of the Colt in Section 5., We present a similar analysis of the $\sigma$ R in Section 5. + We summarize and discuss our results in Section 6., We summarize and discuss our results in Section 6. +" SDSS magnitudes are given in the AB system where mip=48.6095ος, and mag=0 is 3631 Jv.", SDSS magnitudes are given in the AB system where $m_{AB}=-48.60-2.5$ log $F_{\nu}$ and $m_{AB}=0$ is 3631 Jy. +" We assume throughout a spatially Hat cosmology with df,=70 knis INpe1 Oy,2027 and O4=0.73. eiving the age of the Universe as 13.88 Civr."," We assume throughout a spatially flat cosmology with $H_0=70$ km $\rm s^{-1}Mpc^{-1}$, $\Omega_{M}=0.27$ and $\Omega_{\Lambda}=0.73$, giving the age of the Universe as 13.88 Gyr." + Our sample is selected from Data Release 4. of the Sloan Digital Sky Survey (Adclman-A\leCarthy ct al., Our sample is selected from Data Release 4 of the Sloan Digital Sky Survey (Adelman-McCarthy et al. + 2006). which covered 4783 deg? of sky with spectra. [or a total of 673280. sources.," 2006), which covered 4783 $\rm deg^2$ of sky with spectra for a total of 673280 sources." + However. our analysis uses more recent versions of the spectra from SDSS) Data Release 6 CXdelman-MeC'arthy. et al.," However, our analysis uses more recent versions of the spectra from SDSS Data Release 6 (Adelman-McCarthy et al." + 2008). calibrated ab Princeton University (spectro.princeton.edu)," 2008), calibrated at Princeton University (spectro.princeton.edu)." + ‘These reductions include measurements of the line-of-sient velocity dispersion (0) through the 3 aresec diameter aperture., These reductions include measurements of the line-of-signt velocity dispersion $\sigma$ ) through the 3 arcsec diameter aperture. + This dataset. contained 367471 galaxies of all tvpes (but exclucling stars. QSOs and unclassifiable sources) in the range 14.5=0.2., The tilt of the K–band FP where the change in the stellar population is negligible is approximately $\beta=0.2$. + This is indeed iu good agreement with our expectation if the tilt were due only to the nonhomoloey and if color eradieuts inside ealaxies do not change their Sévrsic inclices., This is indeed in good agreement with our expectation if the tilt were due only to the nonhomology and if color gradients inside galaxies do not change their Sérrsic indices. + ludeed. radial VIs evacdicnts iu the surface brightness profiles of ellipticals are on average only 0.16 mae + (Peleticr. Valeutiju Jameson 1990) which is small compared to the variations in surface brightuess within an effective radius.," Indeed, radial V–K gradients in the surface brightness profiles of ellipticals are on average only 0.16 mag $^{-1}$ (Peletier, Valentijn Jameson 1990) which is small compared to the variations in surface brightness within an effective radius." + The homologous FP of our sample has a scatter in log(M/L) of order which is consistent with previous results (BBF: Pahre. Djorsovski Carvalho 1998).," The homologous FP of our sample has a scatter in log(M/L) of order which is consistent with previous results (BBF; Pahre, Djorgovski Carvalho 1998)." + The scatter is not significantly reduced im the non-homologous FP which iudicates that it is mainly a result of population effects aud not of structural variations within a given luninosity bin., The scatter is not significantly reduced in the non-homologous FP which indicates that it is mainly a result of population effects and not of structural variations within a given luminosity bin. + Qur results rule out that even very massive elliptical are strouely dominated by dark matter in thei inuer regions. which is iu agreement with Ris et al. (," Our results rule out that even very massive ellipticals are strongly dominated by dark matter in their inner regions, which is in agreement with Rix et al. (" +1997) and Cerhard et al. (,1997) and Gerhard et al. ( +2001).,2001). + After correcting for nouliomology. the mean value of the mass-to-leht ratio (AL/Lyp) of earbv-tvpe ealaxies iu our hnuuimositv rauge is 7142.8 (lo scatter).," After correcting for nonhomology, the mean value of the mass-to-light ratio $_B$ ) of early-type galaxies in our luminosity range is $\pm$ 2.8 $\sigma$ scatter)." + This value is in good agreement with the value expected for an old stellar populations of AU/Lp=7.8#2.7 (Gerhard et al 2001)., This value is in good agreement with the value expected for an old stellar populations of $_B$ $\pm$ 2.7 (Gerhard et al 2001). + We thaul Nicola Caon and Ποπ Jerjen for providing us with an (updated) clectronic copy of the Virgo Cluster Catalogs and [ausWalter Rix. Marijü Fraus. Alister W. Caaham and Ralf Deuder for interesting discussions.," We thank Nicola Caon and Helmut Jerjen for providing us with an (updated) electronic copy of the Virgo Cluster Catalogs and Hans–Walter Rix, Marijn Franx, Alister W. Graham and Ralf Bender for interesting discussions." + Some data used in this work were been obtained from ITvperLeda database., Some data used in this work were been obtained from HyperLeda database. +Scaunapicco While several theoretical models of eemitters have been developed (c.g.Bartonοἱal.2004:Dave2009:Davaletal.2008:Samuictal9000) we still lack a complete understanding of how mass assembly. ancl star-formation⋅⊀ occurs in. these galaxies.," While several theoretical models of emitters have been developed \citep[e.g.][]{bar04,dav06,tas06,shi07,nag08,del06,kob07,kob09,day08,sam09} + we still lack a complete understanding of how mass assembly and star-formation occurs in these galaxies." +. It is Donlikely that mergers are the dominant. mode of⋅ mass accretion. resulting ..in at. least some fraction (2⋅⊀ 20%)⋅ of Lva (c.g. Pirzkaletal.2007:Bond2009:‘Taniguchietal.2009).," It is likely that mergers are the dominant mode of mass accretion resulting in star-formationin at least some fraction $\geq20\%$ ) of emitters \citep[e.g.][]{pir07,bon09,tan09}." +. tecently. Tilvietal.(2009). developed a physical mocel ol eemitters which is successful in explaining many observable including number density. stellar mass. star-formation rate. and clustering properties of. eemitters from 2=3 to zzc7.," Recently, \citet{til09} developed a physical model of emitters which is successful in explaining many observable including number density, stellar mass, star-formation rate, and clustering properties of emitters from $z\approx 3$ to $z\approx 7$." + This mocdel «τους funclamentally from many of the earlier models (e.g.Llaimanetal.2007:Fernandez&Komatsu2008). in that the of emitters. and hence their [luminosity is proportional to the mass aceretion rate rather than the total halo mass.," This model differs fundamentally from many of the earlier models \citep[e.g.][]{hai99,dij07,mao07,sta07,fer08} + in that the star-formation of emitters, and hence their luminosity is proportional to the mass accretion rate rather than the total halo mass." + In this paper. we combine the above model with a large dark matter cosmological. simulation. to predict. the major. merger. minor merger. and smooth accreting cemitter [fraction from zzc3 to z7.," In this paper, we combine the above model with a large dark matter cosmological simulation to predict the major merger, minor merger, and smooth accreting emitter fraction from $z\approx3$ to $z\approx 7$." + We also carefully asses the uncertainties in our model predictions., We also carefully asses the uncertainties in our model predictions. + We note that currently there are no theoretical. prediction20. of merger [o⋅. να[ contters., We note that currently there are no theoretical prediction of merger fraction of emitters. + On the observational front. only recently it has been possible to estimate the merger fraction of eenmitters.," On the observational front, only recently it has been possible to estimate the merger fraction of emitters." + Atosc0.3. Cowiectal.(2010) found that :30% of enitters either irregulars Oro Dave disturbed morphologies areindicative of mergers.," At $z\sim 0.3$, \citet{cow10} + found that $\geq30\%$ of emitters are either irregulars or have disturbed morphologies indicative of mergers." + jt higher redshifts. 2o3. the observed merger fraction. varies [rom zz20% to zz45% (Pirzkaletal.2007:Bondct2009:‘Taniguchiοἱal. 2009)..," At higher redshifts, $z > 3$, the observed merger fraction varies from $\approx 20\%$ to $\approx 45 \%$ \citep[]{pir07,bon09,tan09}. ." + Recently. Cookeetal.(2010). found that all. Lyman- galaxics (LBGs) that have close companions Cz.15ht Alpe) exhibit strong comission lines.," Recently, \citet{coo10} + found that all Lyman-break galaxies (LBGs) that have close companions $\leq 15 h^{-1}$ Mpc) exhibit strong emission lines." + In. the spectroscopically confirmed. close pairs. the spectra/imaging show double," In the spectroscopically confirmed close pairs, the spectra/imaging show double" +and purity are defined via equations 23 and 24..,and purity are defined via equations \ref{eq:complete} and \ref{eq:pure}. . +" Where Nmatches is the total number of unique or multiple matches, Neiusters is the total number of DFoF clusters found and Άίμαιοες is the total number of mock haloes."," Where $N_{matches}$ is the total number of unique or multiple matches, $N_{clusters}$ is the total number of DFoF clusters found and $N_{haloes}$ is the total number of mock haloes." + Nnatoes 18 calculated ignoring all mock haloes with less than 3 galaxy members as this is the detection limit of the DFoF code., $N_{haloes}$ is calculated ignoring all mock haloes with less than 3 galaxy members as this is the detection limit of the DFoF code. +" Fig.4 shows the total number of clusters found in the 258LAQ mock (top panel), unique completeness (middle left panel), unique purity (middle right panel), non-unique completeness (bottom left panel) and non-unique purity (bottom right panel) as a function of Rfriena(z=0.5) and Ufriend(Z=0.5)."," \ref{fig:rfriends00} shows the total number of clusters found in the 2SLAQ mock (top panel), unique completeness (middle left panel), unique purity (middle right panel), non-unique completeness (bottom left panel) and non-unique purity (bottom right panel) as a function of $R_{friend}(z=0.5)$ and $v_{friend}(z=0.5)$." + This figure clearly shows that the DFoF results are primarily dependent on the choice of Rfriena(z 0.5)., This figure clearly shows that the DFoF results are primarily dependent on the choice of $R_{friend}(z=0.5)$ . +" Looking at the overall contour shape in the top panel, onecan see that the number of clusters found peaks around"," Looking at the overall contour shape in the top panel, onecan see that the number of clusters found peaks around" + , +mag were divided into different magnitude eroups with a bin of 0.5 mae.,mag were divided into different magnitude groups with a bin of 0.5 mag. + For cach maecuitucde eroup of quasars. a Gaussian fiction was used to fit the proper motions in cach componcut in that eroup.," For each magnitude group of quasars, a Gaussian function was used to fit the proper motions in each component in that group." + Figure Ll indicates that there is no obvious maeuitucde dependence of the systematic errors of the USNO-SDSS proper motions iu the both two components., Figure \ref{fg11} indicates that there is no obvious magnitude dependence of the systematic errors of the USNO-SDSS proper motions in the both two components. +" The rms of the systematic errors of the USNO-SDSS proper motions for quasars in different magnitude eroups is 0.3 and 0.1 mias vr| in fi,cosdé and sty. respectively,"," The rms of the systematic errors of the USNO-SDSS proper motions for quasars in different magnitude groups is $0.3$ and $0.4$ mas $^{-1}$ in $\mu_{\alpha}\cos\delta$ and $\mu_{\delta}$, respectively." + This rus is a little sanaller than that for quasars in different magnitudeeroups iu the PPMXLE catalog., This rms is a little smaller than that for quasars in different magnitudegroups in the PPMXL catalog. + Figure 11 also indicates ια the random errors of the USNO-SDSS proper notions in cach component increase along with the SDSS r inaenitude of quasars., Figure \ref{fg11} also indicates that the random errors of the USNO-SDSS proper motions in each component increase along with the SDSS $r$ magnitude of quasars. + Sinular to Figure 6.. ιο vellow dash dot line iu each pauel of Figure 11 shows the best-fittine function which describing the SDSS r maeuitucdeg dependence of the random error of 10 USNO-SDSS proper motions in cach compoucut.," Similar to Figure \ref{fg6}, the yellow dash dot line in each panel of Figure \ref{fg11} shows the best-fitting function which describing the SDSS $r$ magnitude dependence of the random error of the USNO-SDSS proper motions in each component." +" The vest-fitting fiction for the random errors in J6,cosà IS-DQ6—“ye23|JoypeexpκοΤΕ299! nas aud the vost-fitting function for the random errors dm py is Gy,=“ye23|3.9exp"".20-1)2 ας "," The best-fitting function for the random errors in $\mu_{\alpha}\cos\delta$ is$\sigma_{\mu_{\alpha}\cos\delta}=2.3+3.3\exp^{(r-20.5)}$ mas $^{-1}$, and the best-fitting function for the random errors in $\mu_{\delta}$ is $\sigma_{\mu_{\delta}}=2.3+3.9\exp^{(r-20.4)}$ mas $^{-1}$ ." +Tn general. the random error of the USNO-SDSS proper motions in one compoucut changes from ~2.5 mas | to ~6 mas + along with the SDSS r magnitude changing from 16.0 to 21.0 mae.," In general, the random error of the USNO-SDSS proper motions in one component changes from $\sim2.5$ mas $^{-1}$ to $\sim6$ mas $^{-1}$ along with the SDSS $r$ magnitude changing from 16.0 to 21.0 mag." + Siuuilar to Figure 7.. Figure 12 shows the SDSS gor color dependence of the USNO-SDSS proper motions in each component of quasars cross-identified in the PPMXL and SDSS DR7 catalogs.," Similar to Figure \ref{fg7}, Figure \ref{fg12} shows the SDSS $g-r$ color dependence of the USNO-SDSS proper motions in each component of quasars cross-identified in the PPMXL and SDSS DR7 catalogs." + Quasars with SDSS g rcolor iu the range between0.[ aud 1.1xwere divided iuto differeut color groups with a biu of 0.2 mag., Quasars with SDSS $g-r$ color in the range $-0.4$ and 1.4 were divided into different color groups with a bin of 0.2 mag. + For each color eroup of quasars. a Gaussian function was sed to fit the proper motions in cach compoucut in that eroup.," For each color group of quasars, a Gaussian function was used to fit the proper motions in each component in that group." + Figure 12 indicates that there is no obvious color epeudence of the systematic errors of the USNO-SDSS proper motions in the both two componeuts., Figure \ref{fg12} indicates that there is no obvious color dependence of the systematic errors of the USNO-SDSS proper motions in the both two components. +" The riis of the systematic errors ofthe USNO-SDSS proper motions for different quasar color groups is 0.1 aud 0.3 mas vrobdu µεcosd and prs. respectively,"," The rms of the systematic errors of the USNO-SDSS proper motions for different quasar color groups is $0.1$ and $0.3$ mas $^{-1}$ in $\mu_{\alpha}\cos\delta$ and $\mu_{\delta}$, respectively." + This ruis is a little sanaller than that for quasars m different color eroups in the PPMXLE catalog., This rms is a little smaller than that for quasars in different color groups in the PPMXL catalog. + Figure 12. also indicates that the random errors of the USNO-SDSS proper motio-S iu both two compoucuts increase along with the SDSS gvr colors of quasars., Figure \ref{fg12} also indicates that the random errors of the USNO-SDSS proper motions in both two components increase along with the SDSS $g-r$ colors of quasars. +" The color dependence of the random errors of the USNO-SDSS proper motions in cach conrponeut was fitted aud showed as vellow dash dot line in cach panel of Figure 12 using the simular function used iu Figures 6 and Ll o,—01bexp[nrc] . here in isthe SDSSyg) rcolor."," The color dependence of the random errors of the USNO-SDSS proper motions in each component was fitted and showed as yellow dash dot line in each panel of Figure \ref{fg12} using the similar function used in Figures \ref{fg6} and \ref{fg11}: $\sigma_{\mu}=a+b\times\exp^{(m-c)}$ , here $m$ is the SDSS$g-r$ color." +" The best-fittiug function for the random errors dn 4,COSO ds Gy,eus=2.1|3exp!lO qua bound the best-fitting fuuction for the random errors iM fis iS σμ=2.3|XTexp'"""" Linas D."," The best-fitting function for the random errors in $\mu_{\alpha}\cos\delta$ is $\sigma_{\mu_{\alpha}\cos\delta}=2.4+3.9\exp^{(m-1.5)}$ mas $^{-1}$ , and the best-fitting function for the random errors in $\mu_{\delta}$ is $\sigma_{\mu_{\delta}}=2.3+3.7\exp^{(m-1.5)}$ mas $^{-1}$." + In general. he random error of the USNO-SDSS proper motious iu one component changes from ~2.5 mas 1 to ~6 mas t along with the SDSS gor color changing from 0.5 ο 1.5.," In general, the random error of the USNO-SDSS proper motions in one component changes from $\sim2.5$ mas $^{-1}$ to $\sim6$ mas $^{-1}$ along with the SDSS $g-r$ color changing from $-0.5$ to 1.5." + Siuilar to Figure 8.. Figure 15. shows the USNO-SDSS xoper motions in each conipoueut of quasars cross-identified iu the PPAINL aud SDSS DR7 catalogs as a ποοι of a and à.," Similar to Figure \ref{fg8}, Figure \ref{fg13} shows the USNO-SDSS proper motions in each component of quasars cross-identified in the PPMXL and SDSS DR7 catalogs as a function of $\alpha$ and $\delta$." + The top two panels of Figure. 13 indicate that there is no a depeudence of the svstemiatic and random errors of the USNO-SDSS proper motions of quasars in the both two components., The top two panels of Figure \ref{fg13} indicate that there is no $\alpha$ dependence of the systematic and random errors of the USNO-SDSS proper motions of quasars in the both two components. + The xus of the systematic errors of the USNO-SDSS proper motions for quasars in different o. eroups is 0.2 and O. bimas vr+ in Bacos and ps. respectively.," The rms of the systematic errors of the USNO-SDSS proper motions for quasars in different $\alpha$ groups is $0.2$ and $0.4$ mas $^{-1}$ in $\mu_{\alpha}\cos\delta$ and $\mu_{\delta}$ , respectively." +" The rus ofthe random errors of the USNO-SDSS proper motions for quasars iu different © groups is 0.1 and 0.1 mas + in qn,cosó and gis. respectively,"," The rms of the random errors of the USNO-SDSS proper motions for quasars in different $\alpha$ groups is $0.4$ and $0.4$ mas $^{-1}$ in $\mu_{\alpha}\cos\delta$ and $\mu_{\delta}$, respectively." +" The bottom-left panel of Figure 15 indicates that there is no obvious à dependence of he svstematic aud raudom errors of the USNO-SDSS xopoer motions in 445,co80.", The bottom-left panel of Figure \ref{fg13} indicates that there is no obvious $\delta$ dependence of the systematic and random errors of the USNO-SDSS proper motions in $\mu_{\alpha}\cos\delta$. +" The rims of the systematic and random errors of the USNO-SDSS proper motions in 4,cosÓ for quasars iu different ὁ eroups is 0.2 and 0.1 nas Lorespectivelv."," The rms of the systematic and random errors of the USNO-SDSS proper motions in $\mu_{\alpha}\cos\delta$ for quasars in different $\delta$ groups is $0.2$ and $0.4$ mas $^{-1}$, respectively." + The bottom-right paucl of Figure 15 indicates that there is no obvious à dependence of he random errors of the USNO-SDSS proper inotious iu pis.,The bottom-right panel of Figure \ref{fg13} indicates that there is no obvious $\delta$ dependence of the random errors of the USNO-SDSS proper motions in $\mu_{\delta}$. + The rins of the random errors of the USNO-SDSS xoper motious in ffs for quasars in different 9 groups is Obamas d., The rms of the random errors of the USNO-SDSS proper motions in $\mu_{\delta}$ for quasars in different $\delta$ groups is $0.4$ mas $^{-1}$. + Simika to the bottom-right panel of Figure 8.. the bottom-rielit panel of Figure 13. indicates he à dependence of the systeinatic errors of the USNO-SDSS proper motious im jn.," Similar to the bottom-right panel of Figure \ref{fg8}, the bottom-right panel of Figure \ref{fg13} indicates the $\delta$ dependence of the systematic errors of the USNO-SDSS proper motions in $\mu_{\delta}$." + For quasars with à>0. a ine of p=OAS|0.038. was used to best fit the à dependence of the systematic errors of jp ancl showed as vellow dash dot line in the bottom-right paucl of Figure 3..," For quasars with $\delta >0$, a line of $\overline{\mu_{\delta}}=-0.18+0.03\delta$ was used to best fit the $\delta$ dependence of the systematic errors of $\mu_{\delta}$ and showed as yellow dash dot line in the bottom-right panel of Figure \ref{fg13}." + The cocficient 0.03 is half of that derived for the 8 dependence of the systematic errors of srs for quasars iu thePPMXL catalog., The coefficient 0.03 is half of that derived for the $\delta$ dependence of the systematic errors of $\mu_{\delta}$ for quasars in thePPMXL catalog. + As the very distant extragalactie source. the proper notion of a quasar has been assumed to be zero.," As the very distant extragalactic source, the proper motion of a quasar has been assumed to be zero." + Proper notions of quasars with very high accuracy are uceded o check this asswuption., Proper motions of quasars with very high accuracy are needed to check this assumption. + In order to detect the secular aberration drift of the extragalactic radio source proper notions caused by the rotation of the Solu System. xuveenter απο the Calactic center. Titovetal.(2011) derived the absolute proper motious of 555 extragalactic radio sources based ou the observation by the very lone vascline iuterferoiietry (VLBI) between 1990 aud 2010.," In order to detect the secular aberration drift of the extragalactic radio source proper motions caused by the rotation of the Solar System barycenter around the Galactic center, \citet{ti11} derived the absolute proper motions of 555 extragalactic radio sources based on the observation by the very long baseline interferometry (VLBI) between 1990 and 2010." + For the most observed radio sources. the inflated position errors are [0 pas in cach coordinate (Titovctal.2011).," For the most observed radio sources, the inflated position errors are $40\,\mu$ as in each coordinate \citep{ti11}." +. The most of extragalactic radio sources used by Titoyotal.(2011) are quasars. thus. the proper motions derived x Titovetal.(2011) are those with the highest accuracy Or quasars at present.," The most of extragalactic radio sources used by \citet{ti11} are quasars, thus, the proper motions derived by \citet{ti11} are those with the highest accuracy for quasars at present." +" Figure LL shows the histograms of the proper motions derived by Titovetal.(2011) iu 46,coxd and frp with a in of Spas |."," Figure \ref{fg14} shows the histograms of the proper motions derived by \citet{ti11} in $\mu_{\alpha}\cos\delta$ and $\mu_{\delta}$ with a bin of $5\,\mu$ as $^{-1}$." + Not all of 555 sources used by. Titov are showed in Figure LL. aud sources witli he absolute value of proper motion in cach componcut ieecroo than Linas are not showed iu Figure 11..," Not all of 555 sources used by \citet{ti11} are showed in Figure \ref{fg14}, and sources with the absolute value of proper motion in each component bigger than 1 mas $^{-1}$ are not showed in Figure \ref{fg14}. ." +" The ΠΙΟ ofsources not showed in Figure Ll is 13 and 7 in the 46,coxd aud the srs panel. respectively."," The number ofsources not showed in Figure \ref{fg14} is 13 and 7 in the $\mu_{\alpha}\cos\delta$ and the $\mu_{\delta}$ panel, respectively." + Similar ) Figure 5.. a Gaussian fiction was used to fit the proper notions iu each compoucut for all 555 sources in the siuuple of Titovetal.(2011)aud was plotted as red solid ine in cach paucl of Figure L1..," Similar to Figure \ref{fg5}, , a Gaussian function was used to fit the proper motions in each component for all 555 sources in the sample of \citet{ti11} and was plotted as red solid line in each panel of Figure \ref{fg14}." +" Figure Lt indicates that he mean of proper motions derived by Titov for 555 sources is 0.0 and 0.9 pas H iu qr,cos0 aud fs. respectively."," Figure \ref{fg14} indicates that the mean of proper motions derived by \citet{ti11} for 555 sources is $0.0$ and $-0.9$ $\mu$ as $^{-1}$ in $\mu_{\alpha}\cos\delta$ and $\mu_{\delta}$ , respectively." + The ius of the derived. proper motions wv Titovetal.(2011) for555 sources is27.9 shouldand 35.1 pas jdn µεcosÓ and pry. respectively.," The rms of the derived proper motions by \citet{ti11} for 555 sources is $27.9$ and $35.4$ $\mu$ as $^{-1}$ in $\mu_{\alpha}\cos\delta$ and $\mu_{\delta}$ , respectively." + It be noted hat the unit iu Figure LL ds pas not mas + , It should be noted that the unit in Figure \ref{fg14} is $\mu$ as $^{-1}$ not mas $^{-1}$ +not only by faine behavior but also by power law spectra.,not only by fading behavior but also by power law spectra. + Such spectra are relatively rare in the optical sky. which is douunated ly Calactic stars at briel fiux levels and by galaxies at faint fiux levels.," Such spectra are relatively rare in the optical sky, which is dominated by Galactic stars at bright flux levels and by galaxies at faint flux levels." + Relaive to a stellar spectrum. a GRB afterglow is bue at blue wavelengths CE0.La). and red at recL wavelengths (20µη).," Relative to a stellar spectrum, a GRB afterglow is blue at blue wavelengths $\la 0.4 \micron$ ), and red at red wavelengths $\ga 0.6 \micron$ )." + À color-color plot shotId therefore isolate a GRB afterglow froin nearby stars effiientlw. provided it spans a sufficient wiweleneth range to detect spectral curvature (or the Balmer jump) in stars of aux surface temperature.," A color-color plot should therefore isolate a GRB afterglow from nearby stars efficiently, provided it spans a sufficient wavelength range to detect spectral curvature (or the Balmer jump) in stars of any surface temperature." + Under mauy circumstances it will also he xossible to identify afterglows using siupler though less robust single color criteria (either τανjolet excess |-UVN| or infrared excess [IRNj, Under many circumstances it will also be possible to identify afterglows using simpler though less robust single color criteria (either ultraviolet excess [“UVX”] or infrared excess [“IRX”]). + Moreover. absolute photometric calibration is rot required so long as a sufücieut solid anele is observed to enmpircallv. determine the stellar locis in color space.," Moreover, absolute photometric calibration is not required so long as a sufficient solid angle is observed to empirically determine the stellar locus in color space." + Section 2 describes ος] color-color plots that show the expected loci of GRB afterelows. stars. ealaxies. aud quasars.," Section \ref{col_mod_results} describes model color-color plots that show the expected loci of GRB afterglows, stars, galaxies, and quasars." + Section 2.Pa demonstrates empirically that the color-color method could have identified the afterglow of GRB 000301C in a suele epoch., Section \ref{empirical} demonstrates empirically that the color-color method could have identified the afterglow of GRB 000301C in a single epoch. + Finally. section ?? considers advantages and Inaitatious of the method. imcludiug confusion limits as a function of flux level. likely selection effects iu the sample of afterelows found through color-based searches. aud applicability of the method to “orphan afterglow” searches.," Finally, section \ref{discussion} considers advantages and limitations of the method, including confusion limits as a function of flux level, likely selection effects in the sample of afterglows found through color-based searches, and applicability of the method to “orphan afterglow” searches." + To explore this method im detail. [have calculated svuthetic color space locations for (030 afterelows. stars. galaxies. and quasars.," To explore this method in detail, I have calculated synthetic color space locations for GRB afterglows, stars, galaxies, and quasars." + Model caleulatious were performed for the widely available Johusou U. D. aud V filters aud Cousins Roaud I filters. though color-color searches will work for any se of filters spanuing a suffiicicut waveleugth ranec.," Model calculations were performed for the widely available Johnson U, B, and V filters and Cousins R and I filters, though color-color searches will work for any set of filters spanning a sufficient wavelength range." + Filter transmission curves were taken roni Dessell (1990)., Filter transmission curves were taken from Bessell (1990). + The photometric zero pol or all Johuson-Conusms system svuthetic colors was set to the Vega model atinosphere of Ἱνιππιον (1979)., The photometric zero point for all Johnson-Cousins system synthetic colors was set to the Vega model atmosphere of Kurucz (1979). + Model spectra of objects at high redshift were attenuated using the mean intergalactic absorpion eiven by Madan(1995)., Model spectra of objects at high redshift were attenuated using the mean intergalactic absorption given by Madau. +.. For redshifts =2. the flux iu the bluest filter cal be ereatlv reduced by neutra hydrogen absorption in the interealactic ποαι.," For redshifts $z \ga 2$, the flux in the bluest filter can be greatly reduced by neutral hydrogen absorption in the intergalactic medium." + This) absorption consists of a superposition of Lyman à forest ines. higher order Lyman lines. aud »ouud-free Lyiuan continmun absorption (Madii 1995).," This absorption consists of a superposition of Lyman $\alpha$ forest lines, higher order Lyman lines, and bound-free Lyman continuum absorption (Madau 1995)." + The iet effect is a shift in the duest color measured., The net effect is a shift in the bluest color measured. + The relevaut redshift depends on the choice of duest filter., The relevant redshift depends on the choice of bluest filter. +" The Lyman à line is redshitted to the veal, tfrausnison waveleusth of the Johusou U xuidat: 2.041. and the Jolson D filter around =25."," The Lyman $\alpha$ line is redshifted to the peak transmission wavelength of the Johnson U band at $z=2.04$, and the Johnson B filter around $z=2.5$." + Iu additio1. T caleulated reddening vectors for dust both iu he Milkv Wax and in afterglow host ealaxies at ar auge of redshifts. using the empirical fits of Pei (1992) to the extinction laws of the Alilkv Wavy aid the Magellauic Clouds.," In addition, I calculated reddening vectors for dust both in the Milky Way and in afterglow host galaxies at a range of redshifts, using the empirical fits of Pei (1992) to the extinction laws of the Milky Way and the Magellanic Clouds." + Tu the following subsections. I describe the color calculations or each class of object considered. aud then suunuarize the results.," In the following subsections, I describe the color calculations for each class of object considered, and then summarize the results." + Stellar colors Were derived. fro the spectrophotoimoetriic catalog of Comm and Stivker (1983). which spaus spectral types from O to M and luminosity classes from the main sequence to supergiants.," Stellar colors were derived from the spectrophotometric catalog of Gunn and Stryker (1983), which spans spectral types from O to M and luminosity classes from the main sequence to supergiants." +" Afterelows were taken as pure power law spectra. f,XFÉT with indices 0.5xaS1.5."," Afterglows were taken as pure power law spectra, $f_\nu \propto +\nu^{\alpha}$, with indices $0.5 \la -\alpha \la 1.5$." + Such spectra describe svuclirotron Cluission from a power law distribution of electrons away from break [frequencies, Such spectra describe synchrotron emission from a power law distribution of electrons away from break frequencies. + Deviations from power law spectra occur near spectral breaks (see Sari. Dirau. Naravan 1998) aud iu the case of interstellar absorption (section ??)).," Deviations from power law spectra occur near spectral breaks (see Sari, Piran, Narayan 1998) and in the case of interstellar absorption (section \ref{discussion}) )." + The range of spectral indices considered corresponds to the conunonly measured rauge of electron energy indices. 2cp<3.," The range of spectral indices considered corresponds to the commonly measured range of electron energy indices, $2 < p < 3$." + Tere p describes the mumiber-enerey distribution of electrous accelerated at the CRB remuaut’s external shock. N(£)~€/. and T have considered spectra both above aud below the cooling frequency.," Here $p$ describes the number-energy distribution of electrons accelerated at the GRB remnant's external shock, $N(\ee) \propto \ee^{-p}$, and I have considered spectra both above and below the cooling frequency." + Calaxy spectra were taken from the CUSSEL stellar population svuthesis code (Druzual Charlot 1993) for a few representative, Galaxy spectra were taken from the GISSEL stellar population synthesis code (Bruzual Charlot 1993) for a few representative +hydrostatic equilibrimuu by the overall 1iass profiles iu clusters.,hydrostatic equilibrium by the overall mass profiles in clusters. + Tu Riugs ος ο (sine1972:Jones1981).. the hot gas πο deusitv is where is the central nuniber density.," In King's $\beta$ -model \citep{King,Jones}, the hot gas number density is where $n_c$ is the central number density." +" Suppose the hot gas is iu hwdrostatie equilibrimu and the interactions between the barvous iud the ueutriuos are uceleible: then the pressure eradicuts of the hot eas and the ucutrinos are balanced by the total eravitv inside a cluster indepeudenth,.", Suppose the hot gas is in hydrostatic equilibrium and the interactions between the baryons and the neutrinos are negligible; then the pressure gradients of the hot gas and the neutrinos are balanced by the total gravity inside a cluster independently. + Therefore we have where AM(r) is the enclosed. nmuass du a cluster including the masses of galaxies. hot eas. cold dark natter and neutriuos. ig is the average mass of he hot eas particles. and we have assumed that he temperature Tis coustaut throughout the hot eas.," Therefore we have where $M(r)$ is the enclosed mass in a cluster including the masses of galaxies, hot gas, cold dark matter and neutrinos, $m_g$ is the average mass of the hot gas particles, and we have assumed that the temperature $T$ is constant throughout the hot gas." + Although Vikhliuiuetal.(2005) suggested the eniperature niav not be uniformi especially ucar the center of some clusters. the variatious may onlv aout o 20-390 which has little effect on our results dr~|5 ties greater than nydT dr).," Although \citet{Vikhlinin} suggested the temperature may not be uniform especially near the center of some clusters, the variations may only amount to 20-30 , which has little effect on our results $Tdn_g/dr +\sim 4-5$ times greater than $n_gdT/dr$ )." + Also. ChanandClu(2007) show that the teniperature variation m cluster hot gas is not significant because energv transter by conduction is highly eficicut.," Also, \citet{Chan} show that the temperature variation in cluster hot gas is not significant because energy transfer by conduction is highly efficient." + ThereDUE in the followiug analysis. we follow ReiprichaudBohringer(2001) and approximate the teniperature as uniform.," Therefore, in the following analysis, we follow \citet{Reiprich} and approximate the temperature as uniform." +" On the other hand. we suppose that the neutrinos with mass i, are degenerate and iu hydrostatic equilibrium inside the cluster."," On the other hand, we suppose that the neutrinos with mass $m_{\nu}$ are degenerate and in hydrostatic equilibrium inside the cluster." +" Therefore we lave where being the degeueracy. pressure of neutrinos. p, their mass density aud g; the degree of freedom of cach type of neutrinos."," Therefore we have where being the degeneracy pressure of neutrinos, $\rho_{\nu}$ their mass density and $g_s$ the degree of freedom of each type of neutrinos." + We assmue gs=1 aud combine Eqs. (, We assume $g_s=1$ and combine Eqs. ( +3) aud {) to get Using the density profile of the hot eas iu Eq. (,3) and (4) to get Using the density profile of the hot gas in Eq. ( +1) and integrating Eq. (,1) and integrating Eq. ( +"5). we finally obtain Fi (p,—0 forr> R) audthetotal euclosed mass profile (ReiprichaudBoliiuger2001) where is the ceutra ιοΊππο deusitv and ois the radius of the neutrino density profile.","5), we finally obtain for $rR$ ) and the total enclosed mass profile \citep{Reiprich} + where is the central neutrino density and $R$ is the radius of the neutrino density profile." + The total mass profile Eq. (, The total mass profile Eq. ( +7) has a soft core which is ditfereu roni the NEW. profile obtained. by N-body simulat1,7) has a soft core which is different from the NFW profile obtained by N-body simulation. + Nevertheless. recent eravitational lensing data support the existence of soft cores in clusters. in contradiction to the NEW. profile (Tysonctal.1998:Saud2002:Broadhurst2005).," Nevertheless, recent gravitational lensing data support the existence of soft cores in clusters, in contradiction to the NFW profile \citep{Tyson,Sand,Broadhurst}." +. Since there is no robust definition of the radius auc total mass of a cluster. we follow BrownsteinaudMoffat(2005) to define the radius anc otal nass of a cluster A. by assuming a cut off radius where the total mass density = 250 times meancosmological deusitv of barvous (BrownsteinandMoffat2005).," Since there is no robust definition of the radius and total mass of a cluster, we follow \citet{Brownstein} to define the radius and total mass of a cluster $M_c$ by assuming a cut off radius where the total mass density = 250 times meancosmological density of baryons \citep{Brownstein}." +". We can then obtain a relation logM44,=(1.5+0.1)loe(Py)|10.7d0.1) (see Fig."," We can then obtain a relation $\log M_{14}=(1.5 \pm 0.1) \log (\beta T_K)+ +(-10.7 \pm 0.4)$ (see Fig." +" 1). where Mq,=AL101A, and Zu ds the temperatureof theho eas in Ix. or where qz(STO50I0)AZ.. Is a constant which depends seusitivelv ou the definition of the cut off radius."," 1), where $M_{14}=M_c/10^{14}M_{\odot}$ and $T_K$ is the temperatureof thehot gas in K, or where $q \approx (870-5010) M_{\odot}$ $^{-3/2}$ is a constant which depends sensitively on the definition of the cut off radius." + Iu the following. we obtain a relation among the observables à... aud T.," In the following, we obtain a relation among the observables $r_c$, $\beta$ and $T$." + Weiutegrate the density profile in Eq.(6) to eet the total mass of the neutrinos: where aud srr. ty= Ror. p=(BRT ISI).," We integrate the density profile in Eq.(6) to get the total mass of the neutrinos: where and $u=r/r_c$ , $u_0=R/r_c$ , $\tilde{\rho}=(3kT \beta +/5K_{\nu}m_g)^{3/2}$ ." +" Ta a cluster. we assiue the ratio of AM, to AL. to be the sale as the cosinmological value"," In a cluster, we assume the ratio of $M_{\nu}$ to $M_c$ to be the same as the cosmological value" +(1908) τν=0.050 for FOCCO4G ancl cly=0.039 for FCC207).,\cite{sch}~ : $A_R = 0.050$ for FCC046 and $A_R = 0.039$ for FCC207). + The images were nally converted to units of electrons/second/pixel., The images were finally converted to units of electrons/second/pixel. + In order to find the correct scaling for the lt-band images we adopted the following strategv., In order to find the correct scaling for the R-band images we adopted the following strategy. + The pure emission “Em” can be recovered from a narrow-band image “Nb” and an It-band image “Rb” as with e the proper scaling constant and 9 a correction for possible faulty skv-subtraction., The pure emission “Em” can be recovered from a narrow-band image “Nb” and an R-band image “Rb” as with $c$ the proper scaling constant and $\delta$ a correction for possible faulty sky-subtraction. +" To find the best values for e and ὃν we first fitted the isophotes of the narrow-band and lt-band images. in. an annulus between my=.24.5 "" and mg=26.5 mag/"". which in retrospect did not contain any emission (hence Em-0). using the standard command."," To find the best values for $c$ and $\delta$, we first fitted the isophotes of the narrow-band and R-band images in an annulus between $m_R=24.5$ $\Box''$ and $m_R=26.5$ $\Box''$, which in retrospect did not contain any emission (hence $=0$ ), using the standard command." + Thus. a smooth version of this annulus could be constructed for both images.," Thus, a smooth version of this annulus could be constructed for both images." + The optimal e and ὁ can be found by minimising the expression [Nbfe.Rb|8| with Nb and Rh the smoothed. versions of the annulus., The optimal $c$ and $\delta$ can be found by minimising the expression $|{\rm Nb} - (c \times {\rm Rb} + \delta)|$ with Nb and Rb the smoothed versions of the annulus. + With these values in hand. the pure-cmission image can x Obtained using relation (2)).," With these values in hand, the pure-emission image can be obtained using relation \ref{subtr}) )." + 6 was very small for both FCCO46 and. ECC207. which makes us confident that the sky was properly subtracted in all images.," $\delta$ was very small for both FCC046 and FCC207, which makes us confident that the sky was properly subtracted in all images." + Since the Lla anc t-hand overlap. subtracting an R-bancl image in lieu of a continuum image entails a partial removal of some Ho| ight.," Since the $\alpha$ and R-band overlap, subtracting an R-band image in lieu of a continuum image entails a partial removal of some $\alpha+$ ] light." + The error thus introduced is of the order of the ratio of he elfective widths of the filters (B-band: M.=165.0 nm. lla: M=6.4 nm). Le. less thanκι.," The error thus introduced is of the order of the ratio of the effective widths of the filters (R-band: $W=165.0$ nm, $\alpha$: $W=6.4$ nm), i.e. less than." + Since this ellect. is neeligible in. comparison to the other possible sources. oferror. we did not correct for it.," Since this effect is negligible in comparison to the other possible sources oferror, we did not correct for it." + A pixel-value in the purce-emission image (corrected. forboth atmospheric and. interstellar extinction). denoted. by Ny. expressed in electrons/second. can be converted to Dux units.. £5.vw using. the formula. Here. FAO) ds the spectrum. of a. [lux-calibration standard star and ἂν is the measured [ux of that star. expressed. in electrons/second.," A pixel-value in the pure-emission image (corrected forboth atmospheric and interstellar extinction), denoted by $N_g$, expressed in electrons/second, can be converted to flux units, $F'_g$, using the formula Here, ${\cal F}^*_\lambda(\lambda)$ is the spectrum of a flux-calibration standard star and $N_*$ is the measured flux of that star, expressed in electrons/second." +" (A) is the transmission of the Ho. filter and 4, the transmission of the opties (which is basically constant for a narrow-band filter).", $\varphi_{\rm f}(\lambda)$ is the transmission of the $\alpha$ filter and $\varphi_{\rm o}$ the transmission of the optics (which is basically constant for a narrow-band filter). + Phe prime on I indicates that this is the flux incident on the CCD. after going through the telescope and instrument optics and the narrow-band filter.," The prime on $F'_g$ indicates that this is the flux incident on the CCD, after going through the telescope and instrument optics and the narrow-band filter." +" This can also be written as with Fus. Py, and Py, the incoming [luxes i.c. before. going through the telescope and. instrument optics and the narrow-banel filter of respectively the μαG56BA.. the Nu] and the Ni] emission line (approximated as o-Functions)."," This can also be written as with $F_{\rm{H}\alpha}$, $F_{\rm{[N{\sc ii}]}_1}$ and $F_{\rm{[N{\sc +ii}]}_2}$ the incoming fluxes -- i.e. before going through the telescope and instrument optics and the narrow-band filter – of respectively the $\alpha$, the ] and the ] emission line (approximated as $\delta$ -functions)." + This allows one to obtain the true incoming flux of the Ho emission line as The total incoming Ho| Nu] tux is simply Since the Ha filter is relatively Hat-topped and the La and Nu] lines are well inside the filter transmission curve. the total Hux is rather insensitive to the adopted. relative linc-strengths.," This allows one to obtain the true incoming flux of the $\alpha$ emission line as The total incoming $\alpha+$ ] flux is simply Since the $\alpha$ filter is relatively flat-topped and the $\alpha$ and ] lines are well inside the filter transmission curve, the total flux is rather insensitive to the adopted relative line-strengths." +" In the following.we will assume the mean value Pri,(Pir,=3 for the ratio of the line-strengths of the two Nitrogen lines (Alacchetto (1996).. Phillips (1986)))."," In the following,we will assume the mean value $F_{\rm{[N{\sc ii}]}_2}/F_{\rm{[N{\sc ii}]}_1}=3$ for the ratio of the line-strengths of the two Nitrogen lines (Macchetto \cite{mac}, , Phillips \cite{phi}) )." + Phe ratio Pxi4/Pg is not known and is treated as a free parameter. varving between O and 2.," The ratio $F_{\rm{N{\sc +ii}}_2}/F_{\rm{H}\alpha}$ is not known and is treated as a free parameter, varying between 0 and 2." + <110~10ουν (seeLewinetal.1993:Bil," $\la 1-10$$\sim 10-100$ \cite[see][for reviews]{lew93,bil98a}." +"dsten1998.forreviews)... (Lewinetal.1993) AZxa 7; oy (~2.2410.? ft: .X (220.7 ς€ R>Πίνω, Ενο 2001:IKuulkersetal.2002h).. (sec.e.g.tLattimer"," \cite[]{lmxb01} \cite[]{lew93} + $M_{\rm NS}$ $T_{\rm e}$ $\alpha_{\rm T}$ \cite[$\simeq 2.2\times10^{-9}$ $^{-1}$ $X$ $\approx0.7$ $\xi$ $R\ge R_{\rm NS}$ $M_{\rm NS}/R_{\rm NS}$ \cite[e.g.][]{damen90,smale01,kuul01}. \cite[see, e.g.,][]{lp01}," +Iu precision cosmology. a fundamental task ids to distinguish between various candidate models for the cosmic inflation.,"In precision cosmology, a fundamental task is to distinguish between various candidate models for the cosmic inflation." + One wav to perform this task is to measure the degree of nou-Gaussianity in the primordial density field., One way to perform this task is to measure the degree of non-Gaussianity in the primordial density field. + Although the primordial density feld is reearded as nearly Gaussian in all inflationary scenarios (Guth&Pi1982).. the deeree of its non-Cuussiauitv differs between the models.," Although the primordial density field is regarded as nearly Gaussian in all inflationary scenarios \citep{GP82}, the degree of its non-Gaussianity differs between the models." + For stance. iu the sinele-Ποια. slow-roll inflationary ποσο]. the deviation fromm CGaussianity is sinall enough to be unobservable (Verdeetal. 2001).," For instance, in the single-field slow-roll inflationary model, the deviation from Gaussianity is small enough to be unobservable \citep{ver-etal01}." +. Meamwhile in some multi-field inflationary models the uou-Caussianity can be generated to a detectable level (Battefeld&Easther2007.audrefer-ences therein).., Meanwhile in some multi-field inflationary models the non-Gaussianity can be generated to a detectable level \citep[][and references therein]{BE07}. + For a thorough review ou the predictions of various inflationary niodels for the primordial non-Caussianityv. see Bartoloetal.(2001) The cosmic microwave background radiation. (CMD) is a useful probe of the primordial nou-Caussianitv as it reflects the linear density perturbations.," For a thorough review on the predictions of various inflationary models for the primordial non-Gaussianity, see \citet{bar-etal04} + The cosmic microwave background radiation (CMB) is a useful probe of the primordial non-Gaussianity as it reflects the linear density perturbations." + Yet. if he primordial non-Caussianity is scale-dependeut. the constraint from the CAIB analysis is rather restricted o the very large-scale (Verdecetal.2001:I&o1iatsu&Sperecl 2001).," Yet, if the primordial non-Gaussianity is scale-dependent, the constraint from the CMB analysis is rather restricted to the very large-scale \citep{ver-etal01,KS01}." +. The large-scale structure is a powerful alternative probe of the primordial nou-Ciouissiauitv ou he sub-CAIB scale., The large-scale structure is a powerful alternative probe of the primordial non-Gaussianity on the sub-CMB scale. + Tt has been well known that the abuudance of ligh-+ clusters are rare enough to constrain he primordial nou-Caussianity (Lucchin&AMatarreseal.2008:Cirossiet 2009).," It has been well known that the abundance of $z$ clusters are rare enough to constrain the primordial non-Gaussianity \citep{LM88,chi-etal98,mat-etal00,WK03,car-etal08,lov-etal08, +gro-etal09}." +. This probe. however. is ikelv to suffer from large systematics involved im the Inaccurate nieasurenment of the masses of πο]: clusters.," This probe, however, is likely to suffer from large systematics involved in the inaccurate measurement of the masses of $z$ clusters." + The abundance of cosinie voids is another probe of he primordial non-CGaussianity based on the large-scale structure (INamionukowskietal.2009)., The abundance of cosmic voids is another probe of the primordial non-Gaussianity based on the large-scale structure \citep{kam-etal09}. +. One difficulty in using this probe lies in the fact that there is no unique way to define voids (Carbonectal. 2008)..., One difficulty in using this probe lies in the fact that there is no unique way to define voids \citep{car-etal08}. . + Becently. it has been claimed that using the clustering propertics of liehlv biased large-scale structures the primorcial parameter can be measured with accuracy as high as the one obtained from the CMD analysis (Carboneetal.2008:SlosarJeong&Ixo-μιαμα 2009).," Recently, it has been claimed that using the clustering properties of highly biased large-scale structures the primordial parameter can be measured with accuracy as high as the one obtained from the CMB analysis \citep{car-etal08,slo-etal08,jeo-kom09}." +. Tere. we propose the mass functiou of prescut galaxy eroups cinbedded iu void regions as a new probe of the primordial nou-Gaussianity.," Here, we propose the mass function of present galaxy groups embedded in void regions as a new probe of the primordial non-Gaussianity." + It is not ouly the 2 clusters but also the low-: void groups that are so rare that their abundance may depend scusitively on the initial conditions., It is not only the $z$ clusters but also the $z$ void groups that are so rare that their abundance may depend sensitively on the initial conditions. + Furthermore. the mass estimation of low-: ealaxy eroups should be much more reliable than that of high-: clusters (Yangetal.2007).," Furthermore, the mass estimation of $z$ galaxy groups should be much more reliable than that of $z$ clusters \citep{yan-etal07}." +. Throughout this Letter. we assume a WALAP 5 cosinology. (Dunkley 2009)..," Throughout this Letter, we assume a WMAP 5 cosmology \citep{wmap5}." + The Press-Schechter theory (Press&Schechter197L.PShereafter) provides an analytic framework within which the nunuber density of bound objects as a function of mass. dNps/d M. can be obtained: where pis themean background density. 9.(:) is the critical density contrast for gravitational collapse at redshift 2. p(03;) is the probability deusitv distribution of the deusitv field 03; :31100thed on the mass scale of M. and Oaswellas 1 0$, one always finds $a_1 \neq 0$ ) with Eq. \ref{eq:solvephi}) )," + while one finds where C and(' coincide for D—aydaga=0., while one finds where $C_{+}$ and $C_{-}$ coincide for $D \equiv a_1^2 - 4 a_0 a_2 = 0$. + Fig., Fig. +" 6 shows the allowed ranges for r as a function of d using m,—0.5 as example.", \ref{fig:solstruct} shows the allowed ranges for $r$ as a function of $d$ using $m_1 = 0.3$ as example. + However. the structure of the solutions does not depend on the adopted mass fraction.," However, the structure of the solutions does not depend on the adopted mass fraction." + While for given (d.mj). there is at least one and up to three solutions for /)=0. denoted +in the 5following+ by QUIrj. rj;423. ry; 6b..and 7.20=0. denoted by Ql)NE ii2. and ry. there is always just a single solution for 7?=0. denotedrp by rp.," While for given $(d,m_1)$, there is at least one and up to three solutions for $D = 0$, denoted in the following by $r_{D}^{(1)}$, $r_{D}^{(2)}$, $r_{D}^{(3)}$ , and $P_{+} = 0$, denoted by $r_{P_{+}}^{(1)}$, $r_{P_{+}}^{(2)}$, and $r_{P_{+}}^{(3)}$, there is always just a single solution for $P_{-} = 0$, denoted by $r_{P_{-}}$." + The two additional solutions for Z2=0 are only present for close binaries. whereas the two additional solutions for P= (exist for wide binaries.," The two additional solutions for $D = 0$ are only present for close binaries, whereas the two additional solutions for $P_{+} = 0$ exist for wide binaries." + These critical radii can be obtained by interval bisection using the initial bracket intervals listed in Table I.. which are also indicated by small dotted lines in Fig. 6..," These critical radii can be obtained by interval bisection using the initial bracket intervals listed in Table \ref{tab:brackr}, which are also indicated by small dotted lines in Fig. \ref{fig:solstruct}." +" For d=0. one finds. rp=Tl which. reflects the outer critical curve tendings towards the rp,constant +=1 (Einstein circle). while. οiL—rjj.iD2=8 reflects the .inner criticales curves contracting. at the origin."," For $d = 0$, one finds $r_{P_{-}} = r_{P_{+}}^{(1)} = 1$ which reflects the outer critical curve tendings towards the constant $r = 1$ (Einstein circle), while $r_{D}^{(1)} = r_{D}^{(2)} = 0$ reflects the inner critical curves contracting at the origin." + Moreover. DE=my! for d.=0. but this is not a valid value. because cos2 is out of the allowed range.," Moreover, $r_{D}^{(3)} = m_1^{1/4}$ for $d=0$, but this is not a valid value, because $\cos \varphi$ is out of the allowed range." + Table 2. lists the branches of the critical curve detined by the allowed range iinFux] for r and the value for cosqz. either€ or C' as defined by Eq. 1).," Table \ref{tab:branches} lists the branches of the critical curve defined by the allowed range $[r_\rmn{min},r_\rmn{max}]$ for $r$ and the value for $\cos \varphi$, either $C_{+}$ or $C_{-}$ as defined by Eq. \ref{eq:branchphi}) )." + While CI and C? correspond to the small two inner critical curves. C3 and C4 represent the outer critical curve.," While C1 and C2 correspond to the small two inner critical curves, C3 and C4 represent the outer critical curve." +" Branch C4 only exists for d,«ddo. where di is the separation for which the curves Z2=0 and 7?=0 touch."," Branch C4 only exists for $d_\rmn{t} < d < d_\rmn{c}$, where $d_\rmn{t}$ is the separation for which the curves $D = 0$ and $P_{-} = 0$ touch." +" These conditions imply e»=(0. so that a,=2e or a,=2d»."," These conditions imply $a_2 = a_0$, so that $a_1 = 2 a_0$ or $a_1 = 2 a_2$." + Ford—»0. C3 tends to the Einstein circle. whereas Cl and C2 degenerate into points.," For $d \to 0$, C3 tends to the Einstein circle, whereas C1 and C2 degenerate into points." + For d=d... the inner critical curves touch the outer one at the radius (μα>. where CI and C3 merge into Il. and C2 and C4 merge into I2.," For $d = d_\rmn{c}$, the inner critical curves touch the outer one at the radius $r_\rmn{c} = (m_1 d_\rmn{c})^{1/3}$, where C1 and C3 merge into I1, and C2 and C4 merge into I2." +" For the intermediate binary. I? is the branch near the object with mass fraction m, at the coordinate origin. whereas I] is the far branch."," For the intermediate binary, I2 is the branch near the object with mass fraction $m_1$ at the coordinate origin, whereas I1 is the far branch." + For wide binaries. WI] gives the critical curve around the far object. while W2/W3 surround the near object. which both tend to circles around the respective object.," For wide binaries, W1 gives the critical curve around the far object, while W2/W3 surround the near object, which both tend to circles around the respective object." + At d.=dy.the critical curves deseribed by branches WI and W2 merge at radius re=(midYF into D. whereas W3 and I2 are identical.," At $d = d_\rmn{w}$,the critical curves described by branches W1 and W2 merge at radius $r_\rmn{w} = (m_1 d_\rmn{w})^{1/3}$ into I2, whereas W3 and I2 are identical." + In order for the determinant of the Jacobian (09/02) of the lens mapping to vanish. at least one of its eigenvalues must be zero.," In order for the determinant of the Jacobian $(\partial \vec y/\partial \vec x)$ of the lens mapping to vanish, at least one of its eigenvalues must be zero." + In two dimensions. singularities for which there are no non-zero eigenvalues cannot be a generic feature.," In two dimensions, singularities for which there are no non-zero eigenvalues cannot be a generic feature." + In fact. such singularities (known as umbilics) do not exist for any binary point-mass lens (22)...," In fact, such singularities (known as umbilics) do not exist for any binary point-mass lens \citep{SchneiWei:twomass,Erdl}." + Therefore. we can restrict ourselves to the case of exactly one eigenvalue being zero for dicussing the critical curves of binary lenses.," Therefore, we can restrict ourselves to the case of exactly one eigenvalue being zero for dicussing the critical curves of binary lenses." + Since the critical curve is defined as the set of points where aoye Jacobian determinant of the lens mapping vanishes. Eq. (4)).," Since the critical curve is defined as the set of points where the Jacobian determinant of the lens mapping vanishes, Eq. \ref{eq:defcrit}) )," + ye unit normal vector isgiven as n= D/|D|. whereD= ).," the unit normal vector isgiven as $\vec n = \vec D/|\vec D|$ , where$\vec D = \nabla \det \left(\frac{\partial \vec y}{\partial \vec x}\right)$ ." + A corresponding tangent vector then follows as te=(nsn) and ty={ou}Ge is a tangent to the caustic.," A corresponding tangent vector then follows as ${\vec t}_{\vec x} = (-n_2,n_1)$, and ${\vec t}_{\vec y} = \left(\frac{\partial \vec y}{\partial \vec x}\right) {\vec t}_{\vec x}$ is a tangent to the caustic." + Therefore. the caustic is a smooth curve withdefined tangent direction (fold singularity) as long as £4 is not an eigenvector eo of the Jacobian to the eigenvalue zero (cusp singularity).," Therefore, the caustic is a smooth curve withdefined tangent direction (fold singularity) as long as ${\vec t}_{\vec x}$ is not an eigenvector ${\vec e}_0$ of the Jacobian to the eigenvalue zero (cusp singularity)." + A cusp is ctjerefore detined by the scalar equation m+ey= 0.In order to identify cusps as roots of 7?: ej. one needs to find, A cusp is therefore defined by the scalar equation ${\vec n}\cdot {\vec e}_0 = 0$ .In order to identify cusps as roots of ${\vec n} \cdot {\vec e}_0$ one needs to find +due to a poor fit of the Sérrsic function. or a nuclear source.,"due to a poor fit of the Sérrsic function, or a nuclear source." + The extended FUV excess emission is. however. -The residual in the NUV image occurs also at longer wavelengths. and indicates a poor Sérrsic fit.," The extended FUV excess emission is, however, -The residual in the NUV image occurs also at longer wavelengths, and indicates a poor Sérrsic fit." + The FUV excess is. however. stronger and is also extended.," The FUV excess is, however, stronger and is also extended." + -The H-band residual in this galaxy is positive in the very centre. however the observed NUV residual is extended. and is more likely to be due to ongoing star formation.," -The H-band residual in this galaxy is positive in the very centre, however the observed NUV residual is extended, and is more likely to be due to ongoing star formation." + The FUV residual map is very similar to NUV. and the FUV excess is weak. although the colour gradient shows that it is," The FUV residual map is very similar to NUV, and the FUV excess is weak, although the colour gradient shows that it is" + The FUV residual map is very similar to NUV. and the FUV excess is weak. although the colour gradient shows that it is0," The FUV residual map is very similar to NUV, and the FUV excess is weak, although the colour gradient shows that it is" + The FUV residual map is very similar to NUV. and the FUV excess is weak. although the colour gradient shows that it is01," The FUV residual map is very similar to NUV, and the FUV excess is weak, although the colour gradient shows that it is" +The search for motions of the members of the LO under the cosmological initial condition iu equation (2)) commences wit1 a random trial choice of the 1jasses of the four bodies aud the three ('oniponents o ‘the preseit position of the hypothetical third xod.,The search for motions of the members of the LG under the cosmological initial condition in equation \ref{eq:LMC_p_v}) ) commences with a random trial choice of the masses of the four bodies and the three components of the present position of the hypothetical third body. + These seven parameters are used in the numerical action inet]od (NAM: Peebles 1995: Peebles. Phelps. Shaya Tully 2001: ancl 'elereuces the'ejn) {ο sove tle equations of motion under t1e mixed boundary couclitious tiat the »esent positions are given aud the priueval peculiar velociies mateh the growing mode o. linear »erturbation heory in he a»proximatjon describec inSecion ??..," These seven parameters are used in the numerical action method (NAM: Peebles 1995; Peebles, Phelps, Shaya Tully 2001; and references therein) to solve the equations of motion under the mixed boundary conditions that the present positions are given and the primeval peculiar velocities match the growing mode of linear perturbation theory in the approximation described inSection \ref{sec:NAM}." + This is a rapid coiiputation OL ny20 ti1ne step. whic Lis aclegtale to descriye the suoothly varying motious of the three nassive bodies.," This is a rapid computation for $n_x=20$ time steps, which is adequate to describe the smoothly varying motions of the three massive bodies." + [t is adequate [or he rapidly. chaugiug velocity ο‘the LAIC as ita j»proaclies he NW., It is not adequate for the rapidly changing velocity of the LMC as it approaches the MW. + Doibling t Πο of le Ἡeps does οἱ muel improve the precision of the present velocity of the LMC alk Lit cousideraby slows the NAM couputatior., Doubling the number of time steps does not much improve the precision of the present velocity of the LMC and it considerably slows the NAM computation. +" But the NANI xjhlon αἱ Ny=20 gives a useh In‘st approxinati to the initial posilOls aid velocities for a coiventional 1uuerical integration fo""walcd in time | tlie equations of n1οί1011 of he four odies. (", But the NAM solution at $n_x=20$ gives a useful first approximation to the initial positions and velocities for a conventional numerical integration forward in time for the equations of motion of the four bodies. ( +The initial ('onditious are reasonably well fixe bec:se the disslacemel ts0‘the »odies at high redshift scale i proportion to the cosuological expaisjon paraljeter a(t). loaeg OOd approxination. so a linear iterpolation in e is a good approxinati cespite the small luin το“titne stejs.),"The initial conditions are reasonably well fixed because the displacements of the bodies at high redshift scale in proportion to the cosmological expansion parameter $a(t)$, to a good approximation, so a linear interpolation in $a$ is a good approximation despite the small number of time steps.)" + A conventiona forward numerical integration witl Qu2000 tiuie steps take: ittle compatlou time aud is €ute adequate to follow tlie motio Lofte LMC., A conventional forward numerical integration with $p_x=2000$ time steps takes little computation time and is quite adequate to follow the motion of the LMC. + This forward integ‘ation [rou the NAN initia couditious shifts the present position ofte LMC relative to the MW. but that isually is remecliec by a perturbative acjustiment of the initia couditious.," This forward integration from the NAM initial conditions shifts the present position of the LMC relative to the MW, but that usually is remedied by a perturbative adjustment of the initial conditions." + If the resuling yresent veocities of M31 anc the LAC look promisiugly close to what is njeasured then adjustineus of the fi'ee paranieters cal significantly improve the fit to the measured velocities., If the resulting present velocities of M31 and the LMC look promisingly close to what is measured then adjustments of the free parameters can significantly improve the fit to the measured velocities. + This last step is not frequently. called for. but the short computation time for the pjor steps allows many trials.," This last step is not frequently called for, but the short computation time for the prior steps allows many trials." + ] assume a cosinologicale constant aud zero space curvature. and iguore[we radiatiou energyOe deusitv. so the cosinological expansion parameter satisfies #+1—-Q))).," I assume a cosmological constant and zero space curvature, and ignore radiation energy density, so the cosmological expansion parameter satisfies )^2 = + 1 - ), H_ot = ," +We investigate how much of intergalactic space is filled with current and old radio lobes.,We investigate how much of intergalactic space is filled with current and old radio lobes. + Most galaxies seem to have a supermassive black hole at their centres (2)... wich can serve as a central engine for jet ejection.," Most galaxies seem to have a supermassive black hole at their centres \citep{1998AJ....115.2285M}, which can serve as a central engine for jet ejection." + It is possible tlat most massive galaxies have at least one outburst of Jet activity leading to a giant radio source in their lifetime (lasting ~10 vr). ?robably between redshifts 1.5 to 3 during the quasar era (2)...," It is possible that most massive galaxies have at least one outburst of jet activity leading to a giant radio source in their lifetime (lasting $\sim10^8~{\rm yr}$ ), probably between redshifts $1.5$ to $3$ during the quasar era \citep{2001ApJ...560L.115G}." + Tje radio galaxies will have extended emission in the radio as we| as extended X- emission in the keV energies due to inverse-Compton (IC) upscattering bv .10 electrons of photons hat comprise the cosmic microwave background (CMB)., The radio galaxies will have extended emission in the radio as well as extended X-ray emission in the keV energies due to inverse-Compton (IC) upscattering by $\gamma\sim10^3$ electrons of photons that comprise the cosmic microwave background (CMB). + The IC and synchrotron losses will downshift the higher energy electrons 6— 101) responsible for GHz synchrotron radiation more quickly than the ower-energy electrons that give rise to the X-ray emission., The IC and synchrotron losses will downshift the higher energy electrons $\gamma\sim10^4$ ) responsible for GHz synchrotron radiation more quickly than the lower-energy electrons that give rise to the X-ray emission. + Thus or some period of time after the Jet is switched off the source will appear as an inverse-Compton ghost of a radio source before becoming compleely radio and X-ray dark., Thus for some period of time after the jet is switched off the source will appear as an inverse-Compton ghost of a radio source before becoming completely radio and X-ray dark. + The extended X-ray source HDF 130 (2= 1.99) has been interpreted to be such a radio galaxy with its jetsturned off and only showing a double- structure in the X-ray (2).. and the models developed in this duper are applied to that object in a companion paper.," The extended X-ray source HDF 130 $z=1.99$ ) has been interpreted to be such a radio galaxy with its jetsturned off and only showing a double-lobed structure in the X-ray \citep{2009MNRAS.395L..67F}, and the models developed in this paper are applied to that object in a companion paper." + The CMB energy density is proportional to (1|.z)!. cancelling the dimming due to distance. and so extended X-ray emission may be observable at both low and high redshifts.," The CMB energy density is proportional to $(1+z)^4$, cancelling the dimming due to distance, and so extended X-ray emission may be observable at both low and high redshifts." + Previous work on the extended ray emission of radio galaxies range from as early as ?.. which described the cosmic X-ray background (CXB) being attributed to a Compton-blackbody process acting in double radio sources. to 2.. which is an analytic treatment of the time evolution of the radio output of expanding radio lobes incorporating IC losses. to ?.. which considered the relative abundance of double radio galaxies," Previous work on the extended X-ray emission of radio galaxies range from as early as \cite{1969Natur.221..924F}, which described the cosmic X-ray background (CXB) being attributed to a Compton-blackbody process acting in double radio sources, to \cite{1989MNRAS.239..173G}, which is an analytic treatment of the time evolution of the radio output of expanding radio lobes incorporating IC losses, to \cite{2004MNRAS.353..523C}, , which considered the relative abundance of double radio galaxies" +abundance ratios are found to vary considerably [rom around unity in W31RS4 and W31RS5 to ~5 in DR21(OID.,abundance ratios are found to vary considerably from around unity in W3IRS4 and W3IRS5 to $\sim$ 5 in DR21(OH). + They are in good agreement to the integrated intensity ratios of the HCl] and line as suggested by Cernicharoetal...(2010a)., They are in good agreement to the integrated intensity ratios of the HCl and line as suggested by \citet{Cernicharo2010a}. +. The variations of the abundance ratios are lound to be highlv localized., The variations of the abundance ratios are found to be highly localized. + They. could be supported by Che varving vields of nucleosvnthesis of supervoae [rom different progenitors., They could be supported by the varying yields of nucleosynthesis of supervoae from different progenitors. + The low abundance ratios seen in W3IRS4 and. W3IRS5 likely confine the progenitors of the supernovae to stars of relatively high mass (225M.. ) and high metallicity (750.091., The low abundance ratios seen in W3IRS4 and W3IRS5 likely confine the progenitors of the supernovae to stars of relatively high mass $\ga$ $_\sun$ ) and high metallicity $\sim$ 0.02). + Caltech Submillimeter Observatory (CSO) is supported through NSF erant. AST-, Caltech Submillimeter Observatory (CSO) is supported through NSF grant AST-0540882. +instabilities with quasi-periodic behavior but the phase relatiouship between the TEME aud NAMIE is not as well defined as in Figure 2..,instabilities with quasi-periodic behavior but the phase relationship between the TFME and NAME is not as well defined as in Figure \ref{shearmag}. + Some quasi-periodic oscillations are present ou timescales of several vears but louger-terus trends are also evident. comparable to or longer than the duration of the simulation (~ 10 wears).," Some quasi-periodic oscillations are present on timescales of several years but longer-term trends are also evident, comparable to or longer than the duration of the simulation $\sim$ 10 years)." + Such longer-term evolution is to be expected since the growth rate of the clamshell instability decreases with decreasing field streneth., Such longer-term evolution is to be expected since the growth rate of the clam-shell instability decreases with decreasing field strength. + Achieving substantially lower SCS) diffuxon would require higher resolution which is a challenge because of the long integration times necessary to capture multiple evcles., Achieving substantially lower SGS diffusion would require higher resolution which is a challenge because of the long integration times necessary to capture multiple cycles. + The relatively short forcing timescale used for the simulations shown in Figures 1-3 (7-—Q1. corresponding to about 10 hours) is also dn some sense required by the setup of our nuuerical experinenuts.," The relatively short forcing timescale used for the simulations shown in Figures \ref{onlyshear}- \ref{slices} + $\tau = 0.1$, corresponding to about 10 hours) is also in some sense required by the setup of our numerical experiments." + Du a stimulation similar to that shown in Figures 2-25 but with 7=2 (8 davs). the mechanical forcing is msufBcient to overcome the magnetic tension associated with the imposed poloidal field.," In a simulation similar to that shown in Figures \ref{shearmag}- \ref{slices} but with $\tau = 2$ (8 days), the mechanical forcing is insufficient to overcome the magnetic tension associated with the imposed poloidal field." + As a result. the DRKE is oulv of the target value associated with «y aud the clam-shell instability is suppressed.," As a result, the DRKE is only of the target value associated with $u_0$ and the clam-shell instability is suppressed." + The field does exhibit η=1 structure but TEME dominates the magnetic energy and the evolution is quasi-steady. with a slow retrograde wopagation aud uo episodic openiuse up of the σαιπο attr.," The field does exhibit $m=1$ structure but TFME dominates the magnetic energy and the evolution is quasi-steady, with a slow retrograde propagation and no episodic opening up of the clam-shell pattern." + The solar tachocline is uch mere complex than our àiehlv simupliied model, The solar tachocline is much more complex than our highly simplified model. + Forcing timescales are longer mt the diffusion is lower. so strong toroidal fields could )o produced with lower poloidal Ποια strengths and the differential rotation could be maintained with weaker uechanical forcing.," Forcing timescales are longer but the diffusion is lower, so strong toroidal fields could be produced with lower poloidal field strengths and the differential rotation could be maintained with weaker mechanical forcing." + It is therefore difficult to establish roni the simulations alone whether the solar tachocline is Ina regine which exhibits quasi-periodic beliavoir as in Figure 2.., It is therefore difficult to establish from the simulations alone whether the solar tachocline is in a regime which exhibits quasi-periodic behavoir as in Figure \ref{shearmag}. + However. helioscisiaic inversions nmdicate hat the rotational shear in the tacliocline is continually naintained aud luear analysis sugeests that even weak oroidal fields are unstable iu the presence of such shear so it is likely that the tachocline is indeed coutiuuallv nuderegoineg global maegueto-shear instabilities.," However, helioseismic inversions indicate that the rotational shear in the tachocline is continually maintained and linear analysis suggests that even weak toroidal fields are unstable in the presence of such shear so it is likely that the tachocline is indeed continually undergoing global magneto-shear instabilities." + Latitudinal shear in the convective envelope is maintained by Reynolds stresses sud meridional circulations on timescales of order mouths while the nearly uniforui rotation of the radiative interior may be established ou iumch longer time scales (c.g.Gough&Melutvre1998:Talouetal.2002:A\Gesch 2005)..," Latitudinal shear in the convective envelope is maintained by Reynolds stresses and meridional circulations on timescales of order months while the nearly uniform rotation of the radiative interior may be established on much longer time scales \citep[e.g.][]{gough98,talon02,miesc05}. ." + Magnetic flux is coutinually supplied to the tachocline by topological pumping from peuctrative convection (6.8.Tobiasetal. 2001)., Magnetic flux is continually supplied to the tachocline by topological pumping from penetrative convection \citep[e.g.][]{tobia01}. + Although much of this flux is disordered. mean fields may be generated by nonlinear selt-orsanization processes such as inverse cascades or by rotational phase mixing aud turbulent recounection (Spruit1999:Browningctal.2006).," Although much of this flux is disordered, mean fields may be generated by nonlinear self-organization processes such as inverse cascades or by rotational phase mixing and turbulent reconnection \citep{sprui99,brown06}." +. In addition. global meridional circulations may transport axisviuuetric poloidal dux to the tachocline where mean toroidal fields would then be generated by rotational shear (Dikpatietal.200tb:Charbouneau2005).," In addition, global meridional circulations may transport axisymmetric poloidal flux to the tachocline where mean toroidal fields would then be generated by rotational shear \citep{dikpa04b,charb05}." +.. Tn this letter we have demonstrated that the clam-shell instability cau operate continually when rotational shear and magnetic fields are coutinnally replenished., In this letter we have demonstrated that the clam-shell instability can operate continually when rotational shear and magnetic fields are continually replenished. + The temporal evolution is quasi-periodic aud as mniean ποια» alternately build up aud destabilize., The temporal evolution is quasi-periodic and as mean fields alternately build up and destabilize. + This has ie character of a critical phenomenon but it is uot selborganized criticality in the technical seuse because were isa characteristic time aud spatial scale associated with the erowth rate aud xwaveuuniber of the instability (Jensen1998)., This has the character of a critical phenomenon but it is not self-organized criticality in the technical sense because there is a characteristic time and spatial scale associated with the growth rate and wavenumber of the instability \citep{jense98}. +. It is Likely that other instability modes nav simnibulv be maintained coutinually by external forcing., It is likely that other instability modes may similarly be maintained continually by external forcing. + Notable amone these is the s=1 tipping instability which exists for the type of concentrated oroidal bands thought to eive rise to photospleric active reeions (Dikpati&Calman1999:Callyetal.2003:Mi-eschetal. 2007).," Notable among these is the $m=1$ tipping instability which exists for the type of concentrated toroidal bands thought to give rise to photospheric active regions \citep{dikpa99,cally03,miesc07}." +. If elobal imagueto-shear instabilities are iudoeed occuriue in the solu tachocline they would lave wide-ranging iuplieatious for tachocline clwnaimics aud for the coupling between the convective envelope. and the radiative interior., If global magneto-shear instabilities are indeed occurring in the solar tachocline they would have wide-ranging implications for tachocline dynamics and for the coupling between the convective envelope and the radiative interior. + Angulu iuonmentuni transport duced. bv. these instabilities may influence the differential rotation profile in the convection zone and the longer-term rotational evolution of the Suu (Charbonneau&MacGregor1993:Calman2000:Talonetal 2002).," Angular momentum transport induced by these instabilities may influence the differential rotation profile in the convection zone and the longer-term rotational evolution of the Sun \citep{charb93,gilma00b,talon02}." +. Chemical transport across the tachocline also has implications for solu evolution. helioseisuuic structural iuversions. aud photospherie abundance ueasureiieuts (Chiristeuscu-Dalseaard2002:Pinson-reault 1997).," Chemical transport across the tachocline also has implications for solar evolution, helioseismic structural inversions, and photospheric abundance measurements \citep{christ02,pinso97}." +. Tachocliue iustabilities may also play a role in the solu dynamo., Tachocline instabilities may also play a role in the solar dynamo. + Although the simulations reported here suggest that clamshell instabilities may rot be capable of sustaining a dynamo localized cutirely within the tachocline. they may still play a role in xuitv sclection. field propagation. and flux emergence xitteris. (Colman2000:Dikpati&Cilinan2001b:Nor-on&Colman2005:DikpatiCiliuau 2005).," Although the simulations reported here suggest that clam-shell instabilities may not be capable of sustaining a dynamo localized entirely within the tachocline, they may still play a role in parity selection, field propagation, and flux emergence patterns \citep{gilma00b,dikpa01c,norto05,dikpa05}." +. We thauk Peter Calman aud Maus Dikpati for any informative discussions aud for conuneuts on he inauseript., We thank Peter Gilman and Mausumi Dikpati for many informative discussions and for comments on the mauscript. + This work was supported by NASA nuder the work order W-10.177 and made use ofligh- computing resources at the National Center or Atmospheric Research.," This work was supported by NASA under the work order W-10,177 and made use ofhigh-performance computing resources at the National Center for Atmospheric Research." +The authors would like to thaws Eric Feigelson for useful discussions about the counection between CIT. and PAIIs.,The authors would like to thank Eric Feigelson for useful discussions about the connection between $_2$ $_2$ and PAHs. + This work is based ou observations mace with the Spitzer Space Telescope. which is operated by the Jet Propulsion Laboratory. California Iustitute of Technology under a coutract with NASA.," This work is based on observations made with the Spitzer Space Telescope, which is operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract with NASA." + Support for this work was provided by NASA., Support for this work was provided by NASA. + Some of the data presented hereim were obtained at the WAL. Ίνους Observatory. which is operated as a scicutific partucrship among the California Institute of Technologw. the University of California and the National Aeronautics and Space Acininistration.," Some of the data presented herein were obtained at the W.M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California and the National Aeronautics and Space Administration." + The Observatory was made possible by the generous financial support of the WAAL Iseck Foundation., The Observatory was made possible by the generous financial support of the W.M. Keck Foundation. + Support for IMP. was provided by NASA through Hubble Fellowship eraut no., Support for KMP was provided by NASA through Hubble Fellowship grant no. + 01201.01 awarded by the Space Telescope Science Iustitute. which is operated by the Association of Universities for Re- search in Astronomy. Iuc.. for NASA. under contract NAS 5-26555.," 01201.01 awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Re- search in Astronomy, Inc., for NASA, under contract NAS 5-26555." + Research support for JSC was also provided by 6.1 base fundiug at the Naval Research Laboratory., Research support for JSC was also provided by 6.1 base funding at the Naval Research Laboratory. +be in the case of spherical svnumetry.,be in the case of spherical symmetry. + Lf this is correct. one may expect that the asphericity of the explosion with the explosion energy.," If this is correct, one may expect that the asphericity of the explosion with the explosion energy." + ltecentlv. a promising project has been started. (Van Dvk et al.," Recently, a promising project has been started (Van Dyk et al." + 1999: Smartt ct al., 1999; Smartt et al. + 2001. 2002: and. references herein) with the ultimate aim to identify the supernova »rogenitors (presupernovae) or at least to impose conclusive constraints on their masses by inspecting the prediscovery ielel of nearby supernovae.," 2001, 2002; and references therein) with the ultimate aim to identify the supernova progenitors (presupernovae) or at least to impose conclusive constraints on their masses by inspecting the prediscovery field of nearby supernovae." + In. particular. Smartt et. al.," In particular, Smartt et al." + derived. upper mass limits of and for he progenitors of the SNe1999em and 1990&g1. assuming distances D for the host galaxies 1637 and 3184 of Mpce ancl Alpe. respectively.," derived upper mass limits of and for the progenitors of the $\,$ 1999em and 1999gi, assuming distances $D$ for the host galaxies $\,$ 1637 and $\,$ 3184 of $\,$ Mpc and $\,$ Mpc, respectively." + Note that theseper limits depend on 2 and have to be adjusted for other values of D to (D7.5λΙρο) for 1999em and 0DT.Mpc) for 1999e1.," Note that these limits depend on $D$ and have to be adjusted for other values of $D$ to $\left(D/7.5\,{\mathrm{Mpc}}\right)^{0.6}$ for $\,$ 1999em and $\left(D/7.9\,{\mathrm{Mpc}}\right)^{0.6}$ for $\,$ 1999gi." + This follows from. the fact that the mass-luminosity relation can be approximated as LoMP in jo mass interval1., This follows from the fact that the mass-luminosity relation can be approximated as $L\sim {\cal M}^{3.3}$ in the mass interval. +.. For 1999em at Dpop= LLOSAIpe Clable3) follows as the upper mass limit for the 1999em progenitor.," For $\,$ 1999em at $D_{\mathrm{P-T}}= 11.08\,$ Mpc $\,$ 3) follows as the upper mass limit for the $\,$ 1999em progenitor." + Hlence. our result ME=15.0.M.. (lable3) does not contradict to. the observations D(1999om)z10 Mpc.," Hence, our result ${\cal M}=\NMS{15.0}$ $\,$ 3) does not contradict to the observations $D({\mathrm{1999em}})\gsim 10\,$ Mpc." + Phe situation of 1999g1 is similar.," The situation of $\,$ 1999gi is similar." +" The upper mass limit for D(1999ei)=14.53 Alpe CIable3) is Mcο(14.53/7.9)""=13.0M... Le. not in significan contradiction with the .M-value of from 3."," The upper mass limit for $D({\mathrm{1999gi}})=14.53\,$ Mpc $\,$ 3) is ${\cal M} < 9\times(14.53/7.9)^{0.6}=\NMS{13.0}$, i.e. not in significant contradiction with the ${\cal M}$ -value of from $\,$ 3." + There is no contradiction either with the upper mass limi of for the 1999gi progenitor imposed recently by Leonard et al. (," There is no contradiction either with the upper mass limit of for the $\,$ 1999gi progenitor imposed recently by Leonard et al. (" +20025).,2002b). + Equations (1)) (3)) by LNS5. derived. from a grid. of 23 LP models covering a wide parameter space.imply a correlation. between the absolute magnitude AZ (ane hence luminosity £ both measured at the mid-point ofthe plateau) and the expansion velocity (5.," Equations \ref{Evtu}) \ref{Rvtu}) ) by LN85, derived from a grid of 23 $\,$ IIP models covering a wide parameter space,imply a correlation between the absolute magnitude $M_V$ (and hence luminosity $L$ – both measured at the mid-point of the plateau) and the expansion velocity $u_{\mathrm{ph}}$." + Phe correlation is shown in Fies.G and 7 where 23 eri moclels are shown by black clots: the straight lines are the least-squares fits.," The correlation is shown in $\,$ \ref{nadezhfg6} and \ref{nadezhfg7} where 23 grid models are shown by black dots; the straight lines are the least-squares fits." + 1n Fig.7 are also shown the eight observed LWP from ‘Table3 marked by open circles. their absolute magnitudes Aly (Vable3. column2) being calculated from 4... where the plateau-tail distances. Jpp were used. from. 3. column2.," In $\,$ \ref{nadezhfg7} are also shown the eight observed $\,$ IIP from $\,$ 3 marked by open circles, their absolute magnitudes $M_V$ $\,$ 3, $\,$ 2) being calculated from $\,$ \ref{MVAD}, where the plateau-tail distances $D_{\mathrm{P-T}}$ were used from $\,$ 3, $\,$ 2." + These real SNe follow about. the slope of the models. but at a. fixed. value of μι they are fainter by =0.6 mag on average.," These real SNe follow about the slope of the models, but at a fixed value of $u_{\mathrm{ph}}$ they are fainter by $\approx 0.6\,$ mag on average." + Empirically. [αν Pinto (2002) have also found. using the CMD redshift-based clistances. such a correlation.," Empirically, Hamuy Pinto (2002) have also found, using the CMB redshift-based distances, such a correlation." + The slopes of their least-squares fits are virtually the same as shown in 6 and 7..," The slopes of their least-squares fits are virtually the same as shown in $\,$ \ref{nadezhfg6} and \ref{nadezhfg7}." + Thus our models confirm their linding., Thus our models confirm their finding. + The main conclusion one can draw from Figs.6. and 7 ds that our three-parametric eric of only 2:3 SNeILDP properly chosen models is ample enough to reproduce the main features of the real SNe.," The main conclusion one can draw from $\,$ \ref{nadezhfg6} + and \ref{nadezhfg7} is that our three-parametric grid of only 23 $\,$ IIP properly chosen models is ample enough to reproduce the main features of the real SNe." + Alodel calculation by LNS3 and LNS5 of LLP. leading to Eqs. (13). (33). ave combined: with available IPM distances ancl velocity distances (fg=60) to derive the explosion energy ££. the ejected mass ME. and the presupernova radius Roof 14 SNe.," Model calculation by LN83 and LN85 of $\,$ IIP, leading to $\,$ \ref{Evtu}) \ref{Rvtu}) ), are combined with available EPM distances and velocity distances $(H_0=60)$ to derive the explosion energy $E$, the ejected mass $\cal M$, and the presupernova radius $R$ of 14 $\,$ IIP." + Only the apparent. absorption-corrected magnitude V. and the expansion velocity μι at the mid- of the plateau together with its total curation 2M are needed as additional input parameters.," Only the apparent, absorption-corrected magnitude $V$ and the expansion velocity $u_{\mathrm{ph}}$ at the mid-point of the plateau together with its total duration $\Delta t$ are needed as additional input parameters." + The results are presented in “Table2.," The results are presented in $\,$ 2." + Instead of using EPAL or velocity distances it is also possible to use the bolometric Iluxes observed. during the SNUP tail phase to determine the Ni mass and hence new. indepencent clistances called here plateau-tail distances Dycp (ο.," Instead of using EPM or velocity distances it is also possible to use the bolometric fluxes observed during the $\,$ IIP tail phase to determine the Ni mass and hence new, independent distances called here plateau-tail distances $D_{\mathrm{P-T}}$ (cf." + Eq 113).," $\,$ \ref{DMNi}) )." + The Dpp distances vield new values of FE. ME. and & given in Table3 for nine SNe whieh were," The $D_{\mathrm{P-T}}$ distances yield new values of $E$, $\cal M$ and $R$ given in $\,$ 3 for nine SNe which were" +The ποιαίσα properties of disc stars in the solar icielibourliood have been exteusively studied in the past.,The kinematical properties of disc stars in the solar neighbourhood have been extensively studied in the past. + Velocity dispersion increase with age aud vertex deviation rave been well kuown facts for a long time aud have been recently reconfirmed (Dehuen Binney 1997))., Velocity dispersion increase with age and vertex deviation have been well known facts for a long time and have been recently reconfirmed (Dehnen Binney \cite{dehnen}) ). + A feature of local stellar motions which practically osse munoticed is a global asvuunetiy of the star distribution in the (0.0) plane of velocities relative to he Suulo dm addition to the vertex deviation which essentially concerus stars of simall epicyclic energies: the nean Ós-wvelocitv (7) of the old dise stars. as inferred roni various sanuples. appears significantly differcut frou zero even if we correct it for the solar motion. coutrarily o the expectation for a stationary axisvnunetrie galaxy.," A feature of local stellar motions which practically passed unnoticed is a global asymmetry of the star distribution in the $(u,v)$ plane of velocities relative to the Sun, in addition to the vertex deviation which essentially concerns stars of small epicyclic energies: the mean -velocity $\overline{u}$ ) of the old disc stars, as inferred from various samples, appears significantly different from zero even if we correct it for the solar motion, contrarily to the expectation for a stationary axisymmetric galaxy." + This anomaly was already apparent with the (ποσο Jalizeiss (1991)) aud the Woolley (1970)) space-velocities of nearby stars aud could be inferred from the )ositions of Eeecouw's old disc stellar groups in the (αν0) plane (EeeenOD 1987 aud references οσα).," This anomaly was already apparent with the Gliese Jahreiss \cite{gliese}) ) and the Woolley \cite{woolley}) ) space-velocities of nearby stars and could be inferred from the positions of Eggen's old disc stellar groups in the $(u,v)$ plane (Eggen \cite{eggen} and references therein)." + Mavor (1972)) eiipliasized a siguificaut excess ath)>>0 (5 = augular ΠοιοΤΙ) for stars having a ean asviunietrical «rift (5)σε20 - 30 laus +., Mayor \cite{mayor1}) ) emphasized a significant excess $\overline{u}(h) > 0$ $h$ = angular momentum) for stars having a mean asymmetrical drift $\langle S \rangle\ \approx 20$ - 30 km $^{-1}$. + Nevertheless. a quantitative inerpretation of the origin of this phenomenon has never bec1 eiven uutil now.," Nevertheless, a quantitative interpretation of the origin of this phenomenon has never been given until now." + Two new facts allow us to eo iore deeply iuto this question., Two new facts allow us to go more deeply into this question. + At first. after the de Vaucouleurs (1961)) prestuuption. series of recent more or less direct observational evidences indicate tha our Calaxy is definitely barred (see e. Iuijkeu 1996 for a review).," At first, after the de Vaucouleurs \cite{devaucoul}) ) presumption, series of recent more or less direct observational evidences indicate that our Galaxy is definitely barred (see e.g. Kuijken \cite{kuijken} for a review)." + Fux (1997)) realised elobal self-eonsisteunt nmuerical sinulatious of our Galaxy which all develop a loue-lasting bar., Fux \cite{fux}) ) realised global self-consistent numerical simulations of our Galaxy which all develop a long-lasting bar. + Secondly. Crenon observed a large sample of 5113 NLTT (New Luvteus Two Teuths. ic. µ0.18+0.02 arcsec Ly stars for which space velocities and xurtlv cheimica colpositions are available.," Secondly, Grenon observed a large sample of 5443 NLTT (New Luyten's Two Tenths, i.e. $\mu > 0.18 \pm 0.02$ arcsec $^{-1}$ ) stars for which space velocities and partly chemical compositions are available." + The sample will be described iu details iu Sect., The sample will be described in details in Sect. + 2., 2. + Its size allows us to deal with outstaudius questious of galactic structure and evolution., Its size allows us to deal with outstanding questions of galactic structure and evolution. + Iu the present letter. taking benefit of these progresses. we aiu to examine whether the bar could be responsible for the kinematical anomaly 1neutioned above.," In the present letter, taking benefit of these progresses, we aim to examine whether the bar could be responsible for the kinematical anomaly mentioned above." + The nearby star saaples are notoriously poor in halo aud very old dise stars., The nearby star samples are notoriously poor in halo and very old disc stars. + Iu order to test the effect of à bar iu the inner Galaxy. we must consider stars moving ou eccentric orbits bringing them in the bar proximity.," In order to test the effect of a bar in the inner Galaxy, we must consider stars moving on eccentric orbits bringing them in the bar proximity." + The sample used here is an exteusion of the Ciliese's and Woollevs catalogues towards larger volume aud space velocities at he expense of the comipleteness in low space-velocity stars., The sample used here is an extension of the Gliese's and Woolley's catalogues towards larger volume and space velocities at the expense of the completeness in low space-velocity stars. + It is a subset of a vast programe prepared for the HIPPARCOS wission., It is a subset of a vast programme prepared for the HIPPARCOS mission. + The initial set of LOOLT stars was ormed of all stars from Luyteu's NLTT Catalogue with MMRS11.5 if of color class from a to k-ui. or iig<12.5 if the class was ii or ii|.," The initial set of 10047 stars was formed of all stars from Luyten's NLTT Catalogue with $m_{R} < 11.5$ if of color class from a to k-m, or $m_{R} < 12.5$ if the class was m or m+." + According to internal priorities avourmneg the selection of parallaxe stars. namely those within 100 pc. aud to satellite observiug possibilities. 7821 stars have been included iu he IIHIPPARC'OS prograuuac.," According to internal priorities favouring the selection of parallaxe stars, namely those within 100 pc, and to satellite observing possibilities, 7824 stars have been included in the HIPPARCOS programme." +after every object spectrum to monitor the wavelength shifts of the CCD spectra.,after every object spectrum to monitor the wavelength shifts of the CCD spectra. + We also obtained spectra for the telluric standard HD 177724 and the O6-7V((f)) spectral template HD 168075 (Duftonetal.2006)., We also obtained spectra for the telluric standard HD 177724 and the O6-7V((f)) spectral template HD 168075 \citep{Dufton2006}. + Typical continuum-normalized spectra for LS 5039 and HD 168075 are shown in Fig. 1.., Typical continuum-normalized spectra for LS 5039 and HD 168075 are shown in Fig. \ref{longsp}. +" To measure radial velocities we first generated one hour long averaged spectra to get higher SNR — one hour corresponds to 0.01 orbital phase, hence negligible phase smearing appears in the phased radial velocity data."," To measure radial velocities we first generated one hour long averaged spectra to get higher SNR – one hour corresponds to 0.01 orbital phase, hence negligible phase smearing appears in the phased radial velocity data." +" Radial velocities of the HI,, He and He lines were determined by fitting two-component functions (a concentric sum of Gaussian and Lorentzian functions) and calculating the shift of the centroids to laboratory wavelengths."," Radial velocities of the H, He and He lines were determined by fitting two-component functions (a concentric sum of Gaussian and Lorentzian functions) and calculating the shift of the centroids to laboratory wavelengths." +" To check our method we also determined the velocities of some interstellar lines (Ca K, Na D, DIB 45780, DIB 46613) for each night."," To check our method we also determined the velocities of some interstellar lines (Ca K, Na D, DIB $\lambda$ 5780, DIB $\lambda$ 6613) for each night." + We applied heliocentric corrections to the radial velocity for each line at each time., We applied heliocentric corrections to the radial velocity for each line at each time. + The data were phased with an orbital period of 3.906 d (C05)., The data were phased with an orbital period of 3.906 d (C05). + The success in generating a RV curve with this phase folding supports the orbital period of LS 5039 as being that obtained by C05 instead of the longer 4.4 d period obtained by M04., The success in generating a RV curve with this phase folding supports the orbital period of LS 5039 as being that obtained by C05 instead of the longer 4.4 d period obtained by M04. +" To generate the final RV diagrams we used averaged velocities of the H (Ho, H8, Hy, Hd, A3835), He (MATI, A5875) and He (44200, A4686, 5411) lines; there are several other H and He lines in the wavelength region of our spectra (e.g. the frequently used He \4542 line), but they were too noisy or blended to use for velocity determination."," To generate the final RV diagrams we used averaged velocities of the H $\alpha$ , $\beta$, $\gamma$ , $\delta$, $\lambda$ 3835), He $\lambda$ 4471, $\lambda$ 5875) and He $\lambda$ 4200, $\lambda$ 4686, $\lambda$ 5411) lines; there are several other H and He lines in the wavelength region of our spectra (e.g. the frequently used He $\lambda$ 4542 line), but they were too noisy or blended to use for velocity determination." +" 'The resulting RV diagrams are shown in Fig. 2,,"," The resulting RV diagrams are shown in Fig. \ref{rvfit}," + top., top. + The error bars shown in Fig., The error bars shown in Fig. + 2 (typically +10 to +15 km s! in magnitude) represent plus and minus one standard deviation of the measured velocities of two to five lines at different wavelengths., \ref{rvfit} (typically $\pm$ 10 to $\pm$ 15 km $^{-1}$ in magnitude) represent plus and minus one standard deviation of the measured velocities of two to five lines at different wavelengths. +" The relatively large errors were caused partly by observational noise and partly by the high rotational velocity of the O star (votsind = 113 + 8 km s!, C05)."," The relatively large errors were caused partly by observational noise and partly by the high rotational velocity of the O star $v_{\rm rot} \sin i$ = 113 $\pm$ 8 km $^{-1}$, C05)." + We detected systematic increasing blueshifts from the He lines to the He lines to the H Balmer lines., We detected systematic increasing blueshifts from the He lines to the He lines to the H Balmer lines. +" C05 have also described this effect, but found its degree to be smaller (they obtained an ~8 km s! shift between the average RVs of the He and H Balmer lines, as opposed to our 20 km s! value)."," C05 have also described this effect, but found its degree to be smaller (they obtained an $\sim$ 8 km $^{-1}$ shift between the average RVs of the He and H Balmer lines, as opposed to our 20 km $^{-1}$ value)." +" We believe that the RV shift is due to the contamination of wind for the He and H lines (see Pulsetal.(1996))), and so we did not use thoseI two atomic line sets to constrain the orbit."," We believe that the RV shift is due to the contamination of wind for the He and H lines (see \citet{Puls1996}) ), and so we did not use those two atomic line sets to constrain the orbit." +" Additionally, redshifted satellite absorptions were found in the Ca K and NaI D1 and D2absorption lines with a radial velocity around +60 km s! (more precisely, +58.4 + 2.2 km s! by Ca K, +62.9 + 2.3 km s! by Na D1 and +61.9 + 1.7 km s! by Na D2)."," Additionally, redshifted satellite absorptions were found in the Ca K and Na D1 and D2 lines with a radial velocity around +60 km $^{-1}$ (more precisely, +58.4 $\pm$ 2.2 km $^{-1}$ by Ca K, +62.9 $\pm$ 2.3 km $^{-1}$ by Na D1 and +61.9 $\pm$ 1.7 km $^{-1}$ by Na D2)." + These satellite lines may belong to a formerly unknown Galactic Intermediate Velocity Cloud [IVC; see the review by Wakker (1997)]]., These satellite lines may belong to a formerly unknown Galactic Intermediate Velocity Cloud [IVC; see the review by \citet{Wakker1997}] ]. +" In the following analysis we adopted T.g = 39,000 + 1000 K and log g = 3.85 + 0.10 for the O primary (C05)."," In the following analysis we adopted $T_{\rm eff}$ = 39,000 $\pm$ 1000 K and log $g$ = 3.85 $\pm$ 0.10 for the O primary (C05)." + We measured the equivalent widths (EW) of several interstellar lines to estimate the interstellar reddening (see Section ?? for EW measurements of other lines)., We measured the equivalent widths (EW) of several interstellar lines to estimate the interstellar reddening (see Section \ref{starwind} for EW measurements of other lines). +" Using Na D1 [EW = 0.70 + 0.02 wwith the relation to reddening as per Munari (1997)]], DIB 45780and DIB λ6615 [EW = 0.55 + 0.05 aand 0.18 + 0.02A,, respectively with the relation to reddening as per Coxetal. (2005)]] lines, we found E(B—V) = 1.2 « 0.1, which is in agreement with previous results [1.25 to 1.35, Ribóetal.(2002) and 1.28 + 0.02, MO4]."," Using Na D1 [EW = 0.70 $\pm$ 0.02 with the relation to reddening as per \citet{Munari1997}] ], DIB $\lambda$ 5780and DIB $\lambda$ 6613 [EW = 0.55 $\pm$ 0.05 and 0.18 $\pm$ 0.02, respectively with the relation to reddening as per \citet{Cox2005}] ] lines, we found $E(B-V)$ = 1.2 $\pm$ 0.1, which is in agreement with previous results [1.25 to 1.35, \citet{Ribo2002} and 1.28 $\pm$ 0.02, M04]." +" Basedon thisagreement, we adopted the values d=2.5+0.1 kpc, Mo=22.9*$3 Mo and Ro=9.313% Ro obtained by C05."," Basedon thisagreement, we adopted the values $d = 2.5 \pm 0.1$ kpc, $M_{\rm O} = 22.9^{+3.4}_{-2.9}$ $_{\odot}$ and $R_{\rm O} = 9.3^{+0.7}_{-0.6}$ $_{\odot}$ obtained by C05." + Radial velocity curves were modelled using the 2003 of the Wilson-Devinney (WD) code (Wilson&Devin- 2003)..," Radial velocity curves were modelled using the 2003 of the Wilson-Devinney (WD) code \citep{Wilson1971,Wilson1994,Wilson2003}. ." + We used only our own velocity points and did not use previous RV measurements made by others., We used only our own velocity points and did not use previous RV measurements made by others. + Our data set therefore, Our data set therefore +foreground-sereen law.,foreground-screen law. + Tn Section L23.. we analyse the consequences of our dust iodel for IR lwunosity density due to dust. emission.," In Section \ref{sec:further-densities}, we analyse the consequences of our dust model for IR luminosity density due to dust emission." + We can caleulate some derived plivsical properties of the Universe (at οςz 0.1)., We can calculate some derived physical properties of the Universe (at $z\approx0.1$ ). +" The mass density in stars.Ou. is in the range 1.12.0 «107 5.1, and: the SFR density.Pape. is in the range 0.7L1 «10?5."," The mass density in stars, is in the range 1.1–2.0 $\times10^{-3}$ $h^{-1}$, and; the SFR density, is in the range 0.7–4.1 $\times10^{-2}$." + These ranges represeut confidence limits nargimalized over IME aud cosmüc SEIT butrestricted to near-solar metallicity models (Z or Z0.015 0.025)., These ranges represent confidence limits marginalized over IMF and cosmic SFH butrestricted to near-solar metallicity models $\bar{Z}$ or $Z=0.015$ –0.025). + IIowever. the results depend strouglv ou the low-mnass cud of the stellar IMF which is not constrained by our analysis.," However, the results depend strongly on the low-mass end of the stellar IMF which is not constrained by our analysis." + As a test of the varvine the low-mass cud of the IME. we also computed the ranges using the best-fitting IMES aud cosmic SEII« described in Table 2. @vith <95% oof rejection).," As a test of the varying the low-mass end of the IMF, we also computed the ranges using the best-fitting IMFs and cosmic SFHs described in Table \ref{tab:publ-imfs} (with $<95$ of rejection)." +" Frou these. iis in the ranee 0.82.5 «107 7.1, ane: iis in the range 1.1L3 «410?ὃν,"," From these, is in the range 0.8–2.5 $\times10^{-3}$ $h^{-1}$, and; is in the range 1.1–4.3 $\times10^{-2}$." + The lower stellar mass densities are derived frou IMES. with Doa0.5 (IXeunicutt. Salpeter mod.," The lower stellar mass densities are derived from IMFs with $\Gamma_{m<1}\le0.5$ (Kennicutt, Salpeter mod." + D. Scalo 1998) while the higher mass densities are derived from the Isvoupa (2001) BIAIF.," B, Scalo 1998) while the higher mass densities are derived from the Kroupa (2001) B IMF." + The uncertainty in the current SER density is nof increased compared to the measurement based ou the Equation 3 parameterization., The uncertainty in the current SFR density is not increased compared to the measurement based on the Equation \ref{eqn:imf} parameterization. + The lowest SER ceusities (< 0.01) ouly occur in our mocels with Dxd and none of the published INESs in the table have DosL2 which explains the lack of low SER deusities based on those IAIFs., The lowest SFR densities $<0.01$ ) only occur in our models with $\Gamma\la1.1$ and none of the published IMFs in the table have $\Gamma_{m>1}<1.2$ which explains the lack of low SFR densities based on those IMFs. + These results are in good agreement with the results. based on the IKeunicutt. IME. of Coleetal. aand Baldevetabl. and with the results. based ou a modified Salpeter IMF. of Belletal. (2003)...," These results are in good agreement with the results, based on the \citeauthor{Kennicutt83} IMF, of \citeauthor{cole01} and \citeauthor{baldry02}, and with the results, based on a modified Salpeter IMF, of \cite{bell03}. ." + They. are eenerallv not iu agreement with results based on the Salpeter IAIF extending down to, They are generally not in agreement with results based on the Salpeter IMF extending down to +ol spectroscopically confirmed LBGs to the total photometric sample in the magnitude range of 23.5tyta aud rg2rg) are asstuued to preserve the ce. they had when they were accreted., Accreted halos that survive $\tau_{DF} > t_0 - t_a$ and $r_t > r_{\rm max}$ ) are assumed to preserve the $v_c$ they had when they were accreted. + The resulting velocity function of surviving sublialos within the virial radius of the host (~2002tkpe at 0). averaged over all miereer histories. is shown by the thin solid line in Figure 1.," The resulting velocity function of surviving subhalos within the virial radius of the host $\sim 200 \hkpc$ at $z=0$ ), averaged over all merger histories, is shown by the thin solid line in Figure 1." + The error bars reflect the measured dispersion amone different iuerger histories., The error bars reflect the measured dispersion among different merger histories. + The thick straight line is the best fit to the correspoudiug velocity Muction measured in the cosmological N-body simulation O RKKVP99., The thick straight line is the best fit to the corresponding velocity function measured in the cosmological N-body simulation of KKVP99. +" The upper dashed lines show the velocity ""unctiou if the effects of ανασα. friction and/or tidal diszuption are ignored.", The upper dashed lines show the velocity function if the effects of dynamical friction and/or tidal disruption are ignored. + The analytic model reproduces he N-body results remarkably well., The analytic model reproduces the N-body results remarkably well. +" We have not tuned any parameters to obtain this agreement. although we roted abovethat plausible changes in the assuned initial circular radius A, could change the analytic prediction by ο, "," We have not tuned any parameters to obtain this agreement, although we noted abovethat plausible changes in the assumed initial circular radius $R_c$ could change the analytic prediction by $\sim 50\%$." +The good agreement suggests that our analytic uodel captures the esseutial plysics uuderblius the N-)xdy results., The good agreement suggests that our analytic model captures the essential physics underlying the N-body results. + An interesting feature of the model is that he subhalos surviving at 2=0 are ouly a sinall fraction of the halos actually accreted. most of which are destroved w tidal disruption.," An interesting feature of the model is that the subhalos surviving at $z=0$ are only a small fraction of the halos actually accreted, most of which are destroyed by tidal disruption." + We discuss implications of this satellite destruction in 811., We discuss implications of this satellite destruction in 4. + The second step in our model is to determine which of the surviving halos at 2=0 will host observable satellite ealaxies., The second step in our model is to determine which of the surviving halos at $z=0$ will host observable satellite galaxies. + The kev assuuption is that after the reionization redshift 2... gas accretion is suppressed im halos with es 2)., The thick line and shaded region shows the average and scatter in the expected number of observable satellites $z_f > \zre$ ). + The solid raneles show the observed satellite galaxies ofthe Mil Way and M3. within radii of 2005.!Epe from the centers of cach galaxy (note that all results are scaled to a fiducial volume. Lh Mpc?j., The solid triangles show the observed satellite galaxies ofthe Milky Way and M31 within radii of $200 \hkpc$ from the centers of each galaxy (note that all results are scaled to a fiducial volume $1 h^{-3} \rm{Mpc}^{3}$ ). + We see that the theoretical, We see that the theoretical +results for Ad=3.,results for $M=3$. +" Having too many or too few revolutions in Oat pitch angles ji close to zero can result in a numerically, introduced. anisotropy in the perpendicular direction after only a relatively small number of time steps.", Having too many or too few revolutions in $\phi$ at pitch angles $\mu$ close to zero can result in a numerically introduced anisotropy in the perpendicular direction after only a relatively small number of time steps. + Lhe particle cosines 45 are chosen between yp=1.1 with decreasing spacing Ay; such that the total distribution has a net drift with the required velocity., The particle cosines $\mu_i$ are chosen between $\mu_i=-1..1$ with decreasing spacing $\Delta\mu_i$ such that the total distribution has a net drift with the required velocity. + Finally the particles are scattered in the y2 plane using mixed radix. bit-reversed. fractions (Birdsall&Langdon1985)., Finally the particles are scattered in the $y-z$ plane using mixed radix bit-reversed fractions \citep{birdsalllangdon}. +. The two-dimensional magnetic Ποια. is initialised by taking a sum of Fourier nodes in 24) sampled fron a user- spectrum. having random. wave vectors & in the yjc plane (seee.g.Giacalone&Jokipii 1999)..," The two-dimensional magnetic field is initialised by taking a sum of Fourier modes in $A_\|$ sampled from a user-defined spectrum, having random wave vectors $\bm{k}$ in the $y-z$ plane \citep[see e.g.][]{giacalonejokipii99}. ." + For the results shown in Figure 2.. we used a 2D Fourier spectrum. ASQ)x1/1|(KL. )']. such that. perpendicular magnetic 101 will have a power spectrum. peaking close to the eneth Lo.," For the results shown in Figure \ref{fig2}, we used a 2D Fourier spectrum $A_\|^2(k)\propto1/[1+(kL_{\rm c})^{3}]$ , such that perpendicular magnetic field will have a power spectrum peaking close to the length $L_{\rm c}$." + Several cilferent forms for the power spectrum aave been used. and the general results are the same.," Several different forms for the power spectrum have been used, and the general results are the same." + The computational erid is à 512« square mesh with periodic »»undaryconditions in the y and z directions., The computational grid is a $512\times512$ square mesh with periodic boundaryconditions in the $y$ and $z$ directions. + The grid resolution is Aw=0.5. where cimensionless length units are chosen such that mefeBo=1 with Dy the mean magnetic ield strength. out of the plane.," The grid resolution is $\Delta x = 0.5$, where dimensionless length units are chosen such that $mc/eB_0=1$ with $B_0$ the mean magnetic field strength out of the plane." + The Fourier. modes. were selected with uniform logarithmic spacing on the interval 4«bí2x256 with Lo=16. such that most of the magnetic field structure is on scales much smaller than the size of the box.," The Fourier modes were selected with uniform logarithmic spacing on the interval $44 likely originate in cold foreground clouds on the line of sight to the source.,velocity offsets $>$ 4 likely originate in cold foreground clouds on the line of sight to the source. + In contrast. the absorption features at smaller velocity offsets to cold clouds surrounding the dense cores (which other studies call the protostellar envelopes). which are all part of large-scale molecular clouds (see Fig. 2).," In contrast, the absorption features at smaller velocity offsets to cold clouds surrounding the dense cores (which other studies call the protostellar envelopes), which are all part of large-scale molecular clouds (see Fig. \ref{fig:extract-w43-mm1}) )." + The absorptions at aare saturated for G31.412-0.31 and W33A and nearly saturated for the other sources. which indicates. abundances around - 1077—9 forp the outer cold parts of the massive. dense cores e(?)..," The absorptions at are saturated for G31.41+0.31 and W33A and nearly saturated for the other sources, which indicates abundances around $\sim$ $^{-9}$ for the outer cold parts of the massive dense cores \citep{poelman2007}." +" The HO 292-lj, line always appears in emission and shows a broad and a narrower velocity component (Fig. 1)).", The $_2$ O $2_{02}-1_{11}$ line always appears in emission and shows a broad and a narrower velocity component (Fig. \ref{fig:obs}) ). + In addition. the spectra of G31.41+0.31 and W43-MM1 show two well defined self-absorption features whichappear at the source velocity.," In addition, the spectra of G31.41+0.31 and W43-MM1 show two well defined self-absorption features whichappear at the source velocity." + With its high Ευρ. this transition mainly," With its high $E_\mathrm{up}$ , this transition mainly" +We initiated an interferometric follow-up of 6 Sco soon after the opening of the VLTI/AMBER instrument to the scientific,We initiated an interferometric follow-up of $\delta$ Sco soon after the opening of the VLTI/AMBER instrument to the scientific +to suppress accretion disk formation.,to suppress accretion disk formation. + However. as IILO2 note. if a magnetic field is present. then circular polarization should also be present.," However, as HL02 note, if a magnetic field is present, then circular polarization should also be present." + Robinsonetal.(1981). chronicles that repeated. attempts (to measure the circular polarization in MV. Lyr always found a value less than0., \citet{r1981} chronicles that repeated attempts to measure the circular polarization in MV Lyr always found a value less than. +1356.. Robinson οἱ al., Robinson et al. + also note that. if there is a magnetic field present (hat is strong enough to disrupt the accretion disk. Zeeman-splitüng of absorption lines should be detected: it is not.," also note that, if there is a magnetic field present that is strong enough to disrupt the accretion disk, Zeeman-splitting of absorption lines should be detected; it is not." +Thus. there is no evidence for a strong magnetic field associated with the AIV Ταν WD.," Thus, there is no evidence for a strong magnetic field associated with the MV Lyr WD." + Both the intermediate stateZUE spectra and the high state LIST spectra are inconsistent with our calculated Standard Models. having flatter flux profiles.," Both the intermediate state spectra and the high state HST spectra are inconsistent with our calculated Standard Models, having flatter flux profiles." + Our subsequent thin disk simulations. using TLUSTY annulus models. differ from the Standard: Model by assuming a [latter Z'(H) profile: Chev are able to produce [τν eood [fits to the observed. continua.," Our subsequent thin disk simulations, using TLUSTY annulus models, differ from the Standard Model by assuming a flatter $T(R)$ profile; they are able to produce fairly good fits to the observed continua." + Confirmation that the TLUSTY annuli represent a thin disk model is provided by the output data for an annulus ab r/r4=18.5 and for a mass transfer rate of ο10.4.vr.|. close to the value of our high state model.," Confirmation that the TLUSTY annuli represent a thin disk model is provided by the output data for an annulus at $r/r_{\rm wd}=18.5$ and for a mass transfer rate of $4.0{\times}10^{-9}{\cal M}_{\odot}{\rm yr}^{-1}$, close to the value of our high state model." + For this annulus. whose radius is 1.45x10 em. a Rosselancd optical depth of 0.81 is located at 2=194x10? cm. one dex smaller than the radius.," For this annulus, whose radius is $1.45{\times}10^{10}$ cm, a Rosseland optical depth of 0.81 is located at $z=1.94{\times}10^9$ cm, one dex smaller than the radius." + A Rosseland optical depth of 0.001 occurs al 2= L98x10? cm. indicating line formation in a (hin photosphere.," A Rosseland optical depth of 0.001 occurs at $z=1.98{\times}10^9$ cm, indicating line formation in a thin photosphere." + sinak (1994) has discussed peculiar (1.e.. non-Stancdard Model). Z(H) distributions.," Smak (1994) has discussed peculiar (i.e., non-Standard Model), $T(R)$ distributions." + The departures [rom (he Standard. Model in (he svstems he cites (e.g.. 1992)) are in the direction of a too flat £(2) profile. as we find for MV. Lyr.," The departures from the Standard Model in the systems he cites (e.g., \citealt*{rpt92}) ) are in the direction of a too flat $T(R)$ profile, as we find for MV Lyr." + Sinak argues that the departures lor svstems with />75 result from (he assumption of a flat accretion disk., Smak argues that the departures for systems with $i>75{\arcdeg}$ result from the assumption of a flat accretion disk. + That explanation is not applicable for MV Lyr because of its low inclination., That explanation is not applicable for MV Lyr because of its low inclination. + sinak suggests that. For low / cases. heating of the outer part of the accretion disk by the stream collision could be (he explanation.," Smak suggests that, for low $i$ cases, heating of the outer part of the accretion disk by the stream collision could be the explanation." + Duat-Ménnard. LLameury Lasota (2001) discuss the effect of stream impact heating and tidal effects.," Buat-Ménnard, Hameury Lasota (2001) discuss the effect of stream impact heating and tidal effects." + As our high state model indicates. if stream impact heating is (he physical cause of anomalous heating in the outer accretion disk region. the heating elfects extend over an appreciable fraction of the accretion disk radius.," As our high state model indicates, if stream impact heating is the physical cause of anomalous heating in the outer accretion disk region, the heating effects extend over an appreciable fraction of the accretion disk radius." + This effect ciffers from a bright spot. for which the radial extent amounts to a few percent of the component separation (seeWarner1995.sect.2.6.5)..," This effect differs from a bright spot, for which the radial extent amounts to a few percent of the component separation \citep[see][sect.2.6.5]{w95}." + We stress the importance of the low orbital inclination in MV. Lyr and the consequential absence of eclipses., We stress the importance of the low orbital inclination in MV Lyr and the consequential absence of eclipses. + All of the svslenms cited by Smak were shown {ο have peculiar Z() distributions by application of the MEM technique (Horne. 1993)) ancl so were restricted to svstems showing eclipses., All of the systems cited by Smak were shown to have peculiar $T(R)$ distributions by application of the MEM technique \citealt{h93}) ) and so were restricted to systems showing eclipses. + The spectrum svnthesis method used in this paper represents an alternative and independent technique that is applicable to both eclipsing aud non-eclipsing svstenis., The spectrum synthesis method used in this paper represents an alternative and independent technique that is applicable to both eclipsing and non-eclipsing systems. + The presence of high-excitation absorption lines in the MV. Lyr system imply (heir formation in a high temperature region above (both faces of) the accretion disk. possibly," The presence of high-excitation absorption lines in the MV Lyr system imply their formation in a high temperature region above (both faces of) the accretion disk, possibly" +]ilohertz quasi-periodic brigh(iness variations (kllz QPOs) have been detected. [rom more than twenty low-mass N-rayv binaries containing a weakly magnetized neutron star (vanderKlis20060).,Kilohertz quasi-periodic brightness variations (kHz QPOs) have been detected from more than twenty low-mass X-ray binaries containing a weakly magnetized neutron star \citep{vdk06}. +.. A pair of QPOs is often detected. with a lrequency separation that tvpically changes by tens of Hertz as the individual QPO frequencies change by hundreds of llertz.," A pair of QPOs is often detected, with a frequency separation that typically changes by tens of Hertz as the individual QPO frequencies change by hundreds of Hertz." + In lower luminosity svstems (often called atoll sources after the tracks they make in color-color cliagrams). the lower Irequeney QPO can reach quality factors (Q=v/Av) up to 200. whereas the upper kIIz QPO is usually a broader feature with maximum Q around 50 (see.e.g.Barretetal.2005a.b.2006)..," In lower luminosity systems (often called atoll sources after the tracks they make in color-color diagrams), the lower frequency QPO can reach quality factors $\equiv\nu/\Delta\nu$ ) up to 200, whereas the upper kHz QPO is usually a broader feature with maximum Q around 50 \citep[see, +e.g.][]{barret05amnras,barret05bmnras,barret06mnras}." + In brighter svstems (often called Z sources). both the lower and upper klIz QPOs are broader features. wilh maximum Q of a few tens 2010)..," In brighter systems (often called Z sources), both the lower and upper kHz QPOs are broader features, with maximum Q of a few tens \citep{boutelier10mnras}." + In lower luminosity sources. for which the qualitv [actor of the lower κκ QPO can be measured over ils entire frequency span after correcting for (he frequency. 5. Q increases with [frequency until it reaches a maximum around 500900 Iz. bevond which a sharp drop-olfis observed.," In lower luminosity sources, for which the quality factor of the lower kHz QPO can be measured over its entire frequency span after correcting for the frequency drifts, Q increases with frequency until it reaches a maximum around 800–900 Hz, beyond which a sharp drop-off is observed." + The presence of the drop in many systems. and its reproducibility in a given svstem independent of count rate and spectral hardness (Barretοἱal.2007).. led io the suggestion that it may. be related to the existence of an innermost stable circular orbit. a kev prediction of strong field general relativity (Barretetal.2006)..," The presence of the drop in many systems, and its reproducibility in a given system independent of count rate and spectral hardness \citep{barret07mnras}, led to the suggestion that it may be related to the existence of an innermost stable circular orbit, a key prediction of strong field general relativity \citep{barret06mnras}." + ATE JITOl462 is a unique X-rav source. which first beliaved like a Z source at. hieh huninosity. and whieh later behaved like an atoll source at much. lower luminosities.," XTE J1701–462 is a unique X-ray source, which first behaved like a Z source at high luminosity, and which later behaved like an atoll source at much lower luminosities." + The source was Closely monitored with the RNTE Proportional Counter Array. during its 2006- outburst (Iomanetal.2007:Lin2009b:Homan2010)..," The source was closely monitored with the RXTE Proportional Counter Array during its 2006-2007 outburst \citep{homan07apj,lin09apja,homan10apj}." + Type I X-ray bursts were studied by Linetal.(2009a).., Type I X-ray bursts were studied by \citet{lin09apjb}. + The three bursts observed occurred as the source was in Gransition from the (vpical Z-source behavior to the typical atoll-source behavior. at ~LOY ol the Eddington luminosity.," The three bursts observed occurred as the source was in transition from the typical Z-source behavior to the typical atoll-source behavior, at $\sim10$ of the Eddington luminosity." + No significant burst oscillations in (he range 30.4000 IIz were [ος cluring these three bursts., No significant burst oscillations in the range 30–4000 Hz were found during these three bursts. + Linetal.(2009a) also derive a distance estimate of 8.33:1.3 kpe Irom (wo radius expansion bursts (the latter two of the three)., \citet{lin09apjb} also derive a distance estimate of $8.8\pm1.3$ kpc from two radius expansion bursts (the latter two of the three). + In both states. κκ QPOs have been reported. with very. different. properties. vel lollowing the general trend that in the Z state. QPOs showed lower Q and amplitude than in the atoll state (lomanetal.etal. 2010)..," In both states, kHz QPOs have been reported, with very different properties, yet following the general trend that in the Z state, QPOs showed lower Q and amplitude than in the atoll state \citep{homan07apj,homan10apj,sanna10mnras}." + The luminosity range over which kIIz QPOs are detected between the Z ancl atoll state spans a [actor of 15-20., The luminosity range over which kHz QPOs are detected between the Z and atoll state spans a factor of 15-20. + The dramatic changes in the QPO parameters between the two source states could not be due to changes in the neutron star nass. its magnetic field. its spin. or even the inclination of the accretion disk.," The dramatic changes in the QPO parameters between the two source states could not be due to changes in the neutron star mass, its magnetic field, its spin, or even the inclination of the accretion disk." + It is thus more plausible that they. were instead caused by a change in the properties of the accretion flow., It is thus more plausible that they were instead caused by a change in the properties of the accretion flow. + This led Sannaetal.(2010). to conclude first Chat effects other (han the geometry of space time around the neutron star have a strong influence on the coherence and amplitude of the kIIz QPOs. and second that the drop of the coherence and RAIS amplitucle of the lower kllz QPOs. as we have observed it. could not be used to infer the existence of the innermost," This led \citet{sanna10mnras} to conclude first that effects other than the geometry of space time around the neutron star have a strong influence on the coherence and amplitude of the kHz QPOs, and second that the drop of the coherence and RMS amplitude of the lower kHz QPOs, as we have observed it, could not be used to infer the existence of the innermost" +"vepler was NASAIlaunchedhee on 2000""009 AlarehAlarch‘ 6 Giinto à Un5;Z-0 ο.solar‘ orbit. and PEEis observing a 105 square degree area of the sky in between the constellations. of M€vgnus and Lyra (Ixoch.etal. 2010)."," was launched on 2009 March 6 into a 372-d solar orbit, and is observing a 105 square degree area of the sky in between the constellations of Cygnus and Lyra \citep{koch10}." +.. After⋅ a dd commissioning⊲⊲⊀ phase (QU). the regular observations. started on 2009 Alay 12.," After a d commissioning phase (Q0), the regular observations started on 2009 May 12." + In. order to ensure optimal. solar illumination... of the solar panels. a ddegree roll of the telescope is performed at the end of each quarter .. NON ⋅ ∪⇂⊔≱∖⊳∖∪↓⋜," In order to ensure optimal solar illumination of the solar panels, a degree roll of the telescope is performed at the end of each quarter of its solar orbit." +⊔⋅∪↓⋅∣⋡↓↿⊳∐↥∢⊾↓⊔⋅⊳∖⇂⊏↥⋯⊔⋅∩⊾↓⋅↓⋜↧⊳∖↿⋖⋅∠⇂∪⊔↓∙∖⇁⇂∪↓⋅⇀∫≻⇀∫≻⊳⋅↱⊔⇂∠⇂⋅∙∙ (QL).e while: subsequent quarters are all three months long.," The first quarter lasted only for d (Q1), while subsequent quarters are all three months long." + In each of⋅ the four⋅ quarters annually theWvepler targets fall⋅ on cillerent CCDs., In each of the four quarters annually the targets fall on different CCDs. + TheNepler magnitude svstem CAp) refers to the wide Peesowsband (430.— 900nnm) Mtransmission of the telescopeDOO and detector system., The magnitude system $Kp$ ) refers to the wide passband $430-900$ nm) transmission of the telescope and detector system. + Note that. thefvepler magnitudes . (IN were derived.: before. the mission20. launch ancl are only approximatep): values., Note that the magnitudes $Kp$ ) were derived before the mission launch and are only approximate values. + .Currently:Acpíer processing: does. not provide calibratedA'cepéíer magnitudes Ap (Ixolenberg 2010).., Currently processing does not provide calibrated magnitudes $Kp$ \citep{kk10b}. + Both long cadence (LC. mmin. )0)) and short cadence (SC. 5S.9ss.. Παπάοἱal.0b) observations are based on the same 6-5 integrations which are summed. to form the LC and SC data onboard.," Both long cadence (LC, min, ), and short cadence (SC, s, \citealt{gil10b}) ) observations are based on the same $6$ -s integrations which are summed to form the LC and SC data onboard." + In this work we use DJD-corrected. raw LC data (Jenkinsetal.2010) spanning from QO to Q4. ie. dd of quasi- observations.," In this work we use BJD-corrected, raw LC data \citep{jen10a} spanning from Q0 to Q4, i.e. d of quasi-continuous observations." + Some of our targets (VII154CCvg among them) were observed in SC mode as well., Some of our targets Cyg among them) were observed in SC mode as well. + We exploit iis opportunity to compare LC and SC characteristies and investigate the frequeney spectrum to a much higher Nyquist requeney ddl.+ vs. 245dd.+)., We exploit this opportunity to compare LC and SC characteristics and investigate the frequency spectrum to a much higher Nyquist frequency $^{-1}$ vs. $^{-1}$ ). + The saturation limit is between Apcll12mmag depending on the particular chip the star is observed: xiehter than this. accurate photometry can be performed up to Apz Tmmae with judiciously designed: apertures (Szaboetal.2010).," The saturation limit is between $Kp \simeq 11-12$ mag depending on the particular chip the star is observed; brighter than this, accurate photometry can be performed up to $Kp \simeq 7$ mag with judiciously designed apertures \citep{szr10}." +. Since CCvgis much brighter than he saturation limit. it required special treatment. as can be seen in rof FL. which shows a 50 pixel box centered on V1154CCvg.," Since Cyg is much brighter than the saturation limit, it required special treatment, as can be seen in \\ref{FFI}, which shows a 50 pixel box centered on Cyg." + The plot was mace using written by M. Still., The plot was made using written by M. Still. + ‘To illustrate some of the common characteristics of the ata we show in rolvlil54le the rawKepler light curve of V1154CCvg alter normalizing the raw Lux counts and converting the fluxes to the magnitude scale., To illustrate some of the common characteristics of the data we show in \\ref{v1154lc} the raw light curve of Cyg after normalizing the raw flux counts and converting the fluxes to the magnitude scale. + Phe small gaps in the light curve are ue to unplanned safe mode and. loss-ol-line-point events. as well as regular data downlink periods.," The small gaps in the light curve are due to unplanned safe mode and loss-of-fine-point events, as well as regular data downlink periods." + This LC data set spanning Q0O4 data contains 14485 points., This LC data set spanning Q0–Q4 data contains 14485 points. +" 4 shows a dd segment (Q1) where ος data are available for⋅ quCCvg containing""E 49032⋅− data points.", \ref{v1154sc} shows a d segment (Q1) where SC data are available for Cyg containing 49032 data points. +"⊀ sPhe warvingmM amplitude. seen in. 3"" is. ol instrumental. origin.", The varying amplitude seen in \ref{v1154lc} is of instrumental origin. +D. lt is. a result of⋅ the small drift.» of the telescope. coupled: with. different⊀⋅ pixel⊀ sensitivities.," It is a result of the small drift of the telescope, coupled with different pixel sensitivities." +↔↔ In aclelition.Sl differentκ. aperture masks are assigned. to the targets quarterly which. result in. small changes in. the measured Lux.," In addition, different aperture masks are assigned to the targets quarterly which result in small changes in the measured flux." +" s . ∐↥∢⊾⊔↓⇜⇂⊔∪⋯∣⋡↓∢⊾⋜⋯↓↓≻↓↿⋯⇂⋖⋅≼∼↓↥⋜⋯⋏∙≟⋖⋅↓⊳∖⊳∖∢⊾⋖⋅⊔↿∪∖∖⋎⋜⋯⇂⊳∖∣⇂↥⋖⊾⋖⊾⊔∠⇂ . . of ⋅⋅≻O2. which. was noted to be due to flux| flowing. outside. o⋅ the optimal⊀ aperture (bleeding).⊀ alfecting"" the measured brightness."," The most notable amplitude change is seen towards the end of Q2, which was noted to be due to flux flowing outside of the optimal aperture (bleeding), affecting the measured brightness." + Fortunately. in (Q2 a larger mask was also downloaded besides the standard optimal aperture assigned to this star which allowed us to investigate the variation of Hux outside. the optimal: aperture.," Fortunately, in Q2 a larger mask was also downloaded besides the standard optimal aperture assigned to this star which allowed us to investigate the variation of flux outside the optimal aperture." + MMThis confirmed⋅ that the total flux. was indeed.. captured. withinp. the larger∙∙ aperture.m anc hence that the star.. shows no intrinsic.-.. amplitude," This confirmed that the total flux was indeed captured within the larger aperture, and hence that the star shows no intrinsic amplitude" + MMThis confirmed⋅ that the total flux. was indeed.. captured. withinp. the larger∙∙ aperture.m anc hence that the star.. shows no intrinsic.-.. amplitude.," This confirmed that the total flux was indeed captured within the larger aperture, and hence that the star shows no intrinsic amplitude" +timescale ranges.,timescale ranges. + We find that about half of the short period sources have variability timescales shorter than hh. These are again distributed along the main sequence with a [ew objects placed above it., We find that about half of the short period sources have variability timescales shorter than h. These are again distributed along the main sequence with a few objects placed above it. + There are 152 objects showing variability in the 0.25 - 144 range., There are 152 objects showing variability in the 0.25 - d range. + These objects are also mostly. distributed along the main sequence. including ? DDoracdus pulsators amongst others. with some cases found in the extreme colour region.," These objects are also mostly distributed along the main sequence, including $\gamma$ Doradus pulsators amongst others, with some cases found in the extreme colour region." + The RR Lyr variables present in the survey should be Found in this variability range., The RR Lyr variables present in the survey should be found in this variability range. + ΠΕ we combine this with the colours expected for RAR Lyr svstems. ic. Q.1«(D.— V)«0.45. O.1«(V. D)«0.65. (Guldenschuhetal.2005) we find 12 lut Lyr candidates.," If we combine this with the colours expected for RR Lyr systems, i.e. $<$ $-$ $<$ 0.45, $<$ $-$ $<$ 0.65 \cite{glw05} we find 12 RR Lyr candidates." + One of these will be discussed. as an example. in Section +.6..," One of these will be discussed, as an example, in Section \ref{res:example}." + We find 138 sources that show variabilities between 1 and dd again distributed mostly along the main sequence., We find 138 sources that show variabilities between 1 and d again distributed mostly along the main sequence. + This would include 7. Doradus pulsators as well as Pop 11 Cepheids., This would include $\gamma$ Doradus pulsators as well as Pop II Cepheids. + There are 55 point sources that show variabilities on timescales longer than teed. Binary svstems with these periods as well as Pop LE Cepheids are incbuded in this period range., There are 55 point sources that show variabilities on timescales longer than d. Binary systems with these periods as well as Pop II Cepheids are included in this period range. + “Phe blue sources found in these two period. ranges above the blue cutoll could be subdwarf B slow pulsators or binaries., The blue sources found in these two period ranges above the blue cutoff could be subdwarf B slow pulsators or binaries. + Fie., Fig. + Ll presents similar diagrams to those in Fig., \ref{res:ccdiag:fig2} presents similar diagrams to those in Fig. + out. for the sources where the error limits were set το 20 percent., \ref{res:ccdiag:fig1} but for the sources where the error limits were set to 20 percent. + Ehe distribution of variables in the ciagrams is very similar to the initial one., The distribution of variables in the diagrams is very similar to the initial one. + Again about half of the sources show variability timescales shorter than 6hh. Most. of the objects that have disappeared from the diagram come from the shorter period ranges (23 per cent out of the 0.4 - Ghh bin and 22 per cent out of the 0.25 - Leld bin)., Again about half of the sources show variability timescales shorter than h. Most of the objects that have disappeared from the diagram come from the shorter period ranges (23 per cent out of the 0.4 - h bin and 22 per cent out of the 0.25 - d bin). + This could be ue to the fact that if the signal is not sinusoidal or regular. 1e floating mean periodogram tends to calculate. periods gaiorter than the input ones with large errors.," This could be due to the fact that if the signal is not sinusoidal or regular, the floating mean periodogram tends to calculate periods shorter than the input ones with large errors." + It is worth noticing that a lew of the interesting objects above the bluc cut-olf have disappeared., It is worth noticing that a few of the interesting objects above the blue cut-off have disappeared. +"infrared (IR) luminosity (119)) the star-formation rate (SFR), and the stellar mass (M..).","infrared (IR) luminosity ) the star-formation rate (SFR), and the stellar mass $M_*$ )." +" From the SED fitting procedure, we obtain a total Lig6.8x10!!+25%Isun,, and SFR ~119+25% syyr’!."," From the SED fitting procedure, we obtain a total $\sim6.8\times10^{11}\pm25$, and SFR $\sim119\pm$ $^{-1}$." +" This is roughly an order of magnitude lower than the SFRs implied by the few detections of GRB hosts in the submillimeter (Tanviretal.2004), but would definitely qualify the host of aas a dusty luminous star-forming galaxy."," This is roughly an order of magnitude lower than the SFRs implied by the few detections of GRB hosts in the submillimeter \citep{tanvir04}, but would definitely qualify the host of as a dusty luminous star-forming galaxy." +" In the absence of extinction, the inferred SFR is sufficiently high that both aand wwould have been detected at >5σ with the SINFONI spectra."," In the absence of extinction, the inferred SFR is sufficiently high that both and would have been detected at $>5\sigma$ with the SINFONI spectra." +" The (conservative) 5c: upper limits we obtain (in J for aand K for Ho)) give a SFR~30--40Μο .yyr! (usingtheSFRcalibrationsofSavaglioetal.2009)., taking into account the uncertainty in redshift, and the impact of the sky lines on the noise in the observed spectrum."," The (conservative) $\sigma$ upper limits we obtain (in $J$ for and $K$ for ) give a $\sim30-40$ $^{-1}$ \citep[using the SFR calibrations of][]{savaglio09}, taking into account the uncertainty in redshift, and the impact of the sky lines on the noise in the observed spectrum." +" This is a factor of 3 to 4 times lower than the unattenuated SFR inferred from oof the SED analysis; if the latter value is the true one, the extinction of the emission lines would be Ayz| -2mmag, consistent with the SED fitting. (c.f.,Svenssonetal.2010).. (Frailetal.2002)..."," This is a factor of 3 to 4 times lower than the unattenuated SFR inferred from of the SED analysis; if the latter value is the true one, the extinction of the emission lines would be $\ga1-2$ mag, consistent with the SED fitting. \citep[c.f.,][]{svensson10}. \citep{frail02}." +llere. (he spin-up is caused by angular momentum from the core that to the envelope during thermal pulses (Garcia-Seguraetal.1999).,"Here, the spin-up is caused by angular momentum from the core that to the envelope during thermal pulses \citep{1999ApJ...517..767G}." + The validitv of our assumption of angular momentum conservation for the star (hus remains {ο be seen., The validity of our assumption of angular momentum conservation for the star thus remains to be seen. + However. as we will demonstrate in the following section. if this condition is somehow met. some very important observational leatures of AGB stars maw be reproduced.," However, as we will demonstrate in the following section, if this condition is somehow met, some very important observational features of AGB stars may be reproduced." + It is therelore interesting to consider the scenario where the stars angular moment is conserved. despite (he uncertainty of this assuniption.," It is therefore interesting to consider the scenario where the star's angular momentum is conserved, despite the uncertainty of this assumption." +" Strictly speaking. the relationship found between p./p, and à. (see reffig:figurel.. lower panel) is ofcourse only valid for the LAL. AGB star modeled. above."," Strictly speaking, the relationship found between $\rho_{\rm{e}}/\rho_{\rm{p}}$ and $\alpha$ (see \\ref{fig:figure1}, lower panel) is ofcourse only valid for the $1\,\rm{M_{\odot}}$ AGB star modeled above." +" Suill. it may not be unreasonable to assume that p/p, will in first order primarily depend on . since it is the deviation [rom axisvmmetry of the AGB star that leads to an axisvimetric envelope in the first place."," Still, it may not be unreasonable to assume that $\rho_{\rm{e}}/\rho_{\rm{p}}$ will in first order primarily depend on $\alpha$, since it is the deviation from axisymmetry of the AGB star that leads to an axisymmetric envelope in the first place." + If this assumption is correct. we may apply the obtained relationship to other stars as well. and generally study. p./py as a tinction of stellar parameters and evolution (see below).," If this assumption is correct, we may apply the obtained relationship to other stars as well, and generally study $\rho_{\rm{e}}/\rho_{\rm{p}}$ as a function of stellar parameters and evolution (see below)." + IL (he assumption is invalid. the behavior of a still provides information on the general behavior of p./py Lor a given star. since deviations from spherical svummetry ol the AGB star will still be amplified in the cust condensation region 1996)..," If the assumption is invalid, the behavior of $\alpha$ still provides information on the general behavior of $\rho_{\rm{e}}/\rho_{\rm{p}}$ for a given star, since deviations from spherical symmetry of the AGB star will still be amplified in the dust condensation region \citep{1996A&A...313..605D}." + Only the exact relation between a and p./py may not be specified in this case., Only the exact relation between $\alpha$ and $\rho_{\rm{e}}/\rho_{\rm{p}}$ may not be specified in this case. + As AGB stars evolve. their Iuminositv increases. while their mass and elfective temperature decrease.," As AGB stars evolve, their luminosity increases, while their mass and effective temperature decrease." + Following releq:Rerav2.. the effect of £ and Tar is thus to increase a (i.e. lower the degree of axisvyimnietry) over time. while the effect of 37 will be to decrease a (i.e. increase the degree of axisvmnmetry) over (ime.," Following \\ref{eq:Rgrav2}, the effect of $L$ and $T_{\rm{eff}}$ is thus to increase $\alpha$ (i.e. lower the degree of axisymmetry) over time, while the effect of $M$ will be to decrease $\alpha$ (i.e. increase the degree of axisymmetry) over time." + Here. (he stellar mass has the largest effect on a and hence the axisvimetry in the envelope.," Here, the stellar mass has the largest effect on $\alpha$ and hence the axisymmetry in the envelope." + While the luminosity of the star (vpically increases by a factor of 10 during AGB star evolution. a (see releq:Rerav2)) depends on vLi/L. which only decreases by a [actor of 3.," While the luminosity of the star typically increases by a factor of 10 during AGB star evolution, $\alpha$ (see \\ref{eq:Rgrav2}) ) depends on $\sqrt{L_{\rm{i}}/L}$, which only decreases by a factor of 3." + Likewise. while a depends on (1Τι)”. the effective temperature typically decreases [rom KI. to IXIX. so (Tur/Turi)? decreases at most by a factor 2.," Likewise, while $\alpha$ depends on $(T_{\rm{eff}}/T_{\rm{eff,i}})^{2}$, the effective temperature typically decreases from K to K, so $(T_{\rm{eff}}/T_{\rm{eff,i}})^{-2}$ decreases at most by a factor 2." + In constrast. a varies with the stellar mass as (L/M(CM;—M)/(CMMJ).," In constrast, $\alpha$ varies with the stellar mass as $(1/M)((M_{\rm{i}}-M_{\rm{c}})/(M-M_{\rm{c}}))$." +" Assuming its tip of the AGB envelope mass is ~0.01M. (Blócker 1995).. a may therefore varv by a [actor of about 3.6x10* (2.5x 10"") over the lifetime of a 1M. (7 M.) star."," Assuming its tip of the AGB envelope mass is $\sim0.01\,\rm{M_{\odot}}$ \citep{1995A&A...297..727B}, , $\alpha$ may therefore vary by a factor of about $3.6\times10^3$ $2.5\times10^6$ ) over the lifetime of a $1\,\rm{M_{\odot}}$ $7\,\rm{M_{\odot}}$ ) star." + The axisvmmetry in the envelope will thus indeed be primarilv affected by the stellar mass., The axisymmetry in the envelope will thus indeed be primarily affected by the stellar mass. +]t is anticipated that X-ray polarimetry will provide us with a powerful method of probing the physical conditions and geometry of high-energy. astrophysical systems.,It is anticipated that X-ray polarimetry will provide us with a powerful method of probing the physical conditions and geometry of high-energy astrophysical systems. + Accreting X-ray sources are expected to show a significant degree of polarization as a result of photon scattering in non-uniform. distributions of matter in non-spherical geometries. such as accretion disks and columns (seee.g.Mészárosetal.LOSS:Rees 1915).," Accreting X-ray sources are expected to show a significant degree of polarization as a result of photon scattering in non-uniform distributions of matter in non-spherical geometries, such as accretion disks and columns \citep[see e.g.][]{Meszaros88, Rees75}." +. Accreting white cdwarfs are strong X-ray SOULCCS during active states (seee.g.Ixuulkers.ctal.2006:Wuelal.2003:Warner1995.for reviews).," Accreting white dwarfs are strong X-ray sources during active states \citep[see e.g.][for reviews]{Kuulkers06, Wu03, Warner95}." + ln magnetized systems (the magnetic cataclysmic variables. mCVs). the accretion How is confined bv the magnetic field. near the white cdwarf.," In magnetized systems (the magnetic cataclysmic variables, mCVs), the accretion flow is confined by the magnetic field near the white dwarf." + The supersonic accreting material becomes subsonic close to the white-chwarl surface. resulting in a standing shock. which ionizes and heats the plasma to temperatures KDer(1040) keV. (where. & is oltzmann's constant)," The supersonic accreting material becomes subsonic close to the white-dwarf surface, resulting in a standing shock, which ionizes and heats the plasma to temperatures $kT\approx (10-40)$ keV, (where $k$ is Boltzmann's constant)." + The heated. material in the post-shock flow cools by emitting bremsstrahlung N-ravs and optical1. evelotron emission (Lamb&Masters1979:Wing&Lasota 1979).," The heated material in the post-shock flow cools by emitting bremsstrahlung X-rays and optical/IR cyclotron emission \citep{Lamb79, King79}." + Menmsstrahlung radiation emitted. by isotropic thermal electrons is not. polarized., Bremsstrahlung radiation emitted by isotropic thermal electrons is not polarized. + However. in stronely magnetic svstems where evcelotron cooling is very ellicient. Coulomb collisions might not be cllicient chough to ensure an isotropic Alaxwellian distribution for the electrons.," However, in strongly magnetic systems where cyclotron cooling is very efficient, Coulomb collisions might not be efficient enough to ensure an isotropic Maxwellian distribution for the electrons." + Menmsstrahlung X-rays from such systems would be intrinsically polarized. (seec.g.MeMaster.1961)., Bremsstrahlung X-rays from such systems would be intrinsically polarized \citep[see e.g.][]{McMaster61}. +. lor mC'Vs with a high accretion rate. the accretion column can have Thompson optical depths of up to a few. giving rise to substantial Comptonization signatures (seec.g.WuIxuncic.Wu&Cullen2005:MeNamaraetal. 2008).," For mCVs with a high accretion rate, the accretion column can have Thompson optical depths of up to a few, giving rise to substantial Comptonization signatures \citep*[see e.g.][]{Wu99,Kuncic05,McNamara07}." +. Our previous studies (Ixuncicetal.2005:MeNamaraal. 2008).. which used a nonlinear Monte Carlo algorithm for the simulations (Cullen200a.b). demonstrates the substantial effects of Compton scattering on Fe Ka emission lines in the post-shock Lows of mCVs.," Our previous studies \citep{Kuncic05, McNamara07}, which used a nonlinear Monte Carlo algorithm for the simulations \citep{Cullen01a, Cullen01b}, demonstrates the substantial effects of Compton scattering on Fe $\alpha$ emission lines in the post-shock flows of mCVs." + Like the photons in the Fe lines. whose profilesCS are oadened: and: distorted by Compton scattering. the photons in the whole X-ray continuum can undergo multiple scatterings.," Like the photons in the Fe lines, whose profiles are broadened and distorted by Compton scattering, the photons in the whole X-ray continuum can undergo multiple scatterings." + Although Compton scattering woutle not readily introduce prominent spectral signatures in the 011) keV continuum energy band. it can produce a net. polarization. clue to the non-isotropic distribution of electrons in the accretion column. the lack of svmmetry in the viewing geometry anc perhaps the presence. of the magnetic field in the accretion Low.," Although Compton scattering would not readily introduce prominent spectral signatures in the $0.1 - 10$ keV continuum energy band, it can produce a net polarization due to the non-isotropic distribution of electrons in the accretion column, the lack of symmetry in the viewing geometry and perhaps the presence of the magnetic field in the accretion flow." + A study by Matt(2004) has shown that the degree. of polarization is ~44 for a cold. homogeneous and. static accretion column.," A study by \cite{Matt04} has shown that the degree of polarization is $\simeq 4\%$ for a cold, homogeneous and static accretion column." + The degree of X-ray polarization in mC'Vs, The degree of X-ray polarization in mCVs +interpenetrate each other.,interpenetrate each other. + For po20. the contribution of barvons/antibarvons and barvonic resonances is relatively small. but with increasing barvon density. they form an ever larger section of the species present in the matter. aud bevond some barvon density. they become the dominant constituents.," For $\mu \simeq 0$, the contribution of baryons/antibaryons and baryonic resonances is relatively small, but with increasing baryon density, they form an ever larger section of the species present in the matter, and beyond some baryon density, they become the dominant constituents." + Finally. at vanishing temperature. (he medium consists essentially ol nucleons.," Finally, at vanishing temperature, the medium consists essentially of nucleons." + At high barvon density. the dominant interaction is non-resonant.," At high baryon density, the dominant interaction is non-resonant." + Nuclear forces are and strongly attractive at distances of about 1: fm: but [or distances around 0.5 [m. they become strongly repulsive.," Nuclear forces are short-range and strongly attractive at distances of about 1 fm; but for distances around 0.5 fm, they become strongly repulsive." + The former is what makes nuclei. the latter (together with Coulomb aud Fermi repulsion) prevents (hem from collapsing.," The former is what makes nuclei, the latter (together with Coulomb and Fermi repulsion) prevents them from collapsing." + The repulsion between a proton and a neutron shows the purely barvonic “hard-core” effect. and is connected neither (o Coulomb repulsion nor to Pauli blocking of nucleons., The repulsion between a proton and a neutron shows the purely baryonic “hard-core” effect and is connected neither to Coulomb repulsion nor to Pauli blocking of nucleons. + As a consequence. the volumes of nuclei erow Iimearly with the sum of ils protons and neutrons.," As a consequence, the volumes of nuclei grow linearly with the sum of its protons and neutrons." + With increasing barvon density. the mobility of barvons in the medium becomes stronelv restricted by the presence of other barvons (see refhard)). leading to a “jammed” state in which each barvon can only move a small distance before being blocked by others [48]..," With increasing baryon density, the mobility of baryons in the medium becomes strongly restricted by the presence of other baryons (see \\ref{hard}) ), leading to a “jammed” state in which each baryon can only move a small distance before being blocked by others \cite{KS}." + To addresss the situation of high barvon density. we again turn to percolation theory. but now the constituents are hadrons containing a repulsive hare core. which we take for simplicity to be half that of the hadron.," To addresss the situation of high baryon density, we again turn to percolation theory, but now the constituents are hadrons containing a repulsive hard core, which we take for simplicity to be half that of the hadron." + The percolation problem has been solved numerically for such à case as well [49].., The percolation problem has been solved numerically for such a case as well \cite{Kratky}. . +" We thus have (wo percolation scenarios [11]: one for the “bag fusion"" of fully overlapping (or interpenetrating) mesonic spheres of radius rj1 Im. aud one for barvons of the same radius. but having a hard core of radius rj220.5 fm."," We thus have two percolation scenarios \cite{hardcore}: one for the “bag fusion” of fully overlapping (or interpenetrating) mesonic spheres of radius $r_h\simeq 1$ fm, and one for baryons of the same radius, but having a hard core of radius $r_{hc}\simeq 0.5$ fm." + In the T—ji plane. each percolation condition results im a (transition curve. as illustrated in refheperc..," In the $T-\mu$ plane, each percolation condition results in a transition curve, as illustrated in \\ref{hcperc}." + As consequence. we have for low jo a mesonic bag fusion transition to a plasma. while for large ji. the barvonic percolation transition is the first to occur.," As consequence, we have for low $\mu$ a mesonic bag fusion transition to a quark-gluon plasma, while for large $\mu$, the baryonic percolation transition is the first to occur." + It is (hus quite conceivable that the competition between mesonic resonance clustering ancl (he hard-core repulsion of barvons is at the origin of the different transition patterns in the 7—qi plane., It is thus quite conceivable that the competition between mesonic resonance clustering and the hard-core repulsion of baryons is at the origin of the different transition patterns in the $T-\mu$ plane. +" Extending such a scenario even further. one may also consider the large sr region of the T=ji plane below the mesonic transition curve to become a further ""quarkvonic state of matter 101."," Extending such a scenario even further, one may also consider the large $\mu$ region of the $T-\mu$ plane below the mesonic transition curve to become a further “quarkyonic” state of matter \cite{quarky}." + We thus find that at sufficiently high temperatures and/or densities. strongly. interacting malter will be in a new state. consistingof deconfinecl quarks ancl eluons.," We thus find that at sufficiently high temperatures and/or densities, strongly interacting matter will be in a new state, consistingof deconfined quarks and gluons." + Is there some wav, Is there some way +will evolve into a system more massive than either of the oogenitors.,will evolve into a system more massive than either of the progenitors. + During this process the physical evolution of he resulting remnant galaxy will also change. as mergers are potentially the dominant. method. for trigeering star ormation and producing feedback by ejecting. or heating. gas (e.g.. Coxetal. 2004)).," During this process the physical evolution of the resulting remnant galaxy will also change, as mergers are potentially the dominant method for triggering star formation and producing feedback by ejecting, or heating, gas (e.g., \citealt{cox2004}) )." + Mergers can also spur on the ormation of black holes and trigger AGN activity. as both observations and theory have shown (e.g. Hopkins200x Dundyetal. 2008)).," Mergers can also spur on the formation of black holes and trigger AGN activity, as both observations and theory have shown (e.g., \citealt{hopkins2008}; \citealt{bundy2008}) )." + While galaxy mergers are seen in the ocal and distant universe. the exact role of mergers in the ormation and evolution of galaxies over cosmic history is still uncertain.," While galaxy mergers are seen in the local and distant universe, the exact role of mergers in the formation and evolution of galaxies over cosmic history is still uncertain." + There are. two primary methods. for tracing the merecr history of galaxies in observations: morphological identification techniques and the close galaxy. pair method (c.g. Pattonctal. 2000))., There are two primary methods for tracing the merger history of galaxies in observations: morphological identification techniques and the close galaxy pair method (e.g. \citealt{patton2000}) ). + Examples of morphological techniques are. the concentrationasvmmetry.elumpiness method (CAS. hereafter. e.g. Conselice 2003a)) and. the Cini-M20. method. (Lotz.Primack&Alacdau2004).," Examples of morphological techniques are the concentration–asymmetry–clumpiness method (CAS, hereafter, e.g. \citealt{cons2003a}) ) and the Gini-M20 method \citep{lotz2004}." +.. The CAS method identifies galaxies undergoing mergers on the basis of observed morphological properties (e.g... Consclice 2003a)) and is a non-parametric technique for measuring the shapes and structures of galaxies on resolved. CCD images (e.g. Conselice.Bershady&Jangren2000a:: Bershacyetal. 2000: Conselice.ctal. 2002: Conselice 2003a)).," The CAS method identifies galaxies undergoing mergers on the basis of observed morphological properties (e.g., \citealt{cons2003a}) ) and is a non-parametric technique for measuring the shapes and structures of galaxies on resolved CCD images (e.g., \citealt{cons2000a}; \citealt{bershady2000}; \citealt{cons2002}; \citealt{cons2003a}) )." +. ALL methodologies have been demonstrated. to be internally consistent with each other (DeProprisetal.2007:: C'onseliceetal. 2008:: Witzbichler&White 2008))., All methodologies have been demonstrated to be internally consistent with each other \citealt{depropris2007}; \citealt{cons2008}; \citealt{manfred2008}) ). + However. since cach method. identifies galaxies at a different stage during the merger. overall the galaxy. populations investigated by cach method can be substantially different.," However, since each method identifies galaxies at a different stage during the merger, overall the galaxy populations investigated by each method can be substantially different." +" Phe main uncertainty in all methods resides in the time-scale 7,, used to identity ealaxies undergoing mergers (e.g. Conselice2006a:: Lotzetal. 2008b))."," The main uncertainty in all methods resides in the time-scale $\tau_{\rm m}$ used to identify galaxies undergoing mergers (e.g., \citealt{cons2006}; \citealt{lotz2008b}) )." + Currently. the most likely time-scale to which the CAS and. pair methods are sensitive isbelieved. tobe Tu~O41 Cre.," Currently, the most likely time-scale to which the CAS and pair methods are sensitive isbelieved tobe $\tau_{\rm m} \sim 0.4-1$ Gyr." +In the last decadea relatively large sample of galaxy mergers has been collated (Pattonetal.2000:: Pattonctal. 2002: Consclice 2003a:: Hernandez-Toledoetal. 2005:: und.Ellis&Conselice 2005: Bunelyetal. 2006:: Consclice 20062: Conselice2006 X June.Treu&Ellis 2007: 2007: Lotzctal. 2008a:: C'onselicectal. 2008: Patton&Atfield2008: Blucketal. 2009)) and the merger history of galaxies has been traced with sullicient accuracy to perform a detailed comparison with theoretical models.,In the last decadea relatively large sample of galaxy mergers has been collated \citealt{patton2000}; \citealt{patton2002}; \citealt{cons2003a}; \citealt{hernandez2005}; \citealt{bundy2005}; \citealt{bundy2006}; \citealt{cons2006}; \citealt{cons2006b}; \citealt{bundy2007}; \citealt{depropris2007}; \citealt{lotz2008a}; \citealt{cons2008}; ; \citealt{patton2008}; \citealt{bluck2009}) ) and the merger history of galaxies has been traced with sufficient accuracy to perform a detailed comparison with theoretical models. + Mergers are just. now beginning to be identified atoI2 through either close galaxy pairs (e.g.. etal. 2009)). or structural methods (e.g... Conselicectal. 2003b:: Conseliceοἱal. 2008: Lotzctal. 2008b)).," Mergers are just now beginning to be identified at $z > 2$ through either close galaxy pairs (e.g., \citealt{bluck2009}) ), or structural methods (e.g., \citealt{cons2003b}; \citealt{cons2008}; \citealt{lotz2008b}) )." + What is becoming clear is that the merger fraction increases at larger look back times (higher redshifts)., What is becoming clear is that the merger fraction increases at larger look back times (higher redshifts). + This increase can be parameterised as either à power-law. or a combined. power-lawexponential (c.g.. Carlbere1990:: Conselice 2006a:: Conseliceetal.} 2008)).," This increase can be parameterised as either a power-law, or a combined power-law/exponential (e.g., \citealt{carlberg1990}; \citealt{cons2006}; \citealt{cons2008}) )." +" These measured merger fractions in the early universe can be converted into merger rates up to 2o3, and based on these we can attempt to determine the role of major mergers in the formation of galaxies."," These measured merger fractions in the early universe can be converted into merger rates up to $z \sim 3$, and based on these we can attempt to determine the role of major mergers in the formation of galaxies." + In this work. we retrieve the predicted. galaxy merger history. evolution from the Millennium-based. semi-analytic model of Bertoneetal.(2007). asa function of stellar mass.," In this work, we retrieve the predicted galaxy merger history evolution from the Millennium-based semi-analytic model of \citet{bertone2007} as a function of stellar mass." +" We then compare the model. predictions with a selection of observational results ancl examine separately the merger history of galaxies with stellar masses in the intervals 10"" AL<1077AL... AL,>107"" aand M,lott at zx3."," We then compare the model predictions with a selection of observational results and examine separately the merger history of galaxies with stellar masses in the intervals $10^{9}$ $ 10^{10}$ and $M_{\star} > 10^{11}$, at $z < 3$." +" Given the uncertainty in the observational results introduced bv the time-scale τι. in this paper we assume 7,=0.4 Garr as our fiducial value and we investigate how results can change for a longer time-scale of 7,=1 Gye."," Given the uncertainty in the observational results introduced by the time-scale $\tau_{\rm m}$, in this paper we assume $\tau_{\rm m} = 0.4$ Gyr as our fiducial value and we investigate how results can change for a longer time-scale of $\tau_{\rm m} = 1$ Gyr." + In general. we find that the predicted: merger history varies as a function of stellar mass. redshift ancl merger mass ratio.," In general, we find that the predicted merger history varies as a function of stellar mass, redshift and merger mass ratio." + The precicted major and minor merger rates. that is the number of mergers per unit volume and unit time. increase with lower stellar masses.," The predicted major and minor merger rates, that is the number of mergers per unit volume and unit time, increase with lower stellar masses." +" We also find that the predicted: merger rate increases with redshift and reaches a plateau at z«1 for galaxies with Ad,105AL...", We also find that the predicted merger rate increases with redshift and reaches a plateau at $z<1$ for galaxies with $M_{\star} > 10^{11}$. + The predicted: merger rate for less massive galaxies decreases with redshift., The predicted merger rate for less massive galaxies decreases with redshift. + Atos <15 we find a good agreement between predicted and observed merger rates., At $z < 1.5$ we find a good agreement between predicted and observed merger rates. +" However. the predictions for the merger fractions match the observations only for the most massive galaxies with AZ,>Lott aat 2c2."," However, the predictions for the merger fractions match the observations only for the most massive galaxies with $M_{\star} > 10^{11}$ at $z < 2$." +" The predicted. major merger. fractions are about. 10 times smaller than the observational estimates for galaxies with A,2101"" aat zo0.5.", The predicted major merger fractions are about 10 times smaller than the observational estimates for galaxies with $M_{\star} > 10^{10}$ at $z \sim 0.5$. +" We discuss the various ways in which the merger fraction predictions could be incorrect. ancl conclude: that the simulations might not predict enough mergers between ealaxics with Al,105ML.", We discuss the various ways in which the merger fraction predictions could be incorrect and conclude that the simulations might not predict enough mergers between galaxies with $M_{\star} < 10^{11}$. + Phis could. potentially account for other problems with matching observations to semi-analvtical models. including the fact that there are more massive galaxies at hieh redshift than predicted. anc the satellite problem. (e.g.. Mooreetal.L999: Conscliceal. 2007)).," This could potentially account for other problems with matching observations to semi-analytical models, including the fact that there are more massive galaxies at high redshift than predicted and the satellite problem (e.g., \citealt{moore1999}; \citealt{cons2007}) )." + This paper is organised as follows., This paper is organised as follows. + In. £2. we describe the observational data used to compare with the theoretica predictions., In \ref{data} we describe the observational data used to compare with the theoretical predictions. + In particular. we briefly. discuss our criteria for selecting the observational sample and some basie properties of the galaxies in the sample. such as their morphology. ane stellar masses.," In particular, we briefly discuss our criteria for selecting the observational sample and some basic properties of the galaxies in the sample, such as their morphology and stellar masses." + 83. describes the Millennium galaxy catalogue of Bertoneetal.(2007) and how the merger rates aux fractions have been extracted. from the simulation., \ref{millennium} describes the Millennium galaxy catalogue of \citet{bertone2007} and how the merger rates and fractions have been extracted from the simulation. + In &4 we present the model results ancl compare them to the observational data., In \ref{compare} we present the model results and compare them to the observational data. + Finally. 85. discusses our findings aux 8&6 summarises our results.," Finally, \ref{discussion} discusses our findings and \ref{conclusion} summarises our results." + In this Section we give a brick description of the data sets used. for comparison with the Millennium: simulation (Subsections 2.1. and 2.2)) and of how the merger fractions and rates are measured. (Subsection 2.3))., In this Section we give a brief description of the data sets used for comparison with the Millennium simulation (Subsections \ref{sec21} and \ref{sec22}) ) and of how the merger fractions and rates are measured (Subsection \ref{definition}) ). + We use results from. a series of works. based on both the structural asvnimetries of galaxies ancl pair counts. that investigate the merger history for galaxies as a function of stellar mass (C'onselice 20032: DeProprisetal. 2007:: Conseliceetal. 2008: Blucketal. 2009: Conseliceetal. 2009)).," We use results from a series of works, based on both the structural asymmetries of galaxies and pair counts, that investigate the merger history for galaxies as a function of stellar mass \citealt{cons2003a}; ; \citealt{depropris2007}; ; \citealt{cons2008}; ; \citealt{bluck2009}; ; \citealt{cons2009}) )." + Interested. readers should examine these papers for the many details involved., Interested readers should examine these papers for the many details involved. +" The observational quantities we present in this paper are measured using a standard ACDAL cosmology with {ο=70 aand $34,=1.Oy= 0.8.", The observational quantities we present in this paper are measured using a standard $\Lambda$ CDM cosmology with $H_{0} = 70$ and $\Omega_{\rm m} = 1 - \Omega_{\lambda}$= 0.3. + This. dillers sli¢hthy from the, This differs slightly from the +which is sufficiently accurate for our purposes.,which is sufficiently accurate for our purposes. +" In principle, if the jet material consists of a normal electron-proton plasma, we should allow for two species of particles in the shocked gas, each with a different temperature."," In principle, if the jet material consists of a normal electron-proton plasma, we should allow for two species of particles in the shocked gas, each with a different temperature." + We ignore this complication for simplicity., We ignore this complication for simplicity. +" We have three jump conditions across the shock, corresponding to three fundamental conservation laws."," We have three jump conditions across the shock, corresponding to three fundamental conservation laws." +" First, mass conservation implies that the mass fluxes on the two sides of the shock must be equal, i.e., Energy conservation requires the energy fluxes to be equal, le. Finally, momentum conservation gives the condition In the last equation, the terms involving the electric field cancel sinceE,=Ey."," First, mass conservation implies that the mass fluxes on the two sides of the shock must be equal, i.e., Energy conservation requires the energy fluxes to be equal, i.e., Finally, momentum conservation gives the condition In the last equation, the terms involving the electric field cancel since$E_u=E_d$." +" Eliminating uj between equations (8) and (9)) and simplifying, we obtain the following expression for 6;: In addition, equation (8)) can be rewritten in the following simplified form, Given the upstream quantities u, and c, it is straightforward to solve equations and (Τ1)) numerically."," Eliminating $\mu_d$ between equations \ref{energy}) ) and \ref{mmtm}) ) and simplifying, we obtain the following expression for $\theta_d$: In addition, equation \ref{energy}) ) can be rewritten in the following simplified form, Given the upstream quantities $u_u$ and $\sigma$, it is straightforward to solve equations \ref{thetad1}) ) and \ref{thetad2}) ) numerically." + We guess a value for the downstream (Τ0))velocity u; and calculate 6; using equation (I0p)., We guess a value for the downstream velocity $u_d$ and calculate $\theta_d$ using equation \ref{thetad1})). + We then compute /(0;) using the approximation and check whether the condition (ΤΠ) is satisfied., We then compute $h(\theta_d)$ using the approximation \ref{htheta}) ) and check whether the condition \ref{thetad2}) ) is satisfied. +" If it is not, we (6))numerically adjust 4; until the conditionis satisfied."," If it is not, we numerically adjust $u_d$ until the conditionis satisfied." +" We then have the complete solution for all downstream quantities: yy, ua, nq/n,, 04, ua/mc?, Ba/By."," We then have the complete solution for all downstream quantities: $\gamma_d$, $u_d$, $n_d/n_u$, $\theta_d$, $\mu_d/mc^2$, $B_d/B_u$." + The results presented in the following sections use the above numerical approach to solve the jump conditions., The results presented in the following sections use the above numerical approach to solve the jump conditions. + An alternate approach is to make suitable approximations and obtain analytical solutions of the jump conditions., An alternate approach is to make suitable approximations and obtain analytical solutions of the jump conditions. + Appendix presents analytical solutions corresponding to a number of useful [A]limits., Appendix \ref{appendixa} presents analytical solutions corresponding to a number of useful limits. +" We consider two identical blobs, each with magnetization o, approaching each other and colliding."," We consider two identical blobs, each with magnetization $\sigma$, approaching each other and colliding." +" In the center of mass frame, the blobs have Lorentz factorsy and relativistic velocities xAy?-- 1."," In the center of mass frame, the blobs have Lorentz factors$\gamma$ and relativistic velocities $u=\pm\sqrt{\gamma^2-1}$ ." +" As a result of the collision, two identical shocks move (in opposite directions) into the two blobs."," As a result of the collision, two identical shocks move (in opposite directions) into the two blobs." +" For given values of y and c, we solve the jump conditions numerically and calculate all quantities of interest in the shocked gas."," For given values of $\gamma$ and $\sigma$, we solve the jump conditions numerically and calculate all quantities of interest in the shocked gas." + We begin by assuming a value for the upstream Lorentz factor Yu in the frame of one of the shocks., We begin by assuming a value for the upstream Lorentz factor $\gamma_u$ in the frame of one of the shocks. +" Following the procedure described in refsec:jumpconditions,, we solve for the downstream Lorentz factor Ya."," Following the procedure described in \\ref{sec:jumpconditions}, we solve for the downstream Lorentz factor $\gamma_d$." +" From y, and yg, we calculate the relative Lorentz factor Yq between the two regions (relativistic velocity subtraction) and check whether it corresponds to the desired value of y."," From $\gamma_u$ and $\gamma_d$, we calculate the relative Lorentz factor $\gamma_{ud}$ between the two regions (relativistic velocity subtraction) and check whether it corresponds to the desired value of $\gamma$." +" If not, we adjust γι, until we obtain y,4=y."," If not, we adjust $\gamma_u$ until we obtain $\gamma_{ud}=\gamma$." + We then have the solution., We then have the solution. +" Having obtained the solution, we switch to the rest frame of the shocked gas."," Having obtained the solution, we switch to the rest frame of the shocked gas." +" We assume that a fraction ε, of the thermal enthalpy of the shocked gas W,,, goes into electrons and that it is entirely radiated in y-ray].", We assume that a fraction $\epsilon_e$ of the thermal enthalpy of the shocked gas $W_{\rm gas}$ goes into electrons and that it is entirely radiated in $\gamma$ . +" This gives the energy E, that goes into y-rays.", This gives the energy $E_\gamma$ that goes into $\gamma$ -rays. +" The remaining unradiated enthalpy, which consists of rest mass enthalpy Wrst, remaining gas thermal enthalpy (1—&)Woeas and magnetic enthalpy Wg, contributes to the kinetic energy Eo that goes into the afterglow."," The remaining unradiated enthalpy, which consists of rest mass enthalpy $W_{\rm + rest}$, remaining gas thermal enthalpy $(1-\epsilon_e)W_{\rm gas}$ and magnetic enthalpy $W_B$, contributes to the kinetic energy $E_0$ that goes into the afterglow." +" Thus, we estimate the efficiency e, of y-ray emission, the fraction of the total energy that goes into y-rays, to be The quantities W,,, and W,. are easily obtained from the shock solution."," Thus, we estimate the efficiency $\epsilon_\gamma$ of $\gamma$ -ray emission, the fraction of the total energy that goes into $\gamma$ -rays, to be The quantities $W_{\rm gas}$ and $W_{\rm rest}$ are easily obtained from the shock solution." +" Per particle, they are given by To calculate Ws, we first need to calculate the magnetic field of the shocked gas inthe center of mass (CM) frame of the colliding blobs."," Per particle, they are given by To calculate $W_B$, we first need to calculate the magnetic field of the shocked gas inthe center of mass (CM) frame of the colliding blobs." +" This is given by Then the magnetic enthalpy per particle is Thus we obtain Although all quantities have been estimated in the rest frame of the shocked gas, it is easily shown that Lorentz transforming to a different frame, e.g., the observer frame, will leave εν unchanged."," This is given by Then the magnetic enthalpy per particle is Thus we obtain Although all quantities have been estimated in the rest frame of the shocked gas, it is easily shown that Lorentz transforming to a different frame, e.g., the observer frame, will leave $\epsilon_\gamma$ unchanged." +" For a given value of ε,, the y-ray efficiency depends on two parameters, the magnetization o of the blobs and their Lorentz factor y in the center-of-mass frame."," For a given value of $\epsilon_e$, the $\gamma$ -ray efficiency depends on two parameters, the magnetization $\sigma$ of the blobs and their Lorentz factor $\gamma$ in the center-of-mass frame." +" Figure[]] shows how e, varies as a function of σ for selected values of y, as listed in the figure caption."," Figure \ref{fig1} shows how $\epsilon_\gamma$ varies as a function of $\sigma$ for selected values of $\gamma$, as listed in the figure caption." +" Instead of y, we could express the results in terms of the relative inter-blob Lorentz factor of the blobs y;,."," Instead of $\gamma$, we could express the results in terms of the relative inter-blob Lorentz factor of the blobs $\gamma_{\rm ib}$." + The values of yi are also given in the figure caption., The values of $\gamma_{\rm ib}$ are also given in the figure caption. + Figure [I] indicates that the maximum radiative efficiency is obtainedfor unmagnetized blobs., Figure \ref{fig1} indicates that the maximum radiative efficiency is obtainedfor unmagnetized blobs. +" As the magnetization increases, the amount of thermal energy generated in the shock decreases, reducing the radiative efficiency."," As the magnetization increases, the amount of thermal energy generated in the shock decreases, reducing the radiative efficiency." + This result was already discussed by[KC84]., This result was already discussed by. + The analytical approximations in Appendix [A] give further details., The analytical approximations in Appendix \ref{appendixa} give further details. +" From refsec:A3 we see that, for σ«1, the enthalpy of the shocked gas (which is proportional to 67) varies as 1— (5/2)o, i.e., it reduces with increasing magnetization."," From \\ref{sec:A3} we see that, for $\sigma\ll1$, the enthalpy of the shocked gas (which is proportional to $\theta_d$ ) varies as $1-(5/2)\sigma$ , i.e., it reduces with increasing magnetization." +" The reduction is quite pronounced once c> 1; for 0> 1, the enthalpy scales as 1/σ refsec:A1))."," The reduction is quite pronounced once $\sigma>1$ ; for $\sigma\gg1$ , the enthalpy scales as $1/\sigma$ \\ref{sec:A1}) )." +" Note, however, that there is always a shock solution for anychoice of y and σ."," Note, however, that there is always a shock solution for anychoice of $\gamma$ and $\sigma$ ." +" This may appear a little surprising since, as we show in Appendix a magnetized shock is possible only if the upstream velocity u, [A],exceeds Yo."," This may appear a little surprising since, as we show in Appendix \ref{appendixa}, , a magnetized shock is possible only if the upstream velocity $u_u$ exceeds $\sqrt{\sigma}$ ." +" Thus, for strongly magnetized blobs moving in the center-of-mass frame with relatively low"," Thus, for strongly magnetized blobs moving in the center-of-mass frame with relatively low" +" M—10710M... Α~0.2—3 a7~GM/SRy. Α p;/pz0.17. KT.5:10 #=pp/nty 77,) s! fj o7 2KT. Ly T. kT~pR- f»: &T.—2 LyxT? Ponman 2004)."," $M\sim 10^{13} - 10^{15}\, M_{\odot}$ $R\sim 0.2-3$ $\sigma^2 \sim G\, M/5\, +R \sim (0.2 - 2\times 10^3 ~\mathrm{km~s}^{-1})^2$ $R$ $\rho_b/\rho \approx 0.17$ $kT \approx m_p\, \sigma^2/2 \sim 1 - 10$ $n = \rho_b/m_p$ $m_p$ $L_X \propto n^2\, R^3\, +T^{1/2} \sim 10^{42} - 10^{46}$ $^{-1}$ $f_b$ $\sigma^2$ $2\,kT$ $L_X$ $T$ $kT \propto \rho \, R^2$ $L_X\propto T^2$ $f_b$ $kT < 2$ $L_X\propto T^3$ Ponman 2004)." + These low radiation levels witnessing to scarcity of electrons-baryons have stirred a wide debate (see Evrard Henry 1991: Ponman et al., These low radiation levels witnessing to scarcity of electrons-baryons have stirred a wide debate (see Evrard Henry 1991; Ponman et al. + 1999; Cavaliere et al., 1999; Cavaliere et al. + 2002: Lapi et al., 2002; Lapi et al. + 2005: Borgant et al., 2005; Borgani et al. + 2006: Bregman et al., 2006; Bregman et al. + 2007) over the mystery of the baryons missing from the ICP: are they lost somewhere within the wells. or outflown. or just limitedly infallen?," 2007) over the mystery of the baryons missing from the ICP: are they lost somewhere within the wells, or outflown, or just limitedly infallen?" + Here we show that the second alternative is the fitting one. with some help from the third.," Here we show that the second alternative is the fitting one, with some help from the third." + In sorting out these alternatives it helps to note that low emissivity CyXnT7 from the current ICP goes along with enhanced adiabat KxKT7T?' Or excess specific entropy proportional to /5K. as in factον is measured (see Ponman et al.," In sorting out these alternatives it helps to note that low emissivity $\mathcal{L}_X \propto n^2\, T^{1/2}$ from the current ICP goes along with enhanced adiabat $K \propto kT\, +n^{-2/3}\propto T^{5/3}\, \mathcal{L}_X^{-1/3}$ or excess specific entropy proportional to $ln{K}$, as in fact is measured (see Ponman et al." + 2003; Piffaretti et al., 2003; Piffaretti et al. + 2005; Pratt et al., 2005; Pratt et al. + 2006)., 2006). + Baryon sinks may occur within the wells due to radiative cooling. that affects mostly the densest and lowest entropy fractions of the ICP.," Baryon sinks may occur within the wells due to radiative cooling, that affects mostly the densest and lowest entropy fractions of the ICP." + Thereby these tend to lose their pressure support and further condense. radiate and cool even more. and so engage in the classic catastrophic. course ending up into formation of plenty new stars (White Rees 1978; Blanchard et al.," Thereby these tend to lose their pressure support and further condense, radiate and cool even more, and so engage in the classic catastrophic course ending up into formation of plenty new stars (White Rees 1978; Blanchard et al." + 1992)., 1992). + What is left after a Hubble time is the ICP fraction originally in a hot dilute state. exhibiting a high residual entropy today (Voit 2005).," What is left after a Hubble time is the ICP fraction originally in a hot dilute state, exhibiting a high residual entropy today (Voit 2005)." + This indirect mechanism faces limitations. however.," This indirect mechanism faces limitations, however." + For example. cooling would steepen the local Ly—7 correlation to a shape LyxT? only if it proceeded unscathed for a Hubble time throughout the heetic sequence of hierarchical mergers that build up a cluster of today (Voit 2005: for related evidence see Vikhlinin et al.," For example, cooling would steepen the local $L_X - T$ correlation to a shape $L_X \propto T^3$ only if it proceeded unscathed for a Hubble time throughout the hectic sequence of hierarchical mergers that build up a cluster of today (Voit 2005; for related evidence see Vikhlinin et al." + 2007)., 2007). + Even so. the corresponding height still would fall short of the observed luminosity or entropy levels. unless so many stars condensed as to exceed the observational limits (Muanwong et al.," Even so, the corresponding height still would fall short of the observed luminosity or entropy levels, unless so many stars condensed as to exceed the observational limits (Muanwong et al." + 2002)., 2002). +" Finally. cooling does not even dominate the very ""cooling cores” at the center of the ICP: these are observed in many clusters to feature enhanced emissions and short cooling times. but their temperatures are bounded by 7.=T/3 (Molendi Pizzolato 2001:Peterson Fabian2006) atvariance withthecatastrophictrend intrinsicto cooling."," Finally, cooling does not even dominate the very `cooling cores' at the center of the ICP; these are observed in many clusters to feature enhanced emissions and short cooling times, but their temperatures are bounded by $T_c \ga T/3$ (Molendi Pizzolato 2001;Peterson Fabian2006) atvariance withthecatastrophictrend intrinsicto cooling." +Sothelatter must be offset by inputs of energy into the ICP. most likely from,"Sothelatter must be offset by inputs of energy into the ICP, most likely from" +"(6.5%)) and 51 galaxies as SB3 and non- galaxies, respectively.",") and 51 galaxies ) as SB3 and non-barred galaxies, respectively." +" (25.4%))When considering the SB3 galaxies as non-barred systems, the agreement rate between NA10’s and our classification is about85%."," When considering the SB3 galaxies as non-barred systems, the agreement rate between NA10's and our classification is about." +". Note that, in this comparison, fp, is in NA1O0 classification, while (for SB1+SB2) in our classification."," Note that, in this comparison, $\bfr$ is in NA10 classification, while (for SB1+SB2) in our classification." +" Therefore, it is concluded our study and NA10 agree well in morphological classifications and bar fractions."," Therefore, it is concluded our study and NA10 agree well in morphological classifications and bar fractions." +" Among 13,867 early-type galaxies, there are 905 SBO galaxies while we find 3,641 barred galaxies belonging to (6.5%)),SB1-SB3 types among the 10,674 late-type galaxies with b/a>0.60 (far= 34.1%) as shown in Table 2.."," Among 13,867 early-type galaxies, there are 905 SB0 galaxies ), while we find 3,641 barred galaxies belonging to SB1-SB3 types among the 10,674 late-type galaxies with $b/a>0.60$ $\bfr=34.1\%$ ) as shown in Table \ref{table_bf_vis}." +" In some studies, fj, is defined as the the frequency of barred galaxies among disk galaxies including both spirals and lenticulars (Eskridgeetal.etal."," In some studies, $\bfr$ is defined as the the frequency of barred galaxies among disk galaxies including both spirals and lenticulars \citep{esk00,maj07,ree07,barazza08}." +" In this study, however, we do not distinguish lenticulars 2008)..from early-type galaxies."," In this study, however, we do not distinguish lenticulars from early-type galaxies." +" Therefore, hereafter, we define fray as the percentage of barred galaxies among late-type galaxies with b/a>0.60."," Therefore, hereafter, we define $\bfr$ as the percentage of barred galaxies among late-type galaxies with $b/a>0.60$." + We do not use 905 SBO galaxies when calculating the bar fraction of late type galaxies., We do not use 905 SB0 galaxies when calculating the bar fraction of late type galaxies. +" Among the three types for late-type barred galaxies (SB1-SB3), we regard only two types, SB1 and SB2, as barred galaxies."," Among the three types for late-type barred galaxies (SB1-SB3), we regard only two types, SB1 and SB2, as barred galaxies." +" SB3 galaxies have an elongated feature in their central region, but it is uncertain to consider it as a bar."," SB3 galaxies have an elongated feature in their central region, but it is uncertain to consider it as a bar." + Some SB3 galaxies seem to have oval structures in their center., Some SB3 galaxies seem to have oval structures in their center. +" In previous studies some oval galaxies were classified as barred galaxies, but generally they are considered as non-barred ones (Kormendy&Kennicutt 2004)."," In previous studies some oval galaxies were classified as barred galaxies, but generally they are considered as non-barred ones \citep{knk2004}." +. We consider SB3 types as non-barred galaxies from now on., We consider SB3 types as non-barred galaxies from now on. +" In conclusion, we find that the bar fraction for late-type galaxies is barred galaxies)."," In conclusion, we find that the bar fraction for late-type galaxies is (3,240 barred galaxies)." +" This value is in good agreement with (3,240recent studies that used visual inspection to select barred galaxies, 25~33% "," This value is in good agreement with recent studies that used visual inspection to select barred galaxies, $\sim$ " +In a further test caleulation. the expansion part of the energy solver is checked.,"In a further test calculation, the expansion part of the energy solver is checked." + The only energy change considered is the adiabatic cooling due to free expansion of the SN la envelope., The only energy change considered is the adiabatic cooling due to free expansion of the SN Ia envelope. + The energy deposition by y-rays or an energy change due to energy transport is disabled., The energy deposition by $\gamma$ -rays or an energy change due to energy transport is disabled. + For this test case. the expectation is that the atmosphere should just cool down. so the temperature of the atmosphere and the observed luminosity should be decreasiΓια," For this test case, the expectation is that the atmosphere should just cool down, so the temperature of the atmosphere and the observed luminosity should be decreasing." + The observed luminosity is shown in Fig. 2.., The observed luminosity is shown in Fig. \ref{fig:lc_expan_lum}. + The observed luminosity of the SN [a atmosphere decreases in time., The observed luminosity of the SN Ia atmosphere decreases in time. + The temperature structure of the first and the last time step is plotted in Fig. 3.., The temperature structure of the first and the last time step is plotted in Fig. \ref{fig:lc_expan_temp}. + The adiabatic expansion has cooled the atmosphere everywhere. and the new temperature structure is now significantly lower than the initial one.," The adiabatic expansion has cooled the atmosphere everywhere, and the new temperature structure is now significantly lower than the initial one." + To test the energy deposition by the radioactive decay of nickel and cobalt into the SN Ia atmosphere. a test case is considered. where only this y-ray deposition is calculated with the energy solver.," To test the energy deposition by the radioactive decay of nickel and cobalt into the SN Ia atmosphere, a test case is considered, where only this $\gamma$ -ray deposition is calculated with the energy solver." + The energy change due to free expansion and energy transport are neglected to see the direct effect of the additional energy put into the test SN Ia atmosphere., The energy change due to free expansion and energy transport are neglected to see the direct effect of the additional energy put into the test SN Ia atmosphere. + The results of the energy deposition by y-rays calculation with the energy solver is shown in Fig. 4..," The results of the energy deposition by $\gamma$ -rays calculation with the energy solver is shown in Fig. \ref{fig:lc_gamma_lum}," + where the light curve ts plotted., where the light curve is plotted. + Due to the energy added to the atmosphere. the luminosity seen by an observer increases with time.," Due to the energy added to the atmosphere, the luminosity seen by an observer increases with time." + After all single etfects have been tested. we now calculate a test case where all effects are considered for the solution of the energy solver.," After all single effects have been tested, we now calculate a test case where all effects are considered for the solution of the energy solver." + Again. the same initial temperature structure is used and we start our calculation at day 10 after the explosion.," Again, the same initial temperature structure is used and we start our calculation at day 10 after the explosion." + Free expansion as well as energy deposition. and energy transport are active for this computation., Free expansion as well as energy deposition and energy transport are active for this computation. + The observed light curve is shown in Fig. 5., The observed light curve is shown in Fig. \ref{fig:lc_radeq_lum}. + The luminosity increases because of the energy input from deposition of energy from the y-rays produced by decay of nickel and cobalt., The luminosity increases because of the energy input from deposition of energy from the $\gamma$ -rays produced by decay of nickel and cobalt. + It takes a certain time. until the whole atmosphere has relaxed to this new condition.," It takes a certain time, until the whole atmosphere has relaxed to this new condition." + The atmosphere is then in radiative equilibrium state. and the luminosity stays constant.," The atmosphere is then in radiative equilibrium state, and the luminosity stays constant." + The mitial and final temperature structure are plotted in Fig. 6.., The initial and final temperature structure are plotted in Fig. \ref{fig:lc_radeq_temp}. + The energy input caused by radioactive decay has increased the temperature of the whole atmosphere., The energy input caused by radioactive decay has increased the temperature of the whole atmosphere. + The atmosphere is heated by y-ray deposition in the inner part of the atmosphere., The atmosphere is heated by $\gamma$ -ray deposition in the inner part of the atmosphere. + Due to this additional energy. the luminosity of these layers Increases and the heat is radiated away and absorbed by the surrounding layers.," Due to this additional energy, the luminosity of these layers increases and the heat is radiated away and absorbed by the surrounding layers." + This energy transport takes care that the deposited energy is moving through the whole atmosphere so that the temperature increases everywhere and the additional energy from the radioactive decay is radiated, This energy transport takes care that the deposited energy is moving through the whole atmosphere so that the temperature increases everywhere and the additional energy from the radioactive decay is radiated +two-dimensional clustering statistics to obtain the dimensional power spectrum.,two-dimensional clustering statistics to obtain the three-dimensional power spectrum. + They conclude that the turn- which oceurs between 0.02«&<0.06bMpe: can be reproduced by the inversion process.," They conclude that the turn-over, which occurs between $0.02 < k < 0.06 \hmpcrev$, can be reproduced by the inversion process." + However. at these small wavenumbers. the systematic errors in the construction of the ADPM Galaxy Survey ave dillicult to quantify and could perhaps be greater than the random. errors (see. Maddox.Efstathiou&Sutherland.19060 for a detailed. discussion of systematic errors in the ADM survey).," However, at these small wavenumbers, the systematic errors in the construction of the APM Galaxy Survey are difficult to quantify and could perhaps be greater than the random errors (see \pcite{APMlong} for a detailed discussion of systematic errors in the APM survey)." + Lt is therefore cillicult to assign a meanineful statistical significance to this result., It is therefore difficult to assign a meaningful statistical significance to this result. +" The detection of a peak in the power spectrum of the galaxy distribution is one of the main scientific goals ofthe Anelo-Australian 2dE redshift survey (see c.g. 1996)) and the Sloan Digital Sky survey (Gunn&Weinberg 19953) which aim to measure redshifts of ~10"" galaxies.", The detection of a peak in the power spectrum of the galaxy distribution is one of the main scientific goals ofthe Anglo-Australian 2dF redshift survey (see e.g. \pcite{Ef96}) ) and the Sloan Digital Sky survey \pcite{GW95}) ) which aim to measure redshifts of $\sim 10^6$ galaxies. + llowever. in this paper we show that redshift. surveys of much smaller numbers (~ 10°) of rich clusters of galaxies can provide accurate measurements of the power spectrum on large spatial scales.," However, in this paper we show that redshift surveys of much smaller numbers $\sim 10^3$ ) of rich clusters of galaxies can provide accurate measurements of the power spectrum on large spatial scales." + Relatively little work has been done on the three-dimensional power spectrum of rich clusters of galaxies (see Gramman&Einasto1992.. Peacock&West 1992.. Einastoetal. 1993)).," Relatively little work has been done on the three-dimensional power spectrum of rich clusters of galaxies (see \pcite{GE92}, \pcite{PW92}, \pcite{EGST}) )." + Most recent work has focused on measurements of the two-point spatial correlation function of rich. clusters of galaxies. £(r). ancl whether systematic errors in the cluster catalogues allect the amplitude of €(1) on scales 20h!Mpe.," Most recent work has focused on measurements of the two-point spatial correlation function of rich clusters of galaxies, $\xi(r)$, and whether systematic errors in the cluster catalogues affect the amplitude of $\xi(r)$ on scales $\simlt 20 \hmpc$." + The closest. investigation to the one presented here is that of Peacock and Nicholson (1991). who describe a power spectrum analysis of a redshift survey of 310 radio galaxies.," The closest investigation to the one presented here is that of Peacock and Nicholson (1991), who describe a power spectrum analysis of a redshift survey of $310$ radio galaxies." + Their results are described in further detail in Section 4., Their results are described in further detail in Section 4. + In this paper we analyse the redshift) survey of 364 ADM clusters described by Daltonetal.(1994)., In this paper we analyse the redshift survey of $364$ APM clusters described by \scite{DCESMD94}. +. In previous papers (Daltonetal.1992.. Daltonetal. 19949). we have applied a number of tests to show that the APAL cluster catalogue is free of the projection ancl selection biases known to alleet clustering in the Abell cluster catalogues (Sutherland1988.. Efstathiouetal. 1992)).," In previous papers \pcite{DEMS92}, \pcite{DCESMD94}) ), we have applied a number of tests to show that the APM cluster catalogue is free of the projection and selection biases known to affect clustering in the Abell cluster catalogues \pcite{S88}, \pcite{EDSM92}) )." + As we show here. the large volume surveved by the APAL cluster survey (3c3.LOH Mpc?) renders it suitable for an investigation of clustering on very large scales.," As we show here, the large volume surveyed by the APM cluster survey $V \simgt 3 \times 10^7 h^{-3} {\rm Mpc}^3$ ) renders it suitable for an investigation of clustering on very large scales." + This paper is laid out as follows., This paper is laid out as follows. + In Section 2. we summarize the techniques used in the power spectrum analvsis., In Section 2 we summarize the techniques used in the power spectrum analysis. + We apply these techniques to the APAL cluster survey and investigate the sensitivity. of our results to the selection function. weighting function and background cosmological model.," We apply these techniques to the APM cluster survey and investigate the sensitivity of our results to the selection function, weighting function and background cosmological model." + In. Section 3 we construct. simulated ADPM cluster catalogues from large N-bocly simulations to quantify any systematic errors and biases in our power spectrum. estimator., In Section 3 we construct simulated APM cluster catalogues from large N-body simulations to quantify any systematic errors and biases in our power spectrum estimator. + From this analysis we can assess the significance of the observed peak in power spectrum of APAL clusters., From this analysis we can assess the significance of the observed peak in power spectrum of APM clusters. + Our conclusions are presented in Section 4., Our conclusions are presented in Section 4. + The analvsis deseribed here is similar το the power spectrum analysis of the Stromlo-APAL galaxy redshift survey described by Tadros&Efstathiou(1996). (hereafter 'TE96)., The analysis described here is similar to the power spectrum analysis of the Stromlo-APM galaxy redshift survey described by \scite{tad96} (hereafter TE96). + We follow their notation unless otherwise stated., We follow their notation unless otherwise stated. + We apply the power spectrum analysis to the redshift survey of APAIL clusters described by Daltonetal.(1994)..., We apply the power spectrum analysis to the redshift survey of APM clusters described by \scite{DCESMD94}. . +" We use the largest statistically uniform sample of APAL clusters. Sample B of Daltonetal.(1994) containing 364 clusters over the southern APA area (21zAZ5"".τοπnodecn 11.57)."," We use the largest statistically uniform sample of APM clusters, Sample B of \scite{DCESMD94} containing $364$ clusters over the southern APM area $21^{h}\lqt RA \lqt5^{h}, +-72.5^{\circ}\lqt dec \lqt-17.5^{\circ}$ )." + The number density of clusters in this sample is ~34-1070hIMpe)., The number density of clusters in this sample is $\sim 3.4\times 10^{-5} (\hmpc)^{-3}$. +* Phe redshift distribution of the sample is shown in Figure 1.., The redshift distribution of the sample is shown in Figure \ref{nz}. + The median redshift of the sample is tie=0.09 and the cluster distribution extencds to a redshift z02., The median redshift of the sample is $z_{med} = 0.09$ and the cluster distribution extends to a redshift $z \sim 0.2$. + We treat the APAL cluster recshift survey in the same way as a lux limited galaxy survey. anc use the methods of Feldman.Waiser&Peacock(1994) (hereafter FIND). as implemented by TI296. to account for the racially varying selection. function.," We treat the APM cluster redshift survey in the same way as a flux limited galaxy survey, and use the methods of \scite{FKP94} + (hereafter FKP), as implemented by TE96, to account for the radially varying selection function." + To define the selection function of the survey we smooth the velocity distribution shown in Figure with a Gaussian of width vykms+., To define the selection function of the survey we smooth the velocity distribution shown in Figure \ref{nz} with a Gaussian of width $\nu\; \kms$. + Phe fiducial value of v is 4000kms, The fiducial value of $\nu$ is $4000 \;\kms$. + The estimation of the power spectrum may be summarized. as follows (for. further details thereader is referred to TI96)., The estimation of the power spectrum may be summarized as follows (for further details thereader is referred to TE96). + We compute a weighted density Ποιά where the subscript e denotes the cluster density in the real catalogue and s denotes the density. field. for a random catalogue with same angular and racial selection functions as the eluster survey., We compute a weighted density field where the subscript $c$ denotes the cluster density in the real catalogue and $s$ denotes the density field for a random catalogue with same angular and radial selection functions as the cluster survey. + In equation (1). 7(r) is the expected. mean density. of clusters in a catalogue with the same angular and radial selection. functions as the data.," In equation (1), $\overline{n}\left({\bf{r}}\right)$ is the expected mean density of clusters in a catalogue with the same angular and radial selection functions as the data." + The radial selection function is derived. [rom the fits tothe redshift. distribution plotted in Figure 1.., The radial selection function is derived from the fits tothe redshift distribution plotted in Figure \ref{nz}. . + The function T(Y) can be separated into the mean galaxy. density 7r) as a function of radial distance r. multiplied by the angular mask of the catalogue the distribution of the APM," The function $\overline{n}\left({\bf{r}}\right)$ can be separated into the mean galaxy density $\overline{n}\left(r\right)$ as a function of radial distance $r$ , multiplied by the angular mask of the catalogue the distribution of the APM" +posterior distribution of an individual galaxy.,posterior distribution of an individual galaxy. + Making frequent use of Baves rule we can write the conditional redshift posterior distribution described in section + as We will now consider the probability distribution T uus Which basically describes a random. draw. of a particle aguaout of an ensemble of particles.," Making frequent use of Bayes rule we can write the conditional redshift posterior distribution described in section \ref{red_post_dist} as We will now consider the probability distribution ( _n ,z_n| _p ), which basically describes a random draw of a particle out of an ensemble of particles." + Changing the coordinates from spherical redshift coordinates to. co. moving Cartesian coordinates yields where is the derivative of the co-moving radial distance with respect to the redshiftzz., Changing the coordinates from spherical redshift coordinates to co moving Cartesian coordinates yields where is the derivative of the co-moving radial distance with respect to the redshift. +. The Poissonian assumption for the galaxy distribution. assumes. that the number counts. and hence the number of particles inside individual cells. are independent.," The Poissonian assumption for the galaxy distribution, assumes, that the number counts, and hence the number of particles inside individual cells, are independent." + Further. the Poissonian model assumes the particles inside a volume element to be homogeneously distributed.," Further, the Poissonian model assumes the particles inside a volume element to be homogeneously distributed." +" We therefore yield In the following we will omit the arguments of the number counts MMEus ""ο By noting that WC, vVN erem The probability PCr tS merely the probability of randomly picking a particle at a specitic position conditional on the set of number counts.", We therefore yield In the following we will omit the arguments of the number counts _p. We can then write By noting that _i ) = N_i we can write The probability ( is merely the probability of randomly picking a particle at a specific position conditional on the set of number counts. + Hence we can write where is the total number of particles and is the volume of the volume element., Hence we can write where is the total number of particles and is the volume of the volume element. + Next we will consider the fraction where we used the result. obtained in appendix B.. that the density posterior solely depends through the number counts on the set of galaxy coordinates.," Next we will consider the fraction where we used the result, obtained in appendix \ref{Appendix_densitypost}, that the density posterior solely depends through the number counts on the set of galaxy coordinates." + As can be easily seen by applying Bayes law we can write this fraction as the ratio of the Poissonian likelihoods with being the intensity of the Poisson process., As can be easily seen by applying Bayes law we can write this fraction as the ratio of the Poissonian likelihoods with (R_i being the intensity of the Poisson process. +" Since the numberpay densities MandMM diff'eronlvbyoneatthepositionvecx, of the galaxy under consideration. the ratios of the product in equation (C7)) are all equal to one except at this particular galaxy position."," Since the number densities and differ only by one at the position of the galaxy under consideration, the ratios of the product in equation \ref{eq:Lh_ratio_1}) ) are all equal to one except at this particular galaxy position." + we can therefore write Inserting all results into equation (CI) yields Since the produet in the third line of equation (C9)) is only ditferent from one at the galaxy position we can write Also note. since in this work we will use Metropolis-Hastings algorithms to explore the conditional redshift posterior distribution. we do not require to explicitly calculate the normalization constant of the probability distribution given in equation (610).," we can therefore write Inserting all results into equation \ref{eq:cond_redshift_posterior_1a}) ) yields Since the product in the third line of equation \ref{eq:cond_redshift_posterior_1b}) ) is only different from one at the galaxy position we can write Also note, since in this work we will use Metropolis-Hastings algorithms to explore the conditional redshift posterior distribution, we do not require to explicitly calculate the normalization constant of the probability distribution given in equation \ref{eq:cond_redshift_posterior_1c}) )." + Up to an overall normalization constant we can therefore write, Up to an overall normalization constant we can therefore write +from the CPR2002 survey (A32. A23. A27. A29. A36. ALL).,"from the CPR2002 survey (A32, A23, A27, A29, A36, A41)." + The other five. S03. aud MT|91] 632. G01. 612. auk 83 where frou the original optical survey.," The other five, S03, and MT[91] 632, 601, 642, and 83 where from the original optical survey." + The O5 V((É)) star identified by CPR2002 as A387. secus to he two voune for the remainder of the Cve OD2 cluster. indicating au age below 1 million years.," The O5 V((f)) star identified by CPR2002 as A37, seems to be two young for the remainder of the Cyg OB2 cluster, indicating an age below 1 million years." + Sunauuiue thi18s 1p. 7 oft 1ο 11 new stars identified bx CPR2002 show ages inconsistent with the remainder of the cluster. aud are àulikelv 1ieciubers of (νο OB2.," Summing things up, 7 of the 14 new stars identified by CPR2002 show ages inconsistent with the remainder of the cluster, and are unlikely members of Cyg OB2." +" Exteudiug the search for cluster micuibers to larger distances from the ceutral core has lead to an increase in contamination frou, non-member stars.", Extending the search for cluster members to larger distances from the central core has lead to an increase in contamination from non-member stars. + The IME values alc stelar couuts made by. MTOL1 still remain the best estimates for the cluster until the remaining OB candidates ideutified by CPR2002 are observed., The IMF values and stellar counts made by MT91 still remain the best estimates for the cluster until the remaining OB candidates identified by CPR2002 are observed. + However. it is clear that in an effort to move towards ereater completeness of he cluster menibers. we have also moved towards a greater incidence of contamination.," However, it is clear that in an effort to move towards greater completeness of the cluster members, we have also moved towards a greater incidence of contamination." + Wihou reliable nieasures to establish membership. this will be a chronic problem for all studies attempting deep photometric studies of distant clusters within our galaxy.," Without reliable measures to establish membership, this will be a chronic problem for all studies attempting deep photometric studies of distant clusters within our galaxy." +and M (logM = -8.0. -8.5. -9.0. -9.5. -10.0 and -10.5 M. !': see Table 2 in (1993))).,"and $\dot{M}$ $log \dot{M}$ = -8.0, -8.5, -9.0, -9.5, -10.0 and -10.5 $\dot{M}$ $^{-1}$; see Table 2 in \citet{wad98}) )." + The spectra are presented [or six different disk inclinations 7 (8.1. 18.2. 41.4. 60.0. 75.5 and 81.4 degrees).," The spectra are presented for six different disk inclinations $i$ (8.1, 18.2, 41.4, 60.0, 75.5 and 81.4 degrees)." + The models fIuxes include the effects of limb darkening. the projection of fluxes as a funcüon of the inclination angle. ancl are scaled (to a distance of 100 pe where (he distance is related to the scale factor as For a svstem as well-studied as VW Ivi. we adopted widely used parameters in the literature.," The models fluxes include the effects of limb darkening, the projection of fluxes as a function of the inclination angle, and are scaled to a distance of 100 pc where the distance is related to the scale factor as For a system as well-studied as VW Hyi, we adopted widely used parameters in the literature." + We fixed the distance d =65 pc. fixed the orbital inclination al 7=60 degrees but assumed two values of the white dwarl mass. M.," We fixed the distance d $=65$ pc, fixed the orbital inclination at $i = 60$ degrees but assumed two values of the white dwarf mass, $M_{wd}$." + The synthetic disk spectra were then fitted to the three superoutburst spectra by our 4? minimization routine., The synthetic disk spectra were then fitted to the three superoutburst spectra by our $\chi^{2}$ minimization routine. +" The accretion disk models are listed in Table 2 corresponding to. M,=0.55.U. and Af;0.8M..", The best-fitting accretion disk models are listed in Table 2 corresponding to $M_{wd}= 0.55 M_{\odot}$ and $M_{wd}= 0.8 M_{\odot}$. + We list in column (1) the part of the superoutburst in which (he spectrum was taken: (2) the white dwarf mass adopted: (3) the adopted orbital inclination: (4) log of (he accretion rate in solar masses per vear resulting [rom the best-fitting clisk model: (5) the V value corresponding to the best fit: (6) the value of the increment which produced the best refined disk model fit (see section 3)., We list in column (1) the part of the superoutburst in which the spectrum was taken; (2) the white dwarf mass adopted; (3) the adopted orbital inclination; (4) log of the accretion rate in solar masses per year resulting from the best-fitting disk model; (5) the $\chi^{2}$ value corresponding to the best fit; (6) the value of the increment which produced the best refined disk model fit (see section 3). + The best-littàng accretion disk models to the three IST spectra for both values of the white dwarf mass are displaved in Figure 1 for the early spectrum. Figure 2 for the middle spectrum anc Figure 3 for the late spectrum.," The best-fitting accretion disk models to the three HST spectra for both values of the white dwarf mass are displayed in Figure 1 for the early spectrum, Figure 2 for the middle spectrum and Figure 3 for the late spectrum." + All three spectra are well-[it bv steady state accretion disk models except for the observed continuum shortware of Lyman Alpha where the theoretical disk flux overpredicts the observed Πας., All three spectra are well-fit by steady state accretion disk models except for the observed continuum shortward of Lyman Alpha where the theoretical disk flux overpredicts the observed flux. + We discuss the results of these fits in the following section., We discuss the results of these fits in the following section. + The high quality IST STIS together with the currently accepted orbital inclination aud reasonable distance (65 pe) for VW IIvdri enabled a determination of the accretion rate during a superoutburst as a function of (ime within the superoutburst., The high quality HST STIS together with the currently accepted orbital inclination and reasonable distance (65 pc) for VW Hydri enabled a determination of the accretion rate during a superoutburst as a function of time within the superoutburst. +" For assumed white cdwarl masses Mj=0.6... and M,=0.8... the derived average accretion rates during superoutburst are. respectively G(3:—1)x10° ML. /vr and οί—1)x10? NL, /vr."," For assumed white dwarf masses $M_{wd}=0.6 M_{\odot}$ and $M_{wd}=0.8 M_{\odot}$, the derived average accretion rates during superoutburst are, respectively $6(\pm -1) \times 10^{-9}$ $_{\sun}$ /yr and $3(\pm -1) +\times 10^{-9}$ $_{\sun}$ /yr." + All of the best-fitting models show a flux excess relative to the observations., All of the best-fitting models show a flux excess relative to the observations. + This flux deficit relative to the models. shortware of Lyman a. may. be due to the possibilitv that the accretion disk in VW IIvdii is moclestly truncated hence having a cooler inner disk region than the untruncated accretion disk model.," This flux deficit relative to the models, shortward of Lyman $\alpha$, may be due to the possibility that the accretion disk in VW Hydri is modestly truncated hence having a cooler inner disk region than the untruncated accretion disk model." + The accretion rate late in the superoutburst as declined by a [actor of (wo relative to the accretion rate early in the superoutburst., The accretion rate late in the superoutburst as declined by a factor of two relative to the accretion rate early in the superoutburst. +are several approaches to choosing a calibration.,are several approaches to choosing a calibration. + When fitting existiug pan such as galaxy counts. then the effcieucies can be chosen to be the bestfitting values ase.g. LochIxaufftinaun White 1993).," When fitting existing data, such as galaxy counts, then the efficiencies can be chosen to be the best–fitting values (e.g. Kauffmann White 1993)." + Iu. the models of Tainan i(1997. 1998) that extrapolate to high redshifts. the starxluation οποιο was normalized based ou the mean metallicity of the highredshitt Lya forest.," In the models of Haiman Loeb (1997, 1998) that extrapolate to high redshifts, the star–formation efficiency was normalized based on the mean metallicity of the high–redshift $\alpha$ forest." + Iu the present work. our aim is fo maximize hiehredshift ealaxy counts.," In the present work, our aim is to maximize high--redshift galaxy counts." + Accordingly. we regard the overall normalization of the starformation cfiiciency as a free paralucter. and we set it to its maxi allowed value based on existing coustraiuts (see discussion below).," Accordingly, we regard the overall normalization of the starformation efficiency as a free parameter, and we set it to its maximum allowed value based on existing constraints (see discussion below)." + We enviiou that the remnants of the liehredshift starbursts can be identified with the spheroid compoucuts in local galaxies., We envision that the remnants of the high–redshift starbursts can be identified with the spheroid components in local galaxies. +" Accordingly. based ou the FaberJackson relation. we adopt the scaling AfarκOb where Mia is the mass in turned mto stars. aud Aap, 1s the velocity dispersion of the host halo."," Accordingly, based on the Faber–Jackson relation, we adopt the scaling $M_{\rm star}\propto \sigma_{\rm halo}^4$, where $M_{\rm +star}$ is the mass in turned into stars, and $\sigma_{\rm halo}$ is the velocity dispersion of the host halo." + We then normalize the ποσο] as follows: Vi= ) Iu addition. we postulate that no stars form im halos with velocity dispersious less than 30kins|. because of he presence of the UV. backgrouud (see. e.g... Navarro Steietz 1997).," We then normalize the models as follows: )^4= ) In addition, we postulate that no stars form in halos with velocity dispersions less than $30~{\rm km~s^{-1}}$, because of the presence of the UV background (see, e.g., Navarro Steinmetz 1997)." + Prior to reionization (which we rere asstume to occur at redshift τ=— 10). we lower his threshold to 11.7kans!. correspouding to a virial enmperature of 1011. where this cutoff is deteruiued x the requirement of efficient cooling. rather than the eedback from the UV backeround (o5. Waiman. Abel Rees 2000).," Prior to reionization (which we here assume to occur at redshift $z=10$ ), we lower this threshold to $11.7~{\rm +km~s^{-1}}$, corresponding to a virial temperature of $10^4$ K, where this cutoff is determined by the requirement of efficient cooling, rather than the feedback from the UV background (e.g. Haiman, Abel Rees 2000)." + We also note that equation (2.3)) correspouds oa ~3 times higher normalization of the FaberJackson relation than derived for the bulges of local spiral galaxies (Whitinore. Iishuer Schechter 1979).," We also note that equation \ref{eq:fstar}) ) corresponds to a $\sim3$ times higher normalization of the Faber–Jackson relation than derived for the bulges of local spiral galaxies (Whitmore, Kirshner Schechter 1979)." +" Using the standard relation between halo velocity dispersion aud mass (c.g. Navarro. Frenk White 1997). and assuming that the eas available for star formation is Mons=(OQ),/QuAa the stellar mass here corresponds uonünallv to Mia~[enceO78M (for the typical halos at each observed flux)."," Using the standard relation between halo velocity dispersion and mass (e.g. Navarro, Frenk White 1997), and assuming that the gas available for star formation is $M_{\rm gas}=(\Omega_{\rm b}/\Omega_{\rm m})M_{\rm halo}$ the stellar mass here corresponds nominally to $M_{\rm star}\sim 6-7\times M_{\rm +gas}$ (for the typical halos at each observed flux)." + our maximal model is rather extreme. in that it assumes the formation of ο67 eenerations of massive stars. formed in quick succession. to reevele the available gas iuto stars 67 times (for reference. we note that the models in ITEL97 had the much lower overall star formation efficiencies of Maa/Ma~2. 20%).," Hence our maximal model is rather extreme, in that it assumes the formation of $\gsim6-7$ generations of massive stars, formed in quick succession, to recycle the available gas into stars 6–7 times (for reference, we note that the models in HL97 had the much lower overall star formation efficiencies of $M_{\rm star}/M_{\rm gas}\sim +2-20\%$ )." +" A stellar population with a Salpeter IME would return onlv zc30% ofits mass to the iuterstellar inedia in~&105 ve. and would allow reeveline of the eas oulv ων Ίσα,"," A stellar population with a Salpeter IMF would return only $\approx +30\%$ of its mass to the interstellar medium in $\sim 3\times10^8$ yr, and would allow recycling of the gas only $\sim$ twice." +" The requirement iu our model of 67 cvcles could be achieved either with a flatter IAIF (since massive stars return all their mass: aud IME. slope of ~1.8 instead of2.35 ""foris esseutiallythen required). or by postulating a larger eas reservoir a system with a given velocity version."," The requirement in our model of 6–7 cycles could be achieved either with a flatter IMF (since massive stars return essentially all their mass; and IMF slope of $\sim$ 1.8 instead of 2.35 is then required), or by postulating a larger gas reservoir for a system with a given velocity version." + Note that significant metal enrichment. to solar levels. inuplies that ~8 generations of starformation did indeed take place in the Milkv Wav (e.g. Binney Tremaine 1987). aud observed heavy clement abundances in galaxy clusters also favor significant enrichment at high redshifts (Reuzini 1997).," Note that significant metal enrichment, to solar levels, implies that $\sim8$ generations of star–formation did indeed take place in the Milky Way (e.g. Binney Tremaine 1987), and observed heavy element abundances in galaxy clusters also favor significant enrichment at high redshifts (Renzini 1997)." + Existing MIR counts Grom JSOCAAY extend down only to about ~O.lmiJw (Franceschini 2000: Franceschini et al., Existing MIR counts (from ) extend down only to about $\sim0.1$ mJy (Franceschini 2000; Franceschini et al. + 1997: Clements et al., 1997; Clements et al. + 1999). aud we extrapolate the models to several orders of magnitude faiuter flux levels.," 1999), and we extrapolate the models to several orders of magnitude fainter flux levels." + Nevertheless. our normalization has to be cousisteut with faint ealaxy counts in the Hubble Deep Field (IIDE) in both optical aud NIR bands.," Nevertheless, our normalization has to be consistent with faint galaxy counts in the Hubble Deep Field (HDF) in both optical and NIR bands." + In particular. we found that the most coustraining IDF data are the 1.67420 galaxy counts ii à NICMOS followup observationof ~L/sth of the IIDF. area (Thompson et al.," In particular, we found that the most constraining HDF data are the $1.6\mu$ m galaxy counts in a NICMOS follow–up observationof $\sim1/8^{\rm th}$ of the HDF area (Thompson et al." + 1999)., 1999). +" This deep survey has a completion lanit near 287"" mae. and has detected a total of ~300 sources;"," This deep survey has a completion limit near $^{\rm th}$ mag, and has detected a total of $\sim 300$ sources." + We have fouud that models with the template spectra described in 2.2 that are consistent with this abundance always satisfy the limits from optical/UV. counts in the IIubble Deep Field to about the same depth., We have found that models with the template spectra described in \ref{subsec:spectra} that are consistent with this abundance always satisfy the limits from optical/UV counts in the Hubble Deep Field to about the same depth. + Iu Figure 2. we show the 1.6724 counts in our models using the GISSEL spectral models. and with the normalization in equation (2.3)).," In Figure \ref{fig:counts1} we show the $1.6\mu$ m counts in our models using the GISSEL spectral models, and with the normalization in equation \ref{eq:fstar}) )." + The upper curve shows all sources. the lower curve shows only the sources bevoud redshift 2explici=5. aud the dots show the NICAIOS data.," The upper curve shows all sources, the lower curve shows only the sources beyond redshift $z=5$, and the dots show the NICMOS data." + The figure v demonstrates that our model is marginally consistent with the NICMOS counts., The figure explicitly demonstrates that our model is marginally consistent with the NICMOS counts. + An integral coustraint ou the MIR. counts can also be obtained from the upper luit on the total cosmuc imfrared backeround energv density., An integral constraint on the MIR counts can also be obtained from the upper limit on the total cosmic infrared background energy density. + The latter lut derives frou. the TeV emuna ray spectrum of the blazar Ak 501. observed in its high state with ΠΟΙΑ. vielding a stringent Lut on the optical depth to pair production at TeV energies (Stanev Franceschini 1998: Dwek 2001).," The latter limit derives from the TeV gamma ray spectrum of the blazar Mrk 501, observed in its high state with HEGRA, yielding a stringent limit on the optical depth to pair production at TeV energies (Stanev Franceschini 1998; Dwek 2001)." + The upper luit on the MIR backeround at Gpau is ~υπ..., The upper limit on the MIR background at $6\mu$ m is $\sim10^4{\rm Jy~sr^{-1}}$ . +" Tn Figure 1. below. we show as the dashed curve the ratio of the fux from all sources brighter than some flux £F, to this upper But."," In Figure \ref{fig:counts2} below, we show as the dashed curve the ratio of the flux from all sources brighter than some flux $F_\nu$ to this upper limit." + The figure shows that our maximal model. which is marginallv consistent with the 1.67221 NICALOS couuts; is also mareinally cousisteut with the upper luit ou the MIR. backeround.," The figure shows that our maximal model, which is marginally consistent with the $1.6\mu$ m NICMOS counts, is also marginally consistent with the upper limit on the MIR background." + Iu this section. we preseut the galaxy counts at different AOR wavelengths. describe the properties of the fait sources such as typical masses and redshift distributions. and discuss the confusion lianit forTPF.," In this section, we present the galaxy counts at different MIR wavelengths, describe the properties of the faint sources such as typical masses and redshift distributions, and discuss the confusion limit for." + Figure Lo shows the cumulative galaxy counts at 6; in our model. using the effective dust opacity prescription from) Charlot Fall (2000). superinposed onu the dustfree spectral model from GISSELOO (Druzual Charlot 2000).," Figure \ref{fig:counts2} shows the cumulative galaxy counts at $\mu$ m in our model, using the effective dust opacity prescription from Charlot Fall (2000), superimposed on the dust--free spectral model from GISSEL00 (Bruzual Charlot 2000)." +" The upper solid curve shows all galaxies, and the lower curve shows ouly those bevoud redshift 2=|5. t"," The upper solid curve shows all galaxies, and the lower curve shows only those beyond redshift $z=5$ ." +o The dashed curve shows the coutribution of the sources the upper limit on the 6511 backgrouud. as discussed above.," The dashed curve shows the contribution of the sources to the upper limit on the $\mu$ m background, as discussed above." +a mass of LOAL. were to have a surface. it would exhibit Type I bursts with a burst rate only a [actor ~2 smaller than for a NS (Naravan Hey] 2002: Yuan. Narvavan Rees 2004).,"a mass of $10 M_\odot$ were to have a surface, it would exhibit Type I bursts with a burst rate only a factor $\sim 3$ smaller than for a NS (Narayan Heyl 2002; Yuan, Narayan Rees 2004)." + Yet. although thousands of bursts have been observed from NSs. not one burst has been seen from anv BIL candidate!," Yet, although thousands of bursts have been observed from NSs, not one burst has been seen from any BH candidate!" + Naravan Γον] (2002) areued (hat the lack of bursts is strong evidence lor (he presence ol horizons in DII candidates., Narayan Heyl (2002) argued that the lack of bursts is strong evidence for the presence of horizons in BH candidates. + Clearly. if (he object has no surface. then gas cannot accumulate and cannot develop a thermonuclear instability.," Clearly, if the object has no surface, then gas cannot accumulate and cannot develop a thermonuclear instability." + But is the lack of à surface theonly reason why BI candidates do not have bursts?, But is the lack of a surface the reason why BH candidates do not have bursts? + Is there anv reasonable scenario in which the objects might have surfaces and still not burst?, Is there any reasonable scenario in which the objects might have surfaces and still not burst? + There has been some discussion of this point (see Naravan 2003: Yuan et al., There has been some discussion of this point (see Narayan 2003; Yuan et al. + 2004: also Abramowicez. lIuzniak Lasota 2002).," 2004; also Abramowicz, Kluzniak Lasota 2002)." + In brief. il appears (hat one needs (o invoke verv unusual physics if one wishes to explain how DII candidates could have surfaces and vet not produce Type I bursts.," In brief, it appears that one needs to invoke very unusual physics if one wishes to explain how BH candidates could have surfaces and yet not produce Type I bursts." + In fact. the requirements are so extreme (hat itis far more economical simply to accept that DII candidates have event horizons!," In fact, the requirements are so extreme that it is far more economical simply to accept that BH candidates have event horizons!" + Although none of the arguments described above is absolutely rigorous. in combination thev leave almost no room for anv model of DII candidates that does not include an event horizon.," Although none of the arguments described above is absolutely rigorous, in combination they leave almost no room for any model of BH candidates that does not include an event horizon." + Thus. it is fair to sav that there is a compelling case for the presence of event horizons in astrophysical DIIs.," Thus, it is fair to say that there is a compelling case for the presence of event horizons in astrophysical BHs." + The evidence is however indirect. and one wonders whether il is possible to obtain more direct evidence.," The evidence is however indirect, and one wonders whether it is possible to obtain more direct evidence." + The most promising idea is to obtain an image of the region near the event horizon of an accreting DII., The most promising idea is to obtain an image of the region near the event horizon of an accreting BH. + At first sight (his seems impossible. considering how compact astrophysical DlIs are and how [ar away they are Irom us.," At first sight this seems impossible, considering how compact astrophysical BHs are and how far away they are from us." + However. (he situation is not entirely hopeless.," However, the situation is not entirely hopeless." + Consider for concreteness a non-rotating BIT with a horizon at radius A3., Consider for concreteness a non-rotating BH with a horizon at radius $R_S$. + Because of strong light-bending in the vicinity of the BIL. a distant observer will see an apparent boundary of the DIE at a radius of (27)?R5/2 (Faleke. Melia Agol 2000).," Because of strong light-bending in the vicinity of the BH, a distant observer will see an apparent boundary of the BH at a radius of $(27)^{1/2}R_S/2$ (Falcke, Melia Agol 2000)." + Rays with impact parameters inside (his boundary intersect the horizon. while ravs outside the boundary miss the horizon.," Rays with impact parameters inside this boundary intersect the horizon, while rays outside the boundary miss the horizon." + The angular size of the boundary is where mas = nmilliarcsecond = 4.85x10? radian., The angular size of the boundary is where mas = milliarcsecond = $4.85\times10^{-9}$ radian. + A 10... DII candidate at a distance of 1 kpe will have £j~10.° mas. which is much too small to be resolved with any technique in the foreseeable future.," A $10M_\odot$ BH candidate at a distance of 1 kpc will have $\theta_b +\sim 10^{-6}$ mas, which is much too small to be resolved with any technique in the foreseeable future." + However. Sev À* with Mc4x10M. and al a distance of 8 kpc," However, Sgr A* with $M\sim +4\times10^{6}M_\odot$ and at a distance of 8 kpc" +in determining the total Dux from annihilating cark matter.,in determining the total flux from annihilating dark matter. + If recent. simulations are correct. it seems likely that this Hux may be 24 times larger than that predicted for a pure NEW profile: in the extreme case of a Moore profile with an inner cusp limited. only. by. self-annihilation. the total [Lux is 25 times the NEW value.," If recent simulations are correct, it seems likely that this flux may be 2–4 times larger than that predicted for a pure NFW profile; in the extreme case of a Moore profile with an inner cusp limited only by self-annihilation, the total flux is 25 times the NFW value." + Since the dependence on rfr is similar for all profiles. in what follows we will assume the NEW form for f(c). ancl allow that the ux may be a constant 225 times greater than this.," Since the dependence on $r/r_p$ is similar for all profiles, in what follows we will assume the NFW form for $f(c)$, and allow that the flux may be a constant 2–25 times greater than this." + ‘To calculate the background Lux from annihilations within a arge volume. we need to add the relative contributions from regions of different density within this volume.," To calculate the background flux from annihilations within a large volume, we need to add the relative contributions from regions of different density within this volume." + Following the pess-Schechter approximation (Press Schechter 1974). we can consider all the mass in à given (physical) volume V. to »e contained in virialised halos of some (possibly very small) mass.," Following the Press-Schechter approximation (Press Schechter 1974), we can consider all the mass in a given (physical) volume $V$ to be contained in virialised halos of some (possibly very small) mass." + We make the further approximation that these halos are spherical. with a fixed. virial overdensity A. relative to he critical density. and have universal density profiles with a concentration e=r.fr. that depends only on their mass.," We make the further approximation that these halos are spherical, with a fixed virial overdensity $\Delta_c$ relative to the critical density, and have universal density profiles with a concentration $c = r_v/r_s$ that depends only on their mass." + Lf he volume contains V(dpnCAL)/dAL)AAL halos in the mass range Al to AL|AAL. then from equation (2)). the total lux multiplier for the volume will be where p ijs the mean density of dark matter within V. p=Acpe ds the average density of bound. halos. and ολ} is the Bux. multiplier for halos of concentration e=c(Al).," If the volume contains $V\, (dn(M)/dM)\, \Delta M$ halos in the mass range $M$ to $M + \Delta M$, then from equation \ref{fluxm1}) ), the total flux multiplier for the volume will be where $\rho$ is the mean density of dark matter within $V$, ${\bar{\rho}} = \Delta_c\,\rho_c$ is the average density of bound halos, and $f(c(M))$ is the flux multiplier for halos of concentration $c = c(M)$." + Since p=Opi. we can rewrite the dimensionless Hux multiplier for large volumes as: where £(AL) is the fraction of the universe in virialised halos of mass AL or larger.," Since $\rho = \Omega\,\rho_c$, we can rewrite the dimensionless flux multiplier for large volumes as: where $F(M)$ is the fraction of the universe in virialised halos of mass $M$ or larger." +" PF can be estimated. using. the Press-Schechter formalism: with v=à./o(M). where 9, is the critical overdensity and. a(Al) describes the power spectrum of. density Iluctuations."," $F$ can be estimated using the Press-Schechter formalism: with $\nu \equiv \delta_c/\sigma(M)$, where $\delta_c$ is the critical overdensity and $\sigma(M)$ describes the power spectrum of density fluctuations." + Recent simulations JJenkins ct 11998) have suggested. however. that this mass function may overestimate the number of halos near Al. the characteristic mass for which e(M)=D(z)8. (where D(z) is the linear erowth factor at redshift z).," Recent simulations Jenkins et 1998) have suggested, however, that this mass function may overestimate the number of halos near $M_*$, the characteristic mass for which $\sigma(M) = D(z)\,\delta_c$ (where $D(z)$ is the linear growth factor at redshift $z$ )." + An alternative mass function. proposed by Sheth ancl Tormen (1999) ancl based. on the ellipsoidal collapse mocoel. is: with ;1=0.3222 and q= 0.3.," An alternative mass function, proposed by Sheth and Tormen (1999) and based on the ellipsoidal collapse model, is: with $A = 0.3222$ and $q = 0.3$ ." + Since both these mass functions have a power-law behaviour at low masses. where concentrations and thus f(e) are larger. it is not clear the integral in equation (20)) will converge as we include the contribution from smaller. ancl smaller halos. (," Since both these mass functions have a power-law behaviour at low masses, where concentrations and thus $f(c)$ are larger, it is not clear the integral in equation \ref{locvol}) ) will converge as we include the contribution from smaller and smaller halos. (" +Although the total mass per unit. volume must converge. f within a given volume need not converge. as in the case of a pure rL7 density profile.),"Although the total mass per unit volume must converge, $f$ within a given volume need not converge, as in the case of a pure $r^{-1.5}$ density profile.)" + In. practice. we expect barvonic phenomena to complicate structure formation on small mass scales. ancl annihilation itself wil also limit the contribution from very dense material.," In practice, we expect baryonic phenomena to complicate structure formation on small mass scales, and annihilation itself will also limit the contribution from very dense material." + Thus. we will truncate the integral at some limiting mass. anc consider the behaviour of f as a function of this mass limit.," Thus, we will truncate the integral at some limiting mass, and consider the behaviour of $f$ as a function of this mass limit." + The concentration of a halo should rellect the density of the universe at the time when it assembled the materia now in its central core., The concentration of a halo should reflect the density of the universe at the time when it assembled the material now in its central core. + “Phere are several predictions of the concentration-mass relation (Navarro. Frenk White 1997: Bullock et 22001: Eke. (ανατο Steinmetz 2001: Wechsler ct 22002). based on this interpretation.," There are several predictions of the concentration-mass relation (Navarro, Frenk White 1997; Bullock et 2001; Eke, Navarro, Steinmetz 2001; Wechsler et 2002), based on this interpretation." + We will use the most recent analytic model. that of Eke. Navarro. Steinmetz (2001 ENS hereafter). to calcula the dimensionless ux multiplier. though we expect similar results from. the other models.," We will use the most recent analytic model, that of Eke, Navarro, Steinmetz (2001 – ENS hereafter), to calculate the dimensionless flux multiplier, though we expect similar results from the other models." + We use the public code supplied. by the authors to calculate concentrations. and integrate the expressions above numerically.," We use the public code supplied by the authors to calculate concentrations, and integrate the expressions above numerically." + Note that one point of uncertainty in all these models is what minimum concentration to assign to halos that have just formed., Note that one point of uncertainty in all these models is what minimum concentration to assign to halos that have just formed. + The, The +simulations. coupled to an advanced synchrotron radiation code. showing that the standard analytical argument systematically overestimates the jet break time.,"simulations, coupled to an advanced synchrotron radiation code, showing that the standard analytical argument systematically overestimates the jet break time." + We explain the numerical set-up of the simulations in this paper in section 2.., We explain the numerical set-up of the simulations in this paper in section \ref{set_up_section}. + In section 3 we study jet. breaks while ignoring both self-absorption and cooling and find that the basic calculation linking jet break time and opening angle can be olf by days., In section \ref{optically_thin_section} we study jet breaks while ignoring both self-absorption and cooling and find that the basic calculation linking jet break time and opening angle can be off by days. + We derive a relation between jet break time and opening angle in the optically thin case and compare limb-brightening of the afterglow image at clillerent spectral regimes., We derive a relation between jet break time and opening angle in the optically thin case and compare limb-brightening of the afterglow image at different spectral regimes. + In section 4 we calculate the full svnchrotron spectrum. and Compare breaks at cillerent spectral regimes., In section \ref{jetbreaks_full_section} we calculate the full synchrotron spectrum and compare jet breaks at different spectral regimes. + We find that the break jetat radio frequencies is postponed. compared to the jet. breaks observed. at frequencies above the selfabsorption break frequency., We find that the break at radio frequencies is postponed compared to the jet breaks observed at frequencies above the self-absorption break frequency. + Depending on opening angle and. observer frequency. this time dillerence can be on the order of several davs (over a factor 2 in jet break time). even though we did not add any novel radiation physics or make any nonstandard assumptions.," Depending on opening angle and observer frequency, this time difference can be on the order of several days (over a factor 2 in jet break time), even though we did not add any novel radiation physics or make any nonstandard assumptions." + The new aspects of our caleulation are merely the accuracy of the radiation code and the numerical resolution of the fluid. simulation., The new aspects of our calculation are merely the accuracy of the radiation code and the numerical resolution of the fluid simulation. + Selt-absorption is fully treated using linear radiative transfer equations ancl local electron cooling times are numerically calculated through an advection equation., Self-absorption is fully treated using linear radiative transfer equations and local electron cooling times are numerically calculated through an advection equation. + The dillerence in jet break characteristics can be understood. from. the act that dillerent regions of the jet. provide the dominant contribution for. different: observer. frequencies., The difference in jet break characteristics can be understood from the fact that different regions of the jet provide the dominant contribution for different observer frequencies. + We show images of the emission coelficient throughout the blast wave ο visualise the underlying physics., We show images of the emission coefficient throughout the blast wave to visualise the underlying physics. + Up to section 4 we assume that collimated outflow can o represented hy a conic section from a 1D. spherically svmametric simulation., Up to section \ref{jetbreaks_full_section} we assume that collimated outflow can be represented by a conic section from a 1D spherically symmetric simulation. + We test this assumption. which implies that lateral spreading has little effect on the observed jet break. by performing a 2D. simulation in section 5.. lli," We test this assumption, which implies that lateral spreading has little effect on the observed jet break, by performing a 2D simulation in section \ref{2D_simulation_section}." +gher dimensional simulations are not the focus of this προς ancl we will only briefly. discuss the consequences of ateral spreacing., Higher dimensional simulations are not the focus of this paper and we will only briefly discuss the consequences of lateral spreading. + We end with a summary and discussion of our results in section 6.., We end with a summary and discussion of our results in section \ref{jetbreaks_summary_section}. + We have performed one-dimensional blast wave simulations using the relativistic hvdrodynamics module of the adaptive-mesh refinement magnetohycdrodyvnamies code (??7)).," We have performed one-dimensional blast wave simulations using the relativistic hydrodynamics module of the adaptive-mesh refinement magnetohydrodynamics code \citealt{Keppens2003, Meliani2007}) )." + We have used an advanced. equation of state (EOS) that implements an effective aciabatic index that gradually changes from 4/3 in the relativistic regime to 5/3 in the nonrelativistic regime., We have used an advanced equation of state (EOS) that implements an effective adiabatic index that gradually changes from $4/3$ in the relativistic regime to $5/3$ in the nonrelativistic regime. + The upper cut-olf Lorentz factor >i of the shock-aceelerated electron power law distribution is set to a numerically high. value upstream and traced locally using an advection equation., The upper cut-off Lorentz factor $\gamma_M$ of the shock-accelerated electron power law distribution is set to a numerically high value upstream and traced locally using an advection equation. + This cut-olf determines the position of the cooling break κα. in the spectrum., This cut-off determines the position of the cooling break $\nu_c$ in the spectrum. + The application of the advection equation ancl the EOS are introclueed and explained in? (WE09)., The application of the advection equation and the EOS are introduced and explained in \cite{vanEerten2009c} (VE09). + Some modifications to this method are explained. in appendix A.., Some modifications to this method are explained in appendix \ref{numerical_approach_section}. + We assume that little lateral spreading of the jet has taken place. and that a collimated outflow can be adequately represented. by a conie section of a spherically svnunetric simulation.," We assume that little lateral spreading of the jet has taken place, and that a collimated outflow can be adequately represented by a conic section of a spherically symmetric simulation." + The settings for the 2D simulation used to test this assumption are discussed separately in section 5.., The settings for the 2D simulation used to test this assumption are discussed separately in section \ref{2D_simulation_section}. + We have used the following physics settings: explosion energv E=2.61075 erg. (homogeneous). cireumburst number density ny=0.78 . accelerated electron power law slope p=2.1. fraction of thermal energy. density in the accelerated. electrons ce and in the magnetic field cg both equal to 0.27 and the fraction £v. of electrons accelerated ab the shock front equal to 1.0. (unless. explicitly: stated otherwise).," We have used the following physics settings: explosion energy $E = 2.6 \cdot 10^{51}$ erg, (homogeneous) circumburst number density $n_0 = 0.78$ $^{-3}$, accelerated electron power law slope $p = 2.1$, fraction of thermal energy density in the accelerated electrons $\epsilon_E$ and in the magnetic field $\epsilon_B$ both equal to 0.27 and the fraction $\xi_N$ of electrons accelerated at the shock front equal to 1.0 (unless explicitly stated otherwise)." + Unlike in 1¢ simulations performed in. VIEOO. we have kept the fractions £x. cg and eg fixed throughout the simulation. in order to stav as close as possible to the conventional fireball model.," Unlike in the simulations performed in VE09, we have kept the fractions $\xi_N$, $\epsilon_E$ and $\epsilon_B$ fixed throughout the simulation, in order to stay as close as possible to the conventional fireball model." +" We have set the observer luminosity distance r4,=2.45-10 em. but kept the redshift at zero (instead of the matching value 0.1685)."," We have set the observer luminosity distance $r_{obs} = 2.47 \cdot 10^{27}$ cm, but kept the redshift at zero (instead of the matching value 0.1685)." + The observer is assumed to be positioned on the axis of the jeIm, The observer is assumed to be positioned on the axis of the jet. + These physics settings qualitatively describe. CRBO30320 and are identical to those used in VEO9., These physics settings qualitatively describe GRB030329 and are identical to those used in VE09. + They do not provide a quantitative match to the data for CIIRDO30329 however. since they have been derived. using an analytical model by 2 and not by directly. matching simulation results to observational clata.," They do not provide a quantitative match to the data for GRB030329 however, since they have been derived using an analytical model by \cite{vanderHorst2008mar} and not by directly matching simulation results to observational data." + We have run a number of simulations. using a grid with 10 base blocks (of 12 cells each) and up to 19 refinement levels (with the resolution doubling at each next refinement level) that has boundaries at 112:107 em and 112:107 em.," We have run a number of simulations, using a grid with 10 base blocks (of 12 cells each) and up to 19 refinement levels (with the resolution doubling at each next refinement level) that has boundaries at $1.12 \cdot 10^{14}$ cm and $1.12 \cdot 10^{18}$ cm." + A blast wave reaching the outer boundary provides coverage up to an observation time of νο50 days., A blast wave reaching the outer boundary provides coverage up to an observation time of $\backsim 50$ days. + We start. the simulation with a blast wave with shock Lorentz [factor 25. ensuring complete coverage long before one day in observer time.," We start the simulation with a blast wave with shock Lorentz factor 25, ensuring complete coverage long before one day in observer time." + We have checked that this resolution is sullicient. ancl discuss this in appendix A.., We have checked that this resolution is sufficient and discuss this in appendix \ref{numerical_approach_section}. + The svnchrotron radiation has been calculated with the method introduced in 2. anc VEO9. using a linear radiative transfer method. where the number of calculated: ravs is changed dynamically via a process analogous to adaptive mesh refinement for the RID simulation.," The synchrotron radiation has been calculated with the method introduced in \cite{vanEerten2009} and VE09, using a linear radiative transfer method where the number of calculated rays is changed dynamically via a process analogous to adaptive mesh refinement for the RHD simulation." + We have allowed for 19 refinement levels in the radiation caleulation. Just like in the RIID simulation.," We have allowed for 19 refinement levels in the radiation calculation, just like in the RHD simulation." + Phe radiative transfer. calculation uses the output from the dynamics simulation that has been stored at fixed time intervals. and we have used up to 10.000 such snapshots of the Iuid state.," The radiative transfer calculation uses the output from the dynamics simulation that has been stored at fixed time intervals, and we have used up to 10,000 such snapshots of the fluid state." + Alreacdw in a simplified set-up where weignore self-absorption and electron cooling we find a noticable dillerence between the analvtically expected jet. break time ancl the simulation results., Already in a simplified set-up where weignore self-absorption and electron cooling we find a noticable difference between the analytically expected jet break time and the simulation results. +" In figure 1. we have plotted. light curves at two dilferent frequencies. 14-10"" Lz and 5:107 Lz. chosen such that they [ie safely below and. above the svynchrotron peak frequency. ,,,."," In figure \ref{break_curves_nosanoc_figure} we have plotted light curves at two different frequencies, $1.4 \cdot 10^9$ Hz and $5 \cdot 10^{17}$ Hz, chosen such that they lie safely below and above the synchrotron peak frequency $\nu_m$." + Also indicated in the plot are both the conventional estimate for thejet break time and an improved estimate (both explained below)., Also indicated in the plot are both the conventional estimate for the jet break time and an improved estimate (both explained below). +" The jet break time is conventionally linked. to the jet half opening angle 8, using the Blandford-Melxee. (DM) self-similar solution for the blast wave dynamics in the ultrarelativistic regime (2)..", The jet break time is conventionally linked to the jet half opening angle $\theta_h$ using the Blandford-McKee (BM) self-similar solution for the blast wave dynamics in the ultrarelativistic regime \citep{Blandford1976}. . + The argument is as follows., The argument is as follows. +" According to BAL the blast wave shock Lorentz factor E and the emission time ἐς, are related. via", According to BM the blast wave shock Lorentz factor $\Gamma$ and the emission time $t_e$ are related via +dynamically active and have either small (in comparison to their total X-ray luminosities) or no cooling Lows.,dynamically active and have either small (in comparison to their total X-ray luminosities) or no cooling flows. +" Clusters like Abell 1689. Ας]. Abell 2163 and Abell 2218 have unusually high velocity dispersions (CGucehus 1989. Couch Sharples 1987. Squires 19972. Le οσο, Pelló Sanahuja 1992). given their X-ray luminosities. ancl exhibit. clear substructure in. their N-rav emission. ealaxy distributions and total matter distributions (see also Section 4.3 and references therein)."," Clusters like Abell 1689, AC114, Abell 2163 and Abell 2218 have unusually high velocity dispersions (Gudehus 1989, Couch Sharples 1987, Squires 1997a, Le Borgne, Pelló Sanahuja 1992), given their X-ray luminosities, and exhibit clear substructure in their X-ray emission, galaxy distributions and total matter distributions (see also Section 4.3 and references therein)." + Merger events will tend to complicate the temperature structure in clusters. and e&enerate turbulent and bulk motions which may contribute tothe support of the X-ray eas against gravity.," Merger events will tend to complicate the temperature structure in clusters, and generate turbulent and bulk motions which may contribute to the support of the X-ray gas against gravity." + Although the discrepancies between the X-ray and strong lensing masses resulting from such processes should not. in general. exceed 50 per cent (Navarro. Frenk White 1995: Schindler 1996: I5vrard. Metzler Navarro 1996: Ioettiger. Burns Loken 1996) at smaller radii (comparable to the cluster core radii) their elfects may be more important. (see Section 4.6).," Although the discrepancies between the X-ray and strong lensing masses resulting from such processes should not, in general, exceed 50 per cent (Navarro, Frenk White 1995; Schindler 1996; Evrard, Metzler Navarro 1996; Roettiger, Burns Loken 1996) at smaller radii (comparable to the cluster core radii) their effects may be more important (see Section 4.6)." + Substructure and. linc-of-sight. alignments of material towards the cluster cores are also likely to contribute to the mass discrepancies since they will increase the probability of detecting gravitational arcs in the clusters. and enhance the masses determined from the lensing data (Dartelmann Steinmetz 1996).," Substructure and line-of-sight alignments of material towards the cluster cores are also likely to contribute to the mass discrepancies since they will increase the probability of detecting gravitational arcs in the clusters, and enhance the masses determined from the lensing data (Bartelmann Steinmetz 1996)." + However. since magnetic elds are expected to be stronger in the cores of cooling-Iow. rather than non-cooling [ow svstems Soker Sarazin 1990). magnetic pressure seems unlikely to contribute significantly to the illerences between the strong lensing ancl X-ray masses observed.," However, since magnetic fields are expected to be stronger in the cores of cooling-flow, rather than non-cooling flow systems Soker Sarazin 1990), magnetic pressure seems unlikely to contribute significantly to the differences between the strong lensing and X-ray masses observed." + The results presented in Section 4.1 demonstrate excellent agreement between the X-ray and strone-lensing masses for the cooling-Llow clusters in our sample., The results presented in Section 4.1 demonstrate excellent agreement between the X-ray and strong-lensing masses for the cooling-flow clusters in our sample. + Ht is crucial to note. however. that such agreement would not have been obtained if the multiphase nature of the X-ray. emission from these clusters were not accounted for in the N-ray. modelling.," It is crucial to note, however, that such agreement would not have been obtained if the multiphase nature of the X-ray emission from these clusters were not accounted for in the X-ray modelling." + The analysis of the ASCA data for the cooling [Low (ancl intermediate) clusters in Section 3.1. incorporated a, The analysis of the ASCA data for the cooling flow (and intermediate) clusters in Section 3.1 incorporated a +Science frames were grouped by filter and reduced separately.,Science frames were grouped by filter and reduced separately. + Twcho-2 reference stars were identified in the w.y data and weighted. least-squares. conventional “plate” adjustineuts (CPA) run on all applicable frames.," Tycho-2 reference stars were identified in the $x,y$ data and weighted, least-squares, conventional “plate"" adjustments (CPA) run on all applicable frames." + A total of 127 IL 9350 RB. 9115 V. aud 75 D filter frames provided successful solutions (18.667 CCD frames all together)," A total of 127 I, 9350 R, 9115 V, and 75 B filter frames provided successful solutions (18,667 CCD frames all together)." + Of these. a total of Lass CCD fraanes are outside the |19.67 to |907 area which constitutes the published catalog data. thus 16.779 CCD frames were used for the BSCC.," Of these, a total of 1,888 CCD frames are outside the $+49.6^{\circ}$ to $+90^{\circ}$ area which constitutes the published catalog data, thus 16,779 CCD frames were used for the BSCC." + The πα of reference stars used per CCD frame is shown in the listoeram of Fig., The number of reference stars used per CCD frame is shown in the histogram of Fig. + 3., 3. + There are 127. frames with 9 or less reference stars in the area north of |19.57. while the typical number of Twcho-2 reference stars used per frame is about 12 to 35. with a few frames up to about 100.," There are 427 frames with 9 or less reference stars in the area north of $+49.5^{\circ}$, while the typical number of Tycho-2 reference stars used per frame is about 12 to 35, with a few frames up to about 100." + A linear plate model (6 parameters) was adopted without correcting for differcutial refraction or aberration., A linear plate model (6 parameters) was adopted without correcting for differential refraction or aberration. + Also no third order seoimetric distortion was pre-applied. which is iuhereut iu Schinidt telescope imaging (curved focal plane and tangential projected £.;4.," Also no third order geometric distortion was pre-applied, which is inherent in Schmidt telescope imaging (curved focal plane and tangential projected $\xi, \eta$ )." + These procedures are adequate due to the small field of view aud the presence of other distortions for example from the filters., These procedures are adequate due to the small field of view and the presence of other distortions for example from the filters. + Ilowever. the combined effect of all econmetrie distortions is determined curpirically as follows. iud has been corrected.," However, the combined effect of all geometric distortions is determined empirically as follows, and has been corrected." +" A total of 312.522 and 292.957 residuals (with 2 coordinates cach) were available from the astrometric reductions of all R aud V filter observations. respectively,"," A total of 312,522 and 292,957 residuals (with 2 coordinates each) were available from the astrometric reductions of all R and V filter observations, respectively." + The residuals were stacked up in bius as functiou of focal plane wr.y coordinates and slightly smoothed bw weighted average with neighboring bins.," The residuals were stacked up in bins as function of focal plane $x,y$ coordinates and slightly smoothed by weighted average with neighboring bins." + The resulting field distortion patterns (FDP) are shown in Fie., The resulting field distortion patterns (FDP) are shown in Fig. + Ll., 4. + Linear interpolation between the bins were orforined to arrive at the FDP correction values which were applied to the «.y data prior to the ‘ollowing iteration of the CPÀ reduction.," Linear interpolation between the bins were performed to arrive at the FDP correction values which were applied to the $x,y$ data prior to the following iteration of the CPA reduction." + Residuals of the final CPA reductions were plotted as a fiction of ue.g coordinate. racial distance from the frame center. iaenitude. color. and coma term (product of magnitude and coordinate).," Residuals of the final CPA reductions were plotted as a function of $x,y$ coordinate, radial distance from the frame center, magnitude, color, and coma term (product of magnitude and coordinate)." + The largest systematic errors. up to about 20 mas. were found as a fiction of magnitude (Figs.," The largest systematic errors, up to about 20 mas, were found as a function of magnitude (Figs." + 5. 6). with root-mean-square (RAIS) scatter shown in Fie.," 5, 6), with root-mean-square (RMS) scatter shown in Fig." + 7., 7. + For most of these 90 sec exposures in the survey saturation is around R-10 preventing from reaching even smaller positional errors at the bright eud., For most of these 90 sec exposures in the survey saturation is around R=10 preventing from reaching even smaller positional errors at the bright end. + Errors for stars fainter than LOth magnitude are dominated by the refercuce star contribution., Errors for stars fainter than 10th magnitude are dominated by the reference star contribution. + A complex. non-linear dependence for the y coordinate (declination) as a function of coma-x and coma-v is found (uot shown) with amplitudes up to 20 mas.," A complex, non-linear dependence for the $y$ coordinate (declination) as a function of coma-x and coma-y is found (not shown) with amplitudes up to 20 mas." + These systematic errors are at the lauit of the reference star catalog at the epoch of the CCD observations., These systematic errors are at the limit of the reference star catalog at the epoch of the CCD observations. + No further investigation was performed aud no attempt to correct the derived star positions for any such magnitude dependent svsteniatie errors was mado., No further investigation was performed and no attempt to correct the derived star positions for any such magnitude dependent systematic errors was made. + The final catalog positions are obtained from a weielited mean of all individual observations for cach star., The final catalog positions are obtained from a weighted mean of all individual observations for each star. + Objects matching within 2.0 arcsec are assuned to be the same star., Objects matching within 2.0 arcsec are assumed to be the same star. + Thus the positions provided iu this observational catalog are based ou the mean of the V. aud BR. baud. observations. eiven at mean epoch of observation. on the ICRS. as represented by the Tycho-2 catalog.," Thus the positions provided in this observational catalog are based on the mean of the V and R band observations, given at mean epoch of observation, on the ICRS, as represented by the Tycho-2 catalog." + Differeutial photometric reductions were performed with respect to Tycho-2 standards ou individual CCD frames., Differential photometric reductions were performed with respect to Tycho-2 standards on individual CCD frames. + Instrumental maguitudes were derived from) the inteeral (voluue) of the fitted stellar nuage profiles above the local background using the modified UCAC reduction pipcline while performing the astrometric pixel reduction step., Instrumental magnitudes were derived from the integral (volume) of the fitted stellar image profiles above the local background using the modified UCAC reduction pipeline while performing the astrometric pixel reduction step. +" Tn the following. oulv Twcho-2 stars with ""good photometry flag. brighter than V = 12.5. aud not saturated on CCD frames were used."," In the following, only Tycho-2 stars with “good"" photometry flag, brighter than V = 12.5, and not saturated on CCD frames were used." + Furthermore. stars with V) < O2 and V) > 1.5 were excluded and stars in the V) range of 1.1 to 1.5 were used with reduced weielt.," Furthermore, stars with $-$ V) $\le$ $-$ 0.2 and $-$ V) $\ge$ 1.5 were excluded and stars in the $-$ V) range of 1.1 to 1.5 were used with reduced weight." + A magnitude zero-point (Vo) per V-baud CCD frame was fittedto transform the iustruneutal magnitudes (V5) iuto standard V magnitudes (V. ). using Tvcho-2 references for Ὡς in a weighted adjustinent according to ," A magnitude zero-point $V_{0}$ ) per V-band CCD frame was fittedto transform the instrumental magnitudes $V_{i}$ ) into standard V magnitudes $V_{s}$ ), using Tycho-2 references for $V_{s}$ in a weighted least-squares adjustment according to ." +Simularly.," Similarly," +derived in Laing (1980) and [EnBlin et al. (1998)..,"derived in Laing (1980) and lin et al. \nocite{1980MNRAS.193..439L,1998AA...332..395E}." + In these derivations it was assumed that the compression is linear along the How axis and that the fields. follow completely passively., In these derivations it was assumed that the compression is linear along the flow axis and that the fields follow completely passively. + The resulting percentage radio polarisation is then eiven by: The term C. denotes the shock compression factor. 5 the spectral index of the electron. population. and 4 the viewing angle.," The resulting percentage radio polarisation is then given by: The term $C_{\rm gas}$ denotes the shock compression factor, $s$ the spectral index of the electron population, and $\delta$ the viewing angle." + LW the magnetic fields dominate the total pressure one can allow them to expand to pressure ecquilibrium after shock passage., If the magnetic fields dominate the total pressure one can allow them to expand to pressure equilibrium after shock passage. + In this case the polarisation is surprisinely similar to that expected in the weak Ποιά case (EnBlin et al. 1998))., In this case the polarisation is surprisingly similar to that expected in the weak field case lin et al. \nocite{1998AA...332..395E}) ). + This can be seen from the reference curves in Fig., This can be seen from the reference curves in Fig. + Ll ane 12.., \ref{fig:pol.WS20.100MHz} and \ref{fig:pol.WS60.100MHz}. + Also shown in these figures are viewing angle scans of the total polarisation of the radio emission. in the simulation :5sD before. (Fig. 1)), Also shown in these figures are viewing angle scans of the total polarisation of the radio emission in the simulation before (Fig. \ref{fig:pol.WS20.100MHz}) ) + and after (Fig. 12)), and after (Fig. \ref{fig:pol.WS60.100MHz}) ) + garock passage., shock passage. + These figures show that. in addition to the intrinsic. polarisation pattern of the turbulent fields. the garock passage imprints a strong polarisation signature onto 10 radio plasma.," These figures show that, in addition to the intrinsic polarisation pattern of the turbulent fields, the shock passage imprints a strong polarisation signature onto the radio plasma." + lt is remarkable that the characteristics o£ the simulated radio polarisation are similar to the analvtic models of garocked magnetic fields., It is remarkable that the characteristics of the simulated radio polarisation are similar to the analytic models of shocked magnetic fields. + LP the amplitude of the polarisation curves in our simulations are not too strongly allectec by artilacts. such as the decaving field strength. or the incorrect acdiabatic index of the radio plasma. we can conclude that the shock acceleration and the revived. fossil radio plasma are not distinguishable by this.," If the amplitude of the polarisation curves in our simulations are not too strongly affected by artifacts, such as the decaying field strength, or the incorrect adiabatic index of the radio plasma, we can conclude that the shock acceleration and the revived fossil radio plasma are not distinguishable by this." + Alternatively. the simplistic analvtic theory of shocked. fields seems to be a good guide in relating viewing angle and radio polarisation.," Alternatively, the simplistic analytic theory of shocked fields seems to be a good guide in relating viewing angle and radio polarisation." + The reason for the similar polarisation pattern in the cilferent mocels is likely that the magnetic fields in all cases are nearly completely aligned with the shock plane., The reason for the similar polarisation pattern in the different models is likely that the magnetic fields in all cases are nearly completely aligned with the shock plane. + In the extreme case of completely shock plane aligned. fields. but with randomly. distributed orientations within that plane. the polarisation is given by This is not too far from the other models.," In the extreme case of completely shock plane aligned fields, but with randomly distributed orientations within that plane, the polarisation is given by This is not too far from the other models." + Whenever the imprinted: polarisation dominates over he initial intrinsic one. the direction of the E-vector can be used. relatively reliably to infer the shock normal projected onto the plane of the sky (Fig. 13)).," Whenever the imprinted polarisation dominates over the initial intrinsic one, the direction of the E-vector can be used relatively reliably to infer the shock normal projected onto the plane of the sky (Fig. \ref{fig:pol.ang.WS60.100MHz}) )." + The angle with respect o this plane can be estimated roughly from. the total »olarisation., The angle with respect to this plane can be estimated roughly from the total polarisation. + Thus. in principle. the 3-dimensional orientation (modulo a mirror ambiguity) can be derived from the »olarisation data onlv.," Thus, in principle, the 3-dimensional orientation (modulo a mirror ambiguity) can be derived from the polarisation data only." + However. these points will. need aciditional investigations before it is applicable to real data.," However, these points will need additional investigations before it is applicable to real data." + Especially the role of the initial field. geometry. has to be investigated., Especially the role of the initial field geometry has to be investigated. + Our simulated radio ghosts showed deviations from the analytic predictions on the order of the total initial polarisation of the source., Our simulated radio ghosts showed deviations from the analytic predictions on the order of the total initial polarisation of the source. + Such deviations may significantly reduce the accuracy of any polarisation based viewing angle estimate., Such deviations may significantly reduce the accuracy of any polarisation based viewing angle estimate. + However. we think that according to our moclel there should be à correlation between total polarisation and the viewing angle due to the field. ordering action of the shock wave.," However, we think that according to our model there should be a correlation between total polarisation and the viewing angle due to the field ordering action of the shock wave." + See IEnBlin et al., See lin et al. + for an early attempt to compare these quantities for a small smaple of cluster racio relies., \nocite{1998AA...332..395E} for an early attempt to compare these quantities for a small smaple of cluster radio relics. + On the basis of our simulations we speculate that the observed. dimensions of a cluster radio relic with a toroidal shape may be used to get a rough estimate of the shock strength., On the basis of our simulations we speculate that the observed dimensions of a cluster radio relic with a toroidal shape may be used to get a rough estimate of the shock strength. + This is based on the observation that in the numerical simulations the radius 2 of the spherical cocoon and the major radius of the torus after the passage of the shock are approximately equal., This is based on the observation that in the numerical simulations the radius $R$ of the spherical cocoon and the major radius of the torus after the passage of the shock are approximately equal. + Since the major (2) and minor (r) radit of the torus can be read. olf approximately from a sensitive high-resolution radio map. the compression of the radio plasma by the shock can be estimated.," Since the major $R$ ) and minor $r$ ) radii of the torus can be read off approximately from a sensitive high-resolution radio map, the compression of the radio plasma by the shock can be estimated." +" In the idealised case of an initially spherical ancl finally toroiclal radio cocoon. the compression factor is given by Assuming the radio cocoon to be in pressure equilibrium with its environment before and after the shock passage. the pressure jump in the shock is given by S/P,= Cv."," In the idealised case of an initially spherical and finally toroidal radio cocoon, the compression factor is given by Assuming the radio cocoon to be in pressure equilibrium with its environment before and after the shock passage, the pressure jump in the shock is given by ${P_2}/{P_1} = C^{\gamma_{\rm rp}}$ ." +" If the adiabatic index of the radio plasma sy), is assumed to be known. e.g :=4/3 for an ultra-relativistic equation of state. the shock strength can be estimated."," If the adiabatic index of the radio plasma $\gamma_{\rm rp}$ is assumed to be known, e.g $\gamma_{\rm rp}=4/3$ for an ultra-relativistic equation of state, the shock strength can be estimated." + But even if this assumption is not justified and the geometry deviates from the σακο. gcometries assumed here. the strength of the shock wave should be correlated to the ratio of the globa cliameter ofa toroidal relic anc 10 thickness of its Glaments.," But even if this assumption is not justified and the geometry deviates from the idealised geometries assumed here, the strength of the shock wave should be correlated to the ratio of the global diameter of a toroidal relic and the thickness of its filaments." + Unfortunately. the quality of the best current radio maps of relics do not vet allow a quantitative comparison ofthe shock streneth by comparing the 2/r ratios of toroidal relies.," Unfortunately, the quality of the best current radio maps of relics do not yet allow a quantitative comparison of the shock strength by comparing the $R/r$ ratios of toroidal relics." + Bu these maps demonstrate that the necessary sensitivity anc resolution might be reached soon., But these maps demonstrate that the necessary sensitivity and resolution might be reached soon. + IU furthermore. the strength of the shock wave of wel resolved cluster radio relics can be estimated independentIv roni X-ray. maps of the ICM. it would be possible to directly measure the adiabatic index of radio plasma.," If, furthermore, the strength of the shock wave of well resolved cluster radio relics can be estimated independently from X-ray maps of the IGM, it would be possible to directly measure the adiabatic index of radio plasma." + This can be done by estimating the slope ofa log(P»/P) versus log(AI/r7) eot for a sample of well observed radio relies and their shock Waves: Llere 5 parametrises the influence of the deviation from. he above assumed ideal geometry., This can be done by estimating the slope of a $\log(P_2/P_1)$ versus $\log(R/r)$ plot for a sample of well observed radio relics and their shock waves: Here $\varepsilon$ parametrises the influence of the deviation from the above assumed ideal geometry. + The values of ¢ should scatter [rom relic to relic. but any systematic correlation of z with the shock strength should beweak.," The values of $\varepsilon$ should scatter from relic to relic, but any systematic correlation of $\varepsilon$ with the shock strength should beweak." + Even though he present radio ancl X-ray. data donot have the required, Even though the present radio and X-ray data donot have the required +the added advantage that uo additional optics would be required. as the control uses feedback from the the imaging camera.,"the added advantage that no additional optics would be required, as the control uses feedback from the the imaging camera." + Furthermore. we cau iterate the positioning of the two masks if necessary. so only a siugle variable is used at a time.," Furthermore, we can iterate the positioning of the two masks if necessary, so only a single variable is used at a time." + We can then outline an observing procedure as follows: center the telescope between the two target stars. aud obtain au estimate of the angular separation between theur aud their angle relative to horizontal ou the image plane.," We can then outline an observing procedure as follows: center the telescope between the two target stars, and obtain an estimate of the angular separation between them, and their angle relative to horizontal on the image plane." + This would be done with the masks cisplaced from the vicinity of the stars: the astrometric measurement creates an initial placement for the two masks in the image plane., This would be done with the masks displaced from the vicinity of the stars; the astrometric measurement creates an initial placement for the two masks in the image plane. + Closec-loop coutrol. as outlined above. may proceed from there.," Closed-loop control, as outlined above, may proceed from there." + A sizable fraction of the overall planet population is expected to reside in binary systenus: vet most current high-contrast. facilities are not suitably equipped to observe such systems witli coronagraphy., A sizable fraction of the overall planet population is expected to reside in binary systems; yet most current high-contrast facilities are not suitably equipped to observe such systems with coronagraphy. + We have presented a conceptual clesign for a APLC-basecl coronagraph which would allow [aliut companions to be seen arouud binary stars., We have presented a conceptual design for a APLC-based coronagraph which would allow faint companions to be seen around binary stars. + This desigu provides comparable throughput to observatious using existing methods with band-lunited coronagrapls. suppresses the cliffractiou spikes introduced. by central obstructions aud spiders. and allows observations without blocking edee-on systems.," This design provides comparable throughput to observations using existing methods with band-limited coronagraphs, suppresses the diffraction spikes introduced by central obstructions and spiders, and allows observations without blocking edge-on systems." + We also outline a control scheme ancl observing procedure which would allow the coronagraph to lock onto the stars., We also outline a control scheme and observing procedure which would allow the coronagraph to lock onto the stars. + La particular. this would be a prime use lor imulti-object adaptive optics systens.," In particular, this would be a prime use for multi-object adaptive optics systems." + As a next step. we will examine mask toleraucing in simulation: a full elosed-loop control system should be designed aud. closed-loop performance uuder noisy coucitious should be simulated.," As a next step, we will examine mask tolerancing in simulation; a full closed-loop control system should be designed and closed-loop performance under noisy conditions should be simulated." + We would also hope to verily the perlormauce experimentally with a small testbed model. aud show the masks can track effectively.," We would also hope to verify the performance experimentally with a small testbed model, and show the masks can track effectively." + The authors would like to thank Sebastian Eguer for graciously providiug situated wavefrout data. Laurent Pueyo for useful ciscussious. aud Rémi Soumauer lor providiug code lor creating apocdizers for APLCs.," The authors would like to thank Sebastian Egner for graciously providing simulated wavefront data, Laurent Pueyo for useful discussions, and Rémmi Soummer for providing code for creating apodizers for APLCs." + ΝΙΛAL acknowledges support [rom NSF Astronomy Astrophysics Postdoctoral Fellowship under award AST-O901967., M.W.M. acknowledges support from NSF Astronomy Astrophysics Postdoctoral Fellowship under award AST-0901967. +ON 2004R. discovered in the last G-orbit stack obtained 2004 Jan. 13.,"SN 2004R, discovered in the last 6-orbit stack obtained 2004 Jan. 13." + It was not detected. to within 5o. in the 12-orbit stack from 2003 Dec. 24 - 30.," It was not detected, to within $\sigma$, in the 12-orbit stack from 2003 Dec. 24 - 30." + A review of the data obtained 2004 Jan. 1 - ll revealed that the SN was rapidly rising in the F850LP and F175W-bauds. but declining in (he F606M -band.," A review of the data obtained 2004 Jan. 1 - 11 revealed that the SN was rapidly rising in the $F850LP$ and $F775W$ -bands, but declining in the $F606W$ -band." + The phot-z for the host galaxy. was again well constrained al 20.8 (0.561.4$. + To summarize. our searching of the UDF. UDEP. and IRUDE resulted in four SNe of largely unknown tvpes. but we can reject the possibility (han any were SNe Ia at z>1.4.," To summarize, our searching of the UDF, UDFP, and IRUDF resulted in four SNe of largely unknown types, but we can reject the possibility than any were SNe Ia at $z>1.4$." + The sample of SNe Ia from the GOODS has shown for the first ime a distinct rise in the SN Ia rate from 0.5<2«1.0 (Dahlenetal.2004)., The sample of SNe Ia from the GOODS has shown for the first time a distinct rise in the SN Ia rate from $0.51., Perhaps the most intriguing result on the supernovae rates from the GOODS sample has been the dearth of SNe Ia discovered at $z >1$. + Dahlenetal.(2004). have found that there is a steep decline in (he rate al 1.2<21.6 in comparison to the rate al 2= 1.0. a result seemingly at odds with the lack of such a decline in the global star formation rate," \citet{Dahlen2003} have found that there is a steep decline in the rate at $1.2< z <1.6$ in comparison to the rate at $z=1.0$ , a result seemingly at odds with the lack of such a decline in the global star formation rate" +To address the question of the origin of the X-ray emission from Coma galaxies. we study their X-ray colors in Fig. 10..,"To address the question of the origin of the X-ray emission from Coma galaxies, we study their X-ray colors in Fig. \ref{f:hr-g}." + The two grids given in the figure allow us to disentangle the role of the diffuse emission from the AGN activity in determining the X-ray luminosity., The two grids given in the figure allow us to disentangle the role of the diffuse emission from the AGN activity in determining the X-ray luminosity. + Optically luminous gas-poor galaxies. whose emission is dominated by integrated flux from point sources (LMXB) are expected to be found within the power-law grid. as this emission 15 characterized by a power law of photon index 1.4 and galactic nH (e.g. Finoguenov Jones 2001).," Optically luminous gas-poor galaxies, whose emission is dominated by integrated flux from point sources (LMXB) are expected to be found within the power-law grid, as this emission is characterized by a power law of photon index 1.4 and galactic nH (e.g. Finoguenov Jones 2001)." + From 10 itis clear that most of the sources have quite soft spectra. indicating a thermal origin from diffuse gas.," From \ref{f:hr-g} it is clear that most of the sources have quite soft spectra, indicating a thermal origin from diffuse gas." + Some of the sources show spectral hardening. possibly due to non-negligible contribution from an unresolved population of LMXB.," Some of the sources show spectral hardening, possibly due to non-negligible contribution from an unresolved population of LMXB." + The Ly-Lg diagram is a fundamental diagnostic. tool for assessing the nature of the X-ray emission from Coma galaxies compared to galaxies detected in other surveys of the local universe with better spatial and spectral resolution., The $_{X}-$ $_{B}$ diagram is a fundamental diagnostic tool for assessing the nature of the X-ray emission from Coma galaxies compared to galaxies detected in other surveys of the local universe with better spatial and spectral resolution. + presents such a diagram., presents such a diagram. + Approximately 14 objects are consistent with all the emission coming from discrete point sources. When corrected for aperture effects.," Approximately 14 objects are consistent with all the emission coming from discrete point sources, when corrected for aperture effects." + This correction takes into account that only a small fraction of the galaxy ts observed in the present survey., This correction takes into account that only a small fraction of the galaxy is observed in the present survey. + Inclusion of a larger fraction would lead to an overestimate of the flux due to the high level of X-ray emission from the Coma ICM. which determines the effective background of our X-ray data.," Inclusion of a larger fraction would lead to an overestimate of the flux due to the high level of X-ray emission from the Coma ICM, which determines the effective background of our X-ray data." + For the remaining two-thirds of the sample. the contribution from discrete point sources is negligible.," For the remaining two-thirds of the sample, the contribution from discrete point sources is negligible." + To isolate possible star-bursting objects. which are known to have their X-ray luminosity significantly enhanced. we separate the sample according the UV-B color.," To isolate possible star-bursting objects, which are known to have their X-ray luminosity significantly enhanced, we separate the sample according the UV-B color." + There ts one detected dwarf star-forming galaxy with an Ly to Ly ratio similar to the local galaxy Holmberg II (see Zezas et al., There is one detected dwarf star-forming galaxy with an $L_X$ to $L_B$ ratio similar to the local galaxy Holmberg II (see Zezas et al. +" 1999),", 1999). +" To determine the Coma galaxy luminosity function. we divide the number of detected galaxies by the Lagrangian volume Massa//p44. Where M is the total gravitational mass of the cluster)5, surveyed as a function of the flux."," To determine the Coma galaxy luminosity function, we divide the number of detected galaxies by the Lagrangian volume $M_{\rm +surveyed}/\Omega_m/\rho_{\rm crit}$, where $M$ is the total gravitational mass of the cluster) surveyed as a function of the flux." + We perform volume estimates for the main cluster and the infalling NGC 4839 subcluster separately applying the NFW= dark-matter profile. p.~7-7 and the corresponding virial (rjoo) radius estimate of 4.0 and 2.6 Mpe (for ACDM. Pierpaoli et al.," We perform volume estimates for the main cluster and the infalling NGC 4839 subcluster separately applying the NFW dark-matter profile, $\rho\sim r^{-2.4}$ and the corresponding virial $r_{100}$ ) radius estimate of 4.0 and 2.6 Mpc (for $\Lambda$ CDM, Pierpaoli et al." + 2001). using the rsoo—T relation of Finoguenov et al. (," 2001), using the $r_{500}-T$ relation of Finoguenov et al. (" +2001).,2001). + The resulting Lagrangian volume ts plotted in the left panel of Fig.12., The resulting Lagrangian volume is plotted in the left panel of \ref{f:glf}. +. As it can be seen from the figure. 1t is Important to account for the substructure. due to inhomogeneous sensitivity of the survey.," As it can be seen from the figure, it is important to account for the substructure, due to inhomogeneous sensitivity of the survey." +" The estimate of the total Lagrangian volume of the main cluster is 4/3κOyjxri,=103060 Mpe*. where à,;;=100/Q,,= 370. so we survey of the virial mass."," The estimate of the total Lagrangian volume of the main cluster is $4 +\pi /3 \times\delta_{vir} \times r_{vir}^3=103060$ $^3$, where $\delta_{vir}=100/\Omega_m=370$ , so we survey of the virial mass." + The mean radius of the survey in the observer's plane is 1.3 Mpe., The mean radius of the survey in the observer's plane is 1.3 Mpc. + A sphere of this radius is characterized by a Lagrangian volume of 52000 Mpce?. of the survey volume.," A sphere of this radius is characterized by a Lagrangian volume of 52000 $^3$, of the survey volume." +" The local luminosity function of X-ray sources by Hasinger (1998). scaled to our assumption of H,=70 km s! Mpel is given in the right panel of Fig.12."," The local luminosity function of X-ray sources by Hasinger (1998), scaled to our assumption of $H_{\rm o}=70$ km $^{-1}$ $^{-1}$ is given in the right panel of \ref{f:glf}." +. The results of the CfA redshift survey (Santiago Strauss 1992) show that the mean density of the typical volume covered by the local luminosity function of Hasinger (1998) is three times the mean density of the Universe., The results of the CfA redshift survey (Santiago Strauss 1992) show that the mean density of the typical volume covered by the local luminosity function of Hasinger (1998) is three times the mean density of the Universe. + To provide a valid comparison. we further scale down the luminosity function of Hasinger (1998) by a factor of 3 since we normalize our Coma galaxy luminosity function to the mean density of the Universe.," To provide a valid comparison, we further scale down the luminosity function of Hasinger (1998) by a factor of 3 since we normalize our Coma galaxy luminosity function to the mean density of the Universe." + We conclude that the X-ray emission of galaxies in. the Coma cluster is quenched on average by a factor of 5.6., We conclude that the X-ray emission of galaxies in the Coma cluster is quenched on average by a factor of 5.6. + We estimate this factor from the difference between the luminosity function in the field and in the Coma cluster., We estimate this factor from the difference between the luminosity function in the field and in the Coma cluster. + It seems natural to attribute this result to reduced star-formation activity in cluster galaxies., It seems natural to attribute this result to reduced star-formation activity in cluster galaxies. + Finoguenov Miniati (2004) show the ellipticals in Coma have X-ray emission typical of the early-type galaxies, Finoguenov Miniati (2004) show the ellipticals in Coma have X-ray emission typical of the early-type galaxies +Taking into account that the incident stellar radiation is unidirectional (in case of a finite-size star the radiation comes from a given stellar pixel). we obtain where for single scattering and r is the optical depth of the layer in the planetary atmosphere from r= Oat the top.,"Taking into account that the incident stellar radiation is unidirectional (in case of a finite-size star the radiation comes from a given stellar pixel), we obtain where for single scattering and $\tau$ is the optical depth of the layer in the planetary atmosphere from $\tau=0$ at the top." + In the same way the scattered radiation ts reduced due to the optical depth on the way out of the atmosphere., In the same way the scattered radiation is reduced due to the optical depth on the way out of the atmosphere. + The Stokes vector of the reflected light is obtained by solving the radiative transfer problem as deseribed above for a given vertical distribution of the temperature and opacity in a planetary atmosphere., The Stokes vector of the reflected light is obtained by solving the radiative transfer problem as described above for a given vertical distribution of the temperature and opacity in a planetary atmosphere. + The radiation flux is then obtained by integrating the Stokes vector over the illuminated planetary surface with a coordinate grid on the planetary surface., The radiation flux is then obtained by integrating the Stokes vector over the illuminated planetary surface with a coordinate grid on the planetary surface. +" Our tests have shown that a grid of 6°x6"" lis sufficient to achieve the necessary accuracy.", Our tests have shown that a grid of $\times$ is sufficient to achieve the necessary accuracy. + Thus the phase function (o) is in this case numerically evaluated., Thus the phase function $\vec{\Phi}(\alpha)$ is in this case numerically evaluated. +" Our model includes the following opacity sources: (1) Rayleigh scattering on H. Hs. He. H?O. CH,4. and Thomson scattering on electrons. with all scattering species contributing to polarization. and (1) continuum absorption due to H. H. H. Hs. He. Πο. Si. Mg. and Fe."," Our model includes the following opacity sources: (i) Rayleigh scattering on H, $_2$, He, $_2$ O, $_4$, and Thomson scattering on electrons, with all scattering species contributing to polarization, and (ii) continuum absorption due to H, $^-$, $_2$$^+$, $_2$$^-$, He, $^-$, Si, Mg, and Fe." + The number densities of the species were calculated with a chemical equilibrium code described in ?.., The number densities of the species were calculated with a chemical equilibrium code described in \cite{berdyuginaetal2003}. + For an example calculation presented in Sect., For an example calculation presented in Sect. + 2? we employed standard model atmospheres by ?.., \ref{subsec:comparison} we employed standard model atmospheres by \citet{allardetal2001}. + For interpreting real data. models of irradiated atmospheres are to be used.," For interpreting real data, models of irradiated atmospheres are to be used." + The difference between the above two cases is in the angular distribution of the intensity of the scattered light: in the first case. 1t is assumed to be according to the Lambert sphere law. while in the second case. it is according to the Rayleigh law.," The difference between the above two cases is in the angular distribution of the intensity of the scattered light: in the first case, it is assumed to be according to the Lambert sphere law, while in the second case, it is according to the Rayleigh law." + Consequently the corresponding phase functions bj(o) and dq(o) are certainly different. and it is important to evaluate the resulting difference in polarization curves.," Consequently the corresponding phase functions $\vec{\Phi}_\mathrm{L}(\alpha)$ and $\vec{\Phi}_\mathrm{R}(\alpha)$ are certainly different, and it is important to evaluate the resulting difference in polarization curves." +" The shapes of the functions b,(a) and O(a) (normalized to their maxima) are shown in Fig. |...", The shapes of the functions $\vec{\Phi}_\mathrm{L}(\alpha)$ and $\vec{\Phi}_\mathrm{R}(\alpha)$ (normalized to their maxima) are shown in Fig. \ref{fig:LR_phasefunc}. +" Their behavior with the orbital phase (which differs from the phase angle «) is as expected: the maximum illuminated area is observed at the exterior conjunction (""full moon"". phase 0.5). while the minimum is at the interior one (""new moon"". phase 0.0)."," Their behavior with the orbital phase (which differs from the phase angle $\alpha$ ) is as expected: the maximum illuminated area is observed at the exterior conjunction (“full moon"", phase 0.5), while the minimum is at the interior one (“new moon"", phase 0.0)." + Some differences between the two functions are seen in their gradients. which are due to the different angular dependencies of Rayleigh scattering and a Lambert sphere.," Some differences between the two functions are seen in their gradients, which are due to the different angular dependencies of Rayleigh scattering and a Lambert sphere." + The Rayleigh phase function also depends on the wavelength. but this effect is significantly smaller.," The Rayleigh phase function also depends on the wavelength, but this effect is significantly smaller." + Note that we normalized the plotted phase functions to one at their maxima to make the comparison of the shapes more apparent., Note that we normalized the plotted phase functions to one at their maxima to make the comparison of the shapes more apparent. + In reality the two curves differ somewhat in scale depending on the detailed properties of the model atmosphere employed in the Rayleigh scattering case. with negligible influence on polarization.," In reality the two curves differ somewhat in scale depending on the detailed properties of the model atmosphere employed in the Rayleigh scattering case, with negligible influence on polarization." + The polarization curves resulting from these phase functions are shown in Fig. 2.., The polarization curves resulting from these phase functions are shown in Fig. \ref{fig:LR_polcurves}. + The overall scale of polarization obviously differs for the two cases., The overall scale of polarization obviously differs for the two cases. + Therefore we have changed the scale of the Rayleigh law results for an easy comparison of the curve shapes., Therefore we have changed the scale of the Rayleigh law results for an easy comparison of the curve shapes. + The shapes of the polarization curves do not differ by a measurable amount for the case considered in this paper. 1.e.. when the reflected light is significantly dimmer than the direct stellar light and the planet remains spatially unresolved.," The shapes of the polarization curves do not differ by a measurable amount for the case considered in this paper, i.e., when the reflected light is significantly dimmer than the direct stellar light and the planet remains spatially unresolved." + This 15 because of the normalization of the Stokes parameters to the total flux from the system., This is because of the normalization of the Stokes parameters to the total flux from the system. + For resolved planets. the differences between the shapes of the polarizatior curves of the Rayleigh and Lambert cases increase but still remain small.," For resolved planets, the differences between the shapes of the polarization curves of the Rayleigh and Lambert cases increase but still remain small." + This renders the Lambert sphere law a good approximation for the intensity of the reflected light. especially when obtaining orbital parameters of planets. which is the primary goal of our case study.," This renders the Lambert sphere law a good approximation for the intensity of the reflected light, especially when obtaining orbital parameters of planets, which is the primary goal of our case study." + To determine the compositior and thermodynamic properties of the planetary atmosphere. a self-consistent polarized radiative transfer calculation as presented in Sect.," To determine the composition and thermodynamic properties of the planetary atmosphere, a self-consistent polarized radiative transfer calculation as presented in Sect." + ?? is required., \ref{subsec:rayleigh} is required. + We will compare the model deseribed above for an extended host star with the simplified case. in which the star is treated as a point source.," We will compare the model described above for an extended host star with the simplified case, in which the star is treated as a point source." + This case is applicable if the semi- axis of the planetary orbit exceeds the radius of the star. so that all light rays from the star can be assumed to arrive parallel on the planet.," This case is applicable if the semi-major axis of the planetary orbit exceeds the radius of the star, so that all light rays from the star can be assumed to arrive parallel on the planet." + Hence the total flux at the observer with the normalization condition in Eq. (3)), Hence the total flux at the observer with the normalization condition in Eq. \ref{eq:normalization}) ) + is given by, is given by +One obvious feature of Figures 2-4 is that the residuals to the model fit greatly exceed the uncertainties in the Doppler shift determinations (as also shown by the large value of AZ above)., One obvious feature of Figures 2-4 is that the residuals to the model fit greatly exceed the uncertainties in the Doppler shift determinations (as also shown by the large value of $\chi^2_{\nu}$ above). + We also notice no obvious trend in the residuals versus time as would be expected for svstematic timing5 effects. such as a constant precessional period time derivative P.," We also notice no obvious trend in the residuals versus time as would be expected for systematic timing effects, such as a constant precessional period time derivative $\dot P$." + Such large.5 apparently random resicuals have been noticed in previous timing5 studies of 89433 (Andersonοἱal.(1983): Margon&Anderson (1989))).," Such large, apparently random residuals have been noticed in previous timing studies of SS433 \citet{Anderson}; \citet{MargonAnderson}) )." + Previous studies have also noticed that the velocity residuals in $5433 show a pattern ol correlation between τι and το (Margon&Anderson1989)., Previous studies have also noticed that the velocity residuals in SS433 show a pattern of correlation between $z_1$ and $z_2$ \citep{MargonAnderson}. +. Specifically. when we plot the residuals of z4(ob5)—z4Gnod) versus za(0bs)—za(mod). we find that most of the points lie in (he second and fourth quadrants (Figure 5).," Specifically, when we plot the residuals of $z_1(obs)-z_1(mod)$ versus $z_2(obs)-z_2(mod)$, we find that most of the points lie in the second and fourth quadrants (Figure 5)." + In other words. when the absolute value of 24 is greater (han expected. the absolute vlaue of το is also greater than expected. and vice versa.," In other words, when the absolute value of $z_1$ is greater than expected, the absolute vlaue of $z_2$ is also greater than expected, and vice versa." + The number of data points with z4 and το residuals in euadrants 2 and 4 is 271+16. while in quacdrants | and 3 (he number is 110c10 a >36 difference.," The number of data points with $z_1$ and $z_2$ residuals in quadrants 2 and 4 is $271 \pm 16$, while in quadrants 1 and 3 the number is $110 \pm 10$ – a $>8 \sigma$ difference." + The linear correlation coellicient between (he residuals is 7=—0.69220.02.," The linear correlation coefficient between the residuals is $r += -0.69 \pm 0.02$." + We estimate the uncertaintv [rom a Monte Carlo simulation as follows., We estimate the uncertainty from a Monte Carlo simulation as follows. + We take the 381 pairs of z4 and το pesiduals and add to each à random number drawn from a Gaussian distribution with mean of zero and a standard deviation of 0.003 the (vpical uncertainty in the Doppler shift measurements., We take the 381 pairs of $z_1$ and $z_2$ residuals and add to each a random number drawn from a Gaussian distribution with mean of zero and a standard deviation of 0.003 – the typical uncertainty in the Doppler shift measurements. + We then calculate the correlation coefficient of the resulting simulated distribuGon., We then calculate the correlation coefficient of the resulting simulated distribution. +" We repeat this procedure 1000 times and then take the standard deviation in the correlation coefficient as the uncertainty above. σ,=40.02."," We repeat this procedure 1000 times and then take the standard deviation in the correlation coefficient as the uncertainty above, $\sigma_r = \pm 0.02$." + This correlation pattern could have several physical sources., This correlation pattern could have several physical sources. + The effect considered most commonlv« in previous studies (e.g. Margon&Anderson (1989))) is that of phase noise in the precessional motion. with striet svmmetry between z4 and το.," The effect considered most commonly in previous studies (e.g. \citet{MargonAnderson}) ) is that of phase noise in the precessional motion, with strict symmetry between $z_1$ and $z_2$." + As the jet precessional phase either lags or leads the model ephemeris. the projected velocity. amplitudes of the jets on the observers line of sight. will either exceed or [all short of the model prediction.," As the jet precessional phase either lags or leads the model ephemeris, the projected velocity amplitudes of the jets on the observers line of sight will either exceed or fall short of the model prediction." + Another possible physical explanation is modulation of the velocity amplitude = 72-noise? in asvstem which otherwise lollows the 5-parameter kinematic model ideally (e.¢. (1982)))., Another possible physical explanation is modulation of the velocity amplitude – $\beta$ -noise” – in a system which otherwise follows the 5-parameter kinematic model ideally (e.g. \citet{Milgrom}) ). +allows us to consider the frequency dependence of the stellar spectrum in a very efficient manner.,allows us to consider the frequency dependence of the stellar spectrum in a very efficient manner. +" In the first Subsect. 2.1,,"," In the first Subsect. \ref{sect:fld}," + we recapitulate the FLD equation for thermal dust emission., we recapitulate the FLD equation for thermal dust emission. + In the following two Subsects., In the following two Subsects. +" and 2.3,, we explain how this FLD solver can simply be combined with a first order ray-tracing routine (either gray or frequency dependent respectively) to include irradiation feedback from a single central object."," \ref{sect:irradiation} and \ref{sect:freqdepirradiation}, we explain how this FLD solver can simply be combined with a first order ray-tracing routine (either gray or frequency dependent respectively) to include irradiation feedback from a single central object." +" Due to the fact that these rays are aligned with the radial coordinate axis in spherical coordinates, this kind of coordinate system is highly favored, but not required, to solve the ray-tracing step."," Due to the fact that these rays are aligned with the radial coordinate axis in spherical coordinates, this kind of coordinate system is highly favored, but not required, to solve the ray-tracing step." +" In the last Subsect. 2.4,,"," In the last Subsect. \ref{sect:gmres}," +" we comment on the so-called generalized minimal residual method (GMRES), our default implicit solver algorithm for the FLD equation."," we comment on the so-called generalized minimal residual method (GMRES), our default implicit solver algorithm for the FLD equation." + The thermal dust emission is solved in the FLD approximation based on a diffusion equation for the thermal radiation energy Εκ., The thermal dust emission is solved in the FLD approximation based on a diffusion equation for the thermal radiation energy $E_\mathrm{R}$ . +" Within a given spatial density p(X) and temperature T(X) distribution, we start from the time evolution of the internal energy density Επι and thermal radiation energy density Eg: with the corresponding thermal pressureP, dynamical velocity 4, and flux of radiation energy density F."," Within a given spatial density $\rho(\vec{x})$ and temperature $T(\vec{x})$ distribution, we start from the time evolution of the internal energy density $E_\mathrm{int}$ and thermal radiation energy density $E_\mathrm{R}$: with the corresponding thermal pressure$P$, dynamical velocity $\vec{u}$, and flux of radiation energy density $\vec{F}$." +" The radiative heating and cooling of the gas is covered in A=pοKR(aT- Ex). where c is the speed of light, kg the Rosseland mean opacity, and a the radiation constant."," The radiative heating and cooling of the gas is covered in $\Lambda = \rho ~ c ~ \kappa_\mathrm{R} ~ \left(a ~ T^4 - E_\mathrm{R} \right)$ , where $c$ is the speed of light, $\kappa_\mathrm{R}$ the Rosseland mean opacity, and $a$ the radiation constant." + Gas and dust temperatures are assumed to be the same (Tas=TauΤ)., Gas and dust temperatures are assumed to be the same $\left(T_\mathrm{gas} = T_\mathrm{dust} = T\right)$. + We add up the Eqs., We add up the Eqs. +" and and solve the transport term V(Egii) separately, if necessary, in the dynamical problem."," and and solve the transport term $\vec{\nabla} \left(E_\mathrm{R} ~ \vec{u} \right)$ separately, if necessary, in the dynamical problem." +" If we consider the transport of the internal energy V.(Eini) already during the corresponding hydrodynamics step (operator splitting), the remaining terms yield where the source term Q*=—PVat... depends on the physics included and can additionally contain additional source terms such as accretion luminosity from sink cells or viscous heating."," If we consider the transport of the internal energy $\vec{\nabla} \cdot \left(E_\mathrm{int} ~ \vec{u} \right)$ already during the corresponding hydrodynamics step (operator splitting), the remaining terms yield where the source term $Q^+ = - P ~ \vec{\nabla} \cdot \vec{u} + \ldots$ depends on the physics included and can additionally contain additional source terms such as accretion luminosity from sink cells or viscous heating." +" In the following, we use the assumption that the gas and radiation temperature are in equilibrium (also called one-temperature radiation transport), which is e.g. a widely used approach in radiation hydrodynamics simulations of circumstellar disks."," In the following, we use the assumption that the gas and radiation temperature are in equilibrium (also called one-temperature radiation transport), which is e.g. a widely used approach in radiation hydrodynamics simulations of circumstellar disks." +" In a purely FLD radiation transport method, this assumption is justified for optically thick regions (e.g. deeply inside an accretion disk)."," In a purely FLD radiation transport method, this assumption is justified for optically thick regions (e.g. deeply inside an accretion disk)." + The usage of our split radiation scheme guarantees also the correct gas temperature in regions of dominating stellar irradiation (like an optically thin envelope or disk atmosphere)., The usage of our split radiation scheme guarantees also the correct gas temperature in regions of dominating stellar irradiation (like an optically thin envelope or disk atmosphere). +" In residual regions, shielded from the irradiation behind the optically thick circumstellar disk, the gas and radiation temperature will be the same in systems where the flow time is long compared to the gas-radiation equilibrium time only."," In residual regions, shielded from the irradiation behind the optically thick circumstellar disk, the gas and radiation temperature will be the same in systems where the flow time is long compared to the gas-radiation equilibrium time only." +" The flow time is {μοι5l/u, where / and u are the characteristic length and velocity scales of the problem."," The flow time is $t_\mathrm{flow} \approx l / u$, where $l$ and $u$ are the characteristic length and velocity scales of the problem." +" The gas-energy equilibrium time is of the order of {αι3(kpc)!, since the energy exchange rate is Er&xpcEg."," The gas-energy equilibrium time is of the order of $t_\mathrm{eq} \approx (\kappa ~ \rho ~ c)^{-1}$, since the energy exchange rate is $\dot{E}_\mathrm{R} \approx \kappa ~ \rho ~ c ~ E_\mathrm{R}$." +" Thus, the requirement that tow>>{οι reduces to the requirement that τ>>u/c, where tT~«plis the optical depth of the system."," Thus, the requirement that $t_\mathrm{flow} \gg t_\mathrm{eq}$ reduces to the requirement that $\tau \gg u / c$, where $\tau \approx \kappa ~ \rho ~ l$ is the optical depth of the system." + This is the regime that ? identifies as static diffusion., This is the regime that \citet{Mihalas:1984p9889} identifies as static diffusion. +" Thus, the scheme is viable in the static diffusion limit."," Thus, the scheme is viable in the static diffusion limit." + This is consistent with our test results for the radiative shock problem presented in Sect. 5.., This is consistent with our test results for the radiative shock problem presented in Sect. \ref{sect:radiativeshock}. +" In this special case of a strong shock in a shielded, optically thin region, the one-temperature approach yields the correct temperature of the shocked gas, but results in a steeper temperature gradient than a two-temperature radiation transport method in the upstream direction of the radiation flux."," In this special case of a strong shock in a shielded, optically thin region, the one-temperature approach yields the correct temperature of the shocked gas, but results in a steeper temperature gradient than a two-temperature radiation transport method in the upstream direction of the radiation flux." +" Consideration of such small effects at outer regions of the domain goes beyond the scope of this research project, which focuses on the details of stellar radiative feedback on the accretion flow onto a massive star."," Consideration of such small effects at outer regions of the domain goes beyond the scope of this research project, which focuses on the details of stellar radiative feedback on the accretion flow onto a massive star." +" Additionally, ? show that massive star formation is generally in the static diffusion limit."," Additionally, \citet{Krumholz:2007p855} + show that massive star formation is generally in the static diffusion limit." +" In the end, we will benefit from the speedup of the radiation transport solver by cutting the numbers of unknown variables in half."," In the end, we will benefit from the speedup of the radiation transport solver by cutting the numbers of unknown variables in half." +" Moreover, the stiffness of the set of equations is much less if the above local equilibrium assumption is made."," Moreover, the stiffness of the set of equations is much less if the above local equilibrium assumption is made." + Expressing both energies on the left hand side of Eq., Expressing both energies on the left hand side of Eq. + in terms of temperature allows us to derive a relation between the time derivatives of the energies., in terms of temperature allows us to derive a relation between the time derivatives of the energies. + The radiation energy density in absence of irradiation (see following Subsect., The radiation energy density in absence of irradiation (see following Subsect. +" 2.2 for the case including irradiation) is given by This expression plus the internal energy density ρΤ with the specific heat capacity cy yield With this relation, the Eq."," \ref{sect:irradiation} for the case including irradiation) is given by This expression plus the internal energy density $E_\mathrm{int} = c_\mathrm{V} ~ \rho ~ T$ with the specific heat capacity $c_\mathrm{V}$ yield With this relation, the Eq." +" reduces to a standard diffusion equation with {ο=(ονpl(4aT3)+1)-1, depending only on the ratio of internal to radiation energy."," reduces to a standard diffusion equation with $f_\mathrm{c} = \left(c_\mathrm{V} ~ \rho / \left(4 ~ a ~ T^3 \right) + 1\right)^{-1}$, depending only on the ratio of internal to radiation energy." + The flux F of radiation energy density is determined in the FLD approximation via with the diffusion constant D=Ac/(xgp)., The flux $\vec{F}$ of radiation energy density is determined in the FLD approximation via with the diffusion constant $D = \lambda ~ c / \left(\kappa_\mathrm{R} ~ \rho \right)$. + The flux limiter Ais chosen according to ?.., The flux limiter $\lambda$is chosen according to \citet{Levermore:1981p57}. . + Scattering is neglected., Scattering is neglected. + In the most extreme limits the flux becomes either F=—cERVER/IVEg| for highly optically thin regions (free-streaming limit) or F- for highly optically thick regions (diffusion limit)., In the most extreme limits the flux becomes either $\vec{F} = - c ~ E_\mathrm{R} ~ \vec{\nabla} E_\mathrm{R} / |\vec{\nabla} E_\mathrm{R}|$ for highly optically thin regions (free-streaming limit) or $\vec{F} = - c ~ \vec{\nabla} E_\mathrm{R} / \left(3 ~ \kappa_\mathrm{R} ~ \rho \right)$ for highly optically thick regions (diffusion limit). +" Summing up, we can describe the thermal/diffuse radiative processes via:"," Summing up, we can describe the thermal/diffuse radiative processes via:" +While (he accretion belt model has improved (he fits in VW IIvi in many observations (Sionetal.2001).. its existence has not vet been established.,"While the accretion belt model has improved the fits in VW Hyi in many observations \citep{sio01}, its existence has not yet been established." + AC some point. it was suggested [see e.g. (IInangetal. 19962)]] that the second hot component might actually be a hot ring near (he inner edee of the disk.," At some point, it was suggested [see e.g. \citep{hua96a}] ] that the second hot component might actually be a hot ring near the inner edge of the disk." + IIuangetal.(19968). identified the hot ring component as (he “hot state suggested in the accretion disk limit evele model (Cannizzo1993)., \citet{hua96a} identified the hot ring component as the “hot state” suggested in the accretion disk limit cycle model \citep{can93}. +. In that theory. the outburst is triggered near the inner edge of the disk. and a heating [rout propagates to the outer edge. transforming the entire disk to the hot state.," In that theory, the outburst is triggered near the inner edge of the disk, and a heating front propagates to the outer edge, transforming the entire disk to the hot state." + The quiescent state is achieved when a cooling front. propagates back to smaller radii ancl shuts off the flow onto the WD., The quiescent state is achieved when a cooling front propagates back to smaller radii and shuts off the flow onto the WD. + In that particular case. one expects the characteristics of the second component (observed in quiescence) to change rapidly in time. as the [ront moves inwarcl through the disk.," In that particular case, one expects the characteristics of the second component (observed in quiescence) to change rapidly in time, as the front moves inward through the disk." + Recent observations (Sionetal.2001).. however. show that the second component in IIST/STIS spectra of VW IIvi. taken 5 days apart. remains pretty much the sane. making the scenario of the ring unlikely.," Recent observations \citep{sio01}, however, show that the second component in HST/STIS spectra of VW Hyi, taken 5 days apart, remains pretty much the same, making the scenario of the ring unlikely." + While accretion belts were first discussed theoretically by (Ixippenhahn&ThomasKutter&Sparks1987. 1989).. the first observational detectionwas for U Gem's WD during quiescence (Longetal.1993) based onHUT observations followed VW Ilis WD by Sionοἱal.(1996) using HST and Gansicke&Beuermann(1996) using IUE archival spectra.," While accretion belts were first discussed theoretically by \citep{kip78,kut87,kut89}, the first observational detectionwas for U Gem's WD during quiescence \citep{lon93} based on observations followed VW Hyi's WD by \citet{sio96} using HST and \citet{gan96} + using IUE archival spectra." + The physical basis for an accretion belt is the tangential accretion of disk matter al (he stellar equator wilh spin-up of the surface lavers of the WD as it shears into the WD envelope with the slow conversion of kinetic energv to heal as a result of viscous heating in the dilferentially rotating atmosphere., The physical basis for an accretion belt is the tangential accretion of disk matter at the stellar equator with spin-up of the surface layers of the WD as it shears into the WD envelope with the slow conversion of kinetic energy to heat as a result of viscous heating in the differentially rotating atmosphere. + We have confirmed that the modeling of theFUSE spectrum of VW Ενα in quiescence requires al least (wo components. as had been suggested bv the earlier LST and. WoT observations.," We have confirmed that the modeling of the spectrum of VW Hyi in quiescence requires at least two components, as had been suggested by the earlier HST and HUT observations." + The main component in the modeling is identified as the photosphere of a WD with a temperature of about 23. 000. The second component is a continuum relatively featureless wilh an effective temperature zz48. 00019. This discussion mainiv serves to emphasize how far we are from an understanding of VW Ilvi without a knowledge of the location of the emitting regions within the system.," The main component in the modeling is identified as the photosphere of a WD with a temperature of about $23,000$ K. The second component is a continuum relatively featureless with an effective temperature $\approx 48,000$ K. This discussion mainly serves to emphasize how far we are from an understanding of VW Hyi without a knowledge of the location of the emitting regions within the system." + There could be a continuous range of temperatures. along wilh ranges in emitting areas and velocities. (hal contribute to the observed FUV spectrum.," There could be a continuous range of temperatures, along with ranges in emitting areas and velocities, that contribute to the observed FUV spectrum." + The only firi result that has been obtained here is that the second modeling component is [ανν flat. aud one possibility {ο produce such a flat component is wilh a high rotational velocity aud a high temperature.," The only firm result that has been obtained here is that the second modeling component is fairly flat, and one possibility to produce such a flat component is with a high rotational velocity and a high temperature." + This work was supported by a Cycle 2 NASA FUSE grant to Villanova University., This work was supported by a Cycle 2 NASA grant to Villanova University. +signature of Polvevelic Aromatic Lvclrocarbons (PALI).,signature of Polycyclic Aromatic Hydrocarbons (PAH). + While global properties of galaxy populations at mic-LR remain vet uncertain. recent850 data certainly has shown that PALL features are an important factor which cannot be ignored MMattila. Lehtinen Lemke 1999. Genzel Cesarsky 2000).," While global properties of galaxy populations at mid-IR remain yet uncertain, recent data certainly has shown that PAH features are an important factor which cannot be ignored Mattila, Lehtinen Lemke 1999, Genzel Cesarsky 2000)." + This is particularly true for any dusty and infrared. bright objects. which might well dominate counts at micl-LR.," This is particularly true for any dusty and infrared bright objects, which might well dominate counts at mid-IR." + Alodclling of the relevant dust and. re-radiation processes is complicated (see GCuidercdont 1998. Silva 1998. Nu 1998): therefore. to »e às observationallv based. as possible. our chosen recipe or predicting counts for the longer LRAC bands. is to take he newly available πο extragalactic counts at 6.7 pum and shift these to the neighbouring HAC bands.," Modelling of the relevant dust and re-radiation processes is complicated (see Guiderdoni 1998, Silva 1998, Xu 1998); therefore, to be as observationally based as possible, our chosen recipe for predicting counts for the longer IRAC bands, is to take the newly available mid-IR extragalactic counts at 6.7 $\umu$ m and shift these to the neighbouring IRAC bands." +" We thus fitted an experimental source count slope o the 6.7 qun extragalactic counts found by various ISOCANM, surveys: ELAIS (Serjeant 2000). ISO-LLDE woject (Oliver 1997). a survey at. the Lockman llole Claniguchi 1997). and the CERS (Flores ct 11999)."," We thus fitted an experimental source count slope to the 6.7 $\umu$ m extragalactic counts found by various ISOCAM surveys: ELAIS (Serjeant 2000), ISO-HDF project (Oliver 1997), a survey at the Lockman Hole (Taniguchi 1997), and the CFRS (Flores et 1999)." +" ""Phe faint slope bevond the deepest observations is adjusted to twpical shape of existing (evolutionary) models (Franceschini et 11997. Pearson Rowan-Robinson 1996. Roche Eales 1999)."," The faint slope beyond the deepest observations is adjusted to typical shape of existing (evolutionary) models (Franceschini et 1997, Pearson Rowan-Robinson 1996, Roche Eales 1999)." + Preliminary Z50-counts [rom the LIDP-S field are also in excellent. agreement: with this experimental source count model (Oliver et. al., Preliminary -counts from the HDF-S field are also in excellent agreement with this experimental source count model (Oliver et al. + 2001. in preparation).," 2001, in preparation)." + Though various independent counts are in very &ood agreement. it should. be noted that there still are uncertainties in the calibration of the ISOCAM clata (see SSerjeant ct 22000. Aussel et 11999).," Though various independent counts are in very good agreement, it should be noted that there still are uncertainties in the calibration of the ISOCAM data (see Serjeant et 2000, Aussel et 1999)." + Note also that the ELALS counts are not corrected for a possible I5ddington/Malmequist type bias due to à non-Gaussian I[Lux-error distribution (see Figure iin Serjeant et 22000)., Note also that the ELAIS counts are not corrected for a possible Eddington/Malmquist type bias due to a non-Gaussian flux-error distribution (see Figure in Serjeant et 2000). + Fig., Fig. + 2 shows the recent mid-It. counts with our [itte model overplotted as the thick solid curve and the equivalen of the 3.6 tum baseline model as the lower thin solid line., \ref{model67_counts} shows the recent mid-IR counts with our fitted model overplotted as the thick solid curve and the equivalent of the 3.6 $\umu$ m baseline model as the lower thin solid line. + We hen translated both the 6.7 pum counts and the fitted moce o the & qun band (Fig. 3))., We then translated both the 6.7 $\umu$ m counts and the fitted model to the 8 $\umu$ m band (Fig. \ref{model8_counts}) ). + Naturally the translation to the δ qun band is mode dependent. but since the shift is not large (the ISOCAA iler partially overlaps the LRAC δ qun. filter) the uncertainty is low. even given the uncertain mid-lIt spectra eatures.," Naturally the translation to the 8 $\umu$ m band is model dependent, but since the shift is not large (the ISOCAM filter partially overlaps the IRAC 8 $\umu$ m filter), the uncertainty is low, even given the uncertain mid-IR spectral features." + We used the baseline model in the transformation., We used the baseline model in the transformation. + We computed numerous model counts at 6.7 and S qun. with dillerent. LEs. galaxy. mixes. cosmologies. SEDs (with anc without ΟΛΗ features). and found that all these changes in the transformation of counts are well within the error bars of the observed. counts.," We computed numerous model counts at 6.7 and 8 $\umu$ m, with different LFs, galaxy mixes, cosmologies, SEDs (with and without PAH features), and found that all these changes in the transformation of counts are well within the error bars of the observed counts." +oessure forces (?7)..,pressure forces \citep{Jar-Abr-Pac:1980:ACTAS:}. + We here determine the radial and vertical components of the gravitational force. produced by the perturbing sources in a purely Newtonian way., We here determine the radial and vertical components of the gravitational force produced by the perturbing sources in a purely Newtonian way. +" This ji an approxination, but we do not expect that a relativistic analysis would greatly change the qualitative features of our results."," This is an approximation, but we do not expect that a relativistic analysis would greatly change the qualitative features of our results." +" For simplicity the force will be determined in the equatorial plane, ie., in the symmetry dane of the dise: this is completely correct for thin, Keplerian dises, and gives good estimates for slim discs."," For simplicity the force will be determined in the equatorial plane, i.e., in the symmetry plane of the disc; this is completely correct for thin, Keplerian discs, and gives good estimates for slim discs." +" We deterinine the time evolution of the perturbing 'oree. comiponents for a fixed point on the dise with coordinates (RG=2/2. Oat), making the restriction BamORR.R,,."," For the binary companion, we assume $d\gg R,R_{\sssm{B}}$." +" IIeye, aud in the following, we consider the force acting on a colmoving unit mass clement of the accretion dise at a given radius R."," Here, and in the following, we consider the force acting on a comoving unit mass element of the accretion disc at a given radius $R$ ." +" Using the quantities .«=δνΠ and wy=|Q,Oa], the vertical component of the perturbing gravitational force is given by while the radial cox1ponent is given by The vertical force oscillates around its iin value with zuuplitude and the radial force oscillates with amplitude These oscillations have au anharmonic character which means that, when Fourier analysed, they show both the basic frequency wy and also some additional frequencies related to it."," Using the quantities $x\equiv R_{\sssm{A}}/R$ and $\omega_{\sssm{A}} \equiv|\Omega_{\sssm{A}} - +\Omega_{\mathrm{d}}|$, the vertical component of the perturbing gravitational force is given by while the radial component is given by The vertical force oscillates around its mean value with amplitude and the radial force oscillates with amplitude These oscillations have an anharmonic character which means that, when Fourier analysed, they show both the basic frequency $\omega_{\sssm{A}}$ and also some additional frequencies related to it." +" The binary companion is taken to be orbiting the neutron star at a constant distance d, with angular velocity O,."," The binary companion is taken to be orbiting the neutron star at a constant distance $d$, with angular velocity $\Omega_{\sssm{B}}$." +" The vertical aud radial components of the perturbing force acting on the accreting material are then given by where the relative angular velocity wj=οι,οzmQq."," The vertical and radial components of the perturbing force acting on the accreting material are then given by where the relative angular velocity $\omega_{\sssm{B}} = +\left|\Omega_{\sssm{B}}-\Omega_{\mathrm{d}}\right| \approx\Omega_{\mathrm{d}}$ ." +" In general, these relations represent auharmonically oscillating forces but we are taking R/d«1 and they then reduce to zn approximate form: which is harmonic with frequency uyzO4."," In general, these relations represent anharmonically oscillating forces but we are taking $R/d\ll 1$ and they then reduce to an approximate form which is harmonic with frequency $\omega_{\sssm{B}} \approx\Omega_{\mathrm{d}}$." + The vertical force oscillates around its 1uean value with amplitude and the radial force oscillates with amplitude In this section we give estimates for the magnitudes of neutron-star asynmunetries arising in different wavs., The vertical force oscillates around its mean value with amplitude and the radial force oscillates with amplitude In this section we give estimates for the magnitudes of neutron-star asymmetries arising in different ways. +" We fist consider classical crystalline imowntains and magnetically-confined accretion columns: both of these are found to be inadequate for the present purposes, however."," We first consider classical crystalline mountains and magnetically-confined accretion columns; both of these are found to be inadequate for the present purposes, however." + We then turn to some different observationallyanotivated possibilities which seem to be more promising., We then turn to some different observationally-motivated possibilities which seem to be more promising. +" Assuniug that the basic nature of a mountain on the surface of a neutron star is the same as for mountains on plauets, the pressure at the base of the mountain needs to be less than the maxima shear stress of the surface material."," Assuming that the basic nature of a mountain on the surface of a neutron star is the same as for mountains on planets, the pressure at the base of the mountain needs to be less than the maximum shear stress of the surface material." +" This pressure is given by Phu=Gus!Poutant: Where Pur is the average density of the material in the mountain, qu, is the surface gravity of the neutron star and μμ is the height of the mountain."," This pressure is given by $P_{\mathrm{mnt}} = +\rho_{\mathrm{mnt}}g_{\mathrm{ns}}h_{\mathrm{mnt}}$, where $\rho_{\mathrm{mnt}}$ is the average density of the material in the mountain, $g_{\mathrm{ns}}$ is the surface gravity of the neutron star and $h_{\mathrm{mnt}}$ is the height of the mountain." + The base of the mountain would be located at the outermost solid surface layer of the neutron star., The base of the mountain would be located at the outermost solid surface layer of the neutron star. + The relevant density to take for this layer is rather uncertain: we willtake it as being ~ and put pur equal to that.," The relevant density to take for this layer is rather uncertain; we willtake it as being $\sim\! 10^6\,\mathrm{g\,cm^{-3}}$ and put $\rho_{\mathrm{mnt}}$ equal to that." + The surface gravity, The surface gravity +day whether the sky position was above the horizon aud whether the time did uot fall in au exclusion window set up to avoid interference or bad data (Schinicdt1999).,day whether the sky position was above the horizon and whether the time did not fall in an exclusion window set up to avoid interference or bad data \citep{sch99}. +. If so. we converted the limitiug couut of 2 times the square root of the observed background iu the second. brightest. illunuinatec detector into a limiting Dux {η," If so, we converted the limiting count of 5 times the square root of the observed background in the second brightest illuminated detector into a limiting flux $P_{lim}$." +" The resulting distribution G(2,,) has a median at 0.37 ph 7 Ll and 10 aud 90 percentiles at 0.29 ph ? ! and 0.51 ph 7s i|, respectively. in the 50—300 keV bail."," The resulting distribution $G(P_{lim})$ has a median at 0.37 ph $^{-2}$ $^{-1}$, and 10 and 90 percentiles at 0.29 ph $^{-2}$ $^{-1}$ and 0.51 ph $^{-2}$ $^{-1}$, respectively, in the $50-300$ keV band." +" Siuce the number of redshliifts of GRBs is as yet too small for a statistical derivatiou of the luminosity [uuction. we will instead a full luminosity Duuctioi aud then use the observed number of GRBs aud their euclidean «V/Vj,4,2 in the BD2 sample to derive properties such as the local space density and the characteristic luminosity L*."," Since the number of redshifts of GRBs is as yet too small for a statistical derivation of the luminosity function, we will instead a full luminosity function and then use the observed number of GRBs and their euclidean $$ in the BD2 sample to derive properties such as the local space density and the characteristic luminosity $L^*$." + We will Bud that these properties vary relatively little as we chauge the shape of the luminosity [üuction., We will find that these properties vary relatively little as we change the shape of the luminosity function. + Experience has shown that the differential luminosity function of mauy types of extragalactic objects can be represented as a broken power law (cL, Experience has shown that the differential luminosity function of many types of extragalactic objects can be represented as a broken power law (cf. + e.g. Hasinger(1905) for X-ray active ealactic nuclei)., e.g. \citet{has98} for X-ray active galactic nuclei). + We will use a broken power law. and in addition iutroduce upper aud lower limits of Iuminosity. thus allowing both narrow (standard candle) aud more realistic broad. Iuminosity [uuctions.," We will use a broken power law, and in addition introduce upper and lower limits of luminosity, thus allowing both narrow (standard candle) and more realistic broad luminosity functions." + We will also assume cleusityevolutiou. to be introduced below.," We will also assume densityevolution, to be introduced below." + The local luminosity function of peak CRB luminosities £. defiued as the co-moving space density of GRBs iu the interval logL to logL+dlogL. is Given that most types of extragalactic objects show evolution. and consideriug that the rate ol star formation may be relevant for GRBs (Macau.Pozetti.audDickinson1993).. we introduce density evolution p(z).," The local luminosity function of peak GRB luminosities $L$, defined as the co-moving space density of GRBs in the interval $\log L$ to $\log L + d\log L$, is Given that most types of extragalactic objects show evolution, and considering that the rate of star formation may be relevant for GRBs \citep{mad98}, we introduce density evolution $\rho(z)$ ." + In most cases. we have assumed," In most cases, we have assumed" +The very red colours of V2672 Oph suggest a high reddening.,The very red colours of V2672 Oph suggest a high reddening. + This is confirmed by the intensity of the Nal Dj. D» interstellar lines and of the 5780. 5797. 5850. 6270 and 6614 cdeilfuse interstellar bands. (D1IBs) recorded. in our spectra (see later).," This is confirmed by the intensity of the NaI $_1$ , $_2$ interstellar lines and of the 5780, 5797, 5850, 6270 and 6614 diffuse interstellar bands (DIBs) recorded in our spectra (see later)." + The Nal D. D» interstellar lines cannot be used because their very large equivalent width indicates they are largely Oover-saturatec (cfMunar&Zwitter1997).," The NaI $_1$, $_2$ interstellar lines cannot be used because their very large equivalent width indicates they are largely over-saturated \citep[cf.][]{MZ97}." +. They must be the result. of the blend of several individual components. as it is reasonable to expect given the line-of-sight passing ‘lose to the Galactic centre.," They must be the result of the blend of several individual components, as it is reasonable to expect given the line-of-sight passing close to the Galactic centre." + Our spectra lack high enough resolution to resolve the individual components and thus to heck if they are individually saturated or not., Our spectra lack high enough resolution to resolve the individual components and thus to check if they are individually saturated or not. +" The best measurable DIB for V2672 Ophis the one at 6614 (identifiedin Figure 8S)). a"" ", The best measurable DIB for V2672 Oph is the one at 6614 (identified in Figure \ref{fig:early}) ). +It appears superimposed against 16 very broad and Ilo profile. which provides a good contrast. background.," It appears superimposed against the very broad and strong $\alpha$ profile, which provides a good contrast background." + The other DIBs are instead. recorded onto a weak. and therefore more noisy continuum. which makes the measurement of their equivalent: widths rather uncertain.," The other DIBs are instead recorded onto a weak, and therefore more noisy continuum, which makes the measurement of their equivalent widths rather uncertain." + The equivalent width of the 6614 DDIB on the day |1.31 spectrum. is 0.30. 0.02., The equivalent width of the 6614 DIB on the day +1.31 spectrum is 0.30 $\pm$ 0.02. +Α.. ὃν comparison with the relation fp5.3 CX) calibrated by Munari(2010) between reddening ancl the equivalent width of the 6614 DDID. a reddening Jg v1.6 can be derived. for V2672 Oph.," By comparison with the relation $E_{B-V}$ $\times$ ) calibrated by \citet{M10} between reddening and the equivalent width of the 6614 DIB, a reddening $E_{B-V}$$\sim$ 1.6 can be derived for V2672 Oph." +" vandenDergh&uet(1987) derived a mean intrinsic colour (DeV =|(0.2:3 for novae at maximum. and (D 0.02) au+£0.04 ""ifor novae at fo."," \citet{BY87} derived a mean intrinsic colour $(B-V)_\circ$ =+0.23 $\pm$ 0.06 for novae at maximum, and $(B-V)_\circ$ $-$ 0.02 $\pm$ 0.04 for novae at $t_2$." + V2672 Oph cdisplaved L = ab do. to which would. correspond. fp v1.9.," V2672 Oph displayed $B-V$ =+1.77 at $t_2$, to which would correspond $E_{B-V}$$\sim$ 1.79." + The Mat £2V. evolution in Figure 1. suggests that a similar 2 Y=)1.77 could hold for V2672 Oph also at maximum brightness. with a corresponding Leev 71.54.," The flat $B$$-$$V$ evolution in Figure 1, suggests that a similar $B-V$ =+1.77 could hold for V2672 Oph also at maximum brightness, with a corresponding $E_{B-V}$$\sim$ 1.54." + The photometric ancl spectroscopic estimates of the redcdening are in [air agreement. and their average value is adopted in this paper as the recdeening allecting V2672 Oph.," The photometric and spectroscopic estimates of the reddening are in fair agreement, and their average value is adopted in this paper as the reddening affecting V2672 Oph." +" Alost relations between absolute magnitude and the rate of declinetake the form Aus=ἂνlog/,|2,4."," Most relations between absolute magnitude and the rate of declinetake the form $M_{\rm max}\,=\,\alpha_n\,\log\, t_n \, + \, \beta_n$." + The most recent calibration of this relation has been provided Downes&Duerbeck(2000)., The most recent calibration of this relation has been provided by \citet{DD00}. +. heir relation for ο}) glves M)2 10.0 for V2672 Oph. and AJ(1)— 10.41 or {αλ," Their relation for $t_2(V)$ gives $M(V)$ $-$ 10.40 for V2672 Oph, and $M(V)$ $-$ 10.41 for $t_3(V)$." + uAdopting the above fe y=1.6 reddening and a “tonal Ry =3.1 extinction law. the distance to V2672 Oph would be 21 kpc.," Adopting the above $E_{B-V}$ =1.6 reddening and a standard $R_V$ =3.1 extinction law, the distance to V2672 Oph would be 21 kpc." + The remains reasonably arge. even if we adopt the ΑΛΑbe )-f2 nudire calibrated by Cohen(LOSS) that gives. 16 or the iron AZ(V)-/4 relation »v Schmidt(1957) hat provides 17 kpc.," The distance remains reasonably large, even if we adopt the $M(V)$ $t_2$ relation calibrated by \citet{C88} that gives 16 kpc, or the $M(V)$ $t_3$ relation by \citet{S57} that provides 17 kpc." + Assigning a higher weight to the more recent calibration by Downes&Duer-»eck (2000).. we take the average of these determinations as the distance to V2672 Oph.," Assigning a higher weight to the more recent calibration by \citet{DD00}, we take the average of these determinations as the distance to V2672 Oph." + Xt. Galactic coordinates f=001.021 and b= |02.535. the linc-of-5sight to V2672 Oph xwsses close to the Galactic centre. crosses the whole Bulge and ends at a galacto-centric distance larger than that of the Sun.," At Galactic coordinates $l$ =001.021 and $b$ =+02.535, the line-of-sight to V2672 Oph passes close to the Galactic centre, crosses the whole Bulge and ends at a galacto-centric distance larger than that of the Sun." + This is probably a record distance and position among known novae., This is probably a record distance and position among known novae. + The linc-of-sight to V2672 Oph does not cross any of the known Galactic low-extinetion windows through he Bulee listed by Dutra.Santiago.&Biea(2002).. as also confirmed by inspection of SDSS images showing a scarcely »opulated stellar field.," The line-of-sight to V2672 Oph does not cross any of the known Galactic low-extinction windows through the Bulge listed by \citet{DSB02}, as also confirmed by inspection of SDSS images showing a scarcely populated stellar field." + Another peculiaritv of V2672 Oph and its position is he 20.8 kpe height above the galactic plane., Another peculiarity of V2672 Oph and its position is the $z$ =0.8 kpc height above the galactic plane. + dellaValle&Livio(1998) found that He/N novae. such as V2672 Oph (sce Section +). belong to the disk population of the Galaxy and are Joe at small heights above the Galactic plane.," \citet{VL98} found that He/N novae, such as V2672 Oph (see Section 4), belong to the disk population of the Galaxy and are located at small heights above the Galactic plane." + While aboveV2672 Oph is undoubtedly away from the Bulge. its wight the Galactic plane is dillieult to reconcile with he zx: 100-200 pe found by della.Valle&Livio(1998). for Ile/N novae.," While V2672 Oph is undoubtedly away from the Bulge, its height above the Galactic plane is difficult to reconcile with the $z$$\leq$ 100-200 pc found by \citet{VL98} for He/N novae." +" The proportion of He/N novae characterised by ugh z is becoming uncomfortably large in comparison with he dellaValle&Livio(1998) scale height other recent üsgh-z examples being V2491 Cve (= Nova (νο 2008 ""N.2 ab 21.1 kpe (Munarietal.2010).. and V477 Set (= Set 2005 N2). located at 220.6 kpe (Alunarietal.2006)."," The proportion of He/N novae characterised by high $z$ is becoming uncomfortably large in comparison with the \citet{VL98} scale height $-$ other recent $z$ examples being V2491 Cyg (= Nova Cyg 2008 N.2) at $z$ =1.1 kpc \citep{MSD10}, and V477 Sct (= Nova Sct 2005 N2), located at $z$ =0.6 kpc \citep{MSN06}." +. The light-curves of V2672 Oph and U Sco (its 2010 outburst) are compared in Figure 2., The light-curves of V2672 Oph and U Sco (its 2010 outburst) are compared in Figure 2. + The match is remarkable. with the exception of the infection displaved by V2672 Oph around day [5.8 and. described in sect.," The match is remarkable, with the exception of the inflection displayed by V2672 Oph around day +5.8 and described in sect." + 3.1 above. which has no counterpart in U Sco.," 3.1 above, which has no counterpart in U Sco." + The strict similarity extends also to later phases. when U Sco displaved a plateau phase.," The strict similarity extends also to later phases, when U Sco displayed a plateau phase." + Hachisuetal.(2000.2002) and Hachisu.Ixato.&Schaefer(2003). have postulated that a plateau is characteristic of recurrent novae. and in particular of the U Sco subclass of recurrent novae. a position shared. bv. Schaefer.(2010," \citet{HKK00,HKK02} and \citet{HKS03} have postulated that a plateau is characteristic of recurrent novae, and in particular of the U Sco subclass of recurrent novae, a position shared by \citet{S10}." +) Their idea is that the plateau is. caused. by the combination of slightlv irradiated companion star and a fully irradiated Larect clisk with a radius 1.4 times the Roche lobe size., Their idea is that the plateau is caused by the combination of a slightly irradiated companion star and a fully irradiated flared disk with a radius 1.4 times the Roche lobe size. + At the time of the plateau. the outbursting white dwarf is experiencing stable nuclear burning and. supersoft. X-ray emission.," At the time of the plateau, the outbursting white dwarf is experiencing stable nuclear burning and supersoft X-ray emission." + The irradiation of the disk and the companion by a stable central engine Leads to a fairlv constant Dux added to that steadily declining from the expanding ejecta., The irradiation of the disk and the companion by a stable central engine leads to a fairly constant flux added to that steadily declining from the expanding ejecta. + Ehis leads to a lattening of the light curve (the plateau). oll.which lasts until Ίο time when the nuclear burning turns ," This leads to a flattening of the light curve (the plateau), which lasts until the time when the nuclear burning turns off." +The plateau phase of V2672 Oph is well seen in the {ς ight-curve of Figure 2., The plateau phase of V2672 Oph is well seen in the $I_{\rm C}$ light-curve of Figure 2. + Unfortunately. the observations in 16 V band stopped duc to the laintness of the nova right ab the time when it was entering the plateau phase.," Unfortunately, the observations in the $V$ band stopped due to the faintness of the nova right at the time when it was entering the plateau phase." + There are just two observations defining the plateau of V2672 Oph. rut they support a close similarity with the plateau of U Sco hat lasted from cay|12 to dav |19.," There are just two observations defining the plateau of V2672 Oph, but they support a close similarity with the plateau of U Sco that lasted from day+12 to day +19." +" During that. period U Sco was found to be - as - à bright supersoft X-ray source (Schlegelοἱal.""iMτοςpeeet 2010).."," During that period U Sco was found to be - as predicted - a bright supersoft X-ray source \citep{SSP10,OPW10}. ." + The plateau for V2672 is A/-=0.6 nmag brighter than in U Sco as illustrated by Figure 2. the V -band panel seems to support insteacl a similar brightness level.," The plateau for V2672 Oph is $\Delta I_{\rm C}$ =0.6 mag brighter than in U Sco as illustrated by Figure 2, while the $V$ -band panel seems to support instead a similar brightness level." + We do not attach much significance to the Ade ollset., We do not attach much significance to the $\Delta I_{\rm C}$ offset. + Lt, It +for about 2-3 passages through the computational volume.,for about 2–3 passages through the computational volume. + The computational cost for this was 1-3 wallclock days on 36 processors with MPI parallelization., The computational cost for this was 1–3 wallclock days on 36 processors with MPI parallelization. +" To test the flow's ability to penetrate the atmosphere in the setup with shear, Fig."," To test the flow's ability to penetrate the atmosphere in the setup with shear, Fig." +" laa, we compare the jet velocities halfway through the simulated distance against the escape velocity in Fig. 6.."," \ref{fig:emergecases}a a, we compare the jet velocities halfway through the simulated distance against the escape velocity in Fig. \ref{fig:vrvesc}." + The jet velocity decreases with both decreasing rotation velocity My and decreasing magnetic field strength By (or increasing fp)., The jet velocity decreases with both decreasing rotation velocity $\Mb$ and decreasing magnetic field strength $\Bb$ (or increasing $\betab$ ). +" It is, however, much more sensitive to the former parameter: 6, must be changed by orders of magnitude to get a significant impact on jet velocity whereas with M», a factor of order unity suffices."," It is, however, much more sensitive to the former parameter: $\betab$ must be changed by orders of magnitude to get a significant impact on jet velocity whereas with $\Mb$, a factor of order unity suffices." + The bottom panel in Fig., The bottom panel in Fig. +" 6 shows which flows pass this test, with those exceeding the escape speed marked in green, the others in red."," \ref{fig:vrvesc} shows which flows pass this test, with those exceeding the escape speed marked in green, the others in red." + Failed jets do not reach the upper boundary., Failed jets do not reach the upper boundary. +" The background atmosphere, whose equilibrium is perturbed, tends to fall down on them."," The background atmosphere, whose equilibrium is perturbed, tends to fall down on them." + The fixed conditions at the lower boundary avert a pile-up of thermal energy: downward flowing hot gas vanishes across the boundary and the injected gas has a constant temperature., The fixed conditions at the lower boundary avert a pile-up of thermal energy: downward flowing hot gas vanishes across the boundary and the injected gas has a constant temperature. + A delayed onset of a flow due to accumulated heat is unlikely for this reason., A delayed onset of a flow due to accumulated heat is unlikely for this reason. + There are instabilities in all cases where a jet develops., There are instabilities in all cases where a jet develops. +" The instabilities develop mainly after the first passage through the computational domain, in the form of helical displacements and/or a change of direction of the whole jet by up to several degrees."," The instabilities develop mainly after the first passage through the computational domain, in the form of helical displacements and/or a change of direction of the whole jet by up to several degrees." +" The latter are likely modes with wavelengths longer than the computational domain, i.e. one sees only the lower part of what would be a kink if the radial extent of the domain was larger."," The latter are likely modes with wavelengths longer than the computational domain, i.e. one sees only the lower part of what would be a kink if the radial extent of the domain was larger." + Jets created by stronger magnetic fields (By< 4.9) tend to show this kind of incipient instability., Jets created by stronger magnetic fields $\betab \le 4.9$ ) tend to show this kind of incipient instability. + Jets from weaker fields move slower and develop pronounced helical deformations already within the computational domain., Jets from weaker fields move slower and develop pronounced helical deformations already within the computational domain. + The proximity of the upper boundary does not allow for more conclusive statements about differences in instability behavior within the limits of this parameter study., The proximity of the upper boundary does not allow for more conclusive statements about differences in instability behavior within the limits of this parameter study. + A series of large and expensive simulations of the kind presented in the next section would be needed for that., A series of large and expensive simulations of the kind presented in the next section would be needed for that. + If the configuration is shifted such that no shear in the magnetic field occurs (Fig., If the configuration is shifted such that no shear in the magnetic field occurs (Fig. +" 1bb), a jet does not develop."," \ref{fig:emergecases}b b), a jet does not develop." + The middle panel in Fig., The middle panel in Fig. + 7 shows such a case., \ref{fig:wedges} shows such a case. + The magnetic field lines are unconnected to the surrounding atmosphere and the field is not amplified by shear., The magnetic field lines are unconnected to the surrounding atmosphere and the field is not amplified by shear. + This appears to be sufficient to allow them to rotate without producing a magnetically powered flow., This appears to be sufficient to allow them to rotate without producing a magnetically powered flow. +" However, for very large values of My and fj, an outflow forms at the edge of the rotating disk, see bottom panel in Fig. 7.."," However, for very large values of $\Mb$ and $\betab$, an outflow forms at the edge of the rotating disk, see bottom panel in Fig. \ref{fig:wedges}." + This outflow appears to be driven by thermal buoyancy associated with the dissipation of rotational energy at the disk's, This outflow appears to be driven by thermal buoyancy associated with the dissipation of rotational energy at the disk's +complexity of binary dynamical interactions is missing in the present Monte Carlo simulations.,complexity of binary dynamical interactions is missing in the present Monte Carlo simulations. + In Fig., In Fig. + 10 is shown the number of collisions as a function of time for the Monte Carlo and N-body models., \ref{fig:tf-col_comparison} is shown the number of collisions as a function of time for the Monte Carlo and $N$ -body models. + 'The collisions are mainly connected with binary mergers due to stellar evolution or dynamical binary interactions., The collisions are mainly connected with binary mergers due to stellar evolution or dynamical binary interactions. + There are only a few direct physical collisions between single stars., There are only a few direct physical collisions between single stars. +" Up to time about 1.5 Gyr both models give similar results, and then the N-body model shows a larger number of collisions than the Monte Carlo model."," Up to time about 1.5 Gyr both models give similar results, and then the $N$ -body model shows a larger number of collisions than the Monte Carlo model." + Again this can be attributed to the fact that in the Monte Carlo simulations the complex dynamical binary interactions are not followed., Again this can be attributed to the fact that in the Monte Carlo simulations the complex dynamical binary interactions are not followed. +" In the Monte Carlo code a binary can only coallesce if,after the dynamical interaction, the periastron distance is smaller than the sum of the stellar radii."," In the Monte Carlo code a binary can only coallesce if, the dynamical interaction, the periastron distance is smaller than the sum of the stellar radii." +" In the N-body code binary coallescence occurs if,during the interaction, the distance between two stars is smaller than the sum of their radii."," In the $N$ -body code binary coallescence occurs if, the interaction, the distance between two stars is smaller than the sum of their radii." +" Definitely the latter can happen more frequently, in the case of strong interactions such as prolonged resonances (temporary capture)."," Definitely the latter can happen more frequently, in the case of strong interactions such as prolonged resonances (temporary capture)." +" When most collision events are connected with the stellar evolution of nearly isolated binaries, then both models agree."," When most collision events are connected with the stellar evolution of nearly isolated binaries, then both models agree." + The old open cluster M67 is an ideal testing ground for modelling the interactions between dynamical and stellar evolution., The old open cluster M67 is an ideal testing ground for modelling the interactions between dynamical and stellar evolution. +" It has a substantial population of blue stragglers, which are almost certainly the product of stellar collisions, or mergers within primordial binaries."," It has a substantial population of blue stragglers, which are almost certainly the product of stellar collisions, or mergers within primordial binaries." +" Also, it is small enough that its entire life history can be modelled with N-body techniques (Hurleyetal.2005), though this has become possible only within the last few years: though its present mass (of order 2000Mo) makes it seem an easy"," Also, it is small enough that its entire life history can be modelled with $N$ -body techniques \citep{hurleyetal2005}, though this has become possible only within the last few years: though its present mass (of order $2000\msun$ ) makes it seem an easy" +Advances in the spectroscopic survey capabilities of 8-meter class telescopes have allowed us in the recent years to extend detailed studies of the clustering of galaxies to the z~1 Universe (2222222?2?)..,"Advances in the spectroscopic survey capabilities of 8-meter class telescopes have allowed us in the recent years to extend detailed studies of the clustering of galaxies to the $z\simeq1$ Universe \citep{coil04,lefevre05b,pollo06,coil06,meneux06,delatorre07,meneux08,coil08,abbas10}." +" The most recent contribution to this endeavour is the COSMOS survey (?),, and in particular ZCOSMOS, its redshift follow-up with VIMOS at the ESO-VLT (?).."," The most recent contribution to this endeavour is the COSMOS survey \citep{scoville07}, and in particular zCOSMOS, its redshift follow-up with VIMOS at the ESO-VLT \citep{lilly07}." +" Early angular studies of the COSMOS field (?) and more recent analyses of the first ten thousand zCOSMOS redshifts to [ap=22.5, have evidenced significant “excess” clustering in the large-scale shape of the two-point angular and projected correlation function."," Early angular studies of the COSMOS field \citep{mccracken07} and more recent analyses of the first ten thousand zCOSMOS redshifts to $I_{AB}=22.5$, have evidenced significant “excess” clustering in the large-scale shape of the two-point angular and projected correlation function." +" The redshift information from zCOSMOS, in particular, shows this excess to dominate in the redshift range 0.5«z1 (?)."," The redshift information from zCOSMOS, in particular, shows this excess to dominate in the redshift range $0.510? ?) as well as hieh resolution mm/subnmum interferometric imaging will be kev tools in uncovering (he hieh temperatures of the dense UV-shiekded gas in CRDIs expected in compact extreme starbursts.,"The main conclusions of this work are three, namely Sensitive observations of key molecular lines with high critical densities $\rm n_{crit}$$\ga $ $^5$ $^{-3}$ ) as well as high resolution mm/submm interferometric imaging will be key tools in uncovering the high temperatures of the dense UV-shielded gas in CRDRs expected in compact extreme starbursts." + Tracers of the very. high ionization [fractions expected for (heir dense gas can provide an independent assesment of their presense., Tracers of the very high ionization fractions expected for their dense gas can provide an independent assesment of their presense. + All these tests will become possible with ALMA lor large numbers of ULURGs in the local Universe., All these tests will become possible with ALMA for large numbers of ULIRGs in the local Universe. + It is a pleasure to acknowledge many inlormative discussions wilh Drs Wing-Fai Thi and Francesco Miniati., It is a pleasure to acknowledge many informative discussions with Drs Wing-Fai Thi and Francesco Miniati. + Discussions will Dr Marco Spaans regarding NDR/CDR potential diagnostics are also οσα[αν acknowledged., Discussions with Dr Marco Spaans regarding XDR/CDR potential diagnostics are also greatfuly acknowledged. + Finally DI would like to thank the referee [or his/her extensive set of comments that helped helped clarify several issues and significantly widen the scope of this work., Finally I would like to thank the referee for his/her extensive set of comments that helped helped clarify several issues and significantly widen the scope of this work. +"amount (a Ceres-sized asteroid) of accreted mass to explain their spectra (?),, well below the detection/calibration limits of current telescopes.","amount (a Ceres-sized asteroid) of accreted mass to explain their spectra \citep{2010ApJ...722..725Z}, well below the detection/calibration limits of current telescopes." +" Additionally, this mass can be hidden in cool material that is far enough from the white dwarf that it does not emit significantly in the mid-infrared."," Additionally, this mass can be hidden in cool material that is far enough from the white dwarf that it does not emit significantly in the mid-infrared." +" A variety of novel observational techniques, such as interferometry, contrast imaging, and leveraging a nearby luminous companion to illuminate a large portion of the disk (as in the case of Sirius A) will be necessary to study the outer parts of these systems, which might comprise ~1/4 of DA white dwarfs, and ~1/3 of DB white dwarfs (??).."," A variety of novel observational techniques, such as interferometry, high-contrast imaging, and leveraging a nearby luminous companion to illuminate a large portion of the disk (as in the case of Sirius A) will be necessary to study the outer parts of these systems, which might comprise $\sim$ 1/4 of DA white dwarfs, and $\sim$ 1/3 of DB white dwarfs \citep{1998ApJ...505L.143Z,2010ApJ...722..725Z}." +" We used archival Gemini/T-ReCS data to directly image the nearest white dwarf, Sirius D, in 5 filters in the N-band (104m) window."," We used archival Gemini/T-ReCS data to directly image the nearest white dwarf, Sirius B, in 5 filters in the N-band $\micron$ ) window." +" The data were taken over a several year period, where Sirius A was used as a photometric standard for many T-ReCS programs."," The data were taken over a several year period, where Sirius A was used as a photometric standard for many T-ReCS programs." +" Because of Sirius B's non-negligable orbital motion during that timespan, we shifted each image by the binary's calculated orbital ephemeris in order to stack the images on Sirius B. Although ? reported a slight excess in the Ks-band, we find no evidence of a large mid-infrared excess, as would be expected for a DAZd white dwarf with a dusty debris disk (?).."," Because of Sirius B's non-negligable orbital motion during that timespan, we shifted each image by the binary's calculated orbital ephemeris in order to stack the images on Sirius B. Although \citet{2008A&A...489..651B} reported a slight excess in the Ks-band, we find no evidence of a large mid-infrared excess, as would be expected for a DAZd white dwarf with a dusty debris disk \citep{2007ApJ...662..544V}." + White dwarfs in Sirius-like binary systems might be good targets for observing the outer parts of these debris disks., White dwarfs in Sirius-like binary systems might be good targets for observing the outer parts of these debris disks. +" Because of the low-luminosity of white dwarfs, circumstellar material at the separations typically observed in debris disks are too cold to emit significant radiation in the mid-infrared."," Because of the low-luminosity of white dwarfs, circumstellar material at the separations typically observed in debris disks are too cold to emit significant radiation in the mid-infrared." +" However, in binary systems, regions of the white dwarf's disk that are not heated by the white dwarf can be heated by its more luminous companion."," However, in binary systems, regions of the white dwarf's disk that are not heated by the white dwarf can be heated by its more luminous companion." +" The authors thank the anonymous referee for his/her extremely helpful suggestions, and Eric Nielsen for providing us with his orbital ephemeris program."," The authors thank the anonymous referee for his/her extremely helpful suggestions, and Eric Nielsen for providing us with his orbital ephemeris program." + AJS acknowledges the NASA Graduate Student Research Program (GSRP) for its generous support., AJS acknowledges the NASA Graduate Student Research Program (GSRP) for its generous support. + LMC is supported by an NSF CAREER. award., LMC is supported by an NSF CAREER award. +Lt is clear that the light curve of 121740.7-2942 is much closer to th1e light curve of X.1 (see c.g. Ixuznetsov et al.,"It is clear that the light curve of 1E1740.7-2942 is much closer to the light curve of Cyg X–1 (see e.g. Kuznetsov et al.," + 1997). than that of a typical Xorav transicnts.," 1997), than that of a typical X–ray transients." +(νο Phe same is true for GISSI758-258., The same is true for GRS1758-258. + However Cvg X-1 has à massive and accretion is fed by a stellar wind., However Cyg X-1 has a very massive companion and accretion is fed by a stellar wind. + At least for veryCGINSI758-258 the companionhypothesis of the companion massive enough to sullicient stellar wind can be rejected based on the optical and infrared. producelimits (see e.g. Chen. Gehrels & Leventhal. 1994: Marti et al.," At least for GRS1758-258 the hypothesis of the companion massive enough to produce sufficient stellar wind can be rejected based on the optical and infrared limits (see e.g. Chen, Gehrels & Leventhal, 1994; Marti et al.," + 1998)., 1998). +" During the Last. few the hypothesis explaining the ""transient character of the black hole vearsLAINDs due to the thermalviscous insability of an accretion disc in the zone of partial hydrogen ionization was inensively discussed in the literature (see e.g. Van Paraclijs 1996. Ixing et al."," During the last few years the hypothesis explaining the “transient” character of the black hole LMXBs due to the thermal–viscous instability of an accretion disc in the zone of partial hydrogen ionization was intensively discussed in the literature (see e.g. Van Paradijs 1996, King et al." + 1997a. Dubus et al.," 1997a, Dubus et al." + 1998)., 1998). + This instability was successfully applied to catacIvsmic variables (e.g. Alever ancl Mever-Hofpmeister. 1981)., This instability was successfully applied to cataclysmic variables (e.g. Meyer and Meyer-Hofmeister 1981). + Lt is interesing to uncerstand the role of this instability for the GRS 1758-258 and LE sources (Ixuznetsov ct al.," It is interesting to understand the role of this instability for the GRS 1758-258 and 1E1740.7-2942 sources (Kuznetsov et al.," + 1998)., 1998). + The light curves of GRS 1758-258 and 151740.7-2942 seem to indicate that this instability is suppressed in these , The light curves of GRS 1758-258 and 1E1740.7-2942 seem to indicate that this instability is suppressed in these objects. +Menou. Naravan & Lasota (1998) suggested that à po»ulation of faint objects.non-transient. LMDBIIDs can exist in the Galaxy.," Menou, Narayan & Lasota (1998) suggested that a population of faint non-transient LMBHBs can exist in the Galaxy." + In their transient sources the outer regions of the disk are colder than the ionization temperature of while at smaller racdii disk switches to the stable advection dominated: hydrogensolution before the disk. teniperature rises to the critical. value., In their non-transient sources the outer regions of the disk are colder than the ionization temperature of hydrogen while at smaller radii disk switches to the stable advection dominated solution before the disk temperature rises to the critical value. + However expected Iuminosities of such objects are| much smaller than observed values (2107 erg/s) Dor GRS 1758-258 and 2042., However expected luminosities of such objects are much smaller than observed values $\ge 10^{37}~erg/s$ ) for GRS 1758-258 and 1E1740.7-2942. + Another is to assume that even at the outmost regions of the aceretion disk the possibilityure is already above the iorization temperature., Another possibility is to assume that even at the outmost regions of the accretion disk the temperature is already above the hydrogen ionization temperature. + Unlike CVs for temperataccreting black holes the hydrogenirradiation of the outer part of the accretion disc by the N-rays (e.g. Shakura & Sunvaev 1973. Lyuty & Sunvaey 1976) originated. in the inner part of the disk night be important for suppressing this instability (e.g. Van Paraclijs 1996. Ixing et al.," Unlike CVs for accreting black holes the irradiation of the outer part of the accretion disc by the X-rays (e.g. Shakura & Sunyaev 1973, Lyuty & Sunyaev 1976) originated in the inner part of the disk might be important for suppressing this instability (e.g. Van Paradijs 1996, King et al." + 1997a. 1997b. Dubus et al.," 1997a, 1997b, Dubus et al." + 1998)., 1998). + Using their prescriptions for suppression of the instability (in the form of minimal mass aceretion rate as a function of radius) one can a constraint on the orbital peviod of the binary. that outmost placeradius of the disk corresponds tο some fraction of the assuming Roche lobe radius.," Using their prescriptions for suppression of the instability (in the form of minimal mass accretion rate as a function of radius) one can place a constraint on the orbital period of the binary, assuming that outmost radius of the disk corresponds to some fraction of the primary Roche lobe radius." + For reasonable choice ol the black hole mass ancl primarymass ratio the must be less than L0-2¢) hours and the mass accretion rate in GRSIT5S8-258period and. 151740.7-2942 should be, For reasonable choice of the black hole mass and mass ratio the period must be less than 10-20 hours and the mass accretion rate in GRS1758-258 and 1E1740.7-2942 should be +the Galaxy.,the Galaxy. +" If planets are found to orbit around low-a dwarfs in this metallicity range, it will strongly support our conjecture presented in thisletter."," If planets are found to orbit around $\alpha$ dwarfs in this metallicity range, it will strongly support our conjecture presented in this." + The other is to search low-a stars with —2 <[Fe/H]<—1 at the tip of the RGB in the Galaxy., The other is to search $\alpha$ stars with $-2<$ $<-1$ at the tip of the RGB in the Galaxy. +" A few spectroscopic observations have been made for red giants with the surface gravities and metallicities similar to the stars observed in dSph galaxies (e.g.,Hansonetal.1998;Fulbright2000)."," A few spectroscopic observations have been made for red giants with the surface gravities and metallicities similar to the stars observed in dSph galaxies \citep[e.g.,][]{Hanson_98, Fulbright_00}." +. None of these stars is a low-o star., None of these stars is a $\alpha$ star. + The other red giants in the Galaxy observed so far are too metal-poor $—2) and/or have too high surface gravities (loggZ 1)., The other red giants in the Galaxy observed so far are too metal-poor $\ltsim-2$) and/or have too high surface gravities $\log g\gtsim 1$ ). +" The metallicity distribution function of stars with planets is shown to shift toward the metal rich region compared with that of stars without planets (e.g.,Gon-zalez 1998)."," The metallicity distribution function of stars with planets is shown to shift toward the metal rich region compared with that of stars without planets \citep[e.g.,][]{Gonzalez_98}." +. There have been two explanations for this fact., There have been two explanations for this fact. +" One is that only stars with sufficient metals can host planets, because the planet formation needs dust grains (e.g.,Santosetal.2003)."," One is that only stars with sufficient metals can host planets, because the planet formation needs dust grains \citep[e.g.,][]{Santos_03}." +". The other is that stars with planets tend to engulf planetesimals to enhance their metallicities(e.g.,Gonzalez1998;Murray&Chaboyer 2002).."," The other is that stars with planets tend to engulf planetesimals to enhance their \citep[e.g.,][]{Gonzalez_98, Murray_02}. ." + Our scenario favors the latter explanation., Our scenario favors the latter explanation. +thus already included in PO4. or excluded based on (heir selection criteria.,"thus already included in P04, or excluded based on their selection criteria." + Finally. it is important to note that Stanghellini et al. (," Finally, it is important to note that Stanghellini et al. (" +2006) and Pottasch Bernarc-Salas (2006) abundances were ealeulated with the same method and ionization correction factors (ICE) (han those of POF. all utilizng the Ixingsburg Barlow (1994) prescription.,"2006) and Pottasch Bernard-Salas (2006) abundances were calculated with the same method and ionization correction factors (ICF) than those of P04, all utilizing the Kingsburg Barlow (1994) prescription." + On the other hand. νέοι Henry (2001). Milingo et al. (," On the other hand, Kwitter Henry (2001), Milingo et al. (" +2002). IXwitter et al. (,"2002), Kwitter et al. (" +2003). and. Costa et al. (,"2003), and Costa et al. (" +2004) used a slighilv a different ICE lor oxvgen.,2004) used a slightly a different ICF for oxygen. + In this paper we correct lor the differences in ICF(O) by using the ionic abundances given in the relevant papers., In this paper we correct for the differences in ICF(O) by using the ionic abundances given in the relevant papers. + In the case when more than one reference give abundances for a partüeular PN we checked (hat the differences are willin the uncertainties. and then chose (he abundances preferring. alter POF. all references whose abundances were originally ealeulated with the ICF relations by Kineshure Barlow (1994).," In the case when more than one reference give abundances for a particular PN we checked that the differences are within the uncertainties, and then chose the abundances preferring, after P04, all references whose abundances were originally calculated with the ICF relations by Kingsburg Barlow (1994)." + We end up with a sample of 206 PNe with homogeneously calculated. oxveen abundances. while (he sample with neon abundances consists of 167 PNe.," We end up with a sample of 206 PNe with homogeneously calculated oxygen abundances, while the sample with neon abundances consists of 167 PNe." + For more than half of the PNe of these sample we also have the helium ancl nitrogen abundance to determine whether belong to the Type I class (Peimbert Torres-Peimbert 1933)., For more than half of the PNe of these sample we also have the helium and nitrogen abundance to determine whether belong to the Type I class (Peimbert Torres-Peimbert 1983). + We use (he uncertainties in the abundances as quoted in the original papers. when available.," We use the uncertainties in the abundances as quoted in the original papers, when available." + Perinotto et al. (, Perinotto et al. ( +2004) gives formal errors for all abundances. which are used here directly.,"2004) gives formal errors for all abundances, which are used here directly." + The abundances from Stanghellini et al. (, The abundances from Stanghellini et al. ( +2006) have uncertainties of 0.04 dex [or all elements. except for neon where (he uncertainty is of (he order of 0.1 dex.,"2006) have uncertainties of 0.04 dex for all elements, except for neon where the uncertainty is of the order of 0.1 dex." + Ixvitter and collaborators assume that the tvpical uncertainty for the oxvgen abundance is ~3xLO|., Kwitter and collaborators assume that the typical uncertainty for the oxygen abundance is $\sim3\times10^{-4}$. + In the cases where (he uncertainties are not given (e. g.. Costa οἱ al.," In the cases where the uncertainties are not given (e. g., Costa et al." + 2004) we assume an uncertainty of 0.15 dex for a conservative approach., 2004) we assume an uncertainty of 0.15 dex for a conservative approach. + In Table 2 (published electronically) we list all PN abundances used in this paper., In Table 2 (published electronically) we list all PN abundances used in this paper. + A PN is in this Table if at least one elemental abundances among (he ones used in this paper (helium. nitrogen. oxveen. and neon) is available.," A PN is in this Table if at least one elemental abundances among the ones used in this paper (helium, nitrogen, oxygen, and neon) is available." + Column (1) gives the PN name: Columns, Column (1) gives the PN name; Columns +corresponds to the force parallel to the vortex motion.,corresponds to the force parallel to the vortex motion. + The coefficients à and 3 can be caleulated. using a specific theory. of vortex mobility., The coefficients $\alpha$ and $\beta$ can be calculated using a specific theory of vortex mobility. + The third term accounts for the the contribution to the force that arises from local vortex bending., The third term accounts for the the contribution to the force that arises from local vortex bending. + If the vortex lattice is locally undeformed (σι=0). the vortexvelocity [rom eqs. (16))," If the vortex lattice is locally undeformed $\sigmabf_{el}=0$ ), the vortexvelocity from eqs. \ref{fl}) )" + and (13)) is where à—1.7., and \ref{lineforce}) ) is where $\alpha\equiv 1-\beta^\prime$. + Imperfect pinning. that is. “vortex creep”. corresponds to à< as the “pinning coellicients.," We refer to $\alpha$, $\beta$, and $\gamma$ as the “pinning coefficients”." + Perfect. pinning corresponds to the limit à=3=>—0. while no pinning (f.=0) corresponds to00—5=] and 7—0.," Perfect pinning corresponds to the limit $\alpha=\beta=\gamma=0$, while no pinning $\fbf=0$ ) corresponds to $\alpha=\gamma=1$ and $\beta=0$." +" Vortices move with a component along vwv,. so that 0«ax1."," Vortices move with a component along $\vbf-\vbf_n$, so that $0<\alpha\le 1$." + The energy. dissipation rate per unit volume is determined by 3) which must be positive to give local entropy. production.," The energy dissipation rate per unit volume is determined by $\beta$ , which must be positive to give local entropy production." + Vortex creep could be a low-clrag process. with 3<>\alpha$ ." + ln much previous work on pinning. the high-drag limit has been implicitly assumed through the followingrelationship between 3 and. 3”: where R is a dimensionless drag coefficient.," In much previous work on pinning, the high-drag limit has been implicitly assumed through the followingrelationship between $\beta$ and $\beta^\prime$ : where ${\cal R}$ is a dimensionless drag coefficient." + In this drag description. imperfect pinning (a<<1. 3<<1) corresponds to Rm dsothat eq. (18))," In this drag description, imperfect pinning $\alpha<<1$, $\beta<<1$ ) corresponds to ${\cal R}>>1$ so that eq. \ref{drag}) )" + requires 2zza., requires $\beta>>\alpha$. + Eq. (18)) general., Eq. \ref{drag}) ). + Ehe presence of non-dissipative forces between vortices and the solid to whieh they are pinned can give 3<>1. where AR is the thickness of the inner crust. the background Low can be taken to be uniform and the local analysis is valid.," Restricting the analysis to the regime $k\Delta R>> 1$, where $\Delta R$ is the thickness of the inner crust, the background flow can be taken to be uniform and the local analysis is valid." +"We take the unperturbed vortex lattice to be locally undeformed (σι,= 0).",We take the unperturbed vortex lattice to be locally undeformed $\sigmabf_{el}=0$ ). + The unperturbed creep velocity in the rotating frame (ο= 0) follows from eq. (17)):, The unperturbed creep velocity in the rotating frame $\vbf_n=0$ ) follows from eq. \ref{vv}) ): + Below we estimate OrefOl7LOου for a typical neutron star.," Below we estimate $\partial r_{v0}/\partial t\sim 10^{-5}\,v_0$ for a typical neutron star." + Linearizing eqs. (12)), Linearizing eqs. \ref{sfaccel}) ) +" and (13)) about eu. Ore1. and σι—0. and neglecting Or.Οἱ compared to uy. gives where à denotes a perturbed quantity. and ji—pp($3,«7)/2."," and \ref{lineforce}) ) about $\vbf_0$, $\partial\rbf_{v0}/\partial t$, and $\sigmabf_{el}=0$, and neglecting $\partial\rbf_{v0}/\partial t$ compared to $\vbf_0$ , gives where $\delta$ denotes a perturbed quantity, and $\mu^\prime\equiv\mu-\rho(\Omegabf_n\times\rbf)^2/2$." + We assume that à and 3 are constants., We assume that $\alpha$ and $\beta$ are constants. + Phe perturbed force is then The vorticity appearing in this equation is the total vorticity evaluated in the laboratory frame., The perturbed force is then The vorticity appearing in this equation is the total vorticity evaluated in the laboratory frame. +" For V«ου<< 2Q,.a good approximation for most neutron stars. the vorticity: is The final term in eq. (23))."," For $\nabla\times\vbf_0<<2\Omegabf_n$ , a good approximation for most neutron stars, the vorticity is The final term in eq. \ref{df}) )," + associated. with stress in the vortex lattice. will turn out to be negligible for vortex creep driven by a [low ryZZer ancl eyD6g.," associated with stress in the vortex lattice, will turn out to be negligible for vortex creep driven by a flow $v_0>>c_T$ and $v_0>>c_V$." + Wetake the rotation axis to be 2. with the unperturbed How in the azimuthaldirection. and along.F at some point.," Wetake the rotation axis to be $\hat{z}$, with the unperturbed flow in the azimuthaldirection, and along$\hat{x}$ at some point." + kor simplicity. we restrict & to lie in the rs plane. with an angle @ with respect to the rotation axis.," For simplicity, we restrict $\kbf$ to lie in the $x-z$ plane, with an angle $\theta$ with respect to the rotation axis." + We further restrict the analysis to the quadrantQ0x6 z/2., We further restrict the analysis to the quadrant$0\le\theta\le\pi/2$ . + Forshear perturbations. k-de= 0. thatis. the velocity perturbations in the directions fj and =cos@#.r|sind? are orthogonal to k. We now Fourier transform (xeikviat) eqs. (20))-(23))," Forshear perturbations, $\kbf\cdot\delta\vbf=0$ , thatis, the velocity perturbations in the directions $\hat{y}$ and $\hat{e}\equiv-\cos\theta\,\hat{x}+\sin\theta\, \hat{z}$ are orthogonal to $\kbf$ We now Fourier transform $(\propto {\rm e}^{i{\mathbf k}\cdot{\mathbf +r}-i\sigma t})$ eqs. \ref{div}) \ref{df}) )" + and takethe projections onto jj and é., and takethe projections onto $\hat{y}$ and $\hat{e}$ . + Defining σ΄=okey sin. c— cos. and s= sin. we obtain the system of equations: The resulting dispersionrelation is quadratic:," Defining $\sigma^\prime\equiv\sigma-kv_0\sin\theta$ , $c\equiv\cos\theta$ , and $s\equiv\sin\theta$ , we obtain the system of equations: The resulting dispersionrelation is quadratic:" +and (he Gaussian function in equation (8) of 104 (d£/dlogZ) is replaced by the expression The model parameters are log(p.;r/Z.)=—0.3. log(Z./Z.)=—0.08. and w=0.16.,"and the Gaussian function in equation (8) of H04 (df/dlogZ) is replaced by the expression The model parameters are $_{eff}/Z_{\odot}) +=-0.3$ , $Z_{c}/Z_{\odot})=-0.68$ , and $w=0.16$." + This function eould have been used for the blue clusters as well but the fit was marginally better using the Gaussian for them given that only one component was being lit., This function could have been used for the blue clusters as well but the fit was marginally better using the Gaussian for them given that only one component was being fit. + The solid black line (arbitrary. normalization) shows the metallicity distribution of all stars lormed in (he surviving population of building blocks prior to the second major merger phase., The solid black line (arbitrary normalization) shows the metallicity distribution of all stars formed in the surviving population of building blocks prior to the second major merger phase. + This group of stars (called the red spheroid in 104) will be more diffuse. have different kinematies and will possess a metal weak tail.," This group of stars (called the red spheroid in H04) will be more diffuse, have different kinematics and will possess a metal weak tail." + Tle mass ratio between these (wo components (post to prior) for the parameters assumed above is ~0.2., The mass ratio between these two components (post to prior) for the parameters assumed above is $\sim 0.2$. +" Note that any blue clusters (hat formed prior to the first major merger phase and which remained bound (ο its lower mass galaxy while avoiding the first mergers will also have the kinematies of the red spheroil population and hence would be members of the ""old halo component of Zinn (1993).", Note that any blue clusters that formed prior to the first major merger phase and which remained bound to its lower mass galaxy while avoiding the first mergers will also have the kinematics of the red spheroid population and hence would be members of the `old' halo component of Zinn (1993). + The red clusters should have the same kinematics as the stars under (he red. curve of lig 6., The red clusters should have the same kinematics as the stars under the red curve of fig 6. + The closest analog of a thick disk population in (hiis model are these sanie stars., The closest analog of a thick disk population in this model are these same stars. + The main purpose of this discussion is to show Chat the phenomenological model outlined above is at least qualitatively consistent with the new data and with our picture of globular cluster formation., The main purpose of this discussion is to show that the phenomenological model outlined above is at least qualitatively consistent with the new data and with our picture of globular cluster formation. + Further. the general outline lor galaxy evolution clescribed above may help explain additional globular cluster related questions.," Further, the general outline for galaxy evolution described above may help explain additional globular cluster related questions." + For example. the blue-red cluster phenomenon is also present in elliptical galaxies even though Chev are morphologically «uite different [rom the gas rich systems.," For example, the blue-red cluster phenomenom is also present in elliptical galaxies even though they are morphologically quite different from the gas rich systems." + Could it be that ellipticals formed similarly but at the intersection of more than one filaanent?, Could it be that ellipticals formed similarly but at the intersection of more than one filament? + The increased frequency of collisions would convert more eas (o stars and lead (o à higher specific frequency of globular clusters., The increased frequency of collisions would convert more gas to stars and lead to a higher specific frequency of globular clusters. + In both cases variations in the distribution of angular momemlun content could explain the differences in the relative frequency of blue to red clusters., In both cases variations in the distribution of angular momemtum content could explain the differences in the relative frequency of blue to red clusters. + We leave these interesting questions to future work., We leave these interesting questions to future work. + We have given a quantitative model for the Formation of globular clusters based on the early work of Gunn MeCrea., We have given a quantitative model for the formation of globular clusters based on the early work of Gunn McCrea. + Clusters are assumed to form in merger induced. collsions., Clusters are assumed to form in merger induced collsions. + We make use of recent HI data lor cbwarl irregular galaxies ancl earlier observational work to derive (he kev parameters of the model., We make use of recent HI data for dwarf irregular galaxies and earlier observational work to derive the key parameters of the model. + We then combined (his model withasimple, We then combined this model withasimple +For both. Gaussian and not Gaussian models. we perform a 1000 simulations.,"For both, Gaussian and not Gaussian models, we perform a $1000$ simulations." + As commented above. to make the simulations more realistic cach simulation is convolved with a Gaussian filter of /33°.," As commented above, to make the simulations more realistic each simulation is convolved with a Gaussian filter of $33'$." + In aclelition. its power spectrum. CT is normalized to that of a CDAI flat A-mocel using the HEALPix package.," In addition, its power spectrum $C_l$ is normalized to that of a CDM flat $\Lambda$ -model using the HEALPix package." + For each of the simulations the wavelet cocllicients for both the SMIIW and the SLAW are computed., For each of the simulations the wavelet coefficients for both the SMHW and the SHW are computed. + “Phe SMIIW. cocllicients are computed by convolving the CAIB map with the SALW given. in eq. (, The SMHW coefficients are computed by convolving the CMB map with the SMHW given in eq. ( +13).,13). + We again use the LUEALPix package to perform. such convolution in Fourier space. having previously caleulated the Legendre cocllicients of the SALW at. the specified resolution.," We again use the HEALPix package to perform such convolution in Fourier space, having previously calculated the Legendre coefficients of the SMHW at the specified resolution." + “Phe SLAW detail coellicients are computed. by performing the linear combinations of 4 pixels as described in section 3., The SHW detail coefficients are computed by performing the linear combinations of 4 pixels as described in section 3. +" Computation time of wavelet coellicients using HEALDix scale as INS, and NS for SALLIW and SLIW respectively.", Computation time of wavelet coefficients using HEALPix scale as $N^3_{N_{side}}$ and $N^2_{N_{side}}$ for SMHW and SHW respectively. + In figure 4 we show the mean values and. dispersion of the skewness and kurtosis of the Gaussian ancl non-Gaussian models for the temperature map. anc for the first 5 resolution levels of the SIIN diagonal. vertical and horizontal coefficients and SAILW coetficients.," In figure 4 we show the mean values and dispersion of the skewness and kurtosis of the Gaussian and non-Gaussian models for the temperature map, and for the first $5$ resolution levels of the SHW diagonal, vertical and horizontal coefficients and SMHW coefficients." + As expected the cillerences are best seen in the finer resolutions., As expected the differences are best seen in the finer resolutions. + Lt is clear from figure 4 that the dillerences in the skewness for, It is clear from figure 4 that the differences in the skewness for +spectrum of OJ 287 on the CCD and integrating the light within a 7.5 aresec aperture.,spectrum of OJ 287 on the CCD and integrating the light within a 7.5 arcsec aperture. + Optimal extraction was used at this phase to obtain maximum signal-to-noise., Optimal extraction was used at this phase to obtain maximum signal-to-noise. + The spectra were calibrated using five spectrophotometric calibration stars (LTT 4816. EG 274. LTT 7379. LTT 6248 and GD 108) obtained with the same instrumental setup as here during the observations or from the ESO archive observations made in 2005-06.," The spectra were calibrated using five spectrophotometric calibration stars (LTT 4816, EG 274, LTT 7379, LTT 6248 and GD 108) obtained with the same instrumental setup as here during the observations or from the ESO archive observations made in 2005-06." + The average sensitivity curve was derived form these five stars and applied to the spectra of OJ 287., The average sensitivity curve was derived form these five stars and applied to the spectra of OJ 287. + An extinction correction was made to each spectrum using a standard atmospheric extinction curve and the airmass at the time of the observation., An extinction correction was made to each spectrum using a standard atmospheric extinction curve and the airmass at the time of the observation. + Some of the nights were affected by thin clouds. whose absorption cannot be accounted for by the above calibration procedure.," Some of the nights were affected by thin clouds, whose absorption cannot be accounted for by the above calibration procedure." + The calibrated spectra exhibit absorption bands from atmospheric water vapor. which are particularly prominent at AIS100-8400 aand 4L18800-9300 aand whose strength varied from one epoch to another.," The calibrated spectra exhibit absorption bands from atmospheric water vapor, which are particularly prominent at $\lambda\lambda$ 8100-8400 and $\lambda\lambda$ 8800-9300 and whose strength varied from one epoch to another." + To correct for the atmospheric absorption bands a template was derived from the spectrum of the nearby star 10 (2?) observed simultaneously with OJ 287 on 2008-01-05., To correct for the atmospheric absorption bands a template was derived from the spectrum of the nearby star 10 \citep{1996A&AS..116..403F} observed simultaneously with OJ 287 on 2008-01-05. + This template was scaled appropriately to obtain the best correction for each epoch., This template was scaled appropriately to obtain the best correction for each epoch. + During this phase it became evident that due to the variable nature of the atmospheric absorption bands they cannot be completely removed at their cores., During this phase it became evident that due to the variable nature of the atmospheric absorption bands they cannot be completely removed at their cores. + The wavelength regions most affected by this effect were excluded from further analysis (see below)., The wavelength regions most affected by this effect were excluded from further analysis (see below). + Figure | shows an example of a calibrated spectrum of OJ 287 obtained during the monitoring campaign., Figure \ref{spectrum} shows an example of a calibrated spectrum of OJ 287 obtained during the monitoring campaign. + The spectrum shows two noisy areas at U8100-8400 aand 4L18850-9200 ddue to the imperfect subtraction of the atmospheric absorption bands., The spectrum shows two noisy areas at $\lambda\lambda$ 8100-8400 and $\lambda\lambda$ 8850-9200 due to the imperfect subtraction of the atmospheric absorption bands. +" The spectra also show two areas populated by weak emission lines: att~ 8570 us the L16548.6583 [NII] + 165635 Ha group and at .t~ 8780 tthe ,16716.6731 [SII] lines."," The spectra also show two areas populated by weak emission lines: at $\lambda \sim$ 8570 is the $\lambda\lambda$ 6548,6583 [NII] + $\lambda6563$ $\alpha$ group and at $\lambda \sim$ 8780 the $\lambda\lambda$ 6716,6731 [SII] lines." + Horizontal bars in Fig., Horizontal bars in Fig. +" 1. indicate the wavelength areas representing ""pure"" continuum.", \ref{spectrum} indicate the wavelength areas representing “pure” continuum. + These areas. 7750-8100Α.. 8400-8460À.. 8680-8750 aand 8800-8900 aare used in all subsequent work for continuum fitting.," These areas, 7750-8100, 8400-8460, 8680-8750 and 8800-8900 are used in all subsequent work for continuum fitting." + The overall shape of the continuum follows a power-law very well as indicated by the power-law fit in Fig. 1.., The overall shape of the continuum follows a power-law very well as indicated by the power-law fit in Fig. \ref{spectrum}. + In all seven spectra the maximum deviation from the power-law fit is1%., In all seven spectra the maximum deviation from the power-law fit is. +. However. because the main interest of this work is on the line variations of OJ 287. a second order polynomial was chosen for the continuum fit as it gives about two times smaller residuals than the power-law fit and still retains the smooth and monotonous shape of the power-law spectrum.," However, because the main interest of this work is on the line variations of OJ 287, a second order polynomial was chosen for the continuum fit as it gives about two times smaller residuals than the power-law fit and still retains the smooth and monotonous shape of the power-law spectrum." + Figure 2 shows the continuum-subtracted spectra during the seven epochs of the monitoring., Figure \ref{spektrit} shows the continuum-subtracted spectra during the seven epochs of the monitoring. + We note that the continuum level varied by a factor of 2.6 during the monitoring., We note that the continuum level varied by a factor of 2.6 during the monitoring. + During at least two of the epochs (four and seven) a broad spectral feature is seen at the location of the Ha-[NII| lines and epochs five and six show a hint of a similar feature., During at least two of the epochs (four and seven) a broad spectral feature is seen at the location of the $\alpha$ -[NII] lines and epochs five and six show a hint of a similar feature. + However. as is evident from Fig. 2..," However, as is evident from Fig. \ref{spektrit}," + the continuum level is fluctuating around the mean level due to calibration errors etc., the continuum level is fluctuating around the mean level due to calibration errors etc. + Because these fluctuations could be wrongly interpreted as true features. it is important to study thestatistical properties of the fluctuations more closely.," Because these fluctuations could be wrongly interpreted as true features, it is important to study thestatistical properties of the fluctuations more closely." + To study the significance of the spectral features in Fig., To study the significance of the spectral features in Fig. + 2 we employed the method by ?.., \ref{spektrit} we employed the method by \cite{2005AJ....129..559S}. + This method consists of dividing the spectrum into spectral bins. computing the equivalent width (EW) of each bin and deriving the rms fluctuations of the EW through the spectrum.," This method consists of dividing the spectrum into spectral bins, computing the equivalent width (EW) of each bin and deriving the rms fluctuations of the EW through the spectrum." + Any EW exceeding a pre-defined rms limit (e.g. 3c) Is taken as a sign of significant emission or absorption line warranting further study., Any EW exceeding a pre-defined rms limit (e.g. $\sigma$ ) is taken as a sign of significant emission or absorption line warranting further study. + ? computed the continuum level for each bin from two adjacent bins. which works fine for narrow lines. but very broad features may be missed.," \cite{2005AJ....129..559S} computed the continuum level for each bin from two adjacent bins, which works fine for narrow lines, but very broad features may be missed." + Thus the method by ο. was slightly modified by using the fitted continuum value instead of the adjacent bins as the continuum estimate., Thus the method by \cite{2005AJ....129..559S} was slightly modified by using the fitted continuum value instead of the adjacent bins as the continuum estimate. + The rms noise in the EW was computed from the pure continuum areas marked with horizontal bars in Fig. 1.., The rms noise in the EW was computed from the pure continuum areas marked with horizontal bars in Fig. \ref{spectrum}. . + A bin size of 8, A bin size of 8 +recoustiuction is trivial. L6. 09=04|SYjj,"reconstruction is trivial, i.e., $a_0 = a_J + \sum_{j=1}^J w_{j}$." + This algorithni is widely used in astronomical applications and biomedical imaging to detect isotropic objects., This algorithm is widely used in astronomical applications and biomedical imaging to detect isotropic objects. + The IUWT filter bank in q«lincusiou (y= 2) becomes hap.dypo=0hyplayὅο0) where Pj is the tensor product of 4 1D filters Pip.," The IUWT filter bank in $q$ -dimension $q\geq2$ ) becomes $(h_{q\text{D}},g_{q\text{D}}=\delta-h_{q\text{D}},\tilde{h}_{q\text{D}}=\delta,\tilde{g}_{q\text{D}}=\delta)$ where $h_{q\text{D}}$ is the tensor product of $q$ 1D filters $h_{\mathrm{1D}}$." +" Note that yyy is in general nou-separable,", Note that $g_{q\text{D}}$ is in general non-separable. + Now the VST can be combined with the IUWT in the following wav: since the filters 1 at all scales j are low-pass filters (so have unouzero cans). we cau first stabilize the approximation cociiicicnts a; at cach scale using the VST. aud then compute iu the standard way the detail coefficieuts frou the stabilized js. Caiven the particular structure of the IUWT. analysis filters (Pi.g). the stabilization procedure is eiven by rieht.. rieht.," Now the VST can be combined with the IUWT in the following way: since the filters $\bar{h}^{\uparrow j}$ at all scales $j$ are low-pass filters (so have nonzero means), we can first stabilize the approximation coefficients $a_j$ at each scale using the VST, and then compute in the standard way the detail coefficients from the stabilized $a_j$ 's. Given the particular structure of the IUWT analysis filters $(h,g)$, the stabilization procedure is given by . ." +. Note that the VST is now scale-depencent (hence the name MSVST))., Note that the VST is now scale-dependent (hence the name ). + The filtering step ou a;4 can be rewritten as a filtering on ay=X. Le. «;=bY)ag where Wl)=fittaehtxh for j> Land fi!!!=à.," The filtering step on $a_{j-1}$ can be rewritten as a filtering on $a_0=\fX$, i.e., $a_{j} = h^{(j)}\star a_0$, where $h^{(j)} = \bar{h}^{j-1}\star\cdots\star\bar{h}^{1}\star \bar{h}$ for $j\geq 1$ and $h^{(0)} = \delta$." + A/ is the VST operator at scale / ⋅ ∣≽∕⊽⊽↴ ⋅ ≺⊓⋝∙↑∐↸∖↸⊳∪∐↴∖↴↑⋜⋯↑↴∖↴∣↗↾∕⋝⋜, ${\cal{A}}_j$ is the VST operator at scale $j$ Let us define $\tau_k^{(j)} = \sum_i \parenth{h^{(j)}[i]}^k$ . +⋯≺↧↙⋅↾∕⋝⋜↧↴∖↴↴∖↴⋯⊳↕⋜↧↑↸∖≼⊔∪∕∣↾∕⋝∐⋯↴∖↴⊓⋝↸∖∫⇀↸∖↑∏↴∖↴≺∐∖∐∐↸∖∣−∕↽∕∶∑∣∩∣↾∕∿∩∙↽∕∏∐∖∐⋜↧↸⊳↸⊳∪↥⋅≼∐∐∶↴⋁↑∪ set to The coustauts bY) and c) oulv depend ou the filter h aud the scale level j.," Then according to \ref{eq:c}) ), the constants $b^{(j)}$ and $c^{(j)}$ associated to $h^{(j)}$ must be set to The constants $b^{(j)}$ and $c^{(j)}$ only depend on the filter $h$ and the scale level $j$." + They can all be pre-couiputed once for ouv given P., They can all be pre-computed once for any given $h$. + À schematic overview of the decomposition and the inversion of ΤΠΝΤ is depicted iu Fig. 3.., A schematic overview of the decomposition and the inversion of +IUWT is depicted in Fig. \ref{fig:msvst}. + lu sunuuiarv. IUWT denoising with the involves the following three main steps: Fie.," In summary, IUWT denoising with the involves the following three main steps: Fig." + 1 upper left shows a set of objects of different sizes and differeut iutensitics a Poisson noise., \ref{fig_xmm_simu_roset} upper left shows a set of objects of different sizes and different intensities a Poisson noise. + Each object along auy radial brauch has the same integrated intensity and has a iore and more exteuded support aswe oeo farther from the, Each object along any radial branch has the same integrated intensity and has a more and more extended support aswe go farther from the +see that this rises from an initial to as high as around the time that the core-collapse phase is halted.,see that this rises from an initial to as high as around the time that the core-collapse phase is halted. + Alter this time the core binary [raction becomes quite noisy owing to the small size of the core (see Figure 1)) and the small numbers of binaries and stars in the core., After this time the core binary fraction becomes quite noisy owing to the small size of the core (see Figure \ref{f:fig1}) ) and the small numbers of binaries and stars in the core. + llowever. the value always remains greater (han the initial value.," However, the value always remains greater than the initial value." + We see also [rom Figure dae that the binary. frequency within the inner Lagrangian radius rises to a maximum of just prior to the end of the core-collapse phase., We see also from Figure \ref{f:fig3}a a that the binary frequency within the inner Lagrangian radius rises to a maximum of just prior to the end of the core-collapse phase. + It is important to note at (his point (hat we are working with radii derived from spherica cata whereas observational determinations of binary fractions are based on (wo-climensiona projected data., It is important to note at this point that we are working with radii derived from spherical data whereas observational determinations of binary fractions are based on two-dimensional projected data. + With our models it is possible to test the effect of this discrepancy on our findings., With our models it is possible to test the effect of this discrepancy on our findings. + If we calculate the Lagrangian radius for model IX100-5 from a (wo-dimensiona projection we find that the radius is reduced by about across the evolution (the choice of projection axis does not affect this result)., If we calculate the Lagrangian radius for model K100-5 from a two-dimensional projection we find that the radius is reduced by about across the evolution (the choice of projection axis does not affect this result). + This is consistent with the expectation sugeested by Fleck οἱ al. (, This is consistent with the expectation suggested by Fleck et al. ( +2006).,2006). + A similar relationship is reported by Doiungardt. Makino Tat (2005) in that the hall-lHight radius (caleulated fom projected data) is approximately half the size of the hall-mass radius (ealeulated [rom spherical data).," A similar relationship is reported by Baumgardt, Makino Hut (2005) in that the half-light radius (calculated from projected data) is approximately half the size of the half-mass radius (calculated from spherical data)." + However. the binary fraction within the projected Lagrangian radius of our IN100-5 model is almost indistinguishable Irom that of the result shown in Figure 3aa (the dotted curve).," However, the binary fraction within the projected Lagrangian radius of our K100-5 model is almost indistinguishable from that of the result shown in Figure \ref{f:fig3}a a (the dotted curve)." + We now aim (ο understand the processes underlying the evolution of the core binary fraction of star clusters. focussing again on the IX100-5 simulation.," We now aim to understand the processes underlying the evolution of the core binary fraction of star clusters, focussing again on the K100-5 simulation." + Figure 5 shows the number of single stars and binaries in the core. relative to their total number in the cluster. as (he cluster evolves.," Figure \ref{f:fig5} shows the number of single stars and binaries in the core, relative to their total number in the cluster, as the cluster evolves." + For the first 10 Gvr of evolution the ratio of binaries in the core to binaries in the cluster is fairly statie roughly 1 in 10 binaries is in the core.," For the first $10\,$ Gyr of evolution the ratio of binaries in the core to binaries in the cluster is fairly static – roughly 1 in 10 binaries is in the core." + However. the ratio of single stars found in (lie core is decreasing sharply over (he same (ümeframe and (hus single stars are being lost [rom the core al a greater rate than from the cluster in general (comparing Fies.," However, the ratio of single stars found in the core is decreasing sharply over the same timeframe and thus single stars are being lost from the core at a greater rate than from the cluster in general (comparing Figs." + d. and . 5)), \ref{f:fig4} and \ref{f:fig5}) ). + From 10 Gyr onwards the ratio of binaries in the core also decreases.," From $10\,$ Gyr onwards the ratio of binaries in the core also decreases." +" This corresponds to a period of increasing core density: prior to 10 Gyr the core density of stars hovers around the 107>starspe"" mark but [rom 10—15 Gyr it increases by an order of magnitude."," This corresponds to a period of increasing core density: prior to $10\,$ Gyr the core density of stars hovers around the $10^2 \, {\rm stars} \, {\rm pc}^{-3}$ mark but from $10-15\,$ Gyr it increases by an order of magnitude." + The binary [fraction conünues to rise in the core over this period indicating that single stars continue to be lost [rom the core al a greater rate (han binaries., The binary fraction continues to rise in the core over this period indicating that single stars continue to be lost from the core at a greater rate than binaries. + We note (hat mass loss from stellar evolution is reduced considerably at this stage compared to earlier in (he cluster lifetime when more massive stars were present., We note that mass loss from stellar evolution is reduced considerably at this stage compared to earlier in the cluster lifetime when more massive stars were present. + Figure 6 confirms that thenumber of binaries in the core is decreasing with time even though thefraction. fy. is increasing.," Figure \ref{f:fig6} confirms that the of binaries in the core is decreasing with time even though the, $f_{b, {\rm c}}$, is increasing." + We also see [rom this figure that at least half of the binaries in (he core al anv lime were not present in (he core the last time the population was sampled (this is done at intervals of 80 Myr).," We also see from this figure that at least half of the binaries in the core at any time were not present in the core the last time the population was sampled (this is done at intervals of $80\,$ Myr)." + So the core binary population is by πο Ineans static as many binaries are being created/cdestroved. or moving in ancl out of the core.," So the core binary population is by no means static as many binaries are being created/destroyed, or moving in and out of the core," +having supersolar iietallicitv.,having supersolar metallicity. + However. we iueutiou that a significant change in the metallicity progenitor could affect the ACB evolution. and πο-]oss history. as well as the nütial-cfüual mass relation.," However, we mention that a significant change in the metallicity progenitor could affect the AGB evolution and mass-loss history, as well as the initial-final mass relation." + Iu this work. We COLpIted white dwarf sequences with hwdrogeu-rici euvoelopes for ZENNoe abundances of. 0.03. and 0.06 takiug iuto account the energv coutyilttions from ο Νο SCCiuentatiou and carbon-oxyeen pliasc (separation.," In this work, we computed white dwarf sequences with hydrogen-rich envelopes for $^{22}$ Ne abundances of 0.03 and 0.06, taking into account the energy contributions from $^{22}$ Ne sedimentation and carbon-oxygen phase separation." + We compute also additional sequences to assess the impact of these cuerev sources., We compute also additional sequences to assess the impact of these energy sources. +" This inclides he computation of the evolution of a L.OAL.. white darf sequence that was started. in contrast to the other secences, frou au artificially-ecnerated initial model. alc with a carbon- colposition simula to that of the 0.5779M. SCQTLCLICC."," This includes the computation of the evolution of a $1.0 \, M_{\sun}$ white dwarf sequence that was started, in contrast to the other sequences, from an artificially-generated initial model, and with a carbon-oxygen composition similar to that of the $0.8779 \, M_{\sun}$ sequence." + Iu this wav. our sequences cover the eutire white cwarf mass interval for which a carbon-oxvegeni core is expected to be formed.," In this way, our sequences cover the entire white dwarf mass interval for which a carbon-oxygen core is expected to be formed." +" Iu Table 1 «Xe list the stellar tnasses of the white chwarts for which we compute their progenitor evolution. together with the inital masses of the progenitor stars at the ZAMS,"," In Table \ref{tableini} we list the stellar masses of the white dwarfs for which we compute their progenitor evolution, together with the inital masses of the progenitor stars at the ZAMS." + Also listed in Table Lois the central oxvecn abundance at the beeiuuiug of the white dwarf evolutionary track., Also listed in Table \ref{tableini} is the central oxygen abundance at the beginning of the white dwarf evolutionary track. + These sequeuces Were computed from the preavlite dwarf stage down to lostLiL.)5.3., These sequences were computed from the pre-white dwarf stage down to $\log(L/L_{\sun}) \approx -5.3$. + To explore the relevance for the cooling times of uwertaintics in the actual value of the diffusion coefficieu of ?2Ne (Delove Bildsten 2002). we conmpute additional cooling sequences altering the diffusion coefficient by a factor of 2," To explore the relevance for the cooling times of uncertainties in the actual value of the diffusion coefficient of $^{22}$ Ne (Deloye Bildsten 2002), we compute additional cooling sequences altering the diffusion coefficient by a factor of 2." + Finally. we Bud worthwhile to assess the lowest ∐∐∖↑⋜↧∐↕↸⊳↕↑⋅↖↽↕∪↥⋅↖↖↽↕∐↸⊳∐−−⋀∖↸∖↴∖↴↸∖≼∐⋯↸∖∐↑⋜↧⊓∪∐↴∖↴↑⋜∐⋅↑↴∖↴↑∪⋜↧↕−↥↸∖↸⊳↑⋅⋅⋟ ⋅⋅≻⋅≻⇁ ⋅ ⋅ ↴∖↴↕∶↴∙⊾∐↕∐↸⊳⋜⋯↑↕⋅↖⇁↑∐↸∖↸⊳∪∪∐∐∶↴∙⊾↑↕ ⊔↸∖↴∖↴∪↕⋟↖↖↽↕∐↑↸∖≼↧↖↖⇁," Finally, we find worthwhile to assess the lowest metallicity for which $^{22}$ Ne sedimentation starts to affect significantly the cooling times of white dwarfs." +⋜∐⋅↕↸∖↴∙⊺↴∪↑↕∐↴∖↴ end. we compute additional cooling sequences for initial 22N Ne abundances: of4 0.01j and 0.005.," To this end, we compute additional cooling sequences for initial $^{22}$ Ne abundances of 0.01 and 0.005." +r The results preseuted in this work are based on a complete and consistent treatiueut of the differeut energy SOTIECOs that influence the evolution of white πανΕς along he distinct evolutionary 8ages., The results presented in this work are based on a complete and consistent treatment of the different energy sources that influence the evolution of white dwarfs along the distinct evolutionary stages. +COS The ultimate aim is to rovee cooling ages as accurate as possible. according to our best knowledge of the plivsical processes that drive he evolution of these stars.," The ultimate aim is to provide cooling ages as accurate as possible, according to our best knowledge of the physical processes that drive the evolution of these stars." + In particilar. we compute vere tje first exid of white chwart evolutionary sequeuces ∐⋜↧↑∐⊔⊳∪↥⋅↻∪↥⋅⋜↧↑↸∖↴∖↴↑↕∐∖↴∖↴↸∖≼∐⋯↸∖∐↑⋜↧⊓∪∐∪↕−−⋀∖↸," In particular, we compute here the first grid of white dwarf evolutionary sequences that incorporates the sedimentation of $^{22}$ Ne." +∖∙↽∕∏∐∖∶↴∙⊾↥⋅↕≼⊔↴∖↴ ⋅ ⋅ ⊳⋅≻⋅≻⇁↴ ⋅⋅ intened for applications to white dwarS with hieh ??Ne aluud:uices m their cores. namely. those resulting from netalrich progenitors. for which ??Ne sedimentation is expeced to impact f1011 evolution.," The grid is intended for applications to white dwarfs with high $^{22}$ Ne abundances in their cores, namely, those resulting from metal-rich progenitors, for which $^{22}$ Ne sedimentation is expected to impact their evolution." + In the interest of avoiding a leugthv discussion of the results. we will ‘OCIS Oll he consequences of 77Ne sedimentation on he ovution. postponing a conpreheusive description of the standard evolutionary aspects particularly the role of carbon-oxveeu phase separation. to a companion miblication (Renecdo ct al.," In the interest of avoiding a lengthy discussion of the results, we will focus on the consequences of $^{22}$ Ne sedimentation on the evolution, postponing a comprehensive description of the standard evolutionary aspects, particularly the role of carbon-oxygen phase separation, to a companion publication (Renedo et al." + 2010)., 2010). + As shown by Delove Bildsten (2002) and CarciaaBerro οt al. (, As shown by Deloye Bildsten (2002) and a--Berro et al. ( +200s). SN sedimentation is a slow process hat impacts thecevolution of white chwarts oulv after ong onuoug1 fines have elapsed.,"2008), $^{22}$ Ne sedimentation is a slow process that impacts the evolution of white dwarfs only after long enough times have elapsed." + During the evolutionary stages where most oftje white dwarf remains iu a Nei state. this process catses a strone depletion of ?7Ne‘ut in he outer region of fre core. and an enbaucenie of its abundauce in the central regions of the star.," During the evolutionary stages where most of the white dwarf remains in a liquid state, this process causes a strong depletion of $^{22}$ Ne in the outer region of the core, and an enhancement of its abundance in the central regions of the star." + This rchavicx becomes Sustautially more noticeable as the eyavity is increased., This behavior becomes susbtantially more noticeable as the gravity is increased. + Iudeed. a more rapid sedimentation aud faster depletion of ?7Ne in the outer avers is expected in inassive white dwarts.," Indeed, a more rapid sedimentation and a faster depletion of $^{22}$ Ne in the outer layers is expected in massive white dwarfs." + However. because πο white dwarfs crvstallize earher than less massive OUCS. DONC7Noe sedimenta+jon will stop at higher effective temperatures as compared with less massive white dwarts.J thus linitiugHfLI the exteut to whichH Μος.“Ne diffusion∙⋅. constitues an enerev source for the star.," However, because massive white dwarfs crystallize earlier than less massive ones, $^{22}$ Ne sedimentation will stop at higher effective temperatures as compared with less massive white dwarfs, thus limiting the extent to which $^{22}$ Ne diffusion constitutes an energy source for the star." + This is a critical issue regarding the cooling behavior of massive white clwarts., This is a critical issue regarding the cooling behavior of massive white dwarfs. + ⊀≚↴∖↴↸∖↘⋉∖↸⊳↑↸∖≼↧∙↑∐↸∖↸⊳∪∐⊓⋅↕↴⋝∏↑↕∪∐∪↕−−⋀∖↸∖↴∖↴↸∖≼∐↕⊔↸∖∐↑⋜↧↕∪∐⋅⋅ ⊳⋅≻⋅≻⇁ ⋅ to the hnunosity budget of white chvarfs becomes larger as the uetal content of the parent star is iucreased.," As expected, the contribution of $^{22}$ Ne sedimentation to the luminosity budget of white dwarfs becomes larger as the metal content of the parent star is increased." + This is exemplified in Fise. 2..," This is exemplified in Fig. \ref{hr}," + which shows the resulting lunimositv contribution (expressed im solar units) in terms of the effective temperature of the white dwarf for the (17051 aud the 0.5219M.. sequences (upper aud bottoni ucl. respectively) aud for the two moetallicities adopted in this work. Z=0.03 and 0.06.," which shows the resulting luminosity contribution (expressed in solar units) in terms of the effective temperature of the white dwarf for the 0.7051 and the $0.5249 \, M_{\sun}$ sequences (upper and bottom panel, respectively) and for the two metallicities adopted in this work, $Z=0.03$ and 0.06." + This figure gives us a dec] »iusiglit of the importance of 77 Ne sedimentation iuto the elobal cuerectics during the entire white dwarf evolution., This figure gives us a deep insight of the importance of $^{22}$ Ne sedimentation into the global energetics during the entire white dwarf evolution. + Note that the coutribution from this process, Note that the contribution from this process +extinction value will result.,extinction value will result. + But more common will be the cases when this zone of avoidance partially covers a cell., But more common will be the cases when this zone of avoidance partially covers a cell. + In that case. the cell may still have stars enough for the giant branch fitting method to be applied but the resulting κοτος Will be an underestimate of the true one.," In that case, the cell may still have stars enough for the giant branch fitting method to be applied but the resulting $A_{K,2MASS}$ will be an underestimate of the true one." + Note that the ziiprz values will not suller from such bias.," Note that the $A_{K,FIR}$ values will not suffer from such bias." + We may model the latter simply as an average over the entire coll: where the integral is over the cell’s solid angle ancl τω) is the varving A band optical depth within the cell boundaries., We may model the latter simply as an average over the entire cell: where the integral is over the cell's solid angle and $\tau (\omega)$ is the varying $K$ band optical depth within the cell boundaries. + For the 2ALASS. assuming that only regions with 7<2 will contribute with CMD stars. we would have: where the 2MASS integral. limit. on the numerator corresponds to the cell regions where τ<2.," For the 2MASS, assuming that only regions with $\tau < 2$ will contribute with CMD stars, we would have: where the 2MASS integral limit on the numerator corresponds to the cell regions where $\tau < 2$." + We may then estimate the relative bias in the latter quantity by determining the ratio mapωςότι For some moclel for τα)., We may then estimate the relative bias in the latter quantity by determining the ratio $\tau_{2MASS} / \tau_{FIR}$ for some model for $\tau (\omega)$. + An important case of interest. especially for the lowest b regions (Jbl<0.5 (see Fig.," An important case of interest, especially for the lowest $b$ regions $|b| < 0.5^{\circ}$ (see Fig." + 3). will be that of a direction cutting through a dense dust cloud.," 3), will be that of a direction cutting through a dense dust cloud." + We may consider that the cloud will dominate the dust. column density in that direction and therefore ignore the contribution of foreground and background. material., We may consider that the cloud will dominate the dust column density in that direction and therefore ignore the contribution of foreground and background material. + Lowe also assume the cloud to have a central optical depth 75. circular symmetry. and an exponentially falling cust column density. we will have: where 4 is the angle between the direction to the cloud centre and the direction considered and 85 is the cloud exponential scale.," If we also assume the cloud to have a central optical depth $\tau_0$, circular symmetry, and an exponentially falling dust column density, we will have: where $\theta$ is the angle between the direction to the cloud centre and the direction considered and $\theta_0$ is the cloud exponential scale." + Fig., Fig. + S shows ToassTptig asa Function of my for several choices of 64., 8 shows $\tau_{2MASS} / \tau_{FIR}$ as a function of $\tau_0$ for several choices of $\theta_0$. +" For 6,=2 and y;>5. the entire cell would have 72 and therefore. zyspass. would. become undetermined."," For $\theta_0 = 2'$ and $\tau_0 > 5$, the entire cell would have $\tau > 2$ and therefore $\tau_{K,2MASS}$ would become undetermined." + We infer from the figure that the bias on the PALASS data is relatively insensitive to the eloud profile shape but it is clearly dependent on profile normalization., We infer from the figure that the bias on the 2MASS data is relatively insensitive to the cloud profile shape but it is clearly dependent on profile normalization. + For dust. clouds with my«5 (roughly corresponding to a central zl< 55). the systematic ellect on elasayiss wil ρου .," For dust clouds with $\tau_0 < 5$ (roughly corresponding to a central $A_V < 55$ ), the systematic effect on $A_{K,2MASS}$ will be $20$." + Note that these ratios were computed assuming the centre of the dust cloud to coincide. with the cell's centre., Note that these ratios were computed assuming the centre of the dust cloud to coincide with the cell's centre. + For the more common olf-center positions. Aneuassflayrin TROMASsSITEILBR will be larger than shown in Fig.," For the more common off-center positions, $A_{K,2MASS} / A_{K,FIR} \simeq \tau_{K,2MASS} / \tau_{FIR}$ will be larger than shown in Fig." + S., 8. + Also. in the higher extinction regions there may possibly be more than one cloud. per cell. thus increasing this svstematic ellect.," Also, in the higher extinction regions there may possibly be more than one cloud per cell, thus increasing this systematic effect." + Fie., Fig. + 9 shows a grav scale map of the clisurasscdrin ratio. which provides information about the relative," 9 shows a gray scale map of the $A_{K,2MASS}/ A_{K,FIR}$ ratio, which provides information about the relative" +of the error function between the borders of the cells).,of the error function between the borders of the cells). +" Summing the probability for all stars, the end result of this procedure is the number-density of stars in a given cell."," Summing the probability for all stars, the end result of this procedure is the number-density of stars in a given cell." + We do this for the cluster and comparison field cells., We do this for the cluster and comparison field cells. +" Next, the comparison field number-density is converted back into an integer number of stars, which is subtracted from the cluster extraction, on a cell-by-cell basis."," Next, the comparison field number-density is converted back into an integer number of stars, which is subtracted from the cluster extraction, on a cell-by-cell basis." +" Thus, the number of member stars in a given cell is NG""..."," Thus, the number of member stars in a given cell is $N^{cell}_{clean}$." +" Allowing for variations in the cell positioning corresponding to 1/3 of the adopted cell size in each dimension, we are left with 27 different setups."," Allowing for variations in the cell positioning corresponding to 1/3 of the adopted cell size in each dimension, we are left with 27 different setups." +" Each setup produces a total number of member stars, Nmem=icell from which we compute the expected total number of member stars (Nmem) by averaging out Nmem over all combinations."," Each setup produces a total number of member stars, $N_{mem}\,=\,\sum_{cell}N^{cell}_{clean}$, from which we compute the expected total number of member stars $\left$ by averaging out $N_{mem}$ over all combinations." +" Stars are ranked according to the number of times they survive all runs, and only the (Nmem) highest ranked stars are considered cluster members and transposed to the respective decontaminated CMD (bottom panels of reffig:t127.mdto12))."," Stars are ranked according to the number of times they survive all runs, and only the $\left$ highest ranked stars are considered cluster members and transposed to the respective decontaminated CMD (bottom panels of \\ref{fig:t127_cmd} to \ref{fig:newcl4_cmd}) )." +"T'hedif ferencebetweentheexpectednumbero 5 fAeldetqy es uhichinaybe fractional)andthenumberof starseff ectivelysubtr for 1127, 26.4+33.3% for 22, 87.143.7% for 994, 92.1+2.4% for 33 and 90.9+7.5% for 44."," The difference between the expected number of field stars (which may be fractional) and the number of stars effectively subtracted (which is integer) from each cell is the subtraction efficiency, which summed over all cells is $\pm$ for 127, $\pm$ for 2, $\pm$ for 94, $\pm$ for 3 and $\pm$ for 4." + No star has been removed within the area of 11., No star has been removed within the area of 1. + All cluster(J—Ks) CMDs of this sample were fitted by eye with 1MMyr Solar-metallicity (suitable for the Galactic disk in general) Padova isochrones 2008))., All cluster CMDs of this sample were fitted by eye with Myr Solar-metallicity (suitable for the Galactic disk in general) Padova isochrones \citealt{marigo08}) ). +" In addition, PMS isochrones by Siess,Forestini(2000) for the ages 0.2, 1, 2, 3,5, 10, and MMyr, were used when necessary."," In addition, PMS isochrones by \citet*{siess00} for the ages 0.2, 1, 2, 3, 5, 10, and Myr, were used when necessary." + Isochrone fits for each cluster reftab:pho)) correspond to a distance from the Sun kkpc (that matches that of Foster&Routledge 2003))., Isochrone fits for each cluster \\ref{tab:pho}) ) correspond to a distance from the Sun kpc (that matches that of \citealt{fosrou03}) ). + This distance locates 912-132 in the Orion-Cygnus arm (Momanyetal. 2008))., This distance locates Sh2-132 in the Orion-Cygnus arm \citealt{momany08}) ). + Only SBB44 appears to be closer and is not part of the complex Sh2-132., Only 4 appears to be closer and is not part of the complex Sh2-132. + Isochrone fit for the CMD of this cluster yields a distance from the Sun kkpc., Isochrone fit for the CMD of this cluster yields a distance from the Sun kpc. +" We detected MS and PMS stars in all clusters, although"," We detected MS and PMS stars in all clusters, although" +electron gas in a metal. where the energy. barrier they must overcome is the work function of the metal.,"electron gas in a metal, where the energy barrier they must overcome is the work function of the metal." +" In a strong magnetic field. the electron Lux is given by F _ TET where puin=fy2n, ped[Uo]. DoCo is the potentialη energy. of⋅ the electrons in. the metal. €=pz/(2m,)E is. the electron. kineticη. energy. and [f(c))- is the Fermi-Dirac distribution function with ye. the electron chemical potential (excluding potential energy)."," In a strong magnetic field, the electron flux is given by _e = ) , where $p_{\rm min}=\sqrt{2m_e|U_0|}$ , $U_0$ is the potential energy of the electrons in the metal, $\epsilon=p_z^2/(2m_e)$ is the electron kinetic energy, and ) = is the Fermi-Dirac distribution function with $\mu'_e$ the electron chemical potential (excluding potential energy)." + Integrating this expression gives FOLIEEaunqua where 6=[Uo].—pl is the work function of the condensed matter and the second equality assumes ὦAd.," Integrating this expression gives _e = ], where $\phi \equiv |U_0|-\mu'_e$ is the work function of the condensed matter and the second equality assumes $\phi \gg kT$." +" Phe steady-state charge density supplied by the surface is then Po with ο ye 30.. where Z5=T/(10""Ix) and £1, is the spin period in units of 1s. For a typical set of pulsar parameters (e.g.. £4,=1 and dí= 0.5) C.~30. but C. can range from 23 for millisecond pulsars to 35 for some magnetars."," The steady-state charge density supplied by the surface is then _e = = , with C_e = ) 30, where $T_6=T/(10^6~{\rm K})$ and $P_0$ is the spin period in units of 1 s. For a typical set of pulsar parameters (e.g., $P_0=1$ and $T_6=0.5$ ) $C_e \sim 30$, but $C_e$ can range from 23 for millisecond pulsars to 35 for some magnetars." + Note that the requirement O>KT is automatically satified here when |p. is less than gen|.," Note that the requirement $\phi \gg +kT$ is automatically satified here when $|\rho_e|$ is less than $|\rho_{GJ}|$." + Phe electron work function was calculated in MLO6b and is depicted in Fig. 4.., The electron work function was calculated in ML06b and is depicted in Fig. \ref{Wfig}. +" For neutron stars with €:B,«0. the Goldreich-Juliam charge above the polar cap is positive. so we are interested in ion emission from the surface."," For neutron stars with $\mathbf{\Omega}\cdot\mathbf{B}_p < 0$, the Goldreich-Juliam charge above the polar cap is positive, so we are interested in ion emission from the surface." + Unlike the electrons. which form a relatively [ree-moving gas within the condensed matter. the ions are bound to their lattice To escape from the surface. the ions must satislv three conditions.," Unlike the electrons, which form a relatively free-moving gas within the condensed matter, the ions are bound to their lattice To escape from the surface, the ions must satisfy three conditions." + First. they must be located on the surface of the Lattice.," First, they must be located on the surface of the lattice." + Ίος below the surface will encounter too much resistance in trving to move through another ion's cell., Ions below the surface will encounter too much resistance in trying to move through another ion's cell. + Second. they must have enough energy to escape as unbound ions.," Second, they must have enough energy to escape as unbound ions." + This binding energy that must be overcome will be labeled £g., This binding energy that must be overcome will be labeled ${\cal E}_B$. + Phird. they must be thermally activated.," Third, they must be thermally activated." + The energy in the lattice is mostly transferred by conduction. so the ions must wait until they are bumped by atoms below to gain enough energy to escape.," The energy in the lattice is mostly transferred by conduction, so the ions must wait until they are bumped by atoms below to gain enough energy to escape." +" Consider the emission of ions with charge Z,c from the neutron star surface (e... Fe would have Z,= 1)."," Consider the emission of ions with charge $Z_n e$ from the neutron star surface (e.g., $^+$ would have $Z_n=1$ )." + The rate of collisions between any two ions in the lattice is approximately equal to the lattice vibration frequency. 7;. which can he estimated from where Ον=(42Z72mi)is 1/2.the ton plasma. (angular) frequency and⋅ i; =ZeD/(ni;e)is. the. ion evelotron⋅ frequency “nj (m;= ny).," The rate of collisions between any two ions in the lattice is approximately equal to the lattice vibration frequency $\nu_i$, which can be estimated from, where $\Omega_p=\left(4\pi Z^2e^2n_i/m_i\right)^{1/2}$ is the ion plasma (angular) frequency and $\omega_{ci}=ZeB/(m_ic)$ is the ion cyclotron frequency $m_i=Am_p$ )." + Not all collisions will lead to ejection of ions from the surface. since an energy barrier £g must be overcome.," Not all collisions will lead to ejection of ions from the surface, since an energy barrier ${\cal E}_B$ must be overcome." + Thus each surface ion has an effective emission rate of order 4e The energy. barrier €i for ejecting tonsof charge Ze is equivalent to the energy required to release a neutral atom from the surface and ionize it. minus the energve Ingained by returninge the electron to the surface (ο...ὃν Tsongo 1990)).," Thus each surface ion has an effective emission rate of order = _i. The energy barrier ${\cal E}_B$ for ejecting ionsof charge $Z_n e$ is equivalent to the energy required to release a neutral atom from the surface and ionize it, minus the energy gained by returning the electron to the surface (e.g., \citealt{tsong90}) )." + Thus, Thus +wilh PG)x@? while the junction with the propeller track at the current M(I) moves down the dipole track. ahead of the pulsar. but at a slower rate P240)xtrack.PI,"with $P(t)\propto t^{1/2}$ while the junction with the propeller track at the current $\dot{M}(t)$ moves down the dipole track, ahead of the pulsar, but at a slower rate $P_0(t)\propto t^{\eta/4}$ ." + A4 =dg. Ply)=PG) and (he pulsar is just turning into its current propeller ," At $t=t_0$, $P(t_0)=P_0(t_0)$ and the pulsar is just turning into its current propeller track." +For />dy. the pulsar lollows its current. propeller track while (he track itself continues to shift towards the bottom-right corner of the P— diagram. as M(/) continues to decrease.," For $t>t_0$, the pulsar follows its current propeller track while the track itself continues to shift towards the bottom-right corner of the $P-\dot{P}$ diagram, as $\dot{M}(t)$ continues to decrease." +" To derive the form of MU/) "" us use the observation that P069)=P3.Mg)) is similar for all pulsars."," To derive the form of $\dot{M}(t)$ let us use the observation that $P_0(t_0)=P_0(\beta,\dot{M}(t_0))$ is similar for all pulsars." + Taking=(.3 s gives My)=L98x10HB?44.," Taking$P_0=0.3$ s gives $\dot{M}(t_0)=1.98\times10^{11}B_{\bot,12}^2$." +" Dipole spindown (Eq.(6)) until /—li vields uuP,By=1.23xLO1D. ων)=0.3 & or D?44=5.95x10""/Iu(vr)."," Dipole spindown (Eq.(6)) until $t=t_0$ yields $P_0=1.23\times10^{-4} +B_{\bot,12} t_0$ $^{1/2}=0.3$ s or $B_{\bot,12}^2=5.95\times10^6/t_0$ (yr)." + Thus we find thatM(/)=L1»ο ο |. that is. jj=L," Thus we find that $\dot{M}(t)=1.18\times10^{18}$ $t$ $^{-1}$ , that is, $\eta=1$." +" For Boye=d.49 =5.95x10"" vr and MUIiy)=2x1011 em/s are obtained."," For $B_{\bot,12}=1$, $t_0=5.95\times10^{6}$ yr and $\dot{M}(t_0) \cong 2\times10^{11}$ gm/s are obtained." +" The application here to all pulsars accross the P— diagram and its success in fitting the pulsar distribution require and support the presence of low mass. low AZ disks. which are active [or pulsar lifetimes of the order of LO"" vrs ancl remain attached to the light cvlinder."," The application here to all pulsars accross the $P-\dot{P}$ diagram and its success in fitting the pulsar distribution require and support the presence of low mass, low $\dot{M}$ disks, which are active for pulsar lifetimes of the order of $10^7$ yrs and remain attached to the light cylinder." + The time dependence of the disk and the mass inflow rate it supplies could be incorporated in a more detailed calculation., The time dependence of the disk and the mass inflow rate it supplies could be incorporated in a more detailed calculation. + The self similar isolated thin disk models with a power law decay of M(I) were emploved by Menou. Perna and Iernquist (2001b) who point out. that for the Crab pulsar. PSR BO540-09 and PSR D1509-58. thin disks in the M ranges indicated by the braking indices of these pulsars are consistent. wilh observational constraints in the optical though most of the disk huminosity would be in the UY where detections are much harder.," The self similar isolated thin disk models with a power law decay of $\dot{M}(t)$ were employed by Menou, Perna and Hernquist (2001b) who point out that for the Crab pulsar, PSR B0540-09 and PSR B1509-58, thin disks in the $\dot{M}$ ranges indicated by the braking indices of these pulsars are consistent with observational constraints in the optical though most of the disk luminosity would be in the UV where detections are much harder." + For the Vela pulsar only a very small and highly: inclined disk could be compatible with observational constraints., For the Vela pulsar only a very small and highly inclined disk could be compatible with observational constraints. + According to the classification of Alpar (2001) disks are present around all classes of voung neutron stars. providing accretion [or AXPs and acting as propellers on DTNs ancl RQNSs.," According to the classification of Alpar (2001) disks are present around all classes of young neutron stars, providing accretion for AXPs and acting as propellers on DTNs and RQNSs." +" For two AXPs and the RQNS in Cas A luminosities predicted by thin disk models are ruled out or tightly constrained by observations in the optical "" IR (Coe Pightling 1998. ... οἱ al 2000. Hulleman. van Werkwijk Ixullkarni—O—2000. IXaplan. Kulkarni Murray""2001)."," For two AXPs and the RQNS in Cas A luminosities predicted by thin disk models are ruled out or tightly constrained by observations in the optical and IR (Coe Pightling 1998, Hulleman et al 2000, Hulleman, van Kerkwijk Kulkarni 2000, Kaplan, Kulkarni Murray 2001)." + Further. it is likely (hat disks under propeller conditions are not standard disks (Alpar 2001).," Further, it is likely that disks under propeller boundary conditions are not standard thin disks (Alpar 2001)." + As the mass inflow is stopped at the cdisk-magnetosphere boundary aud largely ejected. Lom the svstenm. the disk may be enshrined in a corona and oulllow of ejected matter. possibly with larger effective area and softer spectrum.," As the mass inflow is stopped at the disk-magnetosphere boundary and largely ejected from the system, the disk may be enshrined in a corona and outflow of ejected matter, possibly with larger effective area and softer spectrum." + Menou. Perna and IHernquist (2001a) have shown (hat the thin disks may become neutral and stop evolving as thin disks.," Menou, Perna and Hernquist (2001a) have shown that the thin disks may become neutral and stop evolving as thin disks." + The transition would quench the disks Iuminosity. but it would also suppress the dynamical evolution of the disk if the viscositv of MIID. origin is no longer operational.," The transition would quench the disk's luminosity, but it would also suppress the dynamical evolution of the disk if the viscosity of MHD origin is no longer operational." + However. a smaller but. nonzero viscosity should be operating in a neutral disk.," However, a smaller but nonzero viscosity should be operating in a neutral disk." + Furthermore irradiation by the pulsar will probably keep (he disk ionized and allow the mass inflow to continue. possibly as a power law decay.," Furthermore irradiation by the pulsar will probably keep the disk ionized and allow the mass inflow to continue, possibly as a power law decay." + The mininnun rotational energy loss rate ofthe pulsars is of the order of 10 erg L, The minimum rotational energy loss rate ofthe pulsars is of the order of $10^{30}$ erg $^{-1}$ . + The luminosity of the irradiated disk may beshifted to different spectral bands (Perna, The luminosity of the irradiated disk may beshifted to different spectral bands (Perna +Rucerman (1979) the subpulse polarization patterns can be. in general. allected by the propagation effects if the so called adiabatic walking condition is satisfied.,"Ruderman (1979) the subpulse polarization patterns can be, in general, affected by the propagation effects if the so called adiabatic walking condition is satisfied." + Llowever. a more rigorous treatment for (he radiation mechanism considered here demonstrates that the adiabatic walking condition is not satisfied (see eq. |," However, a more rigorous treatment for the radiation mechanism considered here demonstrates that the adiabatic walking condition is not satisfied (see eq. [" +31] and the corresponding discussion below it in GLAIO4).,31] and the corresponding discussion below it in GLM04). + Therefore the waves escape from the plasma retaining the initial polarization in (he direction perpendicular to the magnetic field line planes. exactly as il is observed in strong and hiehlv linearly polarized subpulses presented in our Fig.," Therefore the waves escape from the plasma retaining the initial polarization in the direction perpendicular to the magnetic field line planes, exactly as it is observed in strong and highly linearly polarized subpulses presented in our Fig." + 2., 2. + The characteristic Lorentz [actors of emitng bunches/solitons should be about 57400. for obtaining the observed [requency and power due to coherent curvature radiation in the maegnetospheric plasma (GLAIOL).," The characteristic Lorentz factors of emitting bunches/solitons should be about $\gamma\simeq 400$, for obtaining the observed frequency and power due to coherent curvature radiation in the magnetospheric plasma (GLM04)." + The typical subpulse widths in Fig., The typical subpulse widths in Fig. + b and 2 is about 122x107? radians. which is several times larger than the width of the radiation cone of an elementary curvature emitter 1/400=0.0025 radians.," 1 and 2 is about $ +1^\circ \simeq 2\times 10^{-2}$ radians, which is several times larger than the width of the radiation cone of an elementary curvature emitter $1/400=0.0025$ radians." + Thus the subpulse should be formecl by the incoherent sum of radiation emitted bv a munber of solitons filling the flux (ube of dipolar field lines with an angular extent of about 0.02 racians in the emission region (which for a (vpical pulsar with a period of 1 sec originates at an emission altitude of about 50 stellar radii. see for e.g. Melikidze et al.," Thus the subpulse should be formed by the incoherent sum of radiation emitted by a number of solitons filling the flux tube of dipolar field lines with an angular extent of about 0.02 radians in the emission region (which for a typical pulsar with a period of 1 sec originates at an emission altitude of about 50 stellar radii, see for e.g. Melikidze et al." + 2000. IXijak Gil 1997).," 2000, Kijak Gil 1997)." + This angular width projected onto the polar cap surface gives about 1: percent of the fractional area. which is consistent with the model in which the base of the subpulse flux (tube is formed by sparks ol electron-positron avalanches (e.g. Ruderman Sutherland 1975. Gil sendvk 2000).," This angular width projected onto the polar cap surface gives about 1 percent of the fractional area, which is consistent with the model in which the base of the subpulse flux tube is formed by sparks of electron-positron avalanches (e.g. Ruderman Sutherland 1975, Gil Sendyk 2000)." + This leads to generation of coherent curvature radiation as proposed in the spark associated soliton model by Melikidze. Gil Patarava (2000).," This leads to generation of coherent curvature radiation as proposed in the spark associated soliton model by Melikidze, Gil Pataraya (2000)." + In this paper we analvse a selection of high quality. almost completely polarized single pulses [rom a number of pulsars.," In this paper we analyse a selection of high quality, almost completely polarized single pulses from a number of pulsars." + We argue that in those cases we observe almost exclusively one polarization mode. which we associate with the extraordinary waves excited bv the coherent curvature radiation (GLMOA).," We argue that in those cases we observe almost exclusively one polarization mode, which we associate with the extraordinary waves excited by the coherent curvature radiation (GLM04)." + It should be mentioned that some earlier observations have already found evidence that single pulse PA variations lollow the mean PA traverse (see Ramachandran et al., It should be mentioned that some earlier observations have already found evidence that single pulse PA variations follow the mean PA traverse (see Ramachandran et al. + 2002)., 2002). + However those observations do not reveal anv Liehly polarized pulses as shown in (hiis paper., However those observations do not reveal any highly polarized pulses as shown in this paper. + Single pulse depolarization can result from incoherent addition of emission overlapping Iron adjacent field lines w.r.t the LOS. presence of orthogonal modes and also propagation effects.," Single pulse depolarization can result from incoherent addition of emission overlapping from adjacent field lines w.r.t the LOS, presence of orthogonal modes and also propagation effects." + Our almost completely polarized pulses. are relatively [ree of depolarization and hence can be associated with one of the polarization mode.," Our almost completely polarized pulses, are relatively free of depolarization and hence can be associated with one of the polarization mode." + In this sense ον seem {ο be ideal to unravel the nature of the pulsar radio emission process., In this sense they seem to be ideal to unravel the nature of the pulsar radio emission process. + Naturally. based on our selected. data we are not able to examine the phenomenon of orthogonally poluized modes.," Naturally, based on our selected data we are not able to examine the phenomenon of orthogonally polarized modes." + Hence. the question about (he origin of orthogonal modes observed in pulsar radio emission is still open.," Hence, the question about the origin of orthogonal modes observed in pulsar radio emission is still open." + While the answer is not vel clear. we speculate that the," While the answer is not yet clear, we speculate that the" +The post-Newtouiau contributions to the velocity. which we introduce here are where the terms with wy aud «ws have been added for reasous that will be mace clear when we discuss the solution.,"The post-Newtonian contributions to the velocity, which we introduce here are where the terms with $w_1$ and $w_2$ have been added for reasons that will be made clear when we discuss the solution." + Note that we could eliminate oue constant by introducing variables to denote qj|q ul qo g. but choose instead to retain the jiotatioun iu The Newtonian ellipsoid is characterized by the seni-najor axes 44202Lxay.," Note that we could eliminate one constant by introducing variables to denote $q_1+q$ and $q_2-q$, but choose instead to retain the notation in The Newtonian ellipsoid is characterized by the semi-major axes $a_1\ge a_2\ge a_3$." + Let us assume for he momeut that. as in the Newtomian setting. the axisviunietrie case is obtained by considering e»= ay. an asstuuption that will be verified shortly.," Let us assume for the moment that, as in the Newtonian setting, the axisymmetric case is obtained by considering $a_2=a_1$ , an assumption that will be verified shortly." + In his case. the index 27 iu the index syiubols «ljji... aud Byjy... usedin CETS aud discussed at leugth in 21 of ? can be replaced. by D as is evideut roni the defiutious.," In this case, the index `2' in the index symbols $A_{ijk\ldots}$ and $B_{ijk\ldots}$ usedin CE78 and discussed at length in 21 of \citet{Chandrasekhar87} can be replaced by `1' as is evident from the definitions." + Using the rolatious giveu iu hat book. it is possible to reduce all the iudex sviubols to Ay and ilo.," Using the relations given in that book, it is possible to reduce all the index symbols to $A_1$ and $A_2$." + At the point a2=e. the value for ly (and thus lo) is given by (36) in 17 of ?..," At the point $a_2=a_1$, the value for $A_1$ (and thus $A_2$ ) is given by (36) in 17 of \citet{Chandrasekhar87}." + Furthermore. (2) from ? shows us that ⋅ ↖↖↽∐↸∖↥⋅↸∖↖↖↽↸∖≼∐∖∱∐∐∖↑∐↸∖↴∖↴∙↖↽∐∐⋝∪↕∶↑∪⋯↸∖⋜⋯↑∐⋜↧↑↑∐↸∖ ↸∖↘↻↥⋅↸∖↴∖∷∖↴↕∪∐↕↴∖↴↸∖↖↽⋜↧↕∏⋜↧↑↸∖≼↧⋜↧↑↑∐↸∖↻∪↕∐↑↙∣⊐∶↙∣⊥⋅↕∙↸∖∙ The value for a3 can be found from the equation which holds for the Dedekind (aud Jacobi) ellipsoids. aud gives the value Throughout this paper. «5 is to be understood asa fiction of e4 aud e». given by1).," Furthermore, (2) from \citet{CE74} shows us that where we define the symbol $\stackrel{a}{=}$ to mean that the expression is evaluated at the point $a_2=a_1$, i.e. The value for $a_3$ can be found from the equation which holds for the Dedekind (and Jacobi) ellipsoids, and gives the value Throughout this paper, $a_3$ is to be understood as a function of $a_1$ and $a_2$, given by." + We can now consider the integrability conditions for the pressure aud the coutinuity equation., We can now consider the integrability conditions for the pressure and the continuity equation. + We again follow CETS auc shall refer to the equation uunbers there by adding a prine., We again follow CE78 and shall refer to the equation numbers there by adding a prime. + It turus out that (38°) (of CETS) remains unchauged despite the inocification to the velocity. so that we fiuc Equation (28) is ideutically ‘ulfilled for a.= ay. lineaninge that q4 is left undetermined. iu contrast to the general case.," It turns out that (38') (of CE78) remains unchanged despite the modification to the velocity, so that we find and then from (24') that Equation (28') is identically fulfilled for $a_2=a_1$ , meaning that $q_1$ is left undetermined, in contrast to the general case." + With the changes to the velocity. equatious (307) and (31°) gain the additional terms (aQus|aS) aud (aQus|πο” respectively.," With the changes to the velocity, equations (30') and (31') gain the additional terms $(a_1^2Q_2w_1+a_2^2Q_1w_2)x_1$ and $(a_1^2Q_2w_1+a_2^2Q_1w_2)x_2$ respectively." +Equations (32°)(38) remain unchauged.,Equations (32')–(38') remain unchanged. + Equation (32°) vields and (37°) gives (we shall see shortly that each f; becomes zero)., Equation (32') yields and (37') gives (we shall see shortly that each $t_i$ becomes zero). +" There are additional terms in (39°) correspouding to adding: (απών.""ασ0)(02)/2B both ay TN.and asTN", There are additional terms in (39') corresponding to adding $-(a_1^2Q_2w_1+a_2^2Q_1w_2)/2=a_2^2Q_1(w_1-w_2)/2$ both $\alpha_1^{78}$ and $\alpha_2^{78}$. + Requiring for the new velocity that its normal component vanish on the surface leads to a change in (50) aud thus the resulting equations (527) bv which the terms with Sy$5 are moclified., Requiring for the new velocity that its normal component vanish on the surface leads to a change in (50') and thus the resulting equations (52')--(56') by which the terms with $S_1-S_2$ are modified. +" ""They now become Using equatious (2). and (8). we can subtract equation (51) from (55°) in CETS to arrive at"," They now become Using equations , and , we can subtract equation (54') from (55') in CE78 to arrive at" +Gravitational instabilities in protostellar disces may be important for several reasons.,Gravitational instabilities in protostellar discs may be important for several reasons. + First. if the gravitational instability is strong enough. the dise may fragment to form a companion (e.g. 22222).," First, if the gravitational instability is strong enough, the disc may fragment to form a companion (e.g. \citealt{bonnell94,bb94a,bb94b,whitworth95,rice05}) )." + This is particularly relevant to the magnetised star formation simulations performed by ?.., This is particularly relevant to the magnetised star formation simulations performed by \citet{hw04b}. + They began with a rotating cloud that. in the absence of magnetic fields formed a single object surrounded by a gravitationally unstable dise that fragmented to form companions.," They began with a rotating cloud that, in the absence of magnetic fields formed a single object surrounded by a gravitationally unstable disc that fragmented to form companions." + With magnetic fields initially aligned with the rotation. axis.. they found. that the dise. was much smaller and did. not fragment.," With magnetic fields initially aligned with the rotation axis, they found that the disc was much smaller and did not fragment." + This is consistent with our simulations in that we also find that magnetic fields reduce the tendency for a dise to be gravitational unstable., This is consistent with our simulations in that we also find that magnetic fields reduce the tendency for a disc to be gravitational unstable. + However. Hosking Whitworth attributed the inhibiting of fragmentation to the loss of angular momentum due to magnetic tension forces.," However, Hosking Whitworth attributed the inhibiting of fragmentation to the loss of angular momentum due to magnetic tension forces." +" Here we find that the effect of magnetic pressure in decreasing the mass infall rate on to the dise may be just as important in suppressing dise fragmentation,", Here we find that the effect of magnetic pressure in decreasing the mass infall rate on to the disc may be just as important in suppressing disc fragmentation. + Second.Sec if a protostellar dise is ↜∙⇤∡∙≕∴∡⋡⊽∼gravitationally unstable (but not so strongly as to fragment). spiral density waves are likely to," Second, if a protostellar disc is gravitationally unstable (but not so strongly as to fragment), spiral density waves are likely to" +SUAISS or NVSS catalogues (see Section 5. [or more details on how these were identified).,SUMSS or NVSS catalogues (see Section \ref{radiodetections} for more details on how these were identified). +" Possible BL-Lac objects are llagged with a comment ""DLLac or ""BLLac?"""," Possible BL-Lac objects are flagged with a comment “BLLac"" or “BLLac?""" + in the final catalogue. where the question mark denotes a higher degree of uncertainty in the classification.," in the final catalogue, where the question mark denotes a higher degree of uncertainty in the classification." + ‘To check for previously known redshifts in the RASSαμα full sample we searched the NASA Extragalactic Database (NED)., To check for previously known redshifts in the RASS–6dFGS full sample we searched the NASA Extragalactic Database (NED). + Excluding redshifts listed with a 1 reference (from previous data releases). it was found that 995 (29.2%) sources already hack known redshifts. of which 496 had a eood quality ((22 3) 6dE redshilt.," Excluding redshifts listed with a 6dFGS reference (from previous data releases), it was found that 995 $\%$ ) sources already had known redshifts, of which 496 had a good quality $Q\geq3$ ) 6dFGS redshift." +" Of the 995 sources with known recdshifts. S26 (83%) sources are optically bright (b,x 17.5) and of these bright sources 409 have a reliable GdGS redshift."," Of the 995 sources with known redshifts, 826 $\%$ ) sources are optically bright $b_{\rm J} \leq 17.5$ ) and of these bright sources 409 have a reliable 6dFGS redshift." + Phe SIAIBAD database was also checked. revealing S stars with existing classifications.," The SIMBAD database was also checked, revealing 8 stars with existing classifications." +" ""This smaller sample of 504 (496 from NED and S from SIMDAD) sources with both Gd€S redshifts and a redshift from an independent source allowed us to check the reliability of the GabGS redshifts.", This smaller sample of 504 (496 from NED and 8 from SIMBAD) sources with both 6dFGS redshifts and a redshift from an independent source allowed us to check the reliability of the 6dFGS redshifts. +The results for the 21 Rc and 65 lHütab stars are documented in Fig. 1.,The results for the 21 RRc and 65 RRab stars are documented in Fig. \ref{oc}. + Three panels are shown for cach variable., Three panels are shown for each variable. + The ο—€' values ancl their errors. estimated as twice the standard deviation of the corresponding part of the light curve from the light-curve template used: to determine the O—C' value. are plotted versus time in the left-side panels.," The $O-C$ values and their errors, estimated as twice the standard deviation of the corresponding part of the light curve from the light-curve template used to determine the $O-C$ value, are plotted versus time in the left-side panels." + For the sake of uniformity and. simplicity. the O C' diagrams have been approximated by polynomials of different: order.," For the sake of uniformity and simplicity, the $O-C$ diagrams have been approximated by polynomials of different order." + Whenever it was possible. à linear or quadratic [it was applied.," Whenever it was possible, a linear or quadratic fit was applied." + Occasionalv. when the period changed. very irregularly. the O6” diagram was composed from two or three polynomials fitted to the dillerent parts of the ο€ diagram.," Occasionaly, when the period changed very irregularly, the $O-C$ diagram was composed from two or three polynomials fitted to the different parts of the $O-C$ diagram." + In these cases. the O6 solution might not be unambiguous because of evele-count uncertainties.," In these cases, the $O-C$ solution might not be unambiguous because of cycle-count uncertainties." + In the micelle panels. the deviations from the average values of the periods (P—2)10 are plotted from clirect period determination for the data subsets.," In the middle panels, the deviations from the average values of the periods $(P-P_{\mathrm{a}})\times10^5$ are plotted from direct period determination for the data subsets." + 2o formal errors of the direct. period. determinations are also shown., $\sigma$ formal errors of the direct period determinations are also shown. + If the period could be determined only with large uncertainty. data subsets were drawn together.," If the period could be determined only with large uncertainty, data subsets were drawn together." + The OC' can be given as the function of time as Consequently. the temporal period. 2(/). can. be approximated using the e; coellicients of Ίσα.," The $O-C$ can be given as the function of time as Consequently, the temporal period, $P(t)$, can be approximated using the $c_i$ coefficients of Eq." + 1.:, 1.: + For comparison. and to confirm the O—C' solution. £’(/) calculated from the derivatives of the polvnomial O6 fits are also drawn in the middle panels of Fig 1..," For comparison, and to confirm the $O-C$ solution, $P(t)$ calculated from the derivatives of the polynomial $O-C$ fits are also drawn in the middle panels of Fig \ref{oc}." + The right-hand. panels show the folded. light curves of the time-transformec data (leq., The right-hand panels show the folded light curves of the time-transformed data (Eq. + 2.), 2.) + calculated fromthe OC polvnoniual fits over the hundred vears of observations., calculated from the $O-C$ polynomial fits over the hundred years of observations. + Two QO)C solutions are shown for some of the stars (VS. VIO. V27. V3s. V62. V65. V7S and VSS).," Two $O-C$ solutions are shown for some of the stars (V8, V19, V27, V38, V62, V65, V78 and V88)." + The first fits the O C' data with linear or parabolic approximation. while the second shows a higher order or multiple fit.," The first fits the $O-C$ data with linear or parabolic approximation, while the second shows a higher order or multiple fit." + ποσο examples illustrate the strengths of the higher order. polynomial or irregular period variations., These examples illustrate the strengths of the higher order polynomial or irregular period variations. + \We also note here that. in some cases (VII. VIT. V56 RRab and V40. Vso RRe stars). a sine-like approximation would also be appropriate. but for the sake of conformity ancl uniformity. as mentioned. a polynonial fit was always applied.," We also note here that, in some cases (V11, V17, V56 RRab and V40, V80 RRc stars), a sine-like approximation would also be appropriate, but for the sake of conformity and uniformity, as mentioned, a polynomial fit was always applied." + Although a visual inspection of the folded light curve was already convincing of the validity of both the ο6 values and their polynomial fits in most cases. we also checked this quantitatively.," Although a visual inspection of the folded light curve was already convincing of the validity of both the $O-C$ values and their polynomial fits in most cases, we also checked this quantitatively." + The residuals of the Fourier fits of the folded. light curves (omitting CCD V. data) of the time-translormed data have been determined: am compared to the mean rms of the observations., The residuals of the Fourier fits of the folded light curves (omitting CCD $V$ data) of the time-transformed data have been determined and compared to the mean rms of the observations. + For variables with period variation that was not too complex. the rms of the time-transflormed data were 0.10.0.15 mae for wel resolved stars. which is in the same range as the tvpica errors of the photographie observations.," For variables with period variation that was not too complex, the rms of the time-transformed data were 0.10–0.15 mag for well resolved stars, which is in the same range as the typical errors of the photographic observations." + The rms of the phicographic observations of these stars ranged from. 0.05 to 0.20-mag (usually the smallest residuals were obtainec from iris photometry) with an average value of about 0.100.15 mag., The rms of the photographic observations of these stars ranged from 0.05 to 0.20-mag (usually the smallest residuals were obtained from iris photometry) with an average value of about 0.10--0.15 mag. + The numerical results for the O6 and period data of the studied S6 variables are available electronically., The numerical results for the $O-C$ and period data of the studied 86 variables are available electronically. + Table shows an example for VI., Table \ref{stars} shows an example for V1. + The [first line of the table identifies the variable. gives the period that was used. to calculate the OC'. the cata sets usec for constructing the normal curve and the rms of the time-transformed light curve.," The first line of the table identifies the variable, gives the period that was used to calculate the $O-C$, the data sets used for constructing the normal curve and the rms of the time-transformed light curve." + In calculating this rms. only photographic and £3 band observations were used.," In calculating this rms, only photographic and $B$ band observations were used." + The first part of Table ὃ lists the ο C' data., The first part of Table \ref{stars} lists the $O-C$ data. + The time intervals. their mean Julian Date. the number of data points. the O—€! value and its le error are given.," The time intervals, their mean Julian Date, the number of data points, the $O-C$ value and its $\sigma$ error are given." + The second part of Table 3. gives similar data for direct. period. determinations., The second part of Table \ref{stars} gives similar data for direct period determinations. + The last column of this part of the table lists the actual period-deviation values. £22P.," The last column of this part of the table lists the actual period-deviation values, $P-P_{\mathrm{a}}$." + We emphasize here that the {δι periods are not. the currently best. periods of the variables: these periods are the best mean periods over the last. century., We emphasize here that the $P_{\mathrm{a}}$ periods are not the currently best periods of the variables; these periods are the best mean periods over the last century. + Phe periods determined for the latest part of the observations match the recent cata., The periods determined for the latest part of the observations match the recent data. + Amplitude and phase modulations of Blazhko stars müght introduce some uncertainty into the derived. zero-voint shifts and ο—€ values in the case of variables showing strong light-curve modulations., Amplitude and phase modulations of Blazhko stars might introduce some uncertainty into the derived zero-point shifts and $O-C$ values in the case of variables showing strong light-curve modulations. + However. most. of he Blazhko stars identified in Juresiketal.(2010). show stronely irregular period variations. which cannot be used to lerive any period-change rate.," However, most of the Blazhko stars identified in \cite{p2} show strongly irregular period variations, which cannot be used to derive any period-change rate." + Pherefore. these uncertainties jwe no elfect on any of the conclusions of this paper.," Therefore, these uncertainties have no effect on any of the conclusions of this paper." + The xiod-change rates of the two Blazhko stars with strong hase modulations (V58 and. V63). that have clominantly continuous period changes are well defined as can be seen in lig. 1..," The period-change rates of the two Blazhko stars with strong phase modulations (V58 and V63), that have dominantly continuous period changes are well defined as can be seen in Fig. \ref{oc}." + We have to admit. however. that the origin of the scatter of the O6 and period variations of these stars may either originate [from the bias of their phase modulation or may rellect real small [Ductuations in the periods.," We have to admit, however, that the origin of the scatter of the $O-C$ and period variations of these stars may either originate from the bias of their phase modulation or may reflect real small fluctuations in the periods." + In the previous section the O—€' diagrams of 21 RRe and 65 RRab stars of the cluster are presented., In the previous section the $O-C$ diagrams of 21 RRc and 65 RRab stars of the cluster are presented. + The main characteristic parameters of the light curves and. period changes of these stars are collected. in Table. 5.., The main characteristic parameters of the light curves and period changes of these stars are collected in Table \ref{tabla}. + In the first three columns the catalogue numbers of the variale in question. its tvpe and the period used to construct the οC diagram are given.," In the first three columns the catalogue numbers of the variable in question, its type and the period used to construct the $O-C$ diagram are given." +" The next four columns contain some data of the light. curves that might have a connection. with the stars evolutionary stage and can be compared with the variables’ period-change rates: 1; and Vi, are the intensitv- ancl magnituce-averagecdl mean | magnitudes. respectively. derived from the combined ROG and KOO CCL V observations for most of the stars."," The next four columns contain some data of the light curves that might have a connection with the stars' evolutionary stage and can be compared with the variables' period-change rates: $V_i$ and $V_m$ are the intensity- and magnitude-averaged mean $V$ magnitudes, respectively, derived from the combined R96 and K00 CCD $V$ observations for most of the stars." + The SOL CCD V photometry was used for the star V? and the Brocatoetal.(1996) CCD V. data for the variables V95 ancl V98., The S91 CCD $V$ photometry was used for the star V7 and the \cite{br96} CCD $V$ data for the variables V95 and V98. + For Blazhko-stars. light. curves of the best-represented. phase of the modulation were used to derive the mean V magnitudes.," For Blazhko-stars, light curves of the best-represented phase of the modulation were used to derive the mean $V$ magnitudes." +" D,, denotes the magnitudce-averaged mean D magnitude of the variables determined from the CCD PD data or. if they are not available then Z, has been derived. [rom the Las"," $B_m$ denotes the magnitude-averaged mean $B$ magnitude of the variables determined from the CCD $B$ data or, if they are not available then $B_m$ has been derived from the Las" +is (hen followed until it crosses (he shock surface. at which point the Lorentz transformation io the downstream plasma rest frame is performed.,"is then followed until it crosses the shock surface, at which point the Lorentz transformation to the downstream plasma rest frame is performed." +" At this side of the shock a free escape boundary is located Tar downstream [rom the shock at à,,,0(£)=Ninerο. behind it (note that Πο£5) is the particle gvroradius in the average downstream magnetic field)."," At this side of the shock a free escape boundary is located “far downstream” from the shock at $x_{max}(E) = X_{max}\, \bar{r}_{g,2}(E_2)$ behind it (note that $\bar{r}_{g,2}(E_2)$ is the particle gyroradius in the average downstream magnetic field)." + The selected value of the coefficient ως€(5.100) depends on the chosen simulation parameters. and it is specilied using numerical tests separately for each shock configuration.," The selected value of the coefficient $X_{max}\in (5,100)$ depends on the chosen simulation parameters, and it is specified using numerical tests separately for each shock configuration." +" This ensures that the results are not influenced by X,,,..", This ensures that the results are not influenced by $X_{max}$. + In the conditions considered by us. very. [ew particles are able to travel/diffiise from such distance back to the shock.," In the conditions considered by us, very few particles are able to travel/diffuse from such distance back to the shock." + A particle trajectory downstream of the shock is integrated until it crosses (his escape boundary or reaches (he shock front., A particle trajectory downstream of the shock is integrated until it crosses this escape boundary or reaches the shock front. + After performing (his procedure for all .N. particles. a simulation evele is finished.," After performing this procedure for all $N$ particles, a simulation cycle is finished." + Then the trajectory splitting procedure is applied. which replaces all escaped particles with the ones still active in the acceleration process. with the respective partition of particle statistical weights.," Then the trajectory splitting procedure is applied, which replaces all escaped particles with the ones still active in the acceleration process, with the respective partition of particle statistical weights." + In (his wav particle spectra are derived with approximately the sime accuracyin a wide energy range (fordetailsseeNiemiec&Ostrowski2004)., In this way particle spectra are derived with approximately the same accuracyin a wide energy range \citep[for details see][]{nie04}. +". The analogous subsequent. eveles are repeated until either more than of particles escape through the downstream boundary in an individual simulation evele. or all particles reach the assumed upper energv init £,,,:5» (given in the downstream rest frame). or the lower limit for the particle weight wis reached."," The analogous subsequent cycles are repeated until either more than of particles escape through the downstream boundary in an individual simulation cycle, or all particles reach the assumed upper energy limit $E_{max,2}$ (given in the downstream rest frame), or the lower limit for the particle weight $w$ is reached." + The lower limit for ie is usually set to LO°6 of the initial weight wy., The lower limit for $w$ is usually set to $10^{-6}$ of the initial weight $w_0$ . + The final spectra and angular distributions are averaged over several (10 - 50) simulation runs. each with statistically different sets of No particles and different. realizations of the perturbed magnetic field.," The final spectra and angular distributions are averaged over several $10$ - $50$ ) simulation runs, each with statistically different sets of $N$ particles and different realizations of the perturbed magnetic field." + At the beginning of a simulation run the particles are injected at the shock front with uniform angular distribution within the range of cos»€(—1.—43) in the downstream plasma rest Lame (0 is the angle between (he particle momentum and the shock normal). so that their momentum vectors in (he upstream rest [rame are in (he cone around the shock normal with the opening angle 0. (sing.= 1/54).," At the beginning of a simulation run the particles are injected at the shock front with uniform angular distribution within the range of $\cos\theta_2\in (-1,-u_2)$ in the downstream plasma rest frame $\theta$ is the angle between the particle momentum and the shock normal), so that their momentum vectors in the upstream rest frame are in the cone around the shock normal with the opening angle $\theta_c$ $\sin\theta_c=1/\gamma_1$ )." + Thev are monoenergetic in the downstream rest frame. and the injection energv £L;=LyeO.1 is such that particle resonance wavevectors ροζ)>Myer," They are monoenergetic in the downstream rest frame, and the injection energy $E_i=E_{0,2}=0.1$ is such that particle resonance wavevectors $k_{res}(E_{0,2}) \gg k_{max}$." + Such initial conditions correspond roughly to the particle injection [rom the thermal plasma., Such initial conditions correspond roughly to the particle injection from the thermal plasma. + For ultrarelativistie shocks considered here. the majoritv of the injected particles escape Far downstream in (he first simulation evele.," For ultrarelativistic shocks considered here, the majority of the injected particles escape far downstream in the first simulation cycle." + In order to improve (he statistical accuracy of the spectra. we continue injecting particles in the first evele until No of those which alter (ransnission downstream succeed in reaching the shock front again are selected.," In order to improve the statistical accuracy of the spectra, we continue injecting particles in the first cycle until $N$ of those which — after transmission downstream — succeed in reaching the shock front again are selected." + These particles are used in agiven simulation run and have ihe same initial weights i., These particles are used in agiven simulation run and have the same initial weights $w_0$ . +Double-lined. eclipsing binaries are the only objects. apart from the Sun. for which fundamental ancl simultaneous determinations of masses and radii can be obtained.,"Double-lined eclipsing binaries are the only objects, apart from the Sun, for which fundamental and simultaneous determinations of masses and radii can be obtained." + These determinations are possible through the analysis of spectroscopic data in the form of radial velocity curves. and from. modelling the photometric data in light curves.," These determinations are possible through the analysis of spectroscopic data in the form of radial velocity curves, and from modelling the photometric data in light curves." + In addition. if we consider detached: double-Ilined. eclipsing binaries. no significant mass transfer has occurred. between the components. since they are smaller than their respective ltoche lobes.," In addition, if we consider detached double-lined eclipsing binaries, no significant mass transfer has occurred between the components, since they are smaller than their respective Roche lobes." + In such a case. the mutual interaction can be safely neglected: ancl the components can be assumed. to evolve like single. individual stars.," In such a case, the mutual interaction can be safely neglected and the components can be assumed to evolve like single, individual stars." + Therefore. these objects vield simultaneous absolute dimensions for two single stars that are supposed to have a common origin both in time and chemical composition.," Therefore, these objects yield simultaneous absolute dimensions for two single stars that are supposed to have a common origin both in time and chemical composition." + In this situation. evolutionary models should be able to predict the same age for both components [or a certain chemical composition.," In this situation, evolutionary models should be able to predict the same age for both components for a certain chemical composition." + I5clipsing binaries that are members of physically bound multiple systems. provide additional. constraints for the analysis of evolutionary mocels., Eclipsing binaries that are members of physically bound multiple systems provide additional constraints for the analysis of evolutionary models. + All the information that can be extracted for the companion/s (Collective temperature. maenituce dillerence. mass. )) should be also fitted by the same isochrone that fits the eclipsing binary pair.," All the information that can be extracted for the companion/s (effective temperature, magnitude difference, mass, ) should be also fitted by the same isochrone that fits the eclipsing binary pair." + Not many stuclics have made use of this possibility up to date. mainly because of the scarce amount. of information available [or the additional stellar companions.," Not many studies have made use of this possibility up to date, mainly because of the scarce amount of information available for the additional stellar companions." + CD Tau (LD 34335. HIP 24663) is a bright eclipsing binary (Vinas= 6.75) composed of two similar FG V stars. which was sugeested by Chambliss (1992) as a possible member of a triple svstem.," CD Tau (HD 34335, HIP 24663) is a bright eclipsing binary $V_{\rm +max}=6.75$ ) composed of two similar F6 V stars, which was suggested by Chambliss (1992) as a possible member of a triple system." + Lt has a Ix-type close visual companion (CD Tau €) at 9.98 aresee (ESA 1997) with a, It has a K-type close visual companion (CD Tau C) at 9.98 arcsec (ESA 1997) with a +The single-spin asymmetry was analyzed bythepQCDwith thehigher (vist,or with the inclusion of spin and transverse-momentum effects in parton +Zadziarski et al.,Zdziarski et al. + 1995) and indeed. if we fit the data alone with a simple power-law. the average photon index turns out to be 2 2.08 + 0.18.," 1995) and indeed, if we fit the data alone with a simple power-law, the average photon index turns out to be $\Gamma$ = 2.08 $\pm$ 0.18." + Furthermore. objects with a flat primary continuum are not characterized by a particularly high reflection component (in fact R tends to be low in these objects).," Furthermore, objects with a flat primary continuum are not characterized by a particularly high reflection component (in fact $R$ tends to be low in these objects)." + Further 2-10 keV data possibly on a complete sample of hard X-ray selected AGN may help understanding if these 4 AGN are peculiar and rare objects or instead belong to a typical and more abundant than previously thought population., Further 2-10 keV data possibly on a complete sample of hard X-ray selected AGN may help understanding if these 4 AGN are peculiar and rare objects or instead belong to a typical and more abundant than previously thought population. + The broad-band spectral analysis allowed us to constrain the high energy cut-off in four out of nine AGN in the sample and for all of them the cut-off energy ts found to be below 150 keV. This is at odds with previous results which located the cut-off energy. on average. at ~ 200 keV for the type | Seyfert galaxies observed withBeppoSAX (Perola et al.," The broad-band spectral analysis allowed us to constrain the high energy cut-off in four out of nine AGN in the sample and for all of them the cut-off energy is found to be below 150 keV. This is at odds with previous results which located the cut-off energy, on average, at $\sim$ 200 keV for the type 1 Seyfert galaxies observed with (Perola et al." + 2002. Malizia et al.," 2002, Malizia et al." + 2003b. Dadina 2008).," 2003b, Dadina 2008)." + Gondek et al. (, Gondek et al. ( +1996). who analyzed the average 1-500 keV spectrum of type | AGN observed withEXOSAT.Ginga. and OSSE. found a cut-off energy > 500 keV: similarly a study by Zdziarski et al. (,"1996), who analyzed the average 1-500 keV spectrum of type 1 AGN observed with, and OSSE, found a cut-off energy $>$ 500 keV; similarly a study by Zdziarski et al. (" +1995) of broad-band and OSSE spectra of a large sample of Seyferts provided Ευ > 250 keV. Moreover. only 6 of the 36 AGN detected by analyzed by Beckmann et al. (,"1995) of broad-band and OSSE spectra of a large sample of Seyferts provided $_{cut-off}$ $>$ 250 keV. Moreover, only 6 of the 36 AGN detected by analyzed by Beckmann et al. (" +2006) and Sazonov et al. (,2006) and Sazonov et al. ( +2004) require a cut-off at energies below 200 keV. On the other hand. there are spurious examples in the literature of type 1 Seyferts with low values of the high energy cut-off (e.g.. Molina et al.,"2004) require a cut-off at energies below 200 keV. On the other hand, there are spurious examples in the literature of type 1 Seyferts with low values of the high energy cut-off (e.g., Molina et al." + 2006. Perola et al.," 2006, Perola et al." + 2002)., 2002). + Also the analysis of the average PDS spectra by Deluit Courvotsier (2003) shows that the lower limit obtained for type 1 Seyfert galaxies is fully consistent with our results (Ευ > 63 keV)., Also the analysis of the average PDS spectra by Deluit Courvoisier (2003) shows that the lower limit obtained for type 1 Seyfert galaxies is fully consistent with our results $_{cut-off}$ $>$ 63 keV). + This is also consistent with recent results by Ajello et al. (, This is also consistent with recent results by Ajello et al. ( +2008) who found a mean cut-off energy at ~ 100 keV in Seyfert 1 galaxies observed by Swift/BAT.,2008) who found a mean cut-off energy at $\sim$ 100 keV in Seyfert 1 galaxies observed by /BAT. + A positive correlation between the cut-off energy versus the photon index was previously found usingBeppoSAX data. first by Piro (1999). then by Petrucci et al. (," A positive correlation between the cut-off energy versus the photon index was previously found using data, first by Piro (1999), then by Petrucci et al. (" +2001) and finally confirmed by Perola et al. (,2001) and finally confirmed by Perola et al. ( +2002).,2002). + In Fig., In Fig. + + (left panel) we plot the cut-off energy (keV) versus the photon index I (data taken from Table 4))., \ref{figure=refl} (left panel) we plot the cut-off energy (keV) versus the photon index $\Gamma$ (data taken from Table \ref{table=cut}) ). + Given the poor statistical quality of our data. we cannot draw any conclusion on the correlation between these two parameters.," Given the poor statistical quality of our data, we cannot draw any conclusion on the correlation between these two parameters." + However. no evidence of a correlation is found with the present data (censored data are not included in the analysis). although the four sources in which the cut-off energy has been constrained are those showing the flattest photon indeces.," However, no evidence of a correlation is found with the present data (censored data are not included in the analysis), although the four sources in which the cut-off energy has been constrained are those showing the flattest photon indeces." + We point out that the known interdependence of the parameters in the model ( 1.e.. the cut-off energy is a variable in the fit which is strongly dependent on I and A) has to be taken into account when these correlations are discussed.," We point out that the known interdependence of the parameters in the model ( i.e., the cut-off energy is a variable in the fit which is strongly dependent on $\Gamma$ and $R$ ) has to be taken into account when these correlations are discussed." + A correlation between the reflection parameter R and the photon index has been claimed by Zdziarski et al. (, A correlation between the reflection parameter $R$ and the photon index has been claimed by Zdziarski et al. ( +1999) from the study of a large number of observations of Seyfert galaxies and Galactic black holes.,1999) from the study of a large number of observations of Seyfert galaxies and Galactic black holes. + However. the validity of this correlation is under debate. since R and E. are strongly correlated im the fitting procedure (Vaughan Edelson 2001) and subsequent works did not confirm the presence of a relatior between these two parameters (Petrucci et al.," However, the validity of this correlation is under debate, since $R$ and $\Gamma$ are strongly correlated in the fitting procedure (Vaughan Edelson 2001) and subsequent works did not confirm the presence of a relation between these two parameters (Petrucci et al." + 2001. Perola et al.," 2001, Perola et al." + 2002)., 2002). + Recently. Mattson. Weaver Reynolds (2007) have shown that the strong correlation found between R and FE i their sample of type | and type 1.2 Seyfert galaxies observed withRXTE. is likely to be an artefact of modeling degeneracy.," Recently, Mattson, Weaver Reynolds (2007) have shown that the strong correlation found between $R$ and $\Gamma$ in their sample of type 1 and type 1.2 Seyfert galaxies observed with, is likely to be an artefact of modeling degeneracy." + The reflection parameter in our sample analysis is constrainec only in IGR J16482-3036 and IGR J17418-1212., The reflection parameter in our sample analysis is constrained only in IGR J16482-3036 and IGR J17418-1212. + Therefore. the poor statistics and the large number of upper limits prevent us from drawing strong conclusions on this point.," Therefore, the poor statistics and the large number of upper limits prevent us from drawing strong conclusions on this point." + The R versus Γ (data taken from Table 5)) plot is shown in Fig. 4..," The $R$ versus $\Gamma$ (data taken from Table \ref{table=pex}) ) plot is shown in Fig. \ref{figure=refl}," + right panel: stronger reflection is indeed measured in steeper spectrum sources. but when upper limits are considered this effect ts not so obvious in our data.," right panel: stronger reflection is indeed measured in steeper spectrum sources, but when upper limits are considered this effect is not so obvious in our data." + IGR J16482-3036. IGR J17418-1212. and possibly IGR J16558-5203 show a reflection component R > 1.," IGR J16482-3036, IGR J17418-1212 and possibly IGR J16558-5203 show a reflection component $R$ $>$ 1." + These high values of R have been found in previous studies using andBeppoSAX data (Cappi et al., These high values of $R$ have been found in previous studies using and data (Cappi et al. + 1996. Dadina 2008) and. more recently. with the satellite (Miniutti et al.," 1996, Dadina 2008) and, more recently, with the satellite (Miniutti et al." + 2007. Comastri et al.," 2007, Comastri et al." + 2007)., 2007). + Such strong reflection might be present when nore primary X-ray radiation is emitted toward the reflector than toward the observer as is possible in the case of strongly variable nuclear emission or when there is a time delay between the underlying continuum and the reflected component. caused by a large distance between the reflecting material and the primary source (Malzac Petrucei 2002).," Such strong reflection might be present when more primary X-ray radiation is emitted toward the reflector than toward the observer as is possible in the case of strongly variable nuclear emission or when there is a time delay between the underlying continuum and the reflected component, caused by a large distance between the reflecting material and the primary source (Malzac Petrucci 2002)." + Another explanation might be a peculiar geometry (Malzac et al., Another explanation might be a peculiar geometry (Malzac et al. + 2001: Malzac 2001) or general relativistic light bending effects (Fabian et al 2004; Miniutti Fabian 2004: Fabian et al 2005)., 2001; Malzac 2001) or general relativistic light bending effects (Fabian et al 2004; Miniutti Fabian 2004; Fabian et al 2005). + Recently. Gandhi et al. (," Recently, Gandhi et al. (" +2007) have shown that. in the synthesis models of the X-ray background spectrum. a significant fraction of this type of source is needed when light bending effects are taken into account.,"2007) have shown that, in the synthesis models of the X-ray background spectrum, a significant fraction of this type of source is needed when light bending effects are taken into account." + Under the hypothesis that the line emission is entirely associated with optically thick material. the equivalent width of the Fe line is expected to correlate linearly with the value of R obtained for an arbitrarily fixed inclination angle.," Under the hypothesis that the line emission is entirely associated with optically thick material, the equivalent width of the Fe line is expected to correlate linearly with the value of $R$ obtained for an arbitrarily fixed inclination angle." + To a first approximation. an equivalent width of 140 eV ts predicted if R = | for a cold. face-on disk and an incident power-law with DL ~ 2 (George Fabian 1991).," To a first approximation, an equivalent width of 140 eV is predicted if $R$ $=$ 1 for a cold, face-on disk and an incident power-law with $\Gamma$ $\sim$ 2 (George Fabian 1991)." + In the case of IGR J16482-3036. the equivalent width (0404753 eV). measured using the model in Table 5)) is consistent with the observed reflection fraction: while in the case of IGR J17418-1212 it is very modest ο. eV).," In the case of IGR J16482-3036, the equivalent width $^{+25}_{-82}$ eV), measured using the model in Table \ref{table=pex}) ) is consistent with the observed reflection fraction; while in the case of IGR J17418-1212 it is very modest $^{+26}_{-26}$ eV)." + Some scatter in the equivalent width could be introduced by a variance in the iron abundance which we do not take into account in our analysis., Some scatter in the equivalent width could be introduced by a variance in the iron abundance which we do not take into account in our analysis. + On the other hand. this discrepancy can be explained in terms of à possible anisotropy of the source of seed photons which might modify the resulting spectrum (Petrucci et al.," On the other hand, this discrepancy can be explained in terms of a possible anisotropy of the source of seed photons which might modify the resulting spectrum (Petrucci et al." + 2001. Merloni et al.," 2001, Merloni et al." + 2006)., 2006). + For a given. R. the equivalent width may also. differ according to the value of Γ.," For a given $R$, the equivalent width may also differ according to the value of $\Gamma$." + The simulations of George Fabian (1991) showed that the equivalent width of the iron line. should. decrease as the spectrum softens. given the presence of fewer photons with energies above the iron photoionization threshold.," The simulations of George Fabian (1991) showed that the equivalent width of the iron line should decrease as the spectrum softens, given the presence of fewer photons with energies above the iron photoionization threshold." + Mattson. Weaver Reynolds," Mattson, Weaver Reynolds" +since F decreases wilh time. (the svstem must approach a steady state as /—2€.,"Since $F$ decreases with time, the system must approach a steady state as $t\to\infty$." + The steady-state solutions of equation (30)) are those in which g(s)/j—e(d?s/dr7) is a linear function of οὓς the periodic boundary. conditions require that the linear (erm vanishes. so (he steady state solutions satisfy gis)4-p—0. where pis a constant.," The steady-state solutions of equation \ref{eq:cha}) ) are those in which $g(s)/\mu-\epsilon(d^2 s/d x^2)$ is a linear function of $x$; the periodic boundary conditions require that the linear term vanishes, so the steady state solutions satisfy g(s)+p=0, where $p$ is a constant." +" This equation is equivalent to motion in the potential ps.so there is an ""energv integral LeisOUOps-qsur the properties of the steady-state solutions ean thus be determined by examining the contours of the left-hand side of (5)) in the phase plane with coordinates (s.εἰςdr)."," This equation is equivalent to motion in the potential $-G(s)/(\epsilon\mu)+ps$ , so there is an “energy” integral G(s)+ps=q; the properties of the steady-state solutions can thus be determined by examining the contours of the left-hand side of \ref{eq:energy}) ) in the phase plane with coordinates $(s,ds/dx)$." + We now introduce dimensionless variables. epstlonmuright))t/7.r. H. BEER24(91 recall Chat e ancl e are positive.," We now introduce dimensionless variables, x, t, s; recall that $a$ and $c$ are positive." + Equation (30)). with the stress-shear relation (5)). becomes ggga - BullOS ger," Equation \ref{eq:cha}) ), with the stress-shear relation \ref{eq:gdef}) ), becomes (y + By|y| +,." + The boundary conditions are periodic. with period A€=(c/eji)?Xr.," The boundary conditions are periodic, with period $\Delta\xi\equiv +(c/\epsilon\mu)^{1/2}\Delta x$." + Equation (38)) is the (ΜΗΓΗΠα equation. which has been widely used to model pattern formation in phase (ransilions.," Equation \ref{eq:chb}) ) is the Cahn-Hilliard equation, which has been widely used to model pattern formation in phase transitions." +seearch of signs of evolution.,earch of signs of evolution. +Type Ia supernovae Ia)) are recoguized for their uear uniformity as staucdarcl cauclles.,Type Ia supernovae ) are recognized for their near uniformity as standard candles. + This has led to the use of in cosmology (το)...," This has led to the use of in cosmology \citep{brancharaa98,garnetal98,riess_scoop98,perletal99}." + The development of empirical calibratious between peak brightuess aud light curve shape (?22???2).. have euliauced the usefulness of aas dist:ice indicators.," The development of empirical calibrations between peak brightness and light curve shape \citep{philm15,hametal96a,rpk96,perlasi97,perlq097,tb99}, have enhanced the usefulness of as distance indicators." + Nevertheless theoretical inodelers have yet to agree ou the source of these appareutly systematic variations., Nevertheless theoretical modelers have yet to agree on the source of these apparently systematic variations. + A primary concern is the evolutionary lifetime of pprogenitors and the possibility of siguilicaut deviations of clistant (rom their well observed. couuterparts in the local galactic neighborhood., A primary concern is the evolutionary lifetime of progenitors and the possibility of significant deviations of distant from their well observed counterparts in the local galactic neighborhood. + If. galactic chemical evolution occurs slowly. then more clistant SNe arise [rom a younger. metal poor population.," If galactic chemical evolution occurs slowly, then more distant SNe arise from a younger, metal poor population." + Ou other hand. the metallicity variations in the local sample may already span the r:ige of the ire observational sample.," On the other hand, the metallicity variations in the local sample may already span the range of the entire observational sample." + We probe the possible effects of progenitor metallicity variatious on the observed spectra. by IOCifving the parameterized dellagration model. W7 (?2).," We probe the possible effects of progenitor metallicity variations on the observed spectra, by modifying the parameterized deflagration model, W7 \citep{nomw7,nomw72}." +. Usiug base fits to observations 2.3)) we have scaled all elements heavier than oxygen in the unburned C+O laver of WT to simulate the elTe‘ts of various metallicities iu the progenitor system., Using base fits to observations \ref{basemod}) ) we have scaled all elements heavier than oxygen in the unburned C+O layer of W7 to simulate the effects of various metallicities in the progenitor system. + ? explored this question by modifying the pre-explosion metal content of a particular inimodel aud noted the differences iu final composition. light curves. aud spectra.," \citet{hwt98} + explored this question by modifying the pre-explosion metal content of a particular model and noted the differences in final composition, light curves, and spectra." + They found tliat the composition of the partially burned layers of the ejecta vielded larger quantities ofFe., They found that the composition of the partially burned layers of the ejecta yielded larger quantities of. +.. A similar effect can be seen in the lowered aabuidauce when W7 is caleulatecl using a pure C+O mixture without other metals (?).., A similar effect can be seen in the lowered abundance when W7 is calculated using a pure C+O mixture without other metals \citep{iwamoto99}. + We have 1nO«cified the aabuidauce of the partially burued layers ofWT. to replicate this effect.," We have modified the abundance of the partially burned layers ofW7, to replicate this effect." + While ? focused mainly on. he ellects of metallicity variations ou the light curve αμα energetics. here we conceutrate exclusively on its effects ou the observed spectra. particularly at early times where the formation of tle spectrum occurs in the unburned C+O layer. which is most sensitive to initial progenitor 1netallicity.," While \citet{hwt98} focused mainly on the effects of metallicity variations on the light curve and energetics, here we concentrate exclusively on its effects on the observed spectra, particularly at early times where the formation of the spectrum occurs in the unburned C+O layer, which is most sensitive to initial progenitor metallicity." + Our computational methods are given in 2., Our computational methods are given in \ref{methods}. + In ὁ we show the eflects of metallicity IOClification of the C+O layer on the synthetic spectra at each epoch., In \ref{zco} we show the effects of metallicity modification of the C+O layer on the synthetic spectra at each epoch. + In { we slow the effects of OOLL day 20 and 35 model spectra., In \ref{feint} we show the effects of on day 20 and 35 model spectra. + In 5.1 we discuss the evolution of the Si HH feature at 6150 A.., In \ref{siii} we discuss the evolution of the Si II feature at 6150 . +isk midplane density is likely higher than assuued iu these moclels.,disk midplane density is likely higher than assumed in these models. + Sipilàetal.(2010) found au ---ιαing importance of D. with increasing deisity at LO Ix. but it is unclear whether this effect is important also at hielier temperatures.," \citet{Sipila10} found an increasing importance of $_3^+$ with increasing density at 10 K, but it is unclear whether this effect is important also at higher temperatures." + Another potential unkuown is the abuudauce of though C'eccarelli&Domiuik(2005) found that its couUribution is uegligible at the high deusities of the isk inidplane.," Another potential unknown is the abundance of $^+$, though \citet{Ceccarelli05} found that its contribution is negligible at the high densities of the disk midplane." +" With these caveats in inind. we use the ratos derived by Casellietal.(2008) with tmaxituuim epletion. Le. minimum amounts of CO aud No in the gas-phase. to calculate upper limits on N(S7 ,D r in the disk midplaue as a Duuction of assumed temperature."," With these caveats in mind, we use the ratios derived by \citet{Caselli08} with maximum depletion, i.e. minimum amounts of CO and $_2$ in the gas-phase, to calculate upper limits on $\sum$ $_{3-x}$ $_x^+$ ) in the disk midplane as a function of assumed temperature." +" Figure 3c shows tlie resuS. with limits that range from 1.5 to 8.5xLOM 7. with the peak value at 13 IK. The modification of the shape compared to the HoD — curve is «iue to the faet that the N(H2D )/N(OSZ Hy,D,) ratio peaks uear 13 Ix aud theu falls off quickly at higher temperatures."," Figure 3c shows the results, with limits that range from $1.5$ to $8.5\times10^{13}$ $^{-2}$, with the peak value at 13 K. The modification of the shape compared to the $_2$ $^+$ curve is due to the fact that the $_2$ $^+$ $\sum$ $_{3-x}$ $_x^+$ ) ratio peaks near 13 K and then falls off quickly at higher temperatures." + Te» derive liuits ou the imidplane ion abuudauces. we adopt the model of the DM Tau disk density aud temperature structure described by Andrewsetal.(2011) based on parametric fitting ol the spectral energy distribution aud resolved «observations of millimeter-wave dust emissiou.," To derive limits on the midplane ion abundances, we adopt the model of the DM Tau disk density and temperature structure described by \citet{Andrews11} based on parametric fitting of the spectral energy distribution and resolved observations of millimeter-wave dust emission." + This mode does not iuclude any. chemistry. but rather provides au observatioually coustrained plivsical structure. which cau be used to derive the gas masses in diflereut temperature lavers iu the disk.," This model does not include any chemistry, but rather provides an observationally constrained physical structure, which can be used to derive the gas masses in different temperature layers in the disk." + This is needed to convert au ion columu deusity into an ion abuudauce., This is needed to convert an ion column density into an ion abundance. + We apply a standard interstellar gas-to-dust ratio of 100 to convert the dust densities in this model to gas densities., We apply a standard interstellar gas-to-dust ratio of 100 to convert the dust densities in this model to gas densities. + To determine a midplaue mass. we defiue thedisk nidplane as all material <16 hk. the temperature or complete No [reeze-out in inmost astropliysical environments based ou laboratory ieasuremenuts (Obereetal.2005:Bisschop2006).. i.e. the region where it is most likely that H4 and its isotopologues become abuncdaut.," To determine a midplane mass, we define thedisk midplane as all material $\lesssim$ 16 K, the temperature for complete $_2$ freeze-out in most astrophysical environments based on laboratory measurements \citep{Oberg05,Bisschop06}, i.e. the region where it is most likely that $_3^+$ and its isotopologues become abundant." +" La this disk layer. the density weighted temperature is 11 Ix. ancl he disk averaged gas column density. Nyy, is 15x107? 7."," In this disk layer, the density weighted temperature is 11 K, and the disk averaged gas column density $_{\rm H_2}$ is $15\times10^{22}$ $^{-2}$." + Using this column density. and the ipper limit ou the ion column density iu the midplane of Lx1055 7 from Table 3 aud Fig.," Using this column density, and the upper limit on the ion column density in the midplane of $4\times10^{13}$ $^{-2}$ from Table 3 and Fig." + |. rm2.x10. ny.," 4, $x_i<2.7\times10^{-10}$ $_{\rm H}$." + Alternatively. if the onset of CO freeze-out at 20 Ix. defines the region where H3D is abuudant rather than No lreeze-0ut at 16 Ix. then tlie density averaged lou temperature is 13]. ando; pc.* (o as high as 10* pe.? in the cores of the densest elobular clusters. which complicates matters for the evolution of their members.," Clusters are crowded stellar environments, ranging in density from $10^2\,$ $\,{\rm pc}^{-3}$ to as high as $10^7\,$ $\,{\rm pc}^{-3}$ in the cores of the densest globular clusters, which complicates matters for the evolution of their members." + Encounters between stars can lead (o collisions aud. in (he case of binary. stars or planetary. svstenis. an exchange interaction or disruption of the orbit.," Encounters between stars can lead to collisions and, in the case of binary stars or planetary systems, an exchange interaction or disruption of the orbit." + For Chis reason. amongst others. it is desirable to model the evolution of a star cluster using a direct /N-body method in which the individual orbits of each star are followed in detailand the internal evolution of each star is also taken into account (IIulevetal.2001).," For this reason, amongst others, it is desirable to model the evolution of a star cluster using a direct $N$ -body method in which the individual orbits of each star are followed in detail the internal evolution of each star is also taken into account \citep{hur01}." +. We have instigated a study of the behaviour of planetary svstenis in star clusters using a state-of-the-art N-bocly code in conjunetion with the powerful GRAPE-G special purpose computer (Alakino2001)., We have instigated a study of the behaviour of planetary systems in star clusters using a state-of-the-art $N$ -body code in conjunction with the powerful GRAPE-6 special purpose computer \citep{mak01}. +. This detailed project will ultimately involve a large number of .N- simulations covering a wide range ofinitial conditions. e.g. metallicity. binary fraction. stellar number density. ancl multiple planets per star.," This detailed project will ultimately involve a large number of $N$ -body simulations covering a wide range of initial conditions, e.g. metallicity, binary fraction, stellar number density, and multiple planets per star." + However. for now we have simply looked al (he case of Jupiters in single-planet systems within moderate density cluster conditions.," However, for now we have simply looked at the case of Jupiters in single-planet systems within moderate density cluster conditions." + Furthermore. we do not consider whether planets should form at all in star clusters (Armitage example). especially in low-metallicity and/or hieh density environments. bul simply ask the question: what happens if thev do?," Furthermore, we do not consider whether planets should form at all in star clusters \citep[for example]{arm00}, especially in low-metallicity and/or high density environments, but simply ask the question: what happens if they do?" + Even though (his project is in its infancy the possible discovery of free-floating planets in M22 (Sahuetal.2001) makes publication ol the initial results very timely., Even though this project is in its infancy the possible discovery of free-floating planets in M22 \citep{sah01} makes publication of the initial results very timely. + To model the evolution of star clusters we use the Aarseth code (Aarseth1999: 2001).," To model the evolution of star clusters we use the Aarseth code \citep{aar99,hur01}." +. Simulations are performed on a prototwpe GRAPE-G board located at the American Museum of Natural History., Simulations are performed on a prototype GRAPE-6 board located at the American Museum of Natural History. + This special purpose hardware. which acts as a Newtonian force accelerator for N-body calculations. performs 0.5 Tflops (30 Πορ per chip).," This special purpose hardware, which acts as a Newtonian force accelerator for $N$ -body calculations, performs $0.5\,$ Tflops $\sim 30\,$ Gflop per chip)." + It represents a factor of 100 increase in computing power compared to its predecessor ihe GRAPE-4 (Makino.Kokubo&Taiji1993) and has brought the possibility of modelling, It represents a factor of 100 increase in computing power compared to its predecessor the GRAPE-4 \citep{mak93} and has brought the possibility of modelling +the fit bright globular clusters. foreground stars. background galaxies and the gap between the individual CCD detectors.,"the fit bright globular clusters, foreground stars, background galaxies and the gap between the individual CCD detectors." + The background-subtraction is based on the average of median values from several 10 10 pixel boxes sampled in regions not allected by ealaxy light., The background-subtraction is based on the average of median values from several $\times$ 10 pixel boxes sampled in regions not affected by galaxy light. + Vhe conversion from the LIST/AC€'S instrumental E475N. and E850W filters system to the AB photometric svstem: is performed using the svnthetic cocllicients Crom Siriannietal.(2005)., The conversion from the HST/ACS instrumental F475W and F850W filters system to the AB photometric system is performed using the synthetic coefficients from \cite{sirianni05}. +".. In particular. the PATSW ancl FS5SOW filters are transformed into gig and zig. respectively,"," In particular, the F475W and F850W filters are transformed into $g_{AB}$ and $z_{AB}$, respectively." + Final magnitudes: were corrected for Galactic extinction using the redcening values from the DIRBE dust maps of Schlegelctal.(1998)., Final magnitudes were corrected for Galactic extinction using the reddening values from the DIRBE dust maps of \cite{sch98}. + The errors in magnitude are computed. from the rms scatter of intensity data along the fitted: ellipse and. the errors in the background subtraction., The errors in magnitude are computed from the rms scatter of intensity data along the fitted ellipse and the errors in the background subtraction. + Errors in the Galactic extinction correction values and in the zero-points are negligible with respect to the errors in the intensity. profiles., Errors in the Galactic extinction correction values and in the zero-points are negligible with respect to the errors in the intensity profiles. + Ellipse geometry parameter errors are obtained. from. the internal errors in the harmonie fit., Ellipse geometry parameter errors are obtained from the internal errors in the harmonic fit. + Hlarmonic. amplitude errors are obtained from the fit errors after removal of all harmonics up to and including. the one being considered.," Harmonic amplitude errors are obtained from the fit errors after removal of all harmonics up to and including, the one being considered." + We present the results of the isophotal analysis for the 14 sample galaxies in Lig. 4..," We present the results of the isophotal analysis for the 14 sample galaxies in Fig. \ref{phot_fornax1}," + Fie. 5..," Fig. \ref{phot_fornax2}," + Fig. 6..," Fig. \ref{phot_virgo1}," + and Fig. 7.., and Fig. \ref{phot_virgo2}. + Photometric parameters are. plotted asfunction. of the geometric mean radius r. defined as r=«1c(a)]7; where α ds the length of the isophotal semi-major axis.," Photometric parameters are plotted asfunction of the geometric mean radius $r$, defined as $r=a[1-\epsilon(a)]^{1/2}$ where $a$ is the length of the isophotal semi-major axis." + This radius is then scaledwith the galaxys elfective radius along the senii-major axis and expressedas rfr., This radius is then scaledwith the galaxy's effective radius along the semi-major axis and expressedas $r/r_{e}$. + For cach galaxy. the Γρ. µε surface brightness profiles and the g -2 colour index. profile are shown.," For each galaxy, the $\mu_{g}$, $\mu_{z}$ surface brightness profiles and the $g$ -$z$ colour index profile are shown." +" We also plot racial profiles of isophotal geometry parameters of cllipticity ο, position angle. 22h and the isophote's deviations from perfect. ellipticity zlu. chi. and Ds. By."," We also plot radial profiles of isophotal geometry parameters of ellipticity $\epsilon$, position angle $P.A.$ and the isophote's deviations from perfect ellipticity $A_{3}$ , $A_{4}$ , and $B_{3}$ , $B_{4}$ ." + These parameters are respectively the third. and fourth cosine ancl sine, These parameters are respectively the third and fourth cosine and sine +them (Zasov Arkhipova 20003).,them (Zasov Arkhipova \cite{Zasov00}) ). + They roughv follow so called luminosity metallicity relation: the least InninotS ealaxies show in general smaller values of Ο/Η., They roughly follow so called luminosity – metallicity relation: the least luminous galaxies show in general smaller values of $O/H$. + VV 182 has a verv low heavy-clement abulance., VV 432 has a very low heavy-element abundance. + It:J4. OfII is among the lowest ten values of the most deficieut BCGs out of more than one thousand ealaxies known up-to-now., Its $O/H$ is among the lowest ten values of the most metal-deficient BCGs out of more than one thousand }-galaxies known up-to-now. + It may be considered as4. an example of uon-evolved galaxy., It may be considered as an example of non-evolved galaxy. + Analysis of th enipirical sugeests that dwarf galaxies witl 12|log(O/II)history< 7.6 correlationscan currently experience oulv the first in their episode of SF (Izotov Tlian 1999))., Analysis of the empirical correlations suggests that dwarf galaxies with 12+log(O/H) $<$ 7.6 can currently experience only the first in their history episode of SF (Izotov Thuan \cite{Izotov99}) ). + Therefore VV. 132 with 12|log(O/II) = 7.58 is very οσους candidate for more detailed study., Therefore VV 432 with 12+log(O/H) = 7.58 is very good candidate for more detailed study. + If it is situated in Virgo cluster. it will |o the most moetal deficient galaxy of this4 ACCTCOOeate. beiug even less chemically evolved than anotleDu well-known metal-poor Hi-galaxy iu the direction of Vireo cluser 1225|01 with 12|log(O/TT) = 7.66 (Salzer et al. L991::," If it is situated in Virgo cluster, it will be the most metal deficient galaxy of this aggregate, being even less chemically evolved than another well-known metal-poor -galaxy in the direction of Virgo cluster 1225+01 with 12+log(O/H) = 7.66 (Salzer et al. \cite{Salzer91};" + Cheuealur et al. 1995))., Chengalur et al. \cite{Chengalur95}) ). + One of the possible wavS to resolve the dileuuua of radial distance to VV. 132 is a deection of brigitest stars and construction of their colormagnitude caerau., One of the possible ways to resolve the dilemma of radial distance to VV 432 is a detection of brightest stars and construction of their color-magnitude diagram. + The galaxies we diseuss have rather close neighbours., The galaxies we discuss have rather close neighbours. + Icke (19853) first has drawn attention to the importance of velatively weak interactions to trieeer gravitational instability in eas disks via generation of shocks., Icke \cite{Icke85}) ) first has drawn attention to the importance of relatively weak interactions to trigger gravitational instability in gas disks via generation of shocks. + Maiuiv observational evidences for the important role of wea- interactions to trigecr SE were obtained since that time. including the detection of low mass Ul-companionus of nearby IHir-ealaxies(Chengaliw et al. 1995:," Many observational evidences for the important role of weak interactions to trigger SF were obtained since that time, including the detection of low mass -companions of nearby -galaxies (Chengalur et al. \cite{Chengalur95};" + Taylor et al. 1993.. 1995::," Taylor et al. \cite{Taylor93}, \cite{Taylor95};" + Tavlor 1997)) aud optical faint companiony. of BCCs (Pustiluik et al. L997))., Taylor \cite{Taylor97}) ) and optical faint companions of BCGs (Pustilnik et al. \cite{Pustilnik97}) ). + Receut results on lat( spiralsbv Reshetuikov Combes (1997)) aud Ruduic- Ris (1998)) also sueeest the tuportance of wea- interactions to modulate SF historyin these galaxies., Recent results on late spirals by Reshetnikov Combes \cite{Reshet97}) ) and Rudnick Rix \cite{Rudnick98}) ) also suggest the importance of weak interactions to modulate SF historyin these galaxies. + From t1C observational data discussed: above ποιο preliminary ¢¢iclusious cui be draw:, From the observational data discussed above some preliminary conclusions can be drawn: +such a model for w Cen has already been developed by Romano et al. (,Such a model for $\omega$ Cen has already been developed by Romano et al. ( +2007) ancl then applied by Romano Matteucci (2007) to explain the low values of Cu/Fe found by Cunha et al. (,2007) and then applied by Romano Matteucci (2007) to explain the low values of Cu/Fe found by Cunha et al. ( +2002) and Pancino οἱ al. (,2002) and Pancino et al. ( +2002).,2002). + This model assumes that &« Cen began its history as a cwarf spheroidal galaxy. Chat evolved iniüiallv in isolation and whose chemical evolution was affected strongly by galactic winds (as with Ser)., This model assumes that $\omega$ Cen began its history as a dwarf spheroidal galaxy that evolved initially in isolation and whose chemical evolution was affected strongly by galactic winds (as with Sgr). + The conclusion bv Romano Maltteucci (2007) concerning copper. was that il was produced via a metallicitv-dependent process in INassive stars; in (his case it is the weak s-process occurring during Ie-burning in (hese stars. wilh (he neutron source beinganne 7 Ne(o.n)' os Me.," The conclusion by Romano Matteucci (2007) concerning copper, was that it was produced via a metallicity-dependent process in massive stars; in this case it is the weak s-process occurring during He-burning in these stars, with the neutron source being $^{22}$ $\alpha$ $^{25}$ Mg." + Since⋅ the amount of oreNe depends on the abundance of !! N. whose value depends on stellar metallicity. (his renders the strength of (he s-process proportional to metallicity.," Since the amount of $^{22}$ Ne depends on the abundance of $^{14}$ N, whose value depends on stellar metallicity, this renders the strength of the s-process proportional to metallicity." + Our result [or w Cen is that Mn behaves as a metallicitv-dependent element. in a similar manner (o that of Cu. and may provide further constraints on both chemical evolution within (his peculiar svstem. as well as the origins of both Mn aud Cu.," Our result for $\omega$ Cen is that Mn behaves as a metallicity-dependent element, in a similar manner to that of Cu, and may provide further constraints on both chemical evolution within this peculiar system, as well as the origins of both Mn and Cu." + Note that Wylie de Boer et al. (, Note that Wylie de Boer et al. ( +2010) used low values of Cu/Fe as one indicator Chat stars in Ixaptevns group may represent an w Cen stream.,2010) used low values of Cu/Fe as one indicator that stars in Kapteyn's group may represent an $\omega$ Cen stream. + Our results here suggest (hat Mn/Fe would also be a useful tracer of possible w Cen tidal streams., Our results here suggest that Mn/Fe would also be a useful tracer of possible $\omega$ Cen tidal streams. + Manganese abundances have been measured for the first time in the peculiar globular cluster w Cen. with the analysis of 10 red giants spanning a range in metallicity from |Fe/II]— -1.9 to -0.9.," Manganese abundances have been measured for the first time in the peculiar globular cluster $\omega$ Cen, with the analysis of 10 red giants spanning a range in metallicity from [Fe/H]= -1.9 to -0.9." + The analvsis is based on Mn I lines using both LTE and non-LTE ealeulations to derive abundances., The analysis is based on Mn I lines using both LTE and non-LTE calculations to derive abundances. + In. addition. (he possible effects of enhanced 11ο abundances on derived AIn abundances were investigated for the more metal-rich w Cen giants and were found to be negligible.," In addition, the possible effects of enhanced He abundances on derived Mn abundances were investigated for the more metal-rich $\omega$ Cen giants and were found to be negligible." + The novel result is that (wo members from the more metal-rich populations with w Cen (RGB MInt2 and MlILQtU3) exhibit low ratios of Mn/Fe in comparison to Galactic field stars. as well as other globular cluster stars at the same metallcitiv ([Fe/1]-1).," The novel result is that two members from the more metal-rich populations with $\omega$ Cen (RGB MInt2 and MInt3) exhibit low ratios of Mn/Fe in comparison to Galactic field stars, as well as other globular cluster stars at the same metallcitiy $\sim$ -1)." + Differences between w Cen and the other Milky Way. populations exist whether (he comparison is mace using LTE or non-LTE abundances., Differences between $\omega$ Cen and the other Milky Way populations exist whether the comparison is made using LTE or non-LTE abundances. + The low abundances of Mn may indicate that low-metallicity progenitors to supernovae (of either core collapse or SNe Ia) dominated the production of manganese within iw Cen., The low abundances of Mn may indicate that low-metallicity progenitors to supernovae (of either core collapse or SNe Ia) dominated the production of manganese within $\omega$ Cen. + This result for Mn is similar to what has been noted previously [or the behavior of copper (which in some nucleosvuthesis processes has metallicitv-dependent vields) in & Cen (Cunha et al., This result for Mn is similar to what has been noted previously for the behavior of copper (which in some nucleosynthesis processes has metallicity-dependent yields) in $\omega$ Cen (Cunha et al. + 2002)., 2002). + The behavior of Mn in the more extrenie metal-rich w Cen population (IRGD-a) remains, The behavior of Mn in the more extreme metal-rich $\omega$ Cen population (RGB-a) remains +"aand abundance variations, using available stars.","and abundance variations, using available stars." + In the case of the lowest surface brightness components of the WIM it is necessary to either modify the characteristic radiation field or to introduce non-photoionization heating processes., In the case of the lowest surface brightness components of the WIM it is necessary to either modify the characteristic radiation field or to introduce non-photoionization heating processes. + Study of the diffuse ionized gas in other galaxies may provide some help in understanding our own WIM and the cause of the systematically higher values of iin the lowest surface brightness components., Study of the diffuse ionized gas in other galaxies may provide some help in understanding our own WIM and the cause of the systematically higher values of in the lowest surface brightness components. +" In the study of other galaxies one has the advantage of easily looking for variations with position and these are commonly found (Tüllmann&Dettmar2000a,b;Otteetal.2001,2002),, but this is at the expense of losing the diagnostically valuable tool of being able to divide the contributors into surface brightness groups and it often appears necessary to invoke non-photoionization processes to explain the observations."," In the study of other galaxies one has the advantage of easily looking for variations with position and these are commonly found \citep{tu00a,tu00b,ott01,ott02}, but this is at the expense of losing the diagnostically valuable tool of being able to divide the contributors into surface brightness groups and it often appears necessary to invoke non-photoionization processes to explain the observations." +" The work that we report on here builds from the physics operating in a succession of photoionized objects of decreasing density and increasing scale (M 43, Barnard’s Loop, theBubble,, and local components of the WIM."," The work that we report on here builds from the physics operating in a succession of photoionized objects of decreasing density and increasing scale (M 43, Barnard's Loop, the, and local components of the WIM." + These final conclusions can then be a jumping-off point in discussion of the diffuse ionized gas in other galaxies., These final conclusions can then be a jumping-off point in discussion of the diffuse ionized gas in other galaxies. + We have been able to reach several important conclusions from this study that began with new observations of the Barnard’s Loop., We have been able to reach several important conclusions from this study that began with new observations of the Barnard's Loop. + These have provided data similar to previous studies but in a new region of the object and at higher spectrophotometric accuracy., These have provided data similar to previous studies but in a new region of the object and at higher spectrophotometric accuracy. + These observations were supplemented by intensive photoionization modelling., These observations were supplemented by intensive photoionization modelling. + The major conclusions are:, The major conclusions are: +contanunation bv the ACN. while the bluer (BW) colours in Sevtert 2s are due to strong star formation in their (their nuclear colours being redder than normal galaxy colours).,"contamination by the AGN, while the bluer $(B-V)$ colours in Seyfert 2s are due to strong star formation in their (their nuclear colours being redder than normal galaxy colours)." + A third observation is that thenuclear colours for cach of the two Sevtert saluples appear to lie along some type of sequence in Figure 16.., A third observation is that the colours for each of the two Seyfert samples appear to lie along some type of sequence in Figure \ref{f9}. + We do not find this to be a sequence of IIubble types. interaction stage or of some other norphological peculiarity.," We do not find this to be a sequence of Hubble types, interaction stage or of some other morphological peculiarity." + In Paper II we have secu hat the Wari Sevfert 1 uuclear colours scale withfracLgingLp., In Paper II we have seen that the Warm Seyfert 1 nuclear colours scale with. + This was interpreted iu terms of dust obscuration. which is likely to be represented bv he sequence in the colour-colour plots.," This was interpreted in terms of dust obscuration, which is likely to be represented by the sequence in the colour-colour plots." + The trend or Sevfert 2 nuclei is more dificult to muderstancl., The trend for Seyfert 2 nuclei is more difficult to understand. + There is one Sevfert 2 ealaxy with apparently very due (VR) colour: this is IRAS 13536|1836. a double nucleus svstem for which ouly the E nucleus is considered here (see also Paper IT).," There is one Seyfert 2 galaxy with apparently very blue $(V-R)$ colour; this is IRAS 13536+1836, a double nucleus system for which only the E nucleus is considered here (see also Paper II)." + Because integrated. colours are usually dominated bv the uucleus. a better approach is to use radial colour profiles. especially for the study of disk populatious.," Because integrated colours are usually dominated by the nucleus, a better approach is to use radial colour profiles, especially for the study of disk populations." + Iu the lower paucls of Figure 16 we plot the (μυμη) vs(pyvpug) tracks starting from radius 2 kpe (filled circles) out to ppp=23 mag (triangles)., In the lower panels of Figure \ref{f9} we plot the $(\mu_{B}-\mu_{R})$ vs $(\mu_{V}-\mu_{R})$ tracks starting from radius 2 kpc (filled circles) out to $\mu_{B}$ =23 mag $^{-1}$ (triangles). + The lone-dashed lines on the Seyfert 2 plot indicate the double uucleus mereers IRAS 13536|1836 and 19251-7215., The long-dashed lines on the Seyfert 2 plot indicate the double nucleus mergers IRAS 13536+1836 and 19254-7245. + Not all objects plotted ou he upper panels appear on the lower (those with shallow images were omitted)., Not all objects plotted on the upper panels appear on the lower (those with shallow images were omitted). + The distribution of points is similar between the upper aud lower panels. but the tracks are quite different and will be discussed below in terms of conrparison with population svuthesis models.," The distribution of points is similar between the upper and lower panels, but the tracks are quite different and will be discussed below in terms of comparison with population synthesis models." + The dotted lines represent an average track for the normal spiral sample of DeJong1996 for O 50 hours with Cherenkov telescopes.," TeV blazars exhibit flares over time scales of weeks, allowing exposure times of $\ge$ 50 hours with Cherenkov telescopes." + Recorded flux levels historically range between 7 0.1 - 10 Crab., Recorded flux levels historically range between $\approx$ 0.1 - 10 Crab. + In [act Mrk 421. Mrk 501 20.03) have shown high flaring levels of > 4 Crab [or longer than several weeks.," In fact Mrk 421, Mrk 501 =0.03) have shown high flaring levels of $\ge$ 4 Crab for longer than several weeks." + When correcting for distance. many blazars show similar intrinsic flaring levels: LES1959+650. PKS2155-304!.. IL1H26--428 and 1ES1101-232.," When correcting for distance, many blazars show similar intrinsic flaring levels: 1ES1959+650, , H1426+428 and 1ES1101-232." + To evaluate the, To evaluate the +transit signal itself (1.0. 0): typically an order-of-magnitude.,transit signal itself (i.e. $\delta$ ); typically an order-of-magnitude. + Further. the time scale over which these changes act is &reater than that of the ingress/egress curvatures (1.6. T) except for grazing transits.," Further, the time scale over which these changes act is greater than that of the ingress/egress curvatures (i.e. $t_F \gg \tau$ ) except for grazing transits." + So we can see that. in eeneral. the errors in our numerical integration techniques will be dominated by the ingress/egress curvatures rather than the Iimb-darkening-induced lishteurve-trough curvatures.," So we can see that, in general, the errors in our numerical integration techniques will be dominated by the ingress/egress curvatures rather than the limb-darkening-induced lightcurve-trough curvatures." + ‘The final source of variation in the lightcurve gradient is that of the discontinuous change located at the contact. points., The final source of variation in the lightcurve gradient is that of the discontinuous change located at the contact points. + Estimating the error due to this discontinuity is most easily estimated by assuming a trapezoid approximated lighteurve and considering the location where maximal error is induced., Estimating the error due to this discontinuity is most easily estimated by assuming a trapezoid approximated lightcurve and considering the location where maximal error is induced. + The largest error (and in [act only error) will occur [or measurements close to contact. points. or more specifically |obag<19 where Fay is the time of one of the contact points.," The largest error (and in fact only error) will occur for measurements close to contact points, or more specifically $|t_i - t_M| < \mathcal{I}/2$ where $t_M$ is the time of one of the contact points." + 3elore the first contact point. we have a flat line at f=1 and after this point we have a linear slope with a eracient (0/7).," Before the first contact point, we have a flat line at $F=1$ and after this point we have a linear slope with a gradient $-(\delta/\tau)$." + The error in Simpson's composite rule will depend upon the relative phasing between the centre of the integration and the contact point. Lo. (ένο£4).," The error in Simpson's composite rule will depend upon the relative phasing between the centre of the integration and the contact point, i.e. $(t_i - t_I)$." +" Generalized to any phase. the true. integrated: flux of the trapezoid approximated lightcurve for the 7""sthtime stamp is given by: For each value of m=1.2.3.. we choose to set the phase to be such that the dillerence between the true integrated: Lux anc that from Simpson's method. is maximized."," Generalized to any phase, the true integrated flux of the trapezoid approximated lightcurve for the $i^{\mathrm{th}}$time stamp is given by: For each value of $m=1,2,3...$ we choose to set the phase to be such that the difference between the true integrated flux and that from Simpson's method is maximized." + Under such a condition. it may be shown that the maximum error is given by: For the svstem parameters of Ixepler-5b. we find that using m=1.2.3 induces a maximal error. of 3T1ppm. 93ppm and 41ppm respectively.," Under such a condition, it may be shown that the maximum error is given by: For the system parameters of Kepler-5b, we find that using $m=1,2,3$ induces a maximal error of $371$ ppm, $93$ ppm and $41$ ppm respectively." + Given that the measurement uncertainties are. I30ppm. (νου ct al., Given that the measurement uncertainties are $130$ ppm (Koch et al. + 2010). a suitable choice for the resolution would be m=2 since this means the maxiniuni possible error of a data point in the Lleast- phasing would be below the measurement error.," 2010), a suitable choice for the resolution would be $m=2$ since this means the maximum possible error of a data point in the least-favourable phasing would be below the measurement error." + It is interesting to see that for m=2 the error was Ü.lppm for the ingress/egress curvature of the same system. suggesting the cliscontinuity error. dominates. the errorbudget.," It is interesting to see that for $m=2$ the error was $0.1$ ppm for the ingress/egress curvature of the same system, suggesting the discontinuity error dominates the errorbudget." + Actually. this is expected from the arguments made earlier in this paper.," Actually, this is expected from the arguments made earlier in this paper." + Therefore. in most applications. a selection for m based on the error induced by the contact point clis¢ontinuities will provide a robust integration resolution.," Therefore, in most applications, a selection for $m$ based on the error induced by the contact point discontinuities will provide a robust integration resolution." + An additional method. for numerically integrating the lighteurve is discussed here., An additional method for numerically integrating the lightcurve is discussed here. + Let us consider that we have observations with integrated time stamps given by the vector [X, Let us consider that we have observations with integrated time stamps given by the vector $\underline{\tilde{t}}$. + second way of calculating £tDis to resample the time vector into a very fine cadence. at which point we may assume f=FF.," A second way of calculating $\underline{\tilde{F}}(\underline{\tilde{t}})$ is to resample the time vector into a very fine cadence, at which point we may assume $\tilde{F}=F$." + Let us define our temporary resampled time vector as Z., Let us define our temporary resampled time vector as $\underline{\tilde{t}'}$. + As an example. for the data. we may choose to resample the 30 minute integrations into 1 minute integrations would be done by expanding cach time stamp. 7; into a sub-veetor of 30 equally spaced time stamps with a mean value given by /;;," As an example, for the data, we may choose to resample the 30 minute integrations into 1 minute integrations would be done by expanding each time stamp, $\tilde{t}_i$ into a sub-vector of 30 equally spaced time stamps with a mean value given by $\tilde{t}_i$." +" Our new temporary time array ds used to generate a lDishteurve using the normal ALAO2. expressions. givingEM us £°D,(f°) (note that f°1 here has no tilde because the ALAO2 equations can only generate instantaneous Lux. not integrated flux)."," Our new temporary time array is used to generate a lightcurve using the normal MA02 expressions giving us $\underline{F'}(\underline{\tilde{t}'})$ (note that $F$ here has no tilde because the MA02 equations can only generate instantaneous flux, not integrated flux)." + We then rebin the model lighteurve back to the original cadence to give £(/)., We then rebin the model lightcurve back to the original cadence to give $\underline{F}(\underline{\tilde{t}})$. + Finally. we make the assumption FU~PD). Le. the high cadence resampled time vector vields a lighteurve model consistent with a time vector of infinite cadence.," Finally, we make the assumption $\underline{\tilde{F}}(\underline{\tilde{t}'}) \simeq \underline{F}(\underline{t})$, i.e. the high cadence resampled time vector yields a lightcurve model consistent with a time vector of infinite cadence." + ]t can be seen that resampling into IN sub-time stamps will increase the computation time by a factor of ΑΝ. since tvpically the NLAO2 subroutine uses the majority of a lighteurve fitting algorithms resources (especially for non-linear limb carkening).," It can be seen that resampling into $N$ sub-time stamps will increase the computation time by a factor of $\sim N$, since typically the MA02 subroutine uses the majority of a lightcurve fitting algorithm's resources (especially for non-linear limb darkening)." + In thenext subsection. we will show that the computation times can be decreased. by.," In thenext subsection, we will show that the computation times can be decreased by." +resempling.. One advantage of resampling is that we can choose to resample in such à way as to account for read-out and cleacl- which may be important if the instruments duty evele is quite.," One advantage of resampling is that we can choose to resample in such a way as to account for read-out and dead-times, which may be important if the instrument's duty cycle is quite." +". The resampling of the 7""th time stamp into N sub-time stamps with labels j=1.2....N.—1..N. can be expressed. as: The lux of the 7 time stamp is found by rebinning all N flux stamps from j= 110 j= NV."," The resampling of the $i^{\mathrm{th}}$ time stamp into $N$ sub-time stamps with labels $j=1,2,...N-1,N$ can be expressed as: The flux of the $i^{\mathrm{th}}$ time stamp is found by rebinning all $N$ flux stamps from $j=1$ to $j=N$ ." +" ""hus for the first few values of NV= 2. N= Sand NV=4 we would have: For a trapezoid. approximated. lighteurve. it can be casily shown that the error in these expressions. as a function of UN. is given by:"," Thus for the first few values of $N=2$ , $N=3$ and $N=4$ we would have: For a trapezoid approximated lightcurve, it can be easily shown that the error in these expressions, as a function of $N$ , is given by:" +The goal of this paper is to describe a method to fit the SED of pre-main sequence stars. using the eode called LLABdisk. which was adapted from the Iared dise model proposed. by DDNOI.,"The goal of this paper is to describe a method to fit the SED of pre-main sequence stars, using the code called HABdisk, which was adapted from the flared disc model proposed by DDN01." + The procedure uses the CoA method in order to finc the best paramcters set; based. on minimum. X7 criterion.," The procedure uses the GA method in order to find the best parameters set, based on minimum $\chi^2$ criterion." + The tests applied to AB Aur confirm that the GA methoc provides a good estimation of the circumstellar parameters. reproducing a canonical DDNOI moclel.," The tests applied to AB Aur confirm that the GA method provides a good estimation of the circumstellar parameters, reproducing a canonical DDN01 model." + Aiming to provide an illustrative application of LIADisk. we selected four225 stars that have similar mass and. effective temperatures. but show different amounts of infrared excess. as indicated by their spectral indices.," Aiming to provide an illustrative application of HABdisk, we selected four stars that have similar mass and effective temperatures, but show different amounts of infrared excess, as indicated by their spectral indices." + The estimated: circumstellar Iuminosities are in agreement with the expected correlation of SIZD shape with f. which vanishes as the spectral index in the infrared decreases.," The estimated circumstellar luminosities are in agreement with the expected correlation of SED shape with $f_c$, which vanishes as the spectral index in the infrared decreases." + The fo behaviour in the sample is consistent with the Ciroups I and LE defined by Meeusetal.(2002)... as summarized below.," The $f_c$ behaviour in the sample is consistent with the Groups I and II defined by \cite{Meeus02}, as summarized below." +" The intermediary f values estimated for DD-14. 1319 and LRAS 06475-0735 are in agreement with the optically thick dise surrounded. by a fared thin region proposed. for Group I. LD 141549 shows the lowest value of f, that is consistent with the Dat cise structure suggested for Croup I", The intermediary $f_c$ values estimated for BD-14 1319 and IRAS 06475-0735 are in agreement with the optically thick disc surrounded by a flared thin region proposed for Group I. HD 141549 shows the lowest value of $f_c$ that is consistent with the flat disc structure suggested for Group II. + Among the four stars. LRAS 07394-1953. is the only one associated with nebulositv. as verified in the LRAS-LSIS images (see Sect. 5.1).," Among the four stars, IRAS 07394-1953 is the only one associated with nebulosity, as verified in the IRAS-ISIS images (see Sect. \ref{sectquality}) )," + ancl probably for this reason it has a rising SED at the far-infrared that could not be fitted by ILADisk., and probably for this reason it has a rising SED at the far-infrared that could not be fitted by HABdisk. + Despite the σους quality of fittings. our results also indicate that some degenerated information from SED mocdelling can occur. as verified in the comparison of dilferent models.," Despite the good quality of fittings, our results also indicate that some degenerated information from SED modelling can occur, as verified in the comparison of different models." + First. the flared. dise model was not able to provide a good SED fitting when the observed cise size was considered for LED. 141569.," First, the flared disc model was not able to provide a good SED fitting when the observed disc size was considered for HD 141569." + A bad performance of the CX method is not the case. since a good fitting was achieved. in a second run of the code. but leading to unrealistic disc paranieters.," A bad performance of the GA method is not the case, since a good fitting was achieved in a second run of the code, but leading to unrealistic disc parameters." + Considering that a Hat cise would. better explain the circumstellar structure of LID 141569. we reanalyse the results from (11102 model. which gave reasonable clise size anc temperature.," Considering that a flat disc would better explain the circumstellar structure of HD 141569, we reanalyse the results from GH02 model, which gave reasonable disc size and temperature." + However. other unrealistic parameters were also derived. probably. due to the adopted. optically thick regime that gives high disc luminosity (see Table C1).," However, other unrealistic parameters were also derived, probably due to the adopted optically thick regime that gives high disc luminosity (see Table \ref{tabapptt}) )." + This is not compatible with the optically thin disc that is observed in scattered. light at large. distances from the central star., This is not compatible with the optically thin disc that is observed in scattered light at large distances from the central star. + The disc parameters determination from the SED fitting remains unsolved since the racial structure of this disc is much more complicated. than it is possible to describe using the adopted simple mocels., The disc parameters determination from the SED fitting remains unsolved since the radial structure of this disc is much more complicated than it is possible to describe using the adopted simple models. + On the view of the good results found for Ηλ 06475-0735 and DD-14 1319. we conclude thatPDS stars within the 1κο<0.7 range have SEDs better fitted by ΗΛαν insteac of the Lat cise mocel.," On the view of the good results found for IRAS 06475-0735 and BD-14 1319, we conclude that stars within the $-1 < \beta_1 < 0.7$ range have SEDs better fitted by HABdisk instead of the flat disc model." + For objects with 3)>0.7 another component seenis to be required in the circumstellar structure. such as a shell for example. to better reproduce the observed excess at longer wavelengths.," For objects with $\beta_1 > 0.7$ another component seems to be required in the circumstellar structure, such as a shell for example, to better reproduce the observed excess at longer wavelengths." + In this case. our previous flat disc model. which includes a thin dust envelope in the system. provided better results than LLXDisk.," In this case, our previous flat disc model, which includes a thin dust envelope in the system, provided better results than HABdisk." +" Even consideringthe degeneracy in the case of LD 141569. its low f, value leach us to expect that. objects showing 9τιl seem to be better explained by Dat disc geometry mocels."," Even consideringthe degeneracy in the case of HD 141569, its low $f_c$ value lead us to expect that objects showing $\beta_1 < -1$ seem to be better explained by flat disc geometry models." +" On the lisht of the above remarks. we conclude that eood estimations of the circumstellar luminosities may be provided. for a largesample of objects. and a statistical analvsis can be done by comparing f. with 2, in order to verify a possible sequence of disc disappearance."," On the light of the above remarks, we conclude that good estimations of the circumstellar luminosities may be provided for a largesample of objects, and a statistical analysis can be done by comparing $f_c$ with $\beta_1$ in order to verify a possible sequence of disc disappearance." + We are aware that no inferences about clisc evolution can be attended from the derived: parameters., We are aware that no inferences about disc evolution can be attended from the derived parameters. + Considering the lack of detailed observations about dise parameters or spectral features related to grain composition. à parameters set must. be carefully evaluated. even when derived: from &ood SED fittings.," Considering the lack of detailed observations about disc parameters or spectral features related to grain composition, a parameters set must be carefully evaluated, even when derived from good SED fittings." + Since these detailed observations are not available for the large majority of thePS sample. the disc parameters must be constrained to realistic ranges.," Since these detailed observations are not available for the large majority of the sample, the disc parameters must be constrained to realistic ranges." + The dilliculty to infer dise parameters for large samples arises [rom the interpretation of details on infrared spectral features and/or high angular resolution data. requiring incliviclual analvsis of the physics. the geometry and chemical composition.," The difficulty to infer disc parameters for large samples arises from the interpretation of details on infrared spectral features and/or high angular resolution data, requiring individual analysis of the physics, the geometry and chemical composition." + This task shall be accomplished with the use of several promising high-sensitive observational facilities that are under operation or will be in a near future., This task shall be accomplished with the use of several promising high-sensitive observational facilities that are under operation or will be in a near future. + In particular. we mention here the near-infrared coronagraphie imager CNICT) that is being used withCerri telescope to search [or exoplanets.," In particular, we mention here the near-infrared coronagraphic imager ) that is being used with telescope to search for exoplanets." + One of the sub-products of this campaign certainly shall be the detailed imagery of protoplanetary discs., One of the sub-products of this campaign certainly shall be the detailed imagery of protoplanetary discs. + Using the CAA method. we seek to select &ood targets among thePOS stars that are in the distance range to be imaged withALCL.," Using the GA method, we seek to select good targets among the stars that are in the distance range to be imaged with." + We acknowledge an anonymous referee for very useful comments on the improvement of the paper presentation., We acknowledge an anonymous referee for very useful comments on the improvement of the paper presentation. + We are also grateful to Kees Dullemonc for his. kindness ancl valuable suggestions., We are also grateful to Kees Dullemond for his kindness and valuable suggestions. + JOLIE thanks partial support from FAPESP (Proc., JGH thanks partial support from FAPESP (Proc. + No., No. + 2005/00397-1)., 2005/00397-1). + ALL) thanks LAG/USP for the opportunity to develop this research during a post-doctoral stay., AHJ thanks IAG/USP for the opportunity to develop this research during a post-doctoral stay. + Vhis work has mace use of the and VizieR databases operated at CDS. Strasbourg. France.," This work has made use of the and databases operated at CDS, Strasbourg, France." +(its main effect is to supply a prompt initial enrichment of the ISM auc [GM as well as provide au ionizing source at high redshift). most observable constraiuts are tied to the normal mode.,"(its main effect is to supply a prompt initial enrichment of the ISM and IGM as well as provide an ionizing source at high redshift), most observable constraints are tied to the normal mode." + Thus. we begiu with a more detailed description of the normal mode aud its observational cousequences.," Thus, we begin with a more detailed description of the normal mode and its observational consequences." + We listed the main parameters of the model in the previous section., We listed the main parameters of the model in the previous section. + The inodel cousists of a superposition of a normal mode of star formation and an early massive mode at high redshift. when the global metallicity in the star-forming structures is still very low (population III stars).," The model consists of a superposition of a normal mode of star formation and an early massive mode at high redshift, when the global metallicity in the star-forming structures is still very low (population III stars)." + We will describe this mocle in section 5.., We will describe this mode in section \ref{sec:popIII}. + We focus here on the normal mode of star formation., We focus here on the normal mode of star formation. +" We fix the mass range of star formation to inar=OLNL, and (ap=100ML. so that the only. parameter ueeded to define the IMF is its slope. namely ory. which is usually estimated to be in the range 1.30 (?) to LT (?).."," We fix the mass range of star formation to $m_\mathrm{inf}=0.1\ \mathrm{M_{\odot}}$ and $m_\mathrm{sup}=100\ \mathrm{M_\odot}$ so that the only parameter needed to define the IMF is its slope, namely $x_{1}$, which is usually estimated to be in the range $1.30$ \citep{salpeter:55} to $1.7$ \citep{scalo:86}." + As noted above. we employ anu exponentially decreasing SFR (which. is representative of elliptical galaxies) as parametrizatious such as a Schimidt-Iaw. vield significautly poorer fits to the observational data.," As noted above, we employ an exponentially decreasing SFR (which is representative of elliptical galaxies) as parametrizations such as a Schmidt-law yield significantly poorer fits to the observational data." + Heuce we take. where Jing is the initial age of the Universe at cing where the star formation starts in themodel. τι is a timescale of the order of 2—3Cyr and vy=fannsasaus0)/74 with fy being a fraction eoverniug the elficieucy of the star Siuce many of the observational constraints used to fix the parameters pertain to relatively low redshift. we performed a detailed scau of the parameter space inclucling ouly the normal mode.," Hence we take, where $t_\mathrm{init}$ is the initial age of the Universe at $z_\mathrm{init}$ where the star formation starts in themodel, $\tau_{1}$ is a timescale of the order of $2-3\ \mathrm{Gyr}$ and $\nu_{1}=f_{1} m_\mathrm{struct}(t) / \tau_{1}$ with $f_{1}$ being a fraction governing the efficiency of the star Since many of the observational constraints used to fix the parameters pertain to relatively low redshift, we performed a detailed scan of the parameter space including only the normal mode." +" The parameter grid was chosento be: μμ= 109. 10*. LOS. 109. and 1011M.: e—0. 103. 2x10 7.3x107.57. 7x 10.7.102. 2x107 and 3xLO7: p,=0.1. 0.2. 0.3. 0.L 0.5. 0.6 and 0.7Gyr.th 7=2.2. 2.L 2.6. 2.8. 3.0. 3.2 Cyr ry=13. 135 :xl Lt."," The parameter grid was chosento be: $M_\mathrm{min}=10^{6}$ , $10^{7}$, $10^{8}$, $10^{9}$, and $10^{11}\ \mathrm{M_{\odot}}$; $\epsilon=0$, $10^{-3}$, $2\times 10^{-3}$ , $3\times 10^{-3}$, $7\times 10^{-3}$ , $10^{-2}$, $2\times 10^{-2}$ and $3\times 10^{-2}$; $\nu_{1}=0.1$, 0.2, 0.3, 0.4, 0.5, 0.6 and $0.7\ \mathrm{Gyr^{-1}}$; $\tau_{1}=2.2$, 2.4, 2.6, 2.8, 3.0, 3.2 Gyr; $x_1=1.3$, 1.35 and 1.4." + In all cases. we have assumed that the ouset of star formation begins when the baryou fraction in structures isνε.," In all cases, we have assumed that the onset of star formation begins when the baryon fraction in structures is." + We have tested that this initial Traction has a very weak iupact on the results coucerniug the normal iode of star formation., We have tested that this initial fraction has a very weak impact on the results concerning the normal mode of star formation. + It is on the other liaud of great unportance for the population HI stars aud its effect will be studied in section 5.., It is on the other hand of great importance for the population III stars and its effect will be studied in section \ref{sec:popIII}. + One should also note that there are additional paraineters associated with the rate of type Ia superuovae., One should also note that there are additional parameters associated with the rate of type Ia supernovae. + These are directly coustrained by observations aud will be fixed in section 1..., These are directly constrained by observations and will be fixed in section \ref{sec:SNae}. + To determine the parameters which best fit the observations. we performed 47 analysis over he parameter grid.," To determine the parameters which best fit the observations, we performed $\chi^2$ analysis over the parameter grid." + Included in the V7 analysis are six sets of observational data: (1) The observed cosinic star formation rate up to z5 (?).., Included in the $\chi^2$ analysis are six sets of observational data: (1) The observed cosmic star formation rate up to $z\sim 5$ \citep{hopkins:04}. + The data were binued aud averaged inredshift leacdiug o somewhat larger observational uncertainties at a given redshift than typically reported for a single measurement: (2) The observed rate of type II supernovae up to zQ.7 (2): (3) The present raction of baryons in structures. fhageitz=0)c6Lx18% (2): (1) The presentfraction of orvousin stars. {ως=0)264 (5.6) The evolution of the metal content iu the ISM," The data were binned and averaged inredshift leading to somewhat larger observational uncertainties at a given redshift than typically reported for a single measurement; (2) The observed rate of type II supernovae up to $z\sim 0.7$ \citep{dahlen:04}; ; (3) The present fraction of baryons in structures, $f_\mathrm{b,struct}(z=0)\simeq 61\pm 18\ \%$ \citep{fukugita:04}; ; (4) The presentfraction of baryonsin stars, $f_\mathrm{b,*}(z=0)\simeq 6\pm 6\ \%$ \citep{fukugita:04}; ; (5,6) The evolution of the metal content in the ISM" +The equation for hydrostatic equilibrium in the z direction is given by (BRohlls 1977) where <(07);> is the mean square random velocity along the 2 direction for the component i.,The equation for hydrostatic equilibrium in the z direction is given by (Rohlfs 1977) where $<(v_{z}^{2})_{i}>$ is the mean square random velocity along the $z$ direction for the component $i$. + We further assume each component to be isothermal lor simplicity. so that the velocity term is constant. wilh z.," We further assume each component to be isothermal for simplicity, so that the velocity term is constant with $z$." +" Eliminating 9,,,, between eq. (", Eliminating $\Phi_{total}$ between eq. ( +2) ancl eq. (,2) and eq. ( +3). ancl assuming an isothermal case. we get which represents a set of three coupled. secouc-orcler differential equations. one for each component of the disk.,"3), and assuming an isothermal case, we get which represents a set of three coupled, second-order differential equations, one for each component of the disk." + From the above equation. it is evident that though there is a common eravitational potential. the response of each component will be different due to the difference in their random velocity dispersions.," From the above equation, it is evident that though there is a common gravitational potential, the response of each component will be different due to the difference in their random velocity dispersions." +" We model the bulge of M31 as a spherically svuunetric mass distribution represented by a Hernquist profile (Llernquist 1990). where M, is the total mass of the bulge. aud rj is ils core radius."," We model the bulge of M31 as a spherically symmetric mass distribution represented by a Hernquist profile (Hernquist 1990), where $M_b$ is the total mass of the bulge, and $r_b$ is its core radius." + The mass profile aud density corresponding to this distribution are given by and, The mass profile and density corresponding to this distribution are given by and +Fie.,Fig. + 2 presents the average of all the data collected on 1996 Feb 28., 2 presents the average of all the data collected on 1996 Feb 28. + Lt is characterised by a [lat continuum. broad Balmer and lines in emission. high excitation lines of11. and ancl numerous faint. narrow absorption features ofr.Cat. and that had. been identified. as signatures of the Ix-tvpe secondary star by. Ixraft. (10964). Gallagher Oinas (1974). CCE and Reinseh (1994).," It is characterised by a flat continuum, broad Balmer and lines in emission, high excitation lines of, and and numerous faint, narrow absorption features of, and that had been identified as signatures of the K-type secondary star by Kraft (1964), Gallagher Oinas (1974), CCF and Reinsch (1994)." + We emploved. Ix star spectral templates to determine which luminosity class best matched the secondary star in this svstem during outburst and search. for signatures of increased X-ray irracliation., We employed K star spectral templates to determine which luminosity class best matched the secondary star in this system during outburst and search for signatures of increased X-ray irradiation. + Using CC's fit to the orbita radial velocity of the secondary star we shifted. out. the orbital motion of the absorption lines with a quadratic rebinning algorithm., Using CCF's fit to the orbital radial velocity of the secondary star we shifted out the orbital motion of the absorption lines with a quadratic rebinning algorithm. + We binned in velocity the spectra of aand the [x-tvpe templates to ensure. that they all hac identical wavelength ranges and clispersions., We binned in velocity the spectra of and the K-type templates to ensure that they all had identical wavelength ranges and dispersions. + We emplovec the optimal subtraction algorithm of Marsh. Robinson Wood (1994) to determine the Ix star spectral type we multiply the template by a monochromatic constant which represents the contribution to the spectrum from non-stellar sources of light and subtract the resulting spectrum from the delata.," We employed the optimal subtraction algorithm of Marsh, Robinson Wood (1994) to determine the K star spectral type – we multiply the template by a monochromatic constant which represents the contribution to the spectrum from non-stellar sources of light and subtract the resulting spectrum from the data." + Phe residual was smoothecl using a high-pass band filter (PWIIAL of gaussian = 18 Aj). and a v test performed between the original ancl smoothecl residual.," The residual was smoothed using a high-pass band filter (FWHM of gaussian = 13 ), and a $\chi^2$ test performed between the original and smoothed residual." + This is an iterative procedure to determine the optimum value of the monochromatic constant which continues until X7 is minimised., This is an iterative procedure to determine the optimum value of the monochromatic constant which continues until $\chi^2$ is minimised. + Table 2 lists the templates. their speetral classes. and the reduced X7 obtained after applying optimal subtraction.," Table 2 lists the templates, their spectral classes, and the reduced $\chi^2$ obtained after applying optimal subtraction." + The best fit template is the star HD197964 which provided. a reduced. 47. of 2.5., The best fit template is the star HD197964 which provided a reduced $\chi^2$ of 2.5. + ‘The secondary star contributes 13 per cent of the total light in this spectral region on the third night of observations., The secondary star contributes 13 per cent of the total light in this spectral region on the third night of observations. + This compares to 33 per cent found. by CCE and. Gallagher Oinas (1974) during quiescence indicating that the accretion How has increased in brightness., This compares to 33 per cent found by CCF and Gallagher Oinas (1974) during quiescence indicating that the accretion flow has increased in brightness. + The best-fit luminosity classes are consistent. with the quiescent Classifications of IxX21vp by Ixraft. ο by Gallagher OOinas (1974). by COE. and by Reinsch (1994).," The best-fit luminosity classes are consistent with the quiescent classifications of p by Kraft (1964), by Gallagher Oinas (1974), by CCF, and by Reinsch (1994)." + We find the spectral type to be constant across our two phase samples - one during which a large area of the white dwarf- surface is visible and the other when it is mostly limb-occulted., We find the spectral type to be constant across our two phase samples - one during which a large area of the white dwarf-facing surface is visible and the other when it is mostly limb-occulted. + Consequently. there is no observational evidence for an increase in irradiating Lux from the accretion regions over the inner face of the companion star. although we are limited by a small range of spectral templates and. poor orbital sampling.," Consequently there is no observational evidence for an increase in irradiating flux from the accretion regions over the inner face of the companion star, although we are limited by a small range of spectral templates and poor orbital sampling." +" lo order to measure integrated emission line lluxes [rom each of the three nights. we fitted a third order polynomial through wavelength bands relatively ree of line. features (AA4147-4212.V... AA4278-4306... AA4560-4608,A... AALTTO- aancl subtracted the fit from the data."," In order to measure integrated emission line fluxes from each of the three nights, we fitted a third order polynomial through wavelength bands relatively free of line features $\lambda\lambda$, $\lambda\lambda$, $\lambda\lambda$, $\lambda\lambda$ and subtracted the fit from the data." + Fluxes were measured by summing under cach line profile and these are provided in Table 3., Fluxes were measured by summing under each line profile and these are provided in Table 3. + The intensity of the continuum. the lines and the relative intensity of wwith respect to the Balmer lines. increases from the first night to the last as the svstem approaches the outburst maximum.," The intensity of the continuum, the lines and the relative intensity of with respect to the Balmer lines, increases from the first night to the last as the system approaches the outburst maximum." +" We fit the emission lines during the three nights with a power law function of time £F—/"". and provide the index à for each line in Table 4."," We fit the emission lines during the three nights with a power law function of time $F \sim t^\alpha$, and provide the index $\alpha$ for each line in Table 4." +" Power-law fits ofthe form fy.=7"" on each consecutive night provide à = — L61 + 0.03. 148 + 0.03 and 1.39 + O11."," Power-law fits ofthe form $f_{\nu}=\nu^{\alpha}$ on each consecutive night provide $\alpha$ = $-$ 1.61 $\pm$ 0.03, $-$ 1.43 $\pm$ 0.03 and $-$ 1.39 $\pm$ 0.11." + Continuum slope changes slightly within statistical uncertainties curing the observing run. the spectra becoming bluer with time consistent with a rise in temperature through the accretion flow.," Continuum slope changes slightly within statistical uncertainties during the observing run, the spectra becoming bluer with time consistent with a rise in temperature through the accretion flow." + These indices are inconsistent with an accretion disc emitting as a cliserete set of blackboclics (Pringle 1981)., These indices are inconsistent with an accretion disc emitting as a discrete set of blackbodies (Pringle 1981). + A comparison of the Feb 28 averaged spectrum with the spectra presented by Reinseh (1994) reveals that the Balmoer line lluxes are 71.7 times larger than during quiescence ad the fleature and the BBowen blend are 75.3 times brighter., A comparison of the Feb 28 averaged spectrum with the spectra presented by Reinsch (1994) reveals that the Balmer line fluxes are $\sim$ 1.7 times larger than during quiescence and the feature and the Bowen blend are $\sim$ 5.3 times brighter. + λΕΗτ1τΑ aand A492 anre LA and 2.23 times brighter during this outburst stage. respectively.," $\lambda$ and $\lambda$ are 1.4 and 2.3 times brighter during this outburst stage, respectively." + In quiescence the Balmer lines are the brightest emission lines. whereas the strongest line in the current data isA4686.," In quiescence the Balmer lines are the brightest emission lines, whereas the strongest line in the current data is." +X.. Szkody. Mattei Mateo (1985) and CCE present spectra of ttaken curing the 1983 outburst maximum and 20 davs after outburst respectively in which this behaviour is also clear.," Szkody, Mattei Mateo (1985) and CCF present spectra of taken during the 1983 outburst maximum and 20 days after outburst respectively in which this behaviour is also clear." + In paper we provided an analysis of the emission line velocities., In paper we provided an analysis of the emission line velocities. + To complete the radial velocity analysis we now consider the absorption lines., To complete the radial velocity analysis we now consider the absorption lines. + In Sec., In Sec. + 3.1 we determined that our best secondary star template has a spectral type of Ixliv., 3.1 we determined that our best secondary star template has a spectral type of . + ὃν masking out the emission lines in individual, By masking out the emission lines in individual +The white cowarf Iniinositv function iu a star cluster. iu the absence of dvuamical evolution. coutaius information ou the initial mass function (AIF) aud age of the cluster.,"The white dwarf luminosity function in a star cluster, in the absence of dynamical evolution, contains information on the initial mass function (IMF) and age of the cluster." + Iu fact. it will eventually be possible to use the white dwarf huuinositv function ia au old star cluster (c.g. a elobular cluster) to extend the observed mein sequeuce niass function up to massive stars that many billious of vears ago evolved in to white dwarts (Richer 1997).," In fact, it will eventually be possible to use the white dwarf luminosity function in an old star cluster (e.g. a globular cluster) to extend the observed main sequence mass function up to massive stars that many billions of years ago evolved in to white dwarfs (Richer 1997)." + White dwarf luuinosity functions for different ages were constructed iu the following manuer. (, White dwarf luminosity functions for different ages were constructed in the following manner. ( +a) The isochrones and the inifial-Bnal mass relation were used to set the ΠΠ aud iininwun iain sequence masses for a cluster of a particular age. (,a) The isochrones and the initial-final mass relation were used to set the maximum and minimum main sequence masses for a cluster of a particular age. ( +b) Based on the IME used. a random extraction of à main sequence lass in this range was πας and this then vielded a white dwarf mass frou the initial-final mass relation. (,"b) Based on the IMF used, a random extraction of a main sequence mass in this range was made and this then yielded a white dwarf mass from the initial-final mass relation. (" +ο) From the isochrones. the My of this white dwarf was then obtained. (,"c) From the isochrones, the $M_V$ of this white dwarf was then obtained. (" +d) This was repeated 1.000 times and eventually renormalized to 100 white cawarfs for cach cluster.,"d) This was repeated 1,000 times and eventually renormalized to 100 white dwarfs for each cluster." +" Figure 6 illustrates such Lbhuuinositv functions for a Salpeter IAIF (o(0)xim"" where a=2.35. solid line) and a much flatter IME (a=1.3. dashed line) which is nore in line with the steepest IMEs being fouud at the low nass end in elobular clusters (Piotto aud. Zoccali: 1999)."," Figure 6 illustrates such luminosity functions for a Salpeter IMF $n(m) \propto m^{-\alpha}$ where $\alpha = 2.35$, solid line) and a much flatter IMF $\alpha = 1.3$, dashed line) which is more in line with the steepest IMFs being found at the low mass end in globular clusters (Piotto and Zoccali 1999)." + The main feature to note in this diagram is the manner in which the peak of the cluster white dwarf Iuuinosity uction marches toward lower luminosity as the cluster age iucreases., The main feature to note in this diagram is the manner in which the peak of the cluster white dwarf luminosity function marches toward lower luminosity as the cluster age increases. + This is then a potentially powerful technique or determining cluster ages that is largely iudepenudoeut of isochrone fitting to the turn off region of a cluster., This is then a potentially powerful technique for determining cluster ages that is largely independent of isochrone fitting to the turn off region of a cluster. + As can © seen. the effect of even a radica change in the IME slope has a rather small iufineuce o1 the morphology of he white dwarf Iuuinositv fiction and it appears that his is wnalikely to be a seusitive mehod of investigating cluster IMES.," As can be seen, the effect of even a radical change in the IMF slope has a rather small influence on the morphology of the white dwarf luminosity function and it appears that this is unlikely to be a sensitive method of investigating cluster IMFs." + For this reason we onvo tabulate functions or Salpeter IAIFs., For this reason we only tabulate functions for Salpeter IMFs. + These luminosity fictions are listed iu Table 5 for those in Joliusou-Ixrou/Cousius filters aud in Table 6 for those calculated in the UST filter set., These luminosity functions are listed in Table 5 for those in Johnson-Kron/Cousins filters and in Table 6 for those calculated in the HST filter set. + In these tables the ποτ’ of white dwarfs is normalized to 100 and the coblunus are. respectively. the absolute V inagnitude of the middle of the iu. the umuber of white dwarfs iu that biu. the cumulative munber of white dwarfs. the mean mass of the white cavarts and of the progenitors.," In these tables the number of white dwarfs is normalized to 100 and the columns are, respectively, the absolute $V$ magnitude of the middle of the bin, the number of white dwarfs in that bin, the cumulative number of white dwarfs, the mean mass of the white dwarfs and of the progenitors." + As a last point regarding white dwarf huninosity uctions in clusters. we inquire whether information about the age of a cluster can be obtained if the turnover in the white dwarf luuinesity function isvot observed. mit oulv if a bright portion (e.g. to Mq= 15) is seen.," As a last point regarding white dwarf luminosity functions in clusters, we inquire whether information about the age of a cluster can be obtained if the turnover in the white dwarf luminosity function is observed, but only if a bright portion (e.g. to $M_V = 15$ ) is seen." + This of course has pochtial practical applications as the erinination points of white dwarf sequences will oulv (f possible to observe iu the nearest globular clusters even with UST aud the Advanced Camera for Survevs., This of course has potential practical applications as the termination points of white dwarf sequences will only be possible to observe in the nearest globular clusters even with HST and the Advanced Camera for Surveys. + To investigate this we superinpose in Figure 7 svuthetic white dwarf hiwnosity fictions for 10. 12 aud 11 Cor old clusters.," To investigate this we superimpose in Figure 7 synthetic white dwarf luminosity functions for 10, 12 and 14 Gyr old clusters." + The nunbers of white dwarts indicated are those expected from a single WFPC2 field at 6 core radii from the ceuter of the elobular cluster ALL., The numbers of white dwarfs indicated are those expected from a single WFPC2 field at 6 core radii from the center of the globular cluster M4. + If the functions in Figure 7 are compared only down to Mq:19. it becomes clear that virtually no useful iuforiuation is obtained regarding the age of the cluster.," If the functions in Figure 7 are compared only down to $M_V = 15$, it becomes clear that virtually no useful information is obtained regarding the age of the cluster." + The turnover in the Iuninositv fiction must be observed im order to constrain the cluster age., The turnover in the luminosity function must be observed in order to constrain the cluster age. +" Tn an earlier paper Richer 1998 presented aud discussed the observed white dwarf Inninositv fiction iu the open cluster M67 which has a turn off age of about | Gyr (Monteonmerv 1993),", In an earlier paper Richer 1998 presented and discussed the observed white dwarf luminosity function in the open cluster M67 which has a turn off age of about 4 Gyr (Montgomery 1993). + IIore we colpare this function with svutretic Luminosity fiuctions in order to derive the white dwarf cooling age o the cluster., Here we compare this function with synthetic luminosity functions in order to derive the white dwarf cooling age of the cluster. + In the previous paper we did not have access to such svuthetic fictions so the cirent derivation o: the cluster cooling age will supercede he results in the earlier paper., In the previous paper we did not have access to such synthetic functions so the current derivation of the cluster cooling age will supercede the results in the earlier paper. +the transition out of the hard state: the X-ray luminosity remains approximately constant. the X-ray hardness shows a sharp turnoff. and the radio-infrared emission quenches (e.g.Homanetal.2005).,"the transition out of the hard state: the X-ray luminosity remains approximately constant, the X-ray hardness shows a sharp turnoff, and the radio-infrared emission quenches \citep[e.g.][]{homanetal05}." +. The X-ray luminosity at which this spectral transition happens. would then depend on the aceretion rate. allowing one source to go through the spectral transition at different luminosities in different outbursts (as in the case of GX 339-4).," The X-ray luminosity at which this spectral transition happens, would then depend on the accretion rate, allowing one source to go through the spectral transition at different luminosities in different outbursts (as in the case of GX 339–4)." + However. GX 339-4 itself has been found to show parallel tracks in the radio/X-ray plane. with the hard-state luminosities from two different outbursts being correlated with the same slope but a factor of ~2 difference in normalization (Nowaketal.2005.Corbelal..inprep.)..," However, GX 339–4 itself has been found to show parallel tracks in the radio/X-ray plane, with the hard-state luminosities from two different outbursts being correlated with the same slope but a factor of $\sim$ 2 difference in normalization \citep[][Corbel et al., in prep.]{nowaketal05}." + This would require. in the context described in this Letter. for the jet magnetic field in GX 339-4 be always at or above the critical value.," This would require, in the context described in this Letter, for the jet magnetic field in GX 339–4 be always at or above the critical value." + Little is known about radio emission in the soft state of BHCs. with only a small number of sources being detected (seee.g.Fenderetal.2009.andreferencestherein)...," Little is known about radio emission in the soft state of BHCs, with only a small number of sources being detected \citep[see e.g.][and references therein]{fenderetal09}." + In XTE J1650-500. the radio spectrum in the soft state is consistent. with being flat or inverted. thus consistent. with thick synchrotron emission from a Jet.," In XTE J1650-500, the radio spectrum in the soft state is consistent with being flat or inverted, thus consistent with thick synchrotron emission from a jet." + However. an interaction of previously ejected matter with the ISM seems more plausible (Corbeletal.2004:Fender2009).," However, an interaction of previously ejected matter with the ISM seems more plausible \citep{corbeletal04,fenderetal09}." +. In order to further test this scenario. intensive and sensitive broad-band monitoring of BHC outbursts will be needed. as to track the full spectral evolution. from radio to X-rays. across all spectral transitions.," In order to further test this scenario, intensive and sensitive broad-band monitoring of BHC outbursts will be needed, as to track the full spectral evolution, from radio to X-rays, across all spectral transitions." + A discussion on the origin of a (variable) jet magnetic field in BHCs is beyond the aims of this Letter., A discussion on the origin of a (variable) jet magnetic field in BHCs is beyond the aims of this Letter. + Here we limit ourselves to a few general considerations., Here we limit ourselves to a few general considerations. + The intensity of the magnetic field in the jet is one of the several unknowns of jet physics., The intensity of the magnetic field in the jet is one of the several unknowns of jet physics. + It is often assumed to be at equipartition with the electrons energy. although this is not always the case [e.g.. Poynting-flux dominated jets are widely discussed in the literature (e.g.Lovelaceetal.2002.andreferences therein)]].," It is often assumed to be at equipartition with the electrons energy, although this is not always the case [e.g., Poynting-flux dominated jets are widely discussed in the literature \citep[e.g.][and references therein]{lovelaceetal02}] ]." + In the model discussed here. low values of the magnetic field are needed. which are not easy to reconcile with the generally recognized need for strong magnetic fields to launch the jet itself (e.g.Blandford&Payne1982).," In the model discussed here, low values of the magnetic field are needed, which are not easy to reconcile with the generally recognized need for strong magnetic fields to launch the jet itself \citep[e.g.][]{BP82}." +. However. models predict that the magnetic fielddisk affects the jet power (e.g.Meier2001).. but no conclusions have been drawn about the remaining magnetic field in the jet.," However, models predict that the magnetic field affects the jet power \citep[e.g.][]{meier01}, but no conclusions have been drawn about the remaining magnetic field in the jet." + Furthermore. the existence of additional sources of particles heating might result in increasing the values considered here.," Furthermore, the existence of additional sources of particles heating might result in increasing the values considered here." + No detailed studies have been performed on the dependencies of the magnetic field in the jet on the black-hole spin. or on the accretion flow properties.," No detailed studies have been performed on the dependencies of the magnetic field in the jet on the black-hole spin, or on the accretion flow properties." + For example. very little or nothing is known about how a possible misalignment between the acceretion. disk rotation axis and the BH spin would affect the jet properties. and in particular the magnetic field.," For example, very little or nothing is known about how a possible misalignment between the accretion disk rotation axis and the BH spin would affect the jet properties, and in particular the magnetic field." + A variable advection of magnetic field through the disc (e.g..Taggeretal.2004;Rothstein&Lovelace2008).. for example because of different magnetic properties of the accreted matter. might in principle also result in a variable jet magnetic field.," A variable advection of magnetic field through the disc \citep[e.g.,][]{taggeretal04,rothstein08}, for example because of different magnetic properties of the accreted matter, might in principle also result in a variable jet magnetic field." + We have discussed the potentially important role played by the jet magnetic field in describing the observed spectral behaviour of BHCs., We have discussed the potentially important role played by the jet magnetic field in describing the observed spectral behaviour of BHCs. + In particular. we showed how a scatter of the jet magnetic field values could be the cause for the observed scatter in the radio/X-ray luminosity correlation shown by BHCs: sources with à stronger jet magnetic field. above a critical value. would have a lower radio luminosities.," In particular, we showed how a scatter of the jet magnetic field values could be the cause for the observed scatter in the radio/X-ray luminosity correlation shown by BHCs: sources with a stronger jet magnetic field, above a critical value, would have a lower radio luminosities." + Furthermore. we discussed how the observed spectral transition. out of the hard state can be qualitatively explained by a jet magnetic field reaching a critical value.," Furthermore, we discussed how the observed spectral transition out of the hard state can be qualitatively explained by a jet magnetic field reaching a critical value." + This would cause a saturation of the X-ray lummosity. a relatively sharp turnoff of the X-ray hardness. and a quenching of the radio-to-infrared jet emission.," This would cause a saturation of the X-ray luminosity, a relatively sharp turnoff of the X-ray hardness, and a quenching of the radio-to-infrared jet emission." + More generally. we have discussed how the radio can no longer be considered a good tracer of the jet power.," More generally, we have discussed how the radio can no longer be considered a good tracer of the jet power." + This implies that the usual conclusion that the Jet is switched off when the radio is quenched. does not necessarily hold any longer.," This implies that the usual conclusion that the jet is switched off when the radio is quenched, does not necessarily hold any longer." + This conclusion is general. and might hold also for other types of sources. as Active Galactic Nuelet and acereting neutron stars.," This conclusion is general, and might hold also for other types of sources, as Active Galactic Nuclei and accreting neutron stars." + In particular. the strong dipolar magnetic field of the neutron star might give an important contribution to the initial radiative losses. if the launching region is close enough to the compact object.," In particular, the strong dipolar magnetic field of the neutron star might give an important contribution to the initial radiative losses, if the launching region is close enough to the compact object." + We would like to thank D. Maitra. D. Russell. O. Jamil. P. Soleri. C. Fragile. S. Markoff. S. Corbel. R. Fender. and T. Maecarone for very useful comments and discussions. and to E. Gallo for providing the original data for Fig. ]..," We would like to thank D. Maitra, D. Russell, O. Jamil, P. Soleri, C. Fragile, S. Markoff, S. Corbel, R. Fender, and T. Maccarone for very useful comments and discussions, and to E. Gallo for providing the original data for Fig. \ref{gallorel}." + PC is particularly grateful to G. Ghisellini for an inspiring conversation on jet physics and to P. Soler for allowing us to plot his unpublished data of SWIFT J1753.5-0127., PC is particularly grateful to G. Ghisellini for an inspiring conversation on jet physics and to P. Soleri for allowing us to plot his unpublished data of SWIFT J1753.5-0127. + We thank the referee for detailed and constructive comments., We thank the referee for detailed and constructive comments. + This work was partially supported by an NWO Spinoza grant to M. van der Klis., This work was partially supported by an NWO Spinoza grant to M. van der Klis. + AP is supported by the Riccardo Giacconi Fellowship award of the Space Telescope Science Institute., AP is supported by the Riccardo Giacconi Fellowship award of the Space Telescope Science Institute. +In Fig. 3..,"In Fig. \ref{testing_fig}," + the power spectrum of (he svnthetic images lor the six different noise levels are presented., the power spectrum of the synthetic images for the six different noise levels are presented. + Table 5- lists the properties of the synthetic images (columns 1 to 3) and the results of the SBF analvsis (columns 4 (0 6)., Table \ref{testing} lists the properties of the synthetic images (columns 1 to 3) and the results of the SBF analysis (columns 4 to 6). + The test goes from images with no noise al all (image @) to completely noise-dominated images (images and /)., The test goes from images with no noise at all (image ) to completely noise-dominated images (images and ). + IIere. σLoise5 Is. |he input noise level. NU. is the number of GCs introduced i1 the image. £4 and P? are the SBF results for each image. and Ve! is the total population «M GCs estimated using equation 7..," Here, $\sigma_{\rm noise}^2$ is the input noise level, $N_{\rm GC}^{\rm in}$ is the number of GCs introduced in the image, $P_0$ and $P_1$ are the SBF results for each image, and $N_{\rm GC}^{\rm out}$ is the total population of GCs estimated using equation \ref{sigma-gc}." + It is verv interesting.e even in the imagese with extrenelv high noise variance. that SBF produces good results.," It is very interesting, even in the images with extremely high noise variance, that SBF produces good results." +" In all cases. there is excellent agreement between (the parameters of the input imageso and those recovered by the SBF technique. both for σLoise> and στι,Ci"," In all cases, there is excellent agreement between the parameters of the input images and those recovered by the SBF technique, both for $\sigma_{\rm +noise}^2$ and $\sigma_{\rm GC}^2$." + We only observe a small svstematic excess in the estimated number of GCs., We only observe a small systematic excess in the estimated number of GCs. + This excess could be due to small differences between (he real input GCLF (which includes random effects) ancl the exact Gaussian-shaped GCLE used to evaluate the final result in equation 7.., This excess could be due to small differences between the real input GCLF (which includes random effects) and the exact Gaussian-shaped GCLF used to evaluate the final result in equation \ref{sigma-gc}. +" In oxder to check this. we calculated oz directly from the magnitudes of all the 100000 GCs added io the images in the following wav: The result was od, = 2926 (e. /pixel)?. in [ull agreement with the obtained SBF results (column 5 in Table 5))."," In order to check this, we calculated $\sigma_{\rm GC}^2$ directly from the magnitudes of all the 000 GCs added to the images in the following way: The result was $\sigma_{\rm GC}^2$ = 2926 $e^-$ $^2$, in full agreement with the obtained SBF results (column 5 in Table \ref{testing}) )." + With the former test we have shown that SBF is a very powerlul. selfconsistent technique. and (hat. verv g00d results can be obtained even wilh completely nolse-dominated images. where traditional techniques do not detect anv object.," With the former test we have shown that SBF is a very powerful, selfconsistent technique, and that very good results can be obtained even with completely noise-dominated images, where traditional techniques do not detect any object." + The following treatment is the same for all stuclied galaxies. but with the aim of ilustrating the methodology. we first present the procedure lor the galaxy NGC 4874 in detail and then the results for the rest of galaxies.," The following treatment is the same for all studied galaxies, but with the aim of illustrating the methodology, we first present the procedure for the galaxy NGC 4874 in detail and then the results for the rest of galaxies." + Once the residual image of NGC 4874 is created. cosmic-ray events ancl bacl pixels are masked.," Once the residual image of NGC 4874 is created, cosmic-ray events and bad pixels are masked." + In order to measure oj. we must detect all objects brighter than to above the zero mean SBF.," In order to measure $\sigma_{\rm BG}^2$, we must detect all objects brighter than $4\sigma$ above the zero mean SBF." + Using the DAOPILOT task DAOFIND. 649 objects were detected.," Using the DAOPHOT task DAOFIND, 649 objects were detected." + The photometry was made using ALLSTAR., The photometry was made using ALLSTAR. + In Fie. 4.. ," In Fig. \ref{ngc4874_bglf}, ," +the Iuminositv function of all detected objects is shown., the luminosity function of all detected objects is shown. + The solid line represents the BGLF (eq. 11)), The solid line represents the BGLF (eq. \ref{bglf}) ) + with +=0.39 and sealed to our counts., with $\gamma=0.39$ \citep{T88} and scaled to our counts. + The BGLF in the case of NGC 4874is:, The BGLF in the case of NGC 4874is: +case.,case. + We then have a=«7 , We then have $\alpha=\omega^{2}-\beta^{2}<0$and $0<\gamma\ll1$. +In this limit case. one can get and From our assumption that a« 0. we have U?x 1 therefore there is a pair of roots with positive real parts.," In this limit case, one can get and From our assumption that $\alpha < 0$ , we have $( 1 - \frac{\omega^2}{\beta^2} )^{-1/2} > 1$ , therefore there is a pair of roots with positive real parts." + When 5 is not infinitesimal. this instability persists as one can check by direct spectrum calculation or by more elegant. approaches.," When $\gamma$ is not infinitesimal, this instability persists as one can check by direct spectrum calculation or by more elegant approaches." + The physical meaning is clear: if the particle loses energy. the magnetic field. cannot ‘curve’ it back as close to the maximum as it was previously. ancl it will spiral further and further from the origin.," The physical meaning is clear: if the particle loses energy, the magnetic field cannot `curve' it back as close to the maximum as it was previously, and it will spiral further and further from the origin." + The previous three-cimensional example is a special case of a general theorem which applies for finite. dimensional systems: a Llamiltonian dynamical svstem with a negative enerev mode (which could be stable without further ivpothesis) becomes spectrally ancl hence linearly and. non-incarly unstable when any kind of dissipation is introduced., The previous three-dimensional example is a special case of a general theorem which applies for finite dimensional systems: a Hamiltonian dynamical system with a negative energy mode (which could be stable without further hypothesis) becomes spectrally and hence linearly and non-linearly unstable when any kind of dissipation is introduced. + This counterintuitive result takes its. genesis. from. the classical works by Thomson (Lord Ixelvin) and ‘Tait (1879). out it was proven only recently in the case of dimensional svstems (Blochetal.1994. and. Ixrechetnikov&Marsden 2007)). and. as suggested. by references in. the alter. appears to be very useful in mechanics.," This counterintuitive result takes its genesis from the classical works by Thomson (Lord Kelvin) and Tait (1879), but it was proven only recently in the case of finite-dimensional systems \citealt{BKMR} and \citealt{KM07}) ), and, as suggested by references in the latter, appears to be very useful in mechanics." + More recent works bv WKerechetnikoy&Alarsden(2009) suggest. that he infinite-dimensional case works similarly. although there is no definitive proof. for the time being.," More recent works by \citet{KM09} suggest that the infinite-dimensional case works similarly, although there is no definitive proof for the time being." + In the context of theoretical astrophysics. it is interesting to note that LL. Ixandrup. used. such kind of arguments to investigate eravitational instabilities for triaxial svstems 1991).. before any actual. formal result.," In the context of theoretical astrophysics, it is interesting to note that H. Kandrup used such kind of arguments to investigate gravitational instabilities for triaxial systems \citep[see][]{Kandrup2}, before any actual, formal result." + As recalled. in section 1.1.. CBP a Hamiltonian inlinite-dimensional svstem. so we can apply this theory of dissipation-induced instability for stability investigations in this context of gravitational plasmas.," As recalled in section \ref{CBPE}, CBP a Hamiltonian infinite-dimensional system, so we can apply this theory of dissipation-induced instability for stability investigations in this context of gravitational plasmas." + In the next. section we will show that. when a spherical ancl anisotropic self-eravitating system becomes more anc more radial. we can choose a certain class of g for which 4/7fu]«0: this proves the existence of negative energy modes. in such systenis.," In the next section we will show that, when a spherical and anisotropic self-gravitating system becomes more and more radial, we can choose a certain class of $g$ for which $H^{(2)}[f_{0}]<0$: this proves the existence of negative energy modes in such systems." + Following the dissipation-induced instability theory such kind of gravitating svstems will become unstable as soon as anv Kind. of dissipation can appear., Following the dissipation-induced instability theory such kind of gravitating systems will become unstable as soon as any kind of dissipation can appear. + As noticed by Ixancdrup in his visionary paper. in physical scll-eravitating svstenis dissipation could take several forms like a little bit of gas. dynamical friction or at minimum gravitational radiation!," As noticed by Kandrup in his visionary paper, in physical self-gravitating systems dissipation could take several forms like a little bit of gas, dynamical friction or at minimum gravitational radiation!" + 1n the context of numerical mocdelizations of self-gravitating svstems where racial orbit instability also appears. dissipation is also inevitably introduced. by numerical algorithms of time integration or by potential computation.," In the context of numerical modelizations of self-gravitating systems where radial orbit instability also appears, dissipation is also inevitably introduced by numerical algorithms of time integration or by potential computation." + A pure radial orbit svstem is characterized. by. particles with L7=0. the corresponding distribution function could then be. written. O°(E.L7).=x(E)8(L) where y is any positive smooth normalized. function. ancl ὁ denotes the Dirac distribution.," A pure radial orbit system is characterized by particles with $L^{2}=0$, the corresponding distribution function could then be written $f_{0}^{\textbf{ro}} \left(E, L^{2} \right) += \varphi \left(E \right) \delta\left(L^{2}\right)$ where $\varphi$ is any positive smooth normalized function, and $\delta$ denotes the Dirac distribution." + Hlowever. this distribution is very irregular in zero which is quite problematic. in addition to being unrealistic (orbits can hardly be perfectly radial).," However, this distribution is very irregular in zero which is quite problematic, in addition to being unrealistic (orbits can hardly be perfectly radial)." + So. instead of actually using the Dirac distribution. we will use functions that approach it.," So, instead of actually using the Dirac distribution, we will use functions that approach it." + The choice we made is to use Gaussian functions., The choice we made is to use Gaussian functions. +" More specifically, we will consider an initial distribution function of the form ὃν direct calculation one can easily check that. for any smooth function Z definedon the phase space. one has. by limited development of Z with respect to po ancl p, ou5 which has a clear limit when e7Q and selects the value of Z at L7=0 as expected."," More specifically, we will consider an initial distribution function of the form By direct calculation one can easily check that, for any smooth function $Z$ definedon the phase space, one has, by limited development of $Z$ with respect to $p_\theta$ and $p_\phi$ $^{,\;}$ which has a clear limit when $a \rightarrow 0$ and selects the value of $Z$ at $L^{2}=0$ as expected." + We could sav that fj tends to a distribution function of purely radial orbits when @7 0., We could say that $f_0^a$ tends to a distribution function of purely radial orbits when $a\rightarrow 0$ . + In the following part. we will consider what happens for arbitrarily small values of a.," In the following part, we will consider what happens for arbitrarily small values of $a$ ." + Our Dgoal in this section is to show that there exist »rturbation fe)generators gthat. for sulliciently small values," Our goal in this section is to show that there exist perturbation generators $g$that, for sufficiently small values" +well.,well. + Obviously. both helium aud in particular mctallicity are now much higher as compared to the previous case ignoring diffusion in the calibration: the latter values are increased by (similar values for the comparison codes).," Obviously, both helium and in particular metallicity are now much higher as compared to the previous case ignoring diffusion in the calibration; the latter values are increased by (similar values for the comparison codes)." + We are using the same solar initial abunudances for the M67 isochrones., We are using the same solar initial abundances for the M67 isochrones. + This is not completely consistent as M67 displaysnow a solar ietallicitv. but due to its slightly vounecr age diffusion should have started with a solmewhat lower metallicity than the Sun.," This is not completely consistent as M67 displays a solar metallicity, but due to its slightly younger age diffusion should have started with a somewhat lower metallicity than the Sun." + However. this effect amounts to afew parts in 10. in Z ouly. such that we did not iterate further the iuitial composition.," However, this effect amounts to a few parts in $10^{-4}$ in $Z$ only, such that we did not iterate further the initial composition." + The final fits to M67 are shown in Figure 2.., The final fits to M67 are shown in Figure \ref{f:ssmdiff}. + We still used the same distance aud reddening values. but the isochrone ages are now lower by 0.3 Cr compared to Figure 1l.," We still used the same distance and reddening values, but the isochrone ages are now lower by 0.3 Gyr compared to Figure \ref{f:vgrep}." + The agreement with the ages by WOOT is purely incidental., The agreement with the ages by VG07 is purely incidental. + Instead. the age for the 6898 mixture of 3.9 Car should be compared to that by Michaudetal.(2001). of 3.7 Cir.," Instead, the age for the GS98 mixture of 3.9 Gyr should be compared to that by \citet{mrrv:2004} of 3.7 Gyr." + Now. for both compositions the CMD morphology is reproduced. and ACGS05 is no longer disfavored.," Now, for both compositions the CMD morphology is reproduced, and AGS05 is no longer disfavored." + The ft itself is of the same quality as before., The fit itself is of the same quality as before. + Iu this section we investigate the iurportance of further plysical and numerical aspects that influence the appearance and size of a convective core ou the iain sequence., In this section we investigate the importance of further physical and numerical aspects that influence the appearance and size of a convective core on the main sequence. + These are obviously the nuclear reaction rates of the CNQO-evele aud the amount of overshooting., These are obviously the nuclear reaction rates of the CNO-cycle and the amount of overshooting. + Overshooting may lead to the persistence of the otherwise trausicut convective core that may appear towards the end of the pre-main sequence. bu may be kept alive due to additional mixing of CNO-nuclei by overshooting.," Overshooting may lead to the persistence of the otherwise transient convective core that may appear towards the end of the pre-main sequence, but may be kept alive due to additional mixing of CNO-nuclei by overshooting." + With this aspect we start our tests., With this aspect we start our tests. +" We first repeated the models of 3.1.. 1,0. diffusion was completely ignored. but included overshooting& according o our standard prescription outlined in 2.1.. Equations 1. and 2.."," We first repeated the models of \ref{s:repro}, i.e. diffusion was completely ignored, but included overshooting according to our standard prescription outlined in \ref{s:garstec}, Equations \ref{eqn:ove}~ and \ref{eqn:ove2}." + The parameter f cau be varied. mt we keep it below the standard value of 0.02 (Herwigetal. 1997).," The parameter $f$ can be varied, but we keep it below the standard value of 0.02 \citep{bloe:97}." +. Iu this work we take f=0.018 because with lis value. in our alternative approach (Equation 3) we are able to reproduce well the evolutionary tracks πο Pietriuferuietal.(2001)... as mentioned in 2.1.," In this work we take $f=0.018$ because with this value, in our alternative approach (Equation \ref{eqn:ove3}) ), we are able to reproduce well the evolutionary tracks from \citet{pietr:04}, as mentioned in \ref{s:garstec}." + Iun Figure 3. the resulting CMD for f=(0.018 ane he standard cluster parameters is displaved., In Figure \ref{f:ov018} the resulting CMD for $f=0.018$ and the standard cluster parameters is displayed. + We recall hat the amount of overshooting is reduced due to our ecolctrical restriction (equation 2)): this reduction cau )o quite restrictive for stars with lower masses. around 1.2AL... and be crucial in this study.," We recall that the amount of overshooting is reduced due to our geometrical restriction (equation \ref{eqn:ove2}) ); this reduction can be quite restrictive for stars with lower masses, around $1.2\,M_\odot$, and be crucial in this study." + However. even if the fit itself is not as good as before. now both mixture cases rave TO masses with a convective core being present.," However, even if the fit itself is not as good as before, now both mixture cases have TO masses with a convective core being present." + The situation seenis to be typical for cases without diffision in both the solar calibration aud the cluster uodels., The situation seems to be typical for cases without diffusion in both the solar calibration and the cluster models. + In VaudeuDerg&Stetson(2001). the authors concluded that a πα amount of overshooting is needed o reproduce best the CMD of M67., In \citet{vdbs:2004} the authors concluded that a small amount of overshooting is needed to reproduce best the CMD of M67. + Overshooting was roeated following the integral criterion bv Roxbureh(1980) and the adaption of a varviug amount of overshooting for verv simnall couvective cores close to Mio. determined by VaudeuDoergetal.(2006).," Overshooting was treated following the integral criterion by \citet{rox:89} and the adaption of a varying amount of overshooting for very small convective cores close to $M_\mathrm{ccc}$, determined by \citet{vbd:2006}." +. We stress the fact that this procedure was calibrated using open clusters with solar abundances on theold GSI scale., We stress the fact that this procedure was calibrated using open clusters with solar abundances on the GS98 scale. + For coniplete consistency. this procedure should be repeated for the new ACSOS5 composition. and this may explain why the same small amount of overshooting used bv VGUOT did not lead to a persistent convective core in case," For complete consistency, this procedure should be repeated for the new AGS05 composition, and this may explain why the same small amount of overshooting used by VG07 did not lead to a persistent convective core in case" + , +One of the most promising ways of detecting very high redshift (2m 5) star-forming galaxies is via narrow-band imaging surveys targeting Lyman-a (Lye).,"One of the most promising ways of detecting very high redshift $z +\gtrsim 5$ ), star-forming galaxies is via narrow-band imaging surveys targeting $\alpha$ $\alpha$ )." + In particular. redshifts τ~5.7 and 6.5 have been extensively surveyed by several groups (e.g. Ajiki et al.," In particular, redshifts $z \sim 5.7$ and $6.5$ have been extensively surveyed by several groups (e.g. Ajiki et al." + 2003: Hu et al., 2003; Hu et al. + 2004: Shimasaku et al., 2004; Shimasaku et al. + 2005: Ouchi et al., 2005; Ouchi et al. + 2005. 2007: Malhotra et al.," 2005, 2007; Malhotra et al." + 2005: Taniguchi et al., 2005; Taniguchi et al. + 2005: Tapken et al., 2005; Tapken et al. + 2006: Kashikawa et al., 2006; Kashikawa et al. + 2006)., 2006). + The current redshift record for a spectroscopically confirmed Lye emitter (LEGO - Ίνα Emitting Galaxy-building Object: see Moller Fynbo 2001) is :=6.96 (lye et al., The current redshift record for a spectroscopically confirmed $\alpha$ emitter (LEGO – $\alpha$ Emitting Galaxy-building Object; see ller Fynbo 2001) is $z = 6.96$ (Iye et al. + 2006) although Stark et al. (, 2006) although Stark et al. ( +2007) have suggested the discovery of two LEGOs at 2=8.99 and 9.32.,"2007) have suggested the discovery of two LEGOs at $z = +8.99$ and $9.32$." + The reason why narrow-band surveys are restricted to a discrete number of narrow redshift windows 1s the night sky OH emission lines., The reason why narrow-band surveys are restricted to a discrete number of narrow redshift windows is the night sky OH emission lines. + According to the OH line atlas of Rousselot et al. (, According to the OH line atlas of Rousselot et al. ( +2000). at Lyn redshifts 274.2.7 (\29s00 A) there are only a few possible wavelengths where a narrow-band filter can fit in between the OH sky lines.,"2000), at $\alpha$ redshifts $z_{Ly\alpha} \gtrsim 7$ $\lambda +\gtrsim 9800$ ) there are only a few possible wavelengths where a narrow-band filter can fit in between the OH sky lines." +" These correspond to :ry,c7.7. 2. SN. OL and 10.1 10.5, "," These correspond to $z_{Ly\alpha} \approx 7.7$, $8.2$, $8.8$, $9.4$ and $10.1 - 10.5$ ." +Several future surveys will target these windows in the sky aiming to detect very high redshift galaxies., Several future surveys will target these windows in the sky aiming to detect very high redshift galaxies. + Three narrow-band surveys for Lya at redshift «~5.5 have already been completed (Parkes. Collins Joseph 1994; Willis Courbin 2005: Cuby et al.," Three narrow-band surveys for $\alpha$ at redshift $z \sim 8.8$ have already been completed (Parkes, Collins Joseph 1994; Willis Courbin 2005; Cuby et al." + 2007) but have only yielded upper limits., 2007) but have only yielded upper limits. + Future surveys planned for these redshifts include DaZle (Dark Ages Z Lyman-o Explorer. Horton et al.," Future surveys planned for these redshifts include DaZle (Dark Ages Z $\alpha$ Explorer, Horton et al." + 2004) and ELVIS (Emission-Line galaxies with VISTA Survey. Nilsson et al.," 2004) and ELVIS (Emission-Line galaxies with VISTA Survey, Nilsson et al." + 2006b)., 2006b). + Observations of very high redshift LEGOs have been proposed as an excellent probe of reionisation. through its effects on the Lya emission line profile (e.g. Miralda-Escudé 1998: Miralda-Escudé Rees 1998; Haiman 2002; Gnedin Prada 2004). the luminosity function (e.g. HaimanCen 2005; Dijkstra. Wyithe Haiman 2007) and the clustering of sources (McQuinn et al.," Observations of very high redshift LEGOs have been proposed as an excellent probe of reionisation, through its effects on the $\alpha$ emission line profile (e.g. Miralda-Escudé 1998; Miralda-Escudé Rees 1998; Haiman 2002; Gnedin Prada 2004), the luminosity function (e.g. HaimanCen 2005; Dijkstra, Wyithe Haiman 2007) and the clustering of sources (McQuinn et al." + 2007)., 2007). + We here focus on Lyo emission from star-forming galaxies. where the Ενα photons are emitted from gas which is by massive young stars.," We here focus on $\alpha$ emission from star-forming galaxies, where the $\alpha$ photons are emitted from gas which is by massive young stars." + During recent years. theoretical work on Ένα emitting galaxies has made significant progress.," During recent years, theoretical work on $\alpha$ emitting galaxies has made significant progress." + There are three main aspects to these studies: predicting the numbers of star-forming galaxies as a function of star formation rate and redshift. calculating the fraction of the Ένα photons which escape from galaxies into the IGM and calculating the factor by which the Ένα flux is attenuated by scattering in the IGM on its way to the observer.," There are three main aspects to these studies: predicting the numbers of star-forming galaxies as a function of star formation rate and redshift, calculating the fraction of the $\alpha$ photons which escape from galaxies into the IGM and calculating the factor by which the $\alpha$ flux is attenuated by scattering in the IGM on its way to the observer." + Accurate treatments of and are complicated because Ένα photons are resonantly scattered by hydrogen atoms. with the consequences that absorption of Lya by dust in galaxies is hugely amplified. thereby reducing the escape fraction. and that even a small neutral fraction in the IGM can be effective at scattering Lyo photons out of the line-of-sight. thus attenuating the flux.," Accurate treatments of and are complicated because $\alpha$ photons are resonantly scattered by hydrogen atoms, with the consequences that absorption of $\alpha$ by dust in galaxies is hugely amplified, thereby reducing the escape fraction, and that even a small neutral fraction in the IGM can be effective at scattering $\alpha$ photons out of the line-of-sight, thus attenuating the flux." + Because of these complications. most theoretical papers have chosen to concentrate on only one aspect. adopting simplified treatments of the other two aspects.," Because of these complications, most theoretical papers have chosen to concentrate on only one aspect, adopting simplified treatments of the other two aspects." + Haiman Spaans (1999) made predictions of the number counts of Ένα emitting galaxies by combining the Press-Schechter formalism with a treatment of the inhomogeneous dust distribution inside galaxies., Haiman Spaans (1999) made predictions of the number counts of $\alpha$ emitting galaxies by combining the Press-Schechter formalism with a treatment of the inhomogeneous dust distribution inside galaxies. + Barton et al. (, Barton et al. ( +2004) and Furlanetto et al. (,2004) and Furlanetto et al. ( +2005) calculated the numbers of Lyo emitters in cosmological hydrodynamical simulations of galaxy formation. but did not directly calculate the radiative transfer of Ένα photons.,"2005) calculated the numbers of $\alpha$ emitters in cosmological hydrodynamical simulations of galaxy formation, but did not directly calculate the radiative transfer of $\alpha$ photons." + Radiative transfer calculations of the escape of Lyn photons from galaxies include those of Zheng Muralda-Escudé (2002). Ahn (2004) and Verhamme. Schaerer Maselli (2006) for idealised geometries. and Tasitsiomi. (2006) and Laursen Sommer-Larsen (2007) for galaxies in cosmological hydrodynamical simulations.," Radiative transfer calculations of the escape of $\alpha$ photons from galaxies include those of Zheng Miralda-Escudé (2002), Ahn (2004) and Verhamme, Schaerer Maselli (2006) for idealised geometries, and Tasitsiomi (2006) and Laursen Sommer-Larsen (2007) for galaxies in cosmological hydrodynamical simulations." + The transmission of Lya through the IGM has been investigated by Miralda-Escudé (1998). Haiman (2002). Santos (2004) and Dijkstra. Lidz Wyithe (2007). among others.," The transmission of $\alpha$ through the IGM has been investigated by Miralda-Escudé (1998), Haiman (2002), Santos (2004) and Dijkstra, Lidz Wyithe (2007), among others." + Several authors (e.g. Haiman. Spaans Quataert 2000; Fardal et al.," Several authors (e.g. Haiman, Spaans Quataert 2000; Fardal et al." + 2001: Furlanetto et al., 2001; Furlanetto et al. + 2005) have studied the effect of cold accretion to describe the nature of so-called Lya blobs (Steidel et al., 2005) have studied the effect of cold accretion to describe the nature of so-called $\alpha$ blobs (Steidel et al. + 2000: Matsuda et al., 2000; Matsuda et al. + 2004: Nilsson et al., 2004; Nilsson et al. + 2006a). see also sec. ??..," 2006a), see also sec. \ref{sec:conclusion}. ." + Two models in particular. dissimilar in. their. physical assumptions. have been shown to besuccessful in reproducing," Two models in particular, dissimilar in their physical assumptions, have been shown to besuccessful in reproducing" +the asviuptotie slope 5.,the asymptotic slope $\gamma$. + We recover the already known difference between core aud power-law ealaxics iu terms of absolute magnitude., We recover the already known difference between core and power-law galaxies in terms of absolute magnitude. + The most hnuninous galaxies are exclusively. associated to core profiles., The most luminous galaxies are exclusively associated to core profiles. + Nonetheless.," Nonetheless," +a compact and elliptical-like morphology.,a compact and elliptical-like morphology. + The case of J124027-1131.0 is more ambiguous because its morphology is compact and weakly disturbed., The case of J124027-1131.0 is more ambiguous because its morphology is compact and weakly disturbed. +" Adopting z=phot, for each object we estimated the limits on the Ha luminosity L(Ho) and on the star formation rate (SFR) through the relation SFR=7.9x10-9? L(Ha) [Me yr] (Kennicutt 1998)."," Adopting $z=z_{{\rm sphot}}$, for each object we estimated the limits on the $\alpha$ luminosity $L($ $\alpha)$ and on the star formation rate $SFR$ ) through the relation $SFR=7.9\times10^{-42}L($ $\alpha)$ $_{\odot}$ $^{-1}$ ] (Kennicutt 1998)." + This was not possible for J202807-2141.1 and J202807-2140.8 because no J spectra were available to us., This was not possible for J202807-2141.1 and J202807-2140.8 because no $J$ spectra were available to us. +" We find limits in the range of L(Ha)«7—40x10*!hz erg s~!, corresponding to SFR<6— 30h52Mc yr-! (Table 1)."," We find limits in the range of $L($ $\alpha)< 7-40 \times 10^{41}h_{50}^{-2}$ erg $^{-1}$, corresponding to $SFR < 6-30$$h_{50}^{-2} $ $_{\odot}$ $^{-1}$ (Table 1)." +" Taken at face value, these limits imply star formation rates at most as high as those of nearby gas rich spiral galaxies (see Kennicutt 1998)."," Taken at face value, these limits imply star formation rates at most as high as those of nearby gas rich spiral galaxies (see Kennicutt 1998)." +" However, in case of dust extinction, such SFRs would increase by a factor of 222-30x for ΕΕνΞ 0.2-0.9."," However, in case of dust extinction, such SFRs would increase by a factor of $\approx$ $\times$ for $E_{{\rm B-V}}=$ 0.2–0.9." +" Finally, we noticed that the four ERGs in the J2027-217 field have all very similar zsphot (Fig.2), and may belong to a same cluster or group."," Finally, we noticed that the four ERGs in the J2027-217 field have all very similar $z_{{\rm sphot}}$ (Fig.2), and may belong to a same cluster or group." +" Our observations showed that neither strong emission lines nor continuum breaks are detected in the ISAAC spectra of 9 ERGs, and that only a fraction of them (2-3 out of 9 in our subsample) require strong dust reddening to"," Our observations showed that neither strong emission lines nor continuum breaks are detected in the ISAAC spectra of 9 ERGs, and that only a fraction of them (2-3 out of 9 in our subsample) require strong dust reddening to" +From Tables 2 and 3 we can see that the proportion of galaxies in the c-drop sample that have a Seyfert nucleus is 65%+11% while in the control sample it is 30%+10%.,From Tables \ref{sigmaproperties} and \ref{controlproperties} we can see that the proportion of galaxies in the $\sigma$ -drop sample that have a Seyfert nucleus is $65\%\pm11\%$ while in the control sample it is $30\%\pm10\%$. + On the other hand. LINERs make up 25%+10% of the c-drop sample but 60%11% of the control sample.," On the other hand, LINERs make up $25\%\pm10\%$ of the $\sigma$ -drop sample but $60\%\pm11\%$ of the control sample." + This points to a link between σ- and Seyferts. and links the other galaxies with à more reduced level of activity.," This points to a link between $\sigma$ -drops and Seyferts, and links the other galaxies with a more reduced level of activity." + If this is indeed the case. assuming that Seyfert nuclei are more active than LINERs. we might intuitively think that more energetic phenomena are related to a bigger inflow of gas.," If this is indeed the case, assuming that Seyfert nuclei are more active than LINERs, we might intuitively think that more energetic phenomena are related to a bigger inflow of gas." + This gas could have been partly spent in a generation of stars in the inner volume of the galaxies., This gas could have been partly spent in a generation of stars in the inner volume of the galaxies. + The signature of this recent star formation would be a c-drop., The signature of this recent star formation would be a $\sigma$ -drop. + This result has to be handled with care because in both samples we have a proportion of AGN of around806c.. which is far higher than the proportion of active galaxies that is found in a randomly taken sample.," This result has to be handled with care because in both samples we have a proportion of AGN of around, which is far higher than the proportion of active galaxies that is found in a randomly taken sample." + A direct explanation might be that HST 1s usually employed to observe “interesting” objects. which implies an enhanced fraction of AGN in the galaxies that have been observed with the space telescope.," A direct explanation might be that $HST$ is usually employed to observe `interesting' objects, which implies an enhanced fraction of AGN in the galaxies that have been observed with the space telescope." + One possibility is that the inflow of gas giving rise to à o-drop feeds the energetic phenomena detected as nuclear activity., One possibility is that the inflow of gas giving rise to a $\sigma$ -drop feeds the energetic phenomena detected as nuclear activity. + When the inflow stops the activity fades. and the σ- gradually relaxes.," When the inflow stops the activity fades, and the $\sigma$ -drop gradually relaxes." + As the timeseale for the former is shorter than that for the latter. any correlation will be only partial.," As the timescale for the former is shorter than that for the latter, any correlation will be only partial." + A way to test if this correlation is indeed true is to study a bigger sample. for example all the galaxies from the papers from which we selected the control sample.," A way to test if this correlation is indeed true is to study a bigger sample, for example all the galaxies from the papers from which we selected the control sample." + That yields 85 c-drop galaxies and 95 control galaxies., That yields 85 $\sigma$ -drop galaxies and 95 control galaxies. + There are around 40 galaxies that are difficult to classify and therefore are not included in this test., There are around 40 galaxies that are difficult to classify and therefore are not included in this test. + We found that of the o-drop galaxies 32%45% are Seyfert hosts and 19%+4% are LINER hosts., We found that of the $\sigma$ -drop galaxies $32\%\pm5\%$ are Seyfert hosts and $19\%\pm4\%$ are LINER hosts. + For the control sample we find that 16%44% are Seyfert hosts and 24%x4% are LINER hosts., For the control sample we find that $16\%\pm4\%$ are Seyfert hosts and $24\%\pm4\%$ are LINER hosts. + These data must be taken with caution because they do not come from matched samples. so the effects that we see may be due to other effects such as differences in morphological type.," These data must be taken with caution because they do not come from matched samples, so the effects that we see may be due to other effects such as differences in morphological type." + More than a half of the galaxies used for this test (as performed on the total sample of 85+95 galaxies. defined above) come from the papers from Hérraudeau Simien (1998). Hérraudeau et al. (," More than a half of the galaxies used for this test (as performed on the total sample of $85+95$ galaxies, defined above) come from the papers from Hérraudeau Simien (1998), Hérraudeau et al. (" +"1999), and Simien Prugniel (1997abe. 1998. 2000. and 2002). which have dispersion profiles from galaxies that are so distant that in many cases they have not been studied in any survey of nuclear activity.","1999), and Simien Prugniel (1997abc, 1998, 2000, and 2002), which have dispersion profiles from galaxies that are so distant that in many cases they have not been studied in any survey of nuclear activity." + From this discussion we may tentatively conclude that c-drop are preferably accompanied by Seyfert nuclei. and that both phenomena can be traced to increased gas inflow.," From this discussion we may tentatively conclude that $\sigma$ -drop are preferably accompanied by Seyfert nuclei, and that both phenomena can be traced to increased gas inflow." + Given the different spatial and time scales involved. exactly why and how this is so is slightly puzzling.," Given the different spatial and time scales involved, exactly why and how this is so is slightly puzzling." + We note that a similar. and similarly puzzling. relation has been reported in the literature between the presence of nuclear activity and that of nuclear rings (see Knapen 2005. in particular the discussion in Section 6 of that paper).," We note that a similar, and similarly puzzling, relation has been reported in the literature between the presence of nuclear activity and that of nuclear rings (see Knapen 2005, in particular the discussion in Section 6 of that paper)." + As a way to check another possible connection between σ- drops and their host galaxies. we searched for a correlation between the presence of a o-drop and the shape of the lummosity profiles of their host galaxies.," As a way to check another possible connection between $\sigma$ -drops and their host galaxies, we searched for a correlation between the presence of a $\sigma$ -drop and the shape of the luminosity profiles of their host galaxies." +" Our aim here was to derive luminosity profiles from the nucleus to the outer parts of the galaxies or to use profiles obtained by other authors,", Our aim here was to derive luminosity profiles from the nucleus to the outer parts of the galaxies or to use profiles obtained by other authors. + We obtained Sloan Digital Sky Survey release 5 (SDSS5) (Adelman-MeCarthyetal.2007)) r-band images to make the profiles., We obtained Sloan Digital Sky Survey release 5 (SDSS5) \cite{AD07}) ) $r$ -band images to make the profiles. + In several cases we had to join two or three SDSS frames to get a complete image of a galaxy., In several cases we had to join two or three SDSS frames to get a complete image of a galaxy. + Each pixel in the SDSS images subtends aaresec. obviously not nearly small enough to do an analysis at the same scale as we did for dust andHa... so we concentrate on the host disc here.," Each pixel in the SDSS images subtends arcsec, obviously not nearly small enough to do an analysis at the same scale as we did for dust and, so we concentrate on the host disc here." + We obtained 13 profiles for the o-drop sample and 13 more for the control subsample., We obtained 13 profiles for the $\sigma$ -drop sample and 13 more for the control subsample. + These subsamples are very well matched in morphological type., These subsamples are very well matched in morphological type. + There are not so well matched in axis ratio but this is only marginally important because ellipse fitting and posterior deprojection allow good photometry., There are not so well matched in axis ratio but this is only marginally important because ellipse fitting and posterior deprojection allow good photometry. + The biggest difference is in the galaxies’ magnitudes., The biggest difference is in the galaxies' magnitudes. + The o-drop subsample is on average 0.23 magnitudes brighter than the control one., The $\sigma$ -drop subsample is on average 0.23 magnitudes brighter than the control one. + To produce the luminosity profile. we start by subtracting the sky background contribution from the images.," To produce the luminosity profile, we start by subtracting the sky background contribution from the images." + That was done using the average of sky measurements over outer parts of an image where the dise of the galaxy is well below the noise level., That was done using the average of sky measurements over outer parts of an image where the disc of the galaxy is well below the noise level. + The sky measures were done by averaging circles of 10 pixels in radius., The sky measures were done by averaging circles of 10 pixels in radius. + Once the sky had been subtracted. we fitted ellipses for increasing radius. which yielded. first of all. the position angle (PA) and the ellipticity of the outer regions of the galaxy.," Once the sky had been subtracted, we fitted ellipses for increasing radius, which yielded, first of all, the position angle (PA) and the ellipticity of the outer regions of the galaxy." + The radial profiles were usually featureless across the outer regions., The radial profiles were usually featureless across the outer regions. + We used this PA and ellipticity to measure surface photometry at increasing radii from the centre of the galaxy until the dise “fades out’., We used this PA and ellipticity to measure surface photometry at increasing radii from the centre of the galaxy until the disc `fades out'. + More details about the method can be found in Erwinetal.(2008)., More details about the method can be found in \cite{ER08}. +.. The results are shown as radial surface brightness profiles for all the galaxies in Appendices C and D (on-line only). for the c-drop and control samples. respectively.," The results are shown as radial surface brightness profiles for all the galaxies in Appendices C and D (on-line only), for the $\sigma$ -drop and control samples, respectively." + The fitted exponentials are overplotted., The fitted exponentials are overplotted. + The vertical dashed-dotted linescorrespond to the position of the end of the bar., The vertical dashed-dotted linescorrespond to the position of the end of the bar. + When there are two vertical lines. they indicate à lower and an upper limit estimate of the end of the bar.," When there are two vertical lines, they indicate a lower and an upper limit estimate of the end of the bar." + We classified each profile following Erwinetal. (2008).. and thus divide the galaxies in three groups:," We classified each profile following \cite{ER08}, , and thus divide the galaxies in three groups:" +"interstellar extinction). Fe and F;: For Ne and O. such a ratio of αμ} functions can be constructed from the O VILL. Ne IX and Ne X resonance lines 152p!P1—152!S and 2p?Ds4;—15?5,,5. combined as follows Drake&Testa(2005) found Go/Ga,=1240.1 for active stars.","interstellar extinction), $F_O$ and $F_{Ne}$: For Ne and O, such a ratio of $G_{ji}(T)$ functions can be constructed from the O VIII, Ne IX and Ne X resonance lines $1s2p\, ^1P_1 +\rightarrow 1s^2\, ^1S_0$ and $2p\, ^2P_{3/2,1/2} \rightarrow 1s\, +^2S_{1/2}$ , combined as follows \citet{Drake.Testa:05} found $\overline{G_{O}/G_{Ne}}=1.2\pm 0.1$ for active stars." + Ne/O abundance ratios derived for BP Tan. TW Ilva ancl TWA 5 using this method are also listed in Table 2.. together with the intervening absorbing columims used to correct the observed line fluxes for attenuation.," Ne/O abundance ratios derived for BP Tau, TW Hya and TWA 5 using this method are also listed in Table \ref{t:flx}, together with the intervening absorbing columns used to correct the observed line fluxes for attenuation." + These Ne/O ratios are compared with those presented by (2005) lor a sample of 21 post-T Tauri stars. including single main-sequence stars. eiants. and tidally-interacting binaries in Figure 2..," These Ne/O ratios are compared with those presented by \citet{Drake.Testa:05} for a sample of 21 post-T Tauri stars, including single main-sequence stars, giants, and tidally-interacting binaries in Figure \ref{f:ne_o}." + Based on the Ne/O ratios found for post-T Tauri stars. Drake&Testa(2005) crew two conclusions: (1) Ne/O is essentially constant in stellar coronae. and in full-disk observations is nol susceptible to fractionation effects thatoften appear to characterise other elements with lower [ist ionisation potentials (FIPs) (e.g.Drake2003): Gi} the Ne/O abundance ratio in stars is significantly larger than current assessments of the solar ratio (also illustrated in Figure 2)). but is in-line with inference from solar oscillations (Antia 2005)..," Based on the Ne/O ratios found for post-T Tauri stars, \citet{Drake.Testa:05} drew two conclusions: (i) Ne/O is essentially constant in stellar coronae, and in full-disk observations is not susceptible to fractionation effects thatoften appear to characterise other elements with lower first ionisation potentials (FIPs) \citep[e.g.\ ][]{Drake:03b}; (ii) the Ne/O abundance ratio in stars is significantly larger than current assessments of the solar ratio (also illustrated in Figure \ref{f:ne_o}) ), but is in-line with inference from solar oscillations \citep{Antia.Basu:05,Bahcall.etal:05}." + The constancy of the coronal Ne/O ratio then allows us (to use these elementV. for diagnostics purposes., The constancy of the coronal Ne/O ratio then allows us to use these elements for diagnostics purposes. + Firstly. we can determine whether or not the suspected accretion shock has an Ne/O ratio consistent with that of the underlving star. as represented by the constant coronal Ne/O ratio illustrated in Figure 2..," Firstly, we can determine whether or not the suspected accretion shock has an Ne/O ratio consistent with that of the underlying star, as represented by the constant coronal Ne/O ratio illustrated in Figure \ref{f:ne_o}." + A ratio significantly different to the coronal value would provide further evidence that these lines are not formed in a “normal” coronal plasma., A ratio significantly different to the coronal value would provide further evidence that these lines are not formed in a “normal” coronal plasma. + Secondly. departures [rom (he coronal Ne/O ratio can then be used to inler conmpositional peculiarities in (he accreting gas.," Secondly, departures from the coronal Ne/O ratio can then be used to infer compositional peculiarities in the accreting gas." +" We conclude from Figure 2 that the Ne/O ratio of As,ο1.0 we find in TW Ilva good agreement with the value obtained earlier by Kastneretal.(2002). based on a differential emission measure analvsisis significantly higher than that of more evolved stars (Figure 2)).", We conclude from Figure \ref{f:ne_o} that the Ne/O ratio of $A_{Ne}/A_{O}\sim 1.0$ we find in TW Hya---in good agreement with the value obtained earlier by \citet{Kastner.etal:02} based on a differential emission measure analysis—is significantly higher than that of more evolved stars (Figure \ref{f:ne_o}) ). + In contrast. Ne/O in BP Tau is perfectly consistent with thatfound for the rest ol the sample of Drake&Testa(2005).. This latter result also supports the interpretation of," In contrast, Ne/O in BP Tau is perfectly consistent with thatfound for the rest of the sample of \citet{Drake.Testa:05}.. This latter result also supports the interpretation of" +G. Perrin? B.The,G. Perrin B. using sophisticated simulations of stellar convection.} +a combination of statistical fluctuations anc the lack of spectroscopic redshift completeness in the samples used by Ixapahi in particular.,a combination of statistical fluctuations and the lack of spectroscopic redshift completeness in the samples used by Kapahi in particular. + We would like to thank Christian Ixaiser and Jasper Wall for their helpful comments on the manuscript. anc Malcolm Sremer. Rob van Ojik ane Bichard Saunders for assistance during the 1993 June WIE observations.," We would like to thank Christian Kaiser and Jasper Wall for their helpful comments on the manuscript, and Malcolm Bremer, Rob van Ojik and Richard Saunders for assistance during the 1993 June WHT observations." + We also thank the stall at the WIUT. MeDonald Observatory. Lick Observatory and the IREE for their assistance.," We also thank the staff at the WHT, McDonald Observatory, Lick Observatory and the IRTF for their assistance." + Ehe WIIT is operated on the island. of La Palma by PPARC in the Spanish Observatorio del Itoque de los Muchachos of the Instituto cle Astrolisica de Canarias., The WHT is operated on the island of La Palma by PPARC in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias. + SER was a visiting astronomer at the NASA Infrared. Telescope Facility. operated. by the University ofLlawaii under contract with NASA.," SER was a visiting astronomer at the NASA Infrared Telescope Facility, operated by the University of Hawaii under contract with NASA." + Olfset star positions were obtained using astrometry from the euicle stars selection system astrometric support svstem (GASP). developed at the Space Telescope Science Institute. which is operated by the Association of Universities for Research in Astronomy. lor NASA.," Offset star positions were obtained using astrometry from the guide stars selection system astrometric support system (GASP), developed at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, for NASA." + This research has mace use of the NASA/IPAC Extragalactic Database (NED) which is operated. by the Jet Propulsion Laboratory. California Institute of Technology. under contract with the National Acronautics and Space Administration.," This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration." + ‘To select a bright comparison sample in a similar manner to the NIEC* sample we used data from two 38 MlIEZ surveys to obtain low frequency Hux densities for radio sources in the sample of LRL. resulting in two different (ux density limits.," To select a bright comparison sample in a similar manner to the NEC* sample we used data from two 38 MHz surveys to obtain low frequency flux densities for radio sources in the sample of LRL, resulting in two different flux density limits." + 1n the region covered by the 38-Mllz survey of tees (1990) we used Sisyest)ffl|2)212 Jv. and in the remainder of the northern sky. Sys)yea)ZEE2)015 Jy using Duxdensity from the 38-MllIZ survey of Williams. Ixenderdine Baldwin (1966) corrected according to Laing Peacock (1980).," In the region covered by the 38-MHz survey of Rees (1990) we used $S_{151\; {\rm (rest)}}/(1+z) +\geq 12$ Jy, and in the remainder of the northern sky, $S_{151\; {\rm (rest)}}/(1+z) \geq 15$ Jy using flux density from the 38-MHz survey of Williams, Kenderdine Baldwin (1966) corrected according to Laing Peacock (1980)." + Flux densities at. higher frequencies were mostIy. obtained. from Laing Peacock (1980)., Flux densities at higher frequencies were mostly obtained from Laing Peacock (1980). + The members of the sample are listed in Table Al. and those of the NEC* sample in Table A2.," The members of the sample are listed in Table A1, and those of the NEC* sample in Table A2." + The redshift distributions of the LRL and 3€* samples are not significantly dillerent statistically: a Ixolmogorov-Smirnov test on the two samples gives a probability of 18 per cent that they are drawn from the same underlving distribution., The redshift distributions of the LRL and 3C* samples are not significantly different statistically; a Kolmogorov-Smirnov test on the two samples gives a probability of 18 per cent that they are drawn from the same underlying distribution. + There does. however. seem to be a relative lack of high redshift objects in the 3€7* sample due to the CSS sources dropping out AAL).," There does, however, seem to be a relative lack of high redshift objects in the 3C* sample due to the CSS sources dropping out A1)." +The algorithin is considered to have couverged to a valid shape measurement if it completes without setting of the flags orCoarseFailure.,The algorithm is considered to have converged to a valid shape measurement if it completes without setting of the flags or. + Tn our tests. postage-stamp images are create : judividual galaxies. as convolved with a known PSF. pixelized. and eiveu noise.," In our tests, postage-stamp images are created of individual galaxies, as convolved with a known PSF, pixelized, and given noise." + We then extract SE2ο and shear measurements from euseibles of Sc1 postage-staimp tests., We then extract shape and shear measurements from ensembles of such postage-stamp tests. + In the real sky and iu end-to-end tests which draw (pre-lensing) ealaxy »es at raudonm. the unucertainties in the outpu shear are usually dominated by the finite variance 1e nean pre-shearing shape (shape noise).," In the real sky and in end-to-end tests which draw (pre-lensing) galaxy shapes at random, the uncertainties in the output shear are usually dominated by the finite variance of the mean pre-shearing shape (shape noise)." + We construct our eusemibles with zero mean shape to eliuinate shape noise. leaving our testing precisiou dominated by the shot noise m the ages.," We construct our ensembles with zero mean shape to eliminate shape noise, leaving our testing precision dominated by the shot noise in the images." + Because we provide the shapeaueasureimenut ieorithnuis with an approximate location for everv simulated ealaxy. our tests do not include the effects of possible selection biases (Ivaiscr200xBJO2: IIS03).," Because we provide the shape-measurement algorithms with an approximate location for every simulated galaxy, our tests do not include the effects of possible selection biases \citep{K00,BJ02,Hirata03}." +. Similarly the PSF is always presumed to be kuown exactly. so we do not test for ¢trots that would result froui PSF measureeit oriiterpolation errors (vanWaerbekeetal.2005:Jainetal. 2006).," Similarly the PSF is always presumed to be known exactly, so we do not test for errors that would result from PSF measurement or interpolation errors \citep{HoekstraXX, +Jarvis06}." +. Effects of galaxw crowdius or OVCLlap. detector nonlinearities. intrinsic galaxv- correlations. or redshift determination errors (Maοal.2006) are nof examined here.," Effects of galaxy crowding or overlap, detector nonlinearities, intrinsic galaxy-shape correlations, or redshift determination errors \citep{Ma} are not examined here." + Lnsteac we concentrate on the sources of systematic error that arise specifically from (1) the shape measurement. (2) removal of the PSF effec‘ts. and (3) the shear estimation. in images with finite noise and samplue.," Instead we concentrate on the sources of systematic error that arise specifically from (1) the shape measurement, (2) removal of the PSF effects, and (3) the shear estimation, in images with finite noise and sampling." + Tn order to test our WL analysis iiethodologv. we lreed to Gud the conditions uudoer which Wweks. and then test for any biasing in the shape lueasurement or shear estimation method.," In order to test our WL analysis methodology, we need to find the conditions under which works, and then test for any biasing in the shape measurement or shear estimation method." + The following is the list of the test conditions or cloices made: For the decouvolution fit. we have the followiug additional choices for the PSF: Iu this paper. the PSF is always known: we do not test for errors due to incomplete knowledge of the PSF.," The following is the list of the test conditions or choices made: For the deconvolution fit, we have the following additional choices for the PSF: In this paper, the PSF is always known; we do not test for errors due to incomplete knowledge of the PSF." +The fields of 0322REX and 4427 were observed in service mode at the VLT 8.2 m telescopes. units Antu and Melipal. during the months of May to September 2001 and May to June 2002 respectively.,"The fields of $-$ 0322 and $-$ 4427 were observed in service mode at the VLT 8.2 m telescopes, units Antu and Melipal, during the months of May to September 2001 and May to June 2002 respectively." + The wavelength of Lyo at the redshift of the z23.15 absorber in the spectrum of 0322 corresponds to the central wavelength of a 59 A-wide [OHI] off-band VLT filter., The wavelength of $\alpha$ at the redshift of the z=3.15 absorber in the spectrum of $-$ 0322 corresponds to the central wavelength of a 59 -wide ] off-band VLT filter. + Similarly. the wavelength of γα at the redshift of the z22.85 absorber in the spectrum of 4427is 2.5 ooff from the central wavelength of a 66 A-wide VLT filter.," Similarly, the wavelength of $\alpha$ at the redshift of the z=2.85 absorber in the spectrum of $-$ 4427 is 2.5 off from the central wavelength of a 66 -wide VLT filter." + Both fields were observed in one of the two narrow-band filters and also in the Bessel B and R broad-band filters., Both fields were observed in one of the two narrow-band filters and also in the Bessel B and R broad-band filters. + The transmission curve of each of the filters is shown in Fig. |., The transmission curve of each of the filters is shown in Fig. \ref{filters}. + The integration times in the B and R filters were set by the criterion that the broad on-band B imaging should reach about half a magnitude deeper than the narrow-band imaging for objects having a pure continuum in the narrow filter so as to get a reliable selection of objects with emission in the narrow filter., The integration times in the B and R filters were set by the criterion that the broad on-band B imaging should reach about half a magnitude deeper than the narrow-band imaging for objects having a pure continuum in the narrow filter so as to get a reliable selection of objects with emission in the narrow filter. + For the broad off-band R imaging. we reached a magnitude deeper (at the 5o significance level) than the spectroscopic limit of R(AB)=25.5 for LBGs.," For the broad off-band R imaging, we reached a magnitude deeper (at the $\sigma$ significance level) than the spectroscopic limit of R(AB)=25.5 for LBGs." + The total integration times. the seeing (FWHM) of the combined images and the 5o detection limits are give for each filter and both fields in Table 1..," The total integration times, the seeing (FWHM) of the combined images and the $\sigma$ detection limits are given for each filter and both fields in Table \ref{journal}." + The images were reduced (de-biased and corrected for CCD pixel-to-pixel variations) using the FORSI pipeline (Grosbel et al., The images were reduced (de-biased and corrected for CCD pixel-to-pixel variations) using the FORS1 pipeline l et al. + 1999)., 1999). + The individual reduced images in each filter were combined using a code that optimizes the Signal-to-Noise (S/N) ratio for faint. sky-dominated sources (see Moller Warren 1993 for details on this code).," The individual reduced images in each filter were combined using a code that optimizes the Signal-to-Noise (S/N) ratio for faint, sky-dominated sources (see ller Warren 1993 for details on this code)." + The broad-band images were calibrated as part of the FORSI calibration plan via observations of Landolt standard stars (Landolt 1992)., The broad-band images were calibrated as part of the FORS1 calibration plan via observations of Landolt standard stars (Landolt 1992). + As the data were collected over a time span of months. we have data from several photometric nights which we used to determine independent zeropoints for the combined images.," As the data were collected over a time span of months, we have data from several photometric nights which we used to determine independent zeropoints for the combined images." + These zero-points are consistent with each other within 0.02 mag., These zero-points are consistent with each other within 0.02 mag. + We transformed the zero-points to the AB system using the relations given by Fukugita et al. (, We transformed the zero-points to the AB system using the relations given by Fukugita et al. ( +1995): 0.11 and |0.17.,1995): $-0.14$ and $+0.17$. + The 4427 images are deeper than the 0322 ones by nearly half a magnitude as the 0322 data were obtained at higher airmass and with slightly larger lunar illumination than the 4427 data., The $-$ 4427 images are deeper than the $-$ 0322 ones by nearly half a magnitude as the $-$ 0322 data were obtained at higher airmass and with slightly larger lunar illumination than the $-$ 4427 data. + For the calibration of the narrow-band images. we used observations of the spectrophotometric standard stars LTT6248 and LDS749-B for. respectively. the 0322 and 27 fields.," For the calibration of the narrow-band images, we used observations of the spectrophotometric standard stars LTT6248 and LDS749-B for, respectively, the $-$ 0322 and $-$ 4427 fields." + Contour images of the combined narrow-band images of the 400.400 aresec? fields surrounding the QSOs 0322 and 4427 are shown in Fig. 2.., Contour images of the combined narrow-band images of the $\times$ 400 $^2$ fields surrounding the QSOs $-$ 0322 and $-$ 4427 are shown in Fig. \ref{field}. +" Both QSOs are identified by an &"" at the field centre and the positions of selected LEGO candidates (see Sect. 2.1.1))", Both QSOs are identified by an $\times$ ” at the field centre and the positions of selected LEGO candidates (see Sect. \ref{LEGOs}) ) + are shown with boxes., are shown with boxes. + For object detection and photometry. we used the software package SExtractor (Bertin Arnouts 1996).," For object detection and photometry, we used the software package SExtractor (Bertin Arnouts 1996)." + As a detection image. we used the weighted sum of the combined narrow- and B-band images. with weight for the narrow-band image and weight for the B-band one to secure an optimal selection of objects with excess in the narrow filter.," As a detection image, we used the weighted sum of the combined narrow- and B-band images, with weight for the narrow-band image and weight for the B-band one to secure an optimal selection of objects with excess in the narrow filter." + However. the selection was not very sensitive to the exact weights given to the narrow-band and B-band images.," However, the selection was not very sensitive to the exact weights given to the narrow-band and B-band images." + Before object detection we convolved the detection image with a Gaussian filter function having a FWHM equal to that of point sources., Before object detection we convolved the detection image with a Gaussian filter function having a FWHM equal to that of point sources. + We used a detection threshold of 1.1 times the background sky-noise in the unfiltered detection image and à minimum area of 5 connected pixels above the detection threshold in the filtered image., We used a detection threshold of 1.1 times the background sky-noise in the unfiltered detection image and a minimum area of 5 connected pixels above the detection threshold in the filtered image. + Isophotal apertures were defined on the detection image and those same isophotal apertures are used in the different bands (narrow. B and R).," Isophotal apertures were defined on the detection image and those same isophotal apertures are used in the different bands (narrow, B and R)." + In our final catalogue. we include only objects with total S/N—95 in the isophotal aperture in either the narrow- or the B-band images.," In our final catalogue, we include only objects with total $>$ 5 in the isophotal aperture in either the narrow- or the B-band images." + In total. we detect," In total, we detect" +According to Table 34 most of the IMF and extinction combinations favour a starburst galaxy.,According to Table \ref{synfitresults} most of the IMF and extinction combinations favour a starburst galaxy. + The exception occurs wher a Pre84 extinction law is assumed., The exception occurs when a Pre84 extinction law is assumed. + In most of those cases a young Elliptical galaxy template is the best fitted SED. with a stellar age 0.128-0.181 Gyr.," In most of those cases a young Elliptical galaxy template is the best fitted SED, with a stellar age 0.128–0.181 Gyr." + In one case (SOL-MiSc79) the Pre84 extinction law ts consistent with a young (0.128 Gyr) Im galaxy template., In one case (SOL-MiSc79) the Pre84 extinction law is consistent with a young (0.128 Gyr) Im galaxy template. + —n the first stages of the SED evolution. when the galaxy is dominated by à young blue stellar population (typically younger than 0.1 Gyr) all the synthetic templates resemble each other.," In the first stages of the SED evolution, when the galaxy is dominated by a young blue stellar population (typically younger than $0.1$ Gyr) all the synthetic templates resemble each other." + The templates start to differentiate at ages >0.1 Gyr. when the 4000 break becomes progressively prominent.," The templates start to differentiate at ages $>0.1$ Gyr, when the 4000 break becomes progressively prominent." + Thus. the ages inferred for the E and Im templates are close to that evolutionary transition present at 0.1 Gyr. when their SEDs are still similar to starbursts.," Thus, the ages inferred for the E and Im templates are close to that evolutionary transition present at $\sim +0.1$ Gyr, when their SEDs are still similar to starbursts." + The low age derived for the E and Im templates is just an indication that undergoing active stellar formation is present in the host. independently of the type assigned to each template (the difference among the young templates is more due to a template name definition than a real physical reason).," The low age derived for the E and Im templates is just an indication that undergoing active stellar formation is present in the host, independently of the type assigned to each template (the difference among the young templates is more due to a template name definition than a real physical reason)." + So. only based on the analysis of synthetic templates we can not completely rule out that the host SED is not a young E or an Im galaxy.," So, only based on the analysis of synthetic templates we can not completely rule out that the host SED is not a young E or an Im galaxy." + However. even for these few cases (which represent 22 of the SED solutions displayed in Table 3)). we can claim that the galaxy harbours a prominent blue stellar formation activity.," However, even for these few cases (which represent 22 of the SED solutions displayed in Table \ref{synfitresults}) ), we can claim that the galaxy harbours a prominent blue stellar formation activity." + Therefore. it is clear that the SED is only reproducible with a young synthetic stellar population and it is incompatible with an evolved population.," Therefore, it is clear that the SED is only reproducible with a young synthetic stellar population and it is incompatible with an evolved population." + The starburst scenario is also supported by the results obtained from fitting the K96 observational templates., The starburst scenario is also supported by the results obtained from fitting the K96 observational templates. + As it is shown in Table 4.. by far the smallest values of \?/dof are obtained with blue. low extinction. starburst templates (Stb2 and a Stbl).," As it is shown in Table \ref{empfitresults}, by far the smallest values of $\chi^2/dof$ are obtained with blue, low extinction, starburst templates (Stb2 and a Stb1)." + The rest of the empirical templates. especially the early type galaxies (SO. E and B). show a high degree of discrepancy with the photometric points (A3/dof>23.71. see Table 4).," The rest of the empirical templates, especially the early type galaxies (S0, E and B), show a high degree of discrepancy with the photometric points $\chi^2/dof > 23.71$, see Table \ref{empfitresults}) )." + Therefore. combining the morphological information and the synthetic and empirical SED fits we conclude that the GRB 000418 host galaxy SED is best reproduced by a Stb template.," Therefore, combining the morphological information and the synthetic and empirical SED fits we conclude that the GRB 000418 host galaxy SED is best reproduced by a Stb template." + This agrees with the independent result reported by Bloom et al. (2003)), This agrees with the independent result reported by Bloom et al. \cite{Bloo03}) ) + who based on the relative intensities of the [OIL].I. LI] and lines. conclude that the host is a starburst galaxy rather than à LINER or a Seyfert 2 galaxy.," who based on the relative intensities of the ], ] and lines, conclude that the host is a starburst galaxy rather than a LINER or a Seyfert 2 galaxy." + The lack of underlying peripheric bright knots of star formation (see Sect. 4.1)), The lack of underlying peripheric bright knots of star formation (see Sect. \ref{ellipse}) ) + supports a model with oe dominant nuclear starburst., supports a model with one dominant nuclear starburst. + This fact makes our photometric points a suitable input for Hyperz. as multiple contemporaneous episodes of star formation can not be fitted with this code.," This fact makes our photometric points a suitable input for Hyperz, as multiple contemporaneous episodes of star formation can not be fitted with this code." + In the upper sub-table of Table 3 we show the results obtained when solar metallicity is assumed for the host galaxy., In the upper sub-table of Table \ref{synfitresults} we show the results obtained when solar metallicity is assumed for the host galaxy. + In the middle sub-table the results are displayed when the metallicity is not fixed., In the middle sub-table the results are displayed when the metallicity is not fixed. + In such case the stars eject heavy elements to the environment. enriching the ISM where new generation of stars are continuously born.," In such case the stars eject heavy elements to the environment, enriching the ISM where new generation of stars are continuously born." + The effect of the ISM enrichment is expected to be maximum for Im galaxies (where the SFR is constant) and negligible for instantaneous starbursts. where all the stars are modeled to be formed at the same epoch (instantaneous SFR idealised by a delta function).," The effect of the ISM enrichment is expected to be maximum for Im galaxies (where the SFR is constant) and negligible for instantaneous starbursts, where all the stars are modeled to be formed at the same epoch (instantaneous SFR idealised by a delta function)." + As it is shown the results of both sub-tables are basically the same., As it is shown the results of both sub-tables are basically the same. + Even if the metallicity is left as a free parameter the Stb template is the one providing the most satisfactory fits., Even if the metallicity is left as a free parameter the Stb template is the one providing the most satisfactory fits. + Thus. we conclude that the metallicity of the host is consistent with Solar metallicity. but that the metallicity is not strongly constrained by our analysis.," Thus, we conclude that the metallicity of the host is consistent with Solar metallicity, but that the metallicity is not strongly constrained by our analysis." + According to the empirical SED templates. the blue SED of the host can only be roughly reproduced with low extinction starburst galaxies (templates Stbl and Stb2).," According to the empirical SED templates, the blue SED of the host can only be roughly reproduced with low extinction starburst galaxies (templates Stb1 and Stb2)." + As it can be seen in Table 4. there is a clear correlation between the goodness of the fit and the colour of the template: the bluer the colour the lower 47/dof., As it can be seen in Table \ref{empfitresults} there is a clear correlation between the goodness of the fit and the colour of the template: the bluer the colour the lower $\chi^2/dof$. + To translate the value of E(BV) to Agen we adopt the value of Ry=AvenE(BVV)05--0.50 proposed for starburst galaxies (Calzetti et al. 2000)).," To translate the value of $E(B-V)$ to $A^{global}_{\rm V}$ we adopt the value of $R_{\rm + V}=A^{global}_{\rm V}/E(B-V)=4.05\pm0.80$ proposed for starburst galaxies (Calzetti et al. \cite{Calz00}) )." + The best fit is achieved with a Stb2 template. which shows by definition a fixed colour excess E(BV)=0.15£0.05 following Cal00).," The best fit is achieved with a Stb2 template, which shows by definition a fixed colour excess $E(B-V) = 0.15 +\pm 0.05$ $A^{global}_{\rm V}=0.61 \pm 0.24$ following Cal00)." +Iu general we have fouud that an (-pole mode of the field decays. at late times. like > 0.(U)where f is the time coordinate.,"In general we have found that an $\ell$ -pole mode of the field decays, at late times, like > 0,where $t$ is the time coordinate." + For (=0. we find that rather than the decay. the field approaches a coustant value PPlfasttoon. where yy scales like AG Fiewre 1 shows plots of [ye] versus f for oa back hole with charge (ο) of 0.5. mass (M) of 1.0 aud a cosiiological coustant CX) of 10.|. tho results being representative of a more geucral choice of (e.M.X).," For $\ell = 0$, we find that rather than the decay, the field approaches a constant value + t, where $\varphi_{0}$ scales like $\Lambda$ \cite{cmc-b40} Figure \ref{cmc-f10} shows plots of $|\varphi|$ versus $t$ for a back hole with charge $e$ ) of $0.5$, mass $M$ ) of $1.0$ and a cosmological constant $\Lambda$ ) of $10^{-4}$, the results being representative of a more general choice of $(e,M,\Lambda)$." +" The field behavior is shown along four different surfaces"" (à) The black hole eveut horizon. (", The field behavior is shown along four different surfaces: (a) The black hole event horizon. ( +b) The cosmological event horizon. (,b) The cosmological event horizon. ( +ο) Future timelike infinity. approached along two surfaces of coustaut racius.,c) Future timelike infinity – approached along two surfaces of constant radius. + Figure 1. (a) shows the behavior of the (=0 mode of the scalar field., Figure \ref{cmc-f10}~ (a) shows the behavior of the $\ell=0$ mode of the scalar field. + At carly times (0<£200) the field is dominated by quasinormalringing. while at late times (f£2200) this behavior is swamped by the radiative tails.," At early times $(0200)$ this behavior is swamped by the radiative tails." +" It is clear that the field yy,y approaches the same coustant value [Eq. 2]]."," It is clear that the field $\varphi_{\ell=0}$ approaches the same constant value [Eq. \ref{cmc-e20}] ]," + along cach smface. at late times.," along each surface, at late times." +" A umuerical investigation of the depeudeuce of wy ou A provides the scaling relation qjx AU999!, "," A numerical investigation of the dependence of $\varphi_{0}$ on $\Lambda$ provides the scaling relation $\varphi_{0} \propto +\Lambda^{0.9994}$ ." +Aq analytic calculation shows that yy varies like A. confirming the numerical result.," An analytic calculation shows that $\varphi_{0}$ varies like $\Lambda$, confirming the numerical result." + Examining Qa has allowed us tofurther conclude that the exponent in Eq.," Examining $\varphi_{,t}$ has allowed us tofurther conclude that the exponent in Eq." + 2) is iudecd (4 to within 1054., \ref{cmc-e20} is indeed $\kappa_{1}$ to within $10\%$. + Figure P. (>) shows the behavior of the (=1 mode of the scalar field., Figure \ref{cmc-f10}~ (b) shows the behavior of the $\ell=1$ mode of the scalar field. + Again. at carly times (0<¢t< 100). the field decay is dominated by quasinormal ringing.," Again, at early times $(0 LOO). the behavior is swamped by an exponential decay. with the field falling off as exp( Aft).," At late times though $(t>400)$ the behavior is swamped by an exponential decay, with the field falling off as $\exp(-k t)$ ." + Numerically we lave ascertained that kocona to within 2%., Numerically we have ascertained that $k \approx \kappa_{1}$ to within $2 \%$ . + An examination ofhigher modes has allowed usto conchile, An examination ofhigher modes has allowed usto conclude +peak appears to end ancl (he bar profile becomes prominent.,peak appears to end and the bar profile becomes prominent. + In some cases. lor example in NGC 4321. there appears (ο be a double bar since (here are two distinct flat portions in the profile (e.g. Ixnapen et al.," In some cases, for example in NGC 4321, there appears to be a double bar since there are two distinct flat portions in the profile (e.g. Knapen et al." + 1995)., 1995). + Double bars are evident both in the isophotes aud in (he intensity profiles., Double bars are evident both in the isophotes and in the intensity profiles. + In such cases. we had to carefully examine the profile in order to distinguish the bulge from the rest of the bar.," In such cases, we had to carefully examine the profile in order to distinguish the bulge from the rest of the bar." + Brieht stars and dust can interlere with the isophote fitting procedure: so to 1ininize this effect. we fitted the bar-defining isophotes using the software suite NEMO (Teuben 1995).," Bright stars and dust can interfere with the isophote fitting procedure; so to minimize this effect, we fitted the bar-defining isophotes using the software suite NEMO (Teuben 1995)." + To determine deprojected values of the bar parameters. the bar was treated as a ellipse and then projected onto the plane of the galaxy.," To determine deprojected values of the bar parameters, the bar was treated as a two-dimensional ellipse and then projected onto the plane of the galaxy." + The parameters involved in (he deprojection are (he inclination angle of the galaxy. and the angle between the bar major axis and galaxy axis., The parameters involved in the deprojection are the inclination angle of the galaxy and the angle between the bar major axis and galaxy axis. + The parameters assumed for the galaxies ancl (the observed bar elliplicilies are listed in Table 1 and the deprojected values in Table 2., The parameters assumed for the galaxies and the observed bar ellipticities are listed in Table 1 and the deprojected values in Table 2. + We have used the rotation curves derived [rom the CO(1-0) emission line observations of BIMA SONG to determine [for our sample of barred. galaxies., We have used the rotation curves derived from the CO(1-0) emission line observations of BIMA SONG to determine for our sample of barred galaxies. + As noted earlier. the CO line traces the molecular gas distribution in the bar and should be a good tracer of the bar potential because it is cold. and hence should settle along closed orbits in the plane of (he galaxy.," As noted earlier, the CO line traces the molecular gas distribution in the bar and should be a good tracer of the bar potential because it is cold, and hence should settle along closed orbits in the plane of the galaxy." + We used the data cube derived [rom the spectral line observations to determine the zeroth and first order moments of the intensity distribution. i.e. (he integrated CO intensity maps ancl (he mean-line-of sight velocity maps for these galaxies.," We used the spatial-velocity data cube derived from the spectral line observations to determine the zeroth and first order moments of the intensity distribution, i.e. the integrated CO intensity maps and the mean-line-of sight velocity maps for these galaxies." + A detailed description of the methods involved in deriving (hese rotation curves has been discussed elsewhere (Degeman 1957: Teuben et al., A detailed description of the methods involved in deriving these rotation curves has been discussed elsewhere (Begeman 1987; Teuben et al. + 2002. in preparation).," 2002, in preparation)." + We summarize the procedure here., We summarize the procedure here. + We used a (wo step process to obtain the CO velocity fields., We used a two step process to obtain the CO velocity fields. + First. we eeneraled a mask eube by smoothing the eube al each velocity channel with a 20” gaussian: onlv those pixels wilh emission brighter (han the 3o level in (his smoothed cube were allowed bv the mask.," First, we generated a mask cube by smoothing the cube at each velocity channel with a $20$ gaussian; only those pixels with emission brighter than the $\sigma$ level in this smoothed cube were allowed by the mask." + Then. we further masked the data by including only pixels with brightness above the 2o level in the unsmoothed cube.," Then, we further masked the data by including only pixels with brightness above the $\sigma$ level in the unsmoothed cube." + Moment maps al the Π resolution of the data were then generated in the standard wav using these (wo masks., Moment maps at the full resolution of the data were then generated in the standard way using these two masks. + The rotation curves were determined [rom the velocity fields using the NEMO task rotcur. which is based on the tilted-ring model fitting method developed for HI rotation curves (Degeman 1989).," The rotation curves were determined from the velocity fields using the NEMO task $\tt{rotcur}$, which is based on the tilted-ring model fitting method developed for HI rotation curves (Begeman 1989)." + The parameters for the rings are the inclination angle. (he position angle. the systemic velocity ol the galaxy and the rotation center of the galaxy.," The parameters for the rings are the inclination angle, the position angle, the systemic velocity of the galaxy and the rotation center of the galaxy." + The dynamical center for a galaxy was assumed to be the brightness centroid derived from the Ix. I or B. band images: this involved," The dynamical center for a galaxy was assumed to be the brightness centroid derived from the K, I or R band images; this involved" +The primary aim of a general investigation of star formation is to obtun reliable measurements of the distribution. of the forming objects in mass. age and spatial structure.,"The primary aim of a general investigation of star formation is to obtain reliable measurements of the distribution of the forming objects in mass, age and spatial structure." + A simultaneous aim of the investigation is to constrain the models used in the determination of these physical parameters., A simultaneous aim of the investigation is to constrain the models used in the determination of these physical parameters. + Further objectives may include details of the time evolution of these properties. and their dependence on other parameters. such as the chemical composition. the total mass of the initial cloud. or the environmental conditions.," Further objectives may include details of the time evolution of these properties, and their dependence on other parameters, such as the chemical composition, the total mass of the initial cloud, or the environmental conditions." + But the fundamental aim is to tune the theoretical models. and to obtain accurate values of masses and ages.," But the fundamental aim is to tune the theoretical models, and to obtain accurate values of masses and ages." + In this context. stellar clusters are the most. reliable tool to measure distances. masses and ages of stars.," In this context, stellar clusters are the most reliable tool to measure distances, masses and ages of stars." + Young open clusters (YOCs). in particular. serve to increase our understanding of stars 1n early evolutionary phases. including the pre-main sequence (PMS) evolution.," Young open clusters (YOCs), in particular, serve to increase our understanding of stars in early evolutionary phases, including the pre-main sequence (PMS) evolution." + Our work deals with YOCs of ages around 10 Myr. which offer some clear advantages to the study of the star formation process in clusters.," Our work deals with YOCs of ages around 10 Myr, which offer some clear advantages to the study of the star formation process in clusters." + These objects are usually not embedded in the remnants of the dust and gas clouds where they formed. and can be studied with multiwavelength photometric observations. covering the optical and the infrared range.," These objects are usually not embedded in the remnants of the dust and gas clouds where they formed, and can be studied with multiwavelength photometric observations, covering the optical and the infrared range." + For these clusters. reliable determinations of distance and absorption are possible. which greatly help in further determinations of physical parameters of the PMS cluster members. such as mass and age.," For these clusters, reliable determinations of distance and absorption are possible, which greatly help in further determinations of physical parameters of the PMS cluster members, such as mass and age." + In recent years. detailed new observations of some particular YOCs have enlarged the data available to test and constrain model predictions.," In recent years, detailed new observations of some particular YOCs have enlarged the data available to test and constrain model predictions." + Primarily. X-ray detections and He emission. together with spectroscopically determined spectral types. provide assessment of cluster members. and. subsequently. models are used to obtain masses and ages (Flaccomio et al.," Primarily, X-ray detections and $\alpha$ emission, together with spectroscopically determined spectral types, provide assessment of cluster members, and, subsequently, models are used to obtain masses and ages (Flaccomio et al." + 2006. FO6 in the following: Dahm et al.," 2006, F06 in the following; Dahm et al." + 2007. DO7 in the following).," 2007, D07 in the following)." + In this context. several sets of PMS isochrone models have been published. which cover different ranges in star mass and other physical parameters (see Hillenbrand White 2004. HO4 in the following).," In this context, several sets of PMS isochrone models have been published, which cover different ranges in star mass and other physical parameters (see Hillenbrand White 2004, H04 in the following)." + Recent studies have compared models to observations on the basis of synthesized clusters. simulated from different models and with assumed contributions from the expected sources of uncertainty (Hillenbrand et al.," Recent studies have compared models to observations on the basis of synthesized clusters, simulated from different models and with assumed contributions from the expected sources of uncertainty (Hillenbrand et al." + 2008)., 2008). + Another approach to assess age determinations of theoretical models has been advanced recently. based on the analysis of stellar pulsation of PMS stars and comparison. with. predictions. of model interiors (Zwintz et al.," Another approach to assess age determinations of theoretical models has been advanced recently, based on the analysis of stellar pulsation of PMS stars and comparison with predictions of model interiors (Zwintz et al." + 2008)., 2008). + The measurement of physical parameters such as mass and age is achieved through the comparison of observations with evolutionary stellar interior models in the HR diagram., The measurement of physical parameters such as mass and age is achieved through the comparison of observations with evolutionary stellar interior models in the HR diagram. + This comparison between models and observations can be performed in two ways., This comparison between models and observations can be performed in two ways. + The first consists of calculating luminosity and effective temperature from observed colours. and afterward the physical parameters are read from. the theoretical isochrones in the HR diagram (examples for by Rebull et al.," The first consists of calculating luminosity and effective temperature from observed colours, and afterward the physical parameters are read from the theoretical isochrones in the HR diagram (examples for by Rebull et al." + 2002. RO2 in the following: FO6).," 2002, R02 in the following; F06)." + This approach ts used in the methods for age measurement reviewed by Naylor et al. (, This approach is used in the methods for age measurement reviewed by Naylor et al. ( +2009).,2009). + This procedure has the advantage of à more accurate consideration of extinction. for the individual stars., This procedure has the advantage of a more accurate consideration of extinction for the individual stars. + But the comparison to models needs additional information. such às spectral types and. most important. membership confirmation. which is usually lacking.," But the comparison to models needs additional information, such as spectral types and, most important, membership confirmation, which is usually lacking." + The second approach consists of translating the theoretical isochrones to colours and absolute visual magnitudes. and of comparing to observations in the photometric diagrams (D07. also for 2264)).," The second approach consists of translating the theoretical isochrones to colours and absolute visual magnitudes, and of comparing to observations in the photometric diagrams (D07, also for )." + For a general sample of clusters. the conversion from. theoretical luminosity and effective temperature to photometric colours is preferred. in. particular if the extinction. does not show too high values or degree of variability.," For a general sample of clusters, the conversion from theoretical luminosity and effective temperature to photometric colours is preferred, in particular if the extinction does not show too high values or degree of variability." + The transformed isochrones can then be used as reference lines to measure colour excess and distance., The transformed isochrones can then be used as reference lines to measure colour excess and distance. + Interestingly. this approach allows the simultaneous study of three issues. a) assignment of cluster membership. b) determination of the physical parameters for the candidate members. and c) test of the performances of different evolutionary caleulations.," Interestingly, this approach allows the simultaneous study of three issues, a) assignment of cluster membership, b) determination of the physical parameters for the candidate members, and c) test of the performances of different evolutionary calculations." + In this paper we present the results of the methodology used to obtain basic physical information on the PMS member, In this paper we present the results of the methodology used to obtain basic physical information on the PMS member +Drizzle places the center of a pixel output exactly where il was observed.,Drizzle places the center of a pixel output exactly where it was observed. + However. the average weight of an output pixel will not necessarily fall at the center of the pixel. and thus there is a jitter between the represented ancl effective position of a pixel.," However, the average weight of an output pixel will not necessarily fall at the center of the pixel, and thus there is a jitter between the represented and effective position of a pixel." + Furthermore the peak of a drizzled PSF will never be greater than the ereatest value in the appropriate region of the input images., Furthermore the peak of a drizzled PSF will never be greater than the greatest value in the appropriate region of the input images. + By contrast iDrizzle attempts to predict the true value of the image al the center of the output. pixel. and (hus the peak of a PSF will sometimes be brighter than anv value of the input images in (he appropriate region.," By contrast iDrizzle attempts to predict the true value of the image at the center of the output pixel, and thus the peak of a PSF will sometimes be brighter than any value of the input images in the appropriate region." + iDrizzle essentially uses estimates of (he derivatives of the data to extrapolate to a position (the center of the output pixel) which is not necessarily exactly saanpled in anv of the input images., iDrizzle essentially uses estimates of the derivatives of the data to extrapolate to a position (the center of the output pixel) which is not necessarily exactly sampled in any of the input images. + This will produce some noise amplification. which will vary with the qualitw of the dithering.," This will produce some noise amplification, which will vary with the quality of the dithering." + In tvpical tests performed on this method the noise amplification has been in the region of10%., In typical tests performed on this method the noise amplification has been in the region of. +.. This noise amplilication. however. does not prevent the method from obtaining extraordinary results in high-signal lo noise images.," This noise amplification, however, does not prevent the method from obtaining extraordinary results in high-signal to noise images." + For instance. when the PSF fitting software DAOPILOT (Stetson 1987) is applied to the PSF based on the UDF bright star. it finds statistically identical photometry when measuring the “true” representation of ACS PSFs (Figure 1) with purely statistical 10ise introduced: and when measuring the iDrizzle reconstruction.," For instance, when the PSF fitting software DAOPHOT (Stetson 1987) is applied to the PSF based on the UDF bright star, it finds statistically identical photometry when measuring the “true” representation of ACS PSFs (Figure 1) with purely statistical noise introduced and when measuring the iDrizzle reconstruction." + Both are at millimag accuracy and challenge the precision of the photometry software., Both are at millimag accuracy and challenge the precision of the photometry software. + As the signal-to-noise level is lowered by using fainter simulated stars against a constant noise background. both the introduced noise and the noise surplus of about caused by the method become evident.," As the signal-to-noise level is lowered by using fainter simulated stars against a constant noise background, both the introduced noise and the noise surplus of about caused by the method become evident." + Nonetheless as can be seen in Figure 3 the image reconstruction remains very accurate., Nonetheless as can be seen in Figure 3 the image reconstruction remains very accurate. + The οίκο is dominated by statistical. rather than svstematic. errors.," The noise is dominated by statistical, rather than systematic, errors." + ]Inmnages produced by Drizzle show correlated noise., Images produced by Drizzle show correlated noise. + Part of this correlation is caused by the cdiizzling process itself à non-zero value of causes Drizzle to place a given input pixel value down on a region of linear size pxf. where p is the value of and / is the linear size of an input pixel.," Part of this correlation is caused by the drizzling process itself – a non-zero value of causes Drizzle to place a given input pixel value down on a region of linear size $p \times l$, where $p$ is the value of and $l$ is the linear size of an input pixel." + As the iteration proceeds. iDrizzle effectivelv forces p to zero.," As the iteration proceeds, iDrizzle effectively forces $p$ to zero." + llowever. as noted earlier. noise correlation is introduced to the image by the application of the tapering ΠΟΙΟΙ Lk).," However, as noted earlier, noise correlation is introduced to the image by the application of the tapering function $L(\vec{k})$." + White noise is turned into redclish (correlated) noise bv this procedure., White noise is turned into reddish (correlated) noise by this procedure. + Thus there is a competition between suppressing ringing near bright unresolved sources while maintaining optimal noise properties across the field., Thus there is a competition between suppressing ringing near bright unresolved sources while maintaining optimal noise properties across the field. + This ringing is not caused by any power in the band-limited image passed by (he telescope. but rather by the Poisson noise of the brieht sources.," This ringing is not caused by any power in the band-limited image passed by the telescope, but rather by the Poisson noise of the bright sources." + The limiting angular frequency of this power is not determinedby the, The limiting angular frequency of this power is not determinedby the +but no RAL or DM can be obtained.,but no RM or DM can be obtained. + On21.. only the two lowest frequencies were observed but. polarisation is clearly seen at 2.4 (11 and we derive an RAL of 5100," On, only the two lowest frequencies were observed but polarisation is clearly seen at 2.4 GHz and we derive an RM of $-5100$." + On24.. the RAL has dropped significantly. however. on the RAL is large and positive but can only be detected in the first. 20 min integration at 48 Cillz as detailed. in the table.," On, the RM has dropped significantly, however, on the RM is large and positive but can only be detected in the first 20 min integration at 4.8 GHz as detailed in the table." + We note that this is the only positive value of RAL obtained., We note that this is the only positive value of RM obtained. + A similar result was obtained during the 1994 periastron. where the IMs. were consistently negative both before ancl after periastron.," A similar result was obtained during the 1994 periastron, where the RMs were consistently negative both before and after periastron." + Finally. as late as the pulsar appears depolarisecl at all but SA Gllz.," Finally, as late as the pulsar appears depolarised at all but 8.4 GHz." + During the first 20 min observation at 4.8 Gllz we measured an RAL of 7700, During the first 20 min observation at 4.8 GHz we measured an RM of $-7700$. + ‘There is only marginal evidence for a variable DM with epoch. with the errors quoted in the table being much larger than the typical 02 0.4 ?pe obtained. using. pulsar timing (7)..," There is only marginal evidence for a variable DM with epoch, with the errors quoted in the table being much larger than the typical 0.2 – 0.4 $^{-3}$ pc obtained using pulsar timing \cite{jml+96}." + Phe mean of the values quoted is 146.8 emi pe. almost exactly the result obtained from timing.," The mean of the values quoted is 146.8 $^{-3}$ pc, almost exactly the result obtained from timing." + We note tha these results are consistent with the values obtained during the 1994 and 1997 periastra., We note that these results are consistent with the values obtained during the 1994 and 1997 periastra. + In 1994. the DÀ (ie. the DA with respect to 1H6.8 em. ρου was 34. om ?peby anc no change in DM was seen post-periastron (2)..," In 1994, the $\Delta$ DM (i.e. the DM with respect to 146.8 $^{-3}$ pc) was 3.7 $^{-3}$ pc by and no change in DM was seen post-periastron \cite{jml+96}." + In 1997. the ADM was 15cm ?peon and dem ?pcon42.," In 1997, the $\Delta$ DM was 1.5 $^{-3}$ pc on and 4 $^{-3}$ pc on." + An upper limit of 0.2 “pe to the ADM was obtaine post-periastron (7)., An upper limit of 0.2 $^{-3}$ pc to the $\Delta$ DM was obtained post-periastron \cite{jwn+01}. + From the current data we therefore set an upper lini to ;NDM on o£ 3.0 em pe and on of 5.5 Phe (i.c. twice the error bars). although from the above discussion the ADAL is likely to be much smaller on the latter date.," From the current data we therefore set an upper limit to $\Delta$ DM on of 3.0 $^{-3}$ pc and on of 5.8 $^{-3}$ pc (i.e. twice the error bars), although from the above discussion the $\Delta$ DM is likely to be much smaller on the latter date." + The magnetic field parallel to the line of, The magnetic field parallel to the line of +Evidently. an increase of the pitch angle o=5y7] at a constant . or an increase of the energy ὅ= at a constant pitch angle. both caused by the perturbed electromagnetic field of the instability discussed above. can liberate the particle from the filament.,"Evidently, an increase of the pitch angle $\phi=\sin^{-1}[\beta_r(1-\gamma^{-2})^{-1/2}]$ at a constant $\gamma$, or an increase of the energy ${\cal E}=\gamma mc^2$ at a constant pitch angle, both caused by the perturbed electromagnetic field of the instability discussed above, can liberate the particle from the filament." + A filament experiencing a growing kink instability continuously sheds particles in this fashion., A filament experiencing a growing kink instability continuously sheds particles in this fashion. + The liberated particles have sufficient energy to visit neighboring filaments of either sign of the current. and can be thought of having joined a thermalized pool.," The liberated particles have sufficient energy to visit neighboring filaments of either sign of the current, and can be thought of having joined a thermalized pool." + The loss of particles implies decrease of the current flowing through the filament. which in tum implies the decay of the magnetic field.," The loss of particles implies decrease of the current flowing through the filament, which in turn implies the decay of the magnetic field." + Only the particles that remain confined to the filaments contribute to the coherent toroidal magnetic field of the filament., Only the particles that remain confined to the filaments contribute to the coherent toroidal magnetic field of the filament. + Rapid field decay can be partially offset by an increase in the current per particle by electric fields induced during flux loss: robustness of the currents depends on the competition between the scattering and the induction., Rapid field decay can be partially offset by an increase in the current per particle by electric fields induced during flux loss; robustness of the currents depends on the competition between the scattering and the induction. + We have argued that the quasi-two-dimensional structure of the transition layer in collisionless shocks is disrupted by pressure-driven instabilities., We have argued that the quasi–two-dimensional structure of the transition layer in collisionless shocks is disrupted by pressure-driven instabilities. + We have also shown that the disruption is accompanied by αᾱ redistribution of particle energies. which can be interpreted as the onset of thermalization and magnetic field decay.," We have also shown that the disruption is accompanied by a redistribution of particle energies, which can be interpreted as the onset of thermalization and magnetic field decay." + Long term evolution of the magnetic field must therefore be addressed in the context of the three-dimensional turbulence that ensues after the Weibel filaments have been disrupted., Long term evolution of the magnetic field must therefore be addressed in the context of the three-dimensional turbulence that ensues after the Weibel filaments have been disrupted. + The latter regime remains poorly understood., The latter regime remains poorly understood. + An alternate interpretation. of the early decay of the magnetic field refers to the hierarchical merging of current filaments due to Lorentz forces (Gruzinov2001:Medvedevetal.2005:Kato 2005).," An alternate interpretation of the early decay of the magnetic field refers to the hierarchical merging of current filaments due to Lorentz forces \citep{Gruzinov:01,Medvedev:05,Kato:05}." + It can be asked whether the merging or the pressure-driven instabilities prevail., It can be asked whether the merging or the pressure-driven instabilities prevail. + Since the maximum current that can flow through a filament is limited (see 2)). magnetic energy density must eventually decay under merging.," Since the maximum current that can flow through a filament is limited (see \ref{sec:equilibrium}) ), magnetic energy density must eventually decay under merging." + However. PIC simulations of e* shocks (Spitkovsky Arons 2005. private communication) show that the current inside a filament is tightly shielded by a reverse current flowing just outside the filament. 1.e.. opposite current filaments are tightly packed and most of the current flows near the edge.," However, PIC simulations of $e^\pm$ shocks (Spitkovsky Arons 2005, private communication) show that the current inside a filament is tightly shielded by a reverse current flowing just outside the filament, i.e., opposite current filaments are tightly packed and most of the current flows near the edge." + The shielding currents reduce the Lorentz attraction and slow the growth of the magnetic field correlation length via merging., The shielding currents reduce the Lorentz attraction and slow the growth of the magnetic field correlation length via merging. + Meanwhile. the filaments are susceptible to the instabilities independently of the shielding.," Meanwhile, the filaments are susceptible to the instabilities independently of the shielding." + Therefore. we expect the dynamics of single filaments to be governed by the instabilities.," Therefore, we expect the dynamics of single filaments to be governed by the instabilities." + In. particular. the instabilities may drive merging between the filament fragments in three dimensions.," In particular, the instabilities may drive merging between the filament fragments in three dimensions." +" The highest-resolution published simulations of cold shell collisions with two particle species by Frederiksenetal.(2004) show clear evidence for progressive bending and kinking of the ""proton"" Gn,/m,= 16) filaments (see their Fig.", The highest-resolution published simulations of cold shell collisions with two particle species by \citet{Frederiksen:04} show clear evidence for progressive bending and kinking of the “proton” $m_p/m_e=16$ ) filaments (see their Fig. + 2)., 2). + Similar mechanism was recently studied by Zenitant&Hoshino (2005)... who carried out two-dimensional PIC simulations of the relativistic drift-kink instability in. an infinite e* current sheet confined between reversed magnetic fields.," Similar mechanism was recently studied by \citet{Zenitani:05}, who carried out two-dimensional PIC simulations of the relativistic drift-kink instability in an infinite $e^\pm$ current sheet confined between reversed magnetic fields." + As the sheet bends in the direction perpendicular to the magnetic field. an alternating electric field is induced parallel to the sheet.," As the sheet bends in the direction perpendicular to the magnetic field, an alternating electric field is induced parallel to the sheet." + The authors compare the growth rates measured in the simulations with predictions from two-fluid theory and find good agreement for kA=0.7. where & is the wave number and À is the thickness of the current sheet.," The authors compare the growth rates measured in the simulations with predictions from two-fluid theory and find good agreement for $k\lambda\lesssim 0.7$, where $k$ is the wave number and $\lambda$ is the thickness of the current sheet." + They also find that in the nonlinear stage of the instability. the electric field becomes coherent in the central region of the current sheet. which accelerates particles and efficiently dissipates the magnetic energy energy.," They also find that in the nonlinear stage of the instability, the electric field becomes coherent in the central region of the current sheet, which accelerates particles and efficiently dissipates the magnetic energy energy." + If external shocks in. GRBs resemble the observed outcome of relativistic shell collisions in PIC simulations. the instability discussed here has implications for. the interpretation of the observed weak linear polarization of the afterglow.," If external shocks in GRBs resemble the observed outcome of relativistic shell collisions in PIC simulations, the instability discussed here has implications for the interpretation of the observed weak linear polarization of the afterglow." + The optical emission of GRB afterglows is linearly polarized at a level of a few percent. implying that the magnetic field in the emitting region is anisotropic.," The optical emission of GRB afterglows is linearly polarized at a level of a few percent, implying that the magnetic field in the emitting region is anisotropic." + There are two different forms of magnetic field anisotropy that can produce this polarization., There are two different forms of magnetic field anisotropy that can produce this polarization. + The first is a field parallel to the plane of the shock that is coherent on scales exceeding the plasma skin depth by many orders of magnitude (Gruzinov&Waxman1999;Granot2003).," The first is a field parallel to the plane of the shock that is coherent on scales exceeding the plasma skin depth by many orders of magnitude \citep{GruzinovWaxman:99,Granot:03}." +. The second is a combination of arandom magnetic field within the plane of the shock and a non-axisymmetric geometry of the emitting region (Gruzinov2003;Nakar.Piran.&WaxmanRossietal. 2004).," The second is a combination of a random magnetic field within the plane of the shock and a non-axisymmetric geometry of the emitting region \citep{Gruzinov:99,Sari:99,Ghisellini:99,GranotKonigl:03,Nakar:03,Rossi:04}." +. A coherent magnetic field within the plane of the shock is unlikely to be produced in the shock itself since there is no preferred direction within the plane of the shock., A coherent magnetic field within the plane of the shock is unlikely to be produced in the shock itself since there is no preferred direction within the plane of the shock. + Such field could in principle result by amplification of a pre-existing. ambient coherent magnetic field.," Such field could in principle result by amplification of a pre-existing, ambient coherent magnetic field." + This possibility. however. is implausible because the field in the medium into which the GRB ejecta plow is expected to be far too weak.," This possibility, however, is implausible because the field in the medium into which the GRB ejecta plow is expected to be far too weak." + The second possibility is that the coherence length of the magnetic field generated the shock grows rapidly., The second possibility is that the coherence length of the magnetic field generated the shock grows rapidly. + Since at any given time the observer sees many causally disconnected regions (Gruzinov&Waxman1999;NakarOren2004). the coherence length of the downstream magnetic field should grow at a rate close to the speed of light in order to produce a polarization at the level of a few percent.," Since at any given time the observer sees many causally disconnected regions \citep{GruzinovWaxman:99,Nakar:04}, the coherence length of the downstream magnetic field should grow at a rate close to the speed of light in order to produce a polarization at the level of a few percent." + We do not know of a mechanism that would facilitate such growth. especially given that the Alfvénn speed in the weakly magnetized relativistic downstream plasma is much smaller than the speed of light.," We do not know of a mechanism that would facilitate such growth, especially given that the Alfvénn speed in the weakly magnetized relativistic downstream plasma is much smaller than the speed of light." + An anisotropic field. but random within the plane of the shock. appears to be à much more appealing possibility because the shock breaks the isotropy and could in principle result in a different mean field strength in the parallel and the perpendicular direction.," An anisotropic field, but random within the plane of the shock, appears to be a much more appealing possibility because the shock breaks the isotropy and could in principle result in a different mean field strength in the parallel and the perpendicular direction." + In this case the level of polarization also depends on the degree to which the axisymmetry of the emitting region is broken., In this case the level of polarization also depends on the degree to which the axisymmetry of the emitting region is broken. + Assuming that the magnetic field lies entirely in the plane of the shock (1e.. B-= 0). and that the geometry of the emitting region is as expected during the jet-break in the light curve. the level of polarization is at most 20%—30% (Sart1999;Rossietal.2004) and in some scenarios it can be as small as a few percent.," Assuming that the magnetic field lies entirely in the plane of the shock (i.e., $B_z=0$ ), and that the geometry of the emitting region is as expected during the jet-break in the light curve, the level of polarization is at most $20\%-30\%$ \citep{Sari:99,Rossi:04} and in some scenarios it can be as small as a few percent." + If B-B. the polarization level is significantly reduced.," If $B_z \approx +B_{xy}$, the polarization level is significantly reduced." +" Therefore. the typical observed polarization of a few percent requires that either Bo2B..."," Therefore, the typical observed polarization of a few percent requires that either $B_z < B_{xy}/2$ or $B_z > 2B_{xy}$." + Even this minor difference between B- and δν. presents a theoretical challenge in view of our results. which suggest that B- arises quickly within the transition layer as the current filaments associated with the small-scale magnetic fields are effectively destroyed.," Even this minor difference between $B_z$ and $B_{xy}$ presents a theoretical challenge in view of our results, which suggest that $B_z$ arises quickly within the transition layer as the current filaments associated with the small-scale magnetic fields are effectively destroyed." + We speculate that the magnetic field quickly becomes isotropic in the rest frame of the shocked plasma., We speculate that the magnetic field quickly becomes isotropic in the rest frame of the shocked plasma. + We are indebted to GGoldreich and PPiran for comments and advice. and AArons and SSpitkovsky for many inspiring discussions and for sharing their numerical," We are indebted to Goldreich and Piran for comments and advice, and Arons and Spitkovsky for many inspiring discussions and for sharing their numerical" +use a power spectrum calculated using and the WMAP7+BAO+5SN Maximum Likelihood parameters from Komatsuetal.(2011)..,use a power spectrum calculated using and the WMAP7+BAO+SN Maximum Likelihood parameters from \cite{Komatsu2011n}. +" Using the halo mass function as a predictor of number densities of haloes n(M), we can construct a probability distribution function (pdf) for halo mass to be used in the calculation of the extreme value distribution outlined above: where the normalisation factor is the total (co-moving) number density of haloes."," Using the halo mass function as a predictor of number densities of haloes $n(M)$, we can construct a probability distribution function (pdf) for halo mass to be used in the calculation of the extreme value distribution outlined above: where the normalisation factor is the total (co-moving) number density of haloes." + For a constant redshift box of volume V the total number of expected haloes N is then given by Ίιοιν., For a constant redshift box of volume $V$ the total number of expected haloes $N$ is then given by $n_{\rm tot}V$. + These distributions can be inserted into equation (3)) to predict the pdf of the highest mass dark matter halo within the volume., These distributions can be inserted into equation \ref{eqn:evs:evs_exact}) ) to predict the pdf of the highest mass dark matter halo within the volume. + The form of halo mass distribution in and alternative cosmologies can also be examined; as an example of deviations from we include the effects of primordial non-Gaussianity., The form of halo mass distribution in and alternative cosmologies can also be examined; as an example of deviations from we include the effects of primordial non-Gaussianity. + The halo mass function has long been known to be sensitive to the presence of primordial non-Gaussianity (Lucchin&Matarrese1988) and these effects have been replicated within N-body simulations (Grossietal.2009;Pillepich2010)..," The halo mass function has long been known to be sensitive to the presence of primordial non-Gaussianity \citep{Lucchin1988a} and these effects have been replicated within N-body simulations \citep{Grossi2009, +Pillepich2010a}." +" We include non- into the model via the non-Gaussian correction factor (fxr) of LoVerdeetal.(2008) (LMSV): where $3 is the normalised skewness of the matter density field, for which we use the approximation: given by equation (2.7) of Enqvistetal.(2011)."," We include non-Gaussianity into the model via the non-Gaussian correction factor $\rnl$ of \cite{LoVerde2008} (LMSV): where $S_3$ is the normalised skewness of the matter density field, for which we use the approximation: given by equation (2.7) of \cite{Enqvist2011}." +". The choice of the LMSV version is motivated by Figure 1,, in which we plot three methods of including primordial non-Gaussianity in the halo mass function; the (fxr.) correction factors of LMSV and Matarreseetal.(2000) (MVJ) and the analytically applied non-Gaussianity of Maggiore&Riotto (MR), all applied to the fwr,=0 MR mass function."," The choice of the LMSV version is motivated by Figure \ref{fig:rnl_comp}, in which we plot three methods of including primordial non-Gaussianity in the halo mass function; the $\rnl$ correction factors of LMSV and \cite{Matarrese2000} (MVJ) and the analytically applied non-Gaussianity of \cite{Maggiore2010c} (MR), all applied to the $\fnl = 0$ MR mass function." +" As can be seen (and as observed by Enqvistetal.(2011) when applied to the Tinkeretal.(2008) mass function), the MVJ correction factor leads to a divergence in the mass function in the high-mass limit, which in this analysis we are still required to integrate over."," As can be seen (and as observed by \cite{Enqvist2011} when applied to the \cite{Tinker2008} mass function), the MVJ correction factor leads to a divergence in the mass function in the high-mass limit, which in this analysis we are still required to integrate over." +" By applying non-Gaussianity to the MR mass function we can explicitly see that it is the R(fni) factor which leads to this divergence, rather than the mass function itself."," By applying non-Gaussianity to the MR mass function we can explicitly see that it is the $\rnl$ factor which leads to this divergence, rather than the mass function itself." +" In order to evaluate the efficacy of this formulation of the extreme value statistics of the halo mass function, we compare the extreme value pdf calculated from (9--11)) to Monte Carlo simulations of the most massive halo in a universe with a given mass function."," In order to evaluate the efficacy of this formulation of the extreme value statistics of the halo mass function, we compare the extreme value pdf calculated from \ref{eqn:hmf_evs:evs_exact}- \ref{eqn:evs_exact:norm}) ) to Monte Carlo simulations of the most massive halo in a universe with a given mass function." +" In each cosmology, we construct an ensemble of realisations of the halo mass function; each realisation is constructed by calculating the expected number of haloes in a bin of width Alogm and drawing from a Poisson distribution with this mean."," In each cosmology, we construct an ensemble of realisations of the halo mass function; each realisation is constructed by calculating the expected number of haloes in a bin of width $\Delta \log m$ and drawing from a Poisson distribution with this mean." +" The drawn value is then taken as the number of haloes in this bin for this realisation, generating a mock catalogue of uncorrelated haloes in the volume V."," The drawn value is then taken as the number of haloes in this bin for this realisation, generating a mock catalogue of uncorrelated haloes in the volume $V$." + The largest cluster mass for the realisation is determined as the central value of the highest occupied bin (which is always singly occupied)., The largest cluster mass for the realisation is determined as the central value of the highest occupied bin (which is always singly occupied). + The distribution of highest-mass cluster in each catalogue is then recorded over 103 realisations., The distribution of highest-mass cluster in each catalogue is then recorded over $10^4$ realisations. + Figure 2. shows the results of the above procedure for the Sheth&Tormen(1999) mass function with WMAP7 cosmological parameters., Figure \ref{fig:hmf_dist} shows the results of the above procedure for the \cite{Sheth1999e} mass function with WMAP7 cosmological parameters. +" Plotted are Monte Carlo results with Poisson errors, the exact extreme value distribution calculated using (3)) and asymptotic Type-I (Gumbel) and GEV distributions fitted using a maximum likelihood method."," Plotted are Monte Carlo results with Poisson errors, the exact extreme value distribution calculated using \ref{eqn:evs:evs_exact}) ) and asymptotic Type-I (Gumbel) and GEV distributions fitted using a maximum likelihood method." + It can be seen that the predictions of the exact extreme value distribution (3)) well match the results of the Monte-Carlo simulations., It can be seen that the predictions of the exact extreme value distribution \ref{eqn:evs:evs_exact}) ) well match the results of the Monte-Carlo simulations. +" As can be expected, including the extra degree of freedom of the shape parameter y greatly improves the fit of the GEV distribution over the Type-I. Figure 3 shows the convergence of the shape parameter y for a variety of spherical volumes and values of the non-Gaussianity parameter fwr."," As can be expected, including the extra degree of freedom of the shape parameter $\gamma$ greatly improves the fit of the GEV distribution over the Type-I. Figure \ref{fig:convergence} shows the convergence of the shape parameter $\gamma$ for a variety of spherical volumes and values of the non-Gaussianity parameter $\fnl$." + Values of are estimated with a maximum likelihood method and error bars represent 9596 confidence intervals., Values of $\gamma$ are estimated with a maximum likelihood method and error bars represent $95\%$ confidence intervals. +" As can be seen, whilst the shape parameter appear well converged for volumes above r=30,, there is enough statistical noise so as to wash out any potential detection of fwr,<300 by using y as a test statistic, even in this simple case with uncorrelated haloes."," As can be seen, whilst the shape parameter appear well converged for volumes above $r\gtrsim30$, there is enough statistical noise so as to wash out any potential detection of $\fnl \lesssim 300$ by using $\gamma$ as a test statistic, even in this simple case with uncorrelated haloes." +" Davisetal.(2011) also consider the extreme value statistics of the halo mass function, forming the extreme value distribution as the differential of the void probability:"," \cite{Davis2011} also consider the extreme value statistics of the halo mass function, forming the extreme value distribution as the differential of the void probability:" +irrotational svstems (Urvu&Exiguchi1998).. and configurations that are stationary in the inertial frame (Urvi&Eriguehi1996).,"irrotational systems \citep{UE98}, and configurations that are stationary in the inertial frame \citep{UE96}." +. Our aim is to find à method by which a much wider class of nonaxisvunnetric configurations can be readily constructed., Our aim is to find a method by which a much wider class of nonaxisymmetric configurations can be readily constructed. + This will permit us to more Clearly understand the viability of evolutionary sequences of triaxial configurations ancl will provide models whose stability properties can be readily analvzec., This will permit us to more clearly understand the viability of evolutionary sequences of triaxial configurations and will provide models whose stability properties can be readily analyzed. + Previous linear stability. analvses (Chandrasekhar1969:Lifschitz&Lebovitz1993:Lebovitz&Lilschitz1996:Saldanha1999) have revealed a number of hyvdrodvnamical instabiliües (hat müght arise in incompressible Riemann ellipsoids. but no. corresponding nunmerical work using state-ol-the-art 3D hbvevodvuamic techniques has been carried out.," Previous linear stability analyses \citep{Ch69,LL93,LL96,LS99} have revealed a number of hydrodynamical instabilities that might arise in incompressible Riemann ellipsoids, but no corresponding numerical work using state-of-the-art 3D hydrodynamic techniques has been carried out." + In particular. Riemann S-tvpe ellipsoids have been found to be subject to a hvdrodynanmic strain instability. associated. with elliptical stveam lines (Lebovitz&Lilschitz1996).. which raises concerns about the stability of certain tvpes of geophivsical flows and leads to suspicions about the evolutionary path of stars that are driven by gravitational-radiation-reaction (GRR) forces toward the Dedekind-sequence.," In particular, Riemann S-type ellipsoids have been found to be subject to a hydrodynamic strain instability associated with elliptical stream lines \citep{LL96}, which raises concerns about the stability of certain types of geophysical flows and leads to suspicions about the evolutionary path of stars that are driven by gravitational-radiation-reaction (GRR) forces toward the Dedekind-sequence." + In a recent nonlinear study of the secular bar- instability induced by GRR (Ou.Tohline.&Lindblom2004).. a uniformly rotating. axisvmmeltrie neutron star. which was secularly unstable and driven by artifically enhanced GRR. evolved into a bar-like configuration with a verv slow pattern speed.," In a recent nonlinear study of the secular bar-mode instability induced by GRR \citep{OTL04}, a uniformly rotating, axisymmetric neutron star, which was secularly unstable and driven by artifically enhanced GRR, evolved into a bar-like configuration with a very slow pattern speed." + However. this special bar configuration became unstable to some kind of turbulence-like instability while evolving toward the Dedekind-secuence. (hat is. toward a stationary ellipsoidal structure in (he inertial fame maintained purely by (he internal motion of the [Iuid.," However, this special bar configuration became unstable to some kind of turbulence-like instability while evolving toward the Dedekind-sequence, that is, toward a stationary ellipsoidal structure in the inertial frame maintained purely by the internal motion of the fluid." + It is suspected that (his turbulence-like instability may be the elliptical strain instability identified in Che earlier linear stability analvses., It is suspected that this turbulence-like instability may be the elliptical strain instability identified in the earlier linear stability analyses. + But no clefinite conclusion ean be drawn because the stability of only one Dedekind-like configuration was studied., But no definite conclusion can be drawn because the stability of only one Dedekind-like configuration was studied. +" Following Ou.Tohline.&Lindblom(2004).. one might consiler generating additional ellipsoidal structures Lvdrodvnamically, but. the eeneration of each additional ellipsoidal model would be expensive in the sense (hal one has lo evolve an initially axisvmmetric model for a verv long time. even with artificially enhanced GRR (Shibata&Ixarimmo2004:Ou.Tohline.Lindblom2004)."," Following \cite{OTL04}, one might consider generating additional ellipsoidal structures hydrodynamically, but the generation of each additional ellipsoidal model would be expensive in the sense that one has to evolve an initially axisymmetric model for a very long time, even with artificially enhanced GRR \citep{SK04,OTL04}." +. This approach would make ib impractical to undertake a full stability investigation through the entire parameter space of ellipsoidal moclels., This approach would make it impractical to undertake a full stability investigation through the entire parameter space of ellipsoidal models. + lere we present a new 3D SCF technique that is capable of building the full range of incompressible Riemann S-(wpe ellipsoids with nontrivial internal flows (ie.. not just the uniformly rotating Jacobi configurations. which are thought to be the end point οἱ secularlv unstable stars driven by viscosity. ancl stationary Declekincl configurations) as well as compressible triaxial models that share the same clivergence-lree velocity lield as Riemann S-type ellipsoids.," Here we present a new 3D SCF technique that is capable of building the full range of incompressible Riemann S-type ellipsoids with nontrivial internal flows (i.e., not just the uniformly rotating Jacobi configurations, which are thought to be the end point of secularly unstable stars driven by viscosity, and stationary Dedekind configurations) as well as compressible triaxial models that share the same divergence-free velocity field as Riemann S-type ellipsoids." +" Our compressible models satisfy the steady-state Euler's equation exaclly, but only satisfy (he steady-state conlinuily equation approximately, hence {μον are only in quasi-equilibrium."," Our compressible models satisfy the steady-state Euler's equation exactly, but only satisfy the steady-state continuity equation approximately, hence they are only in quasi-equilibrium." + However. the violation of the steadi-state conlinuily equation is," However, the violation of the steady-state continuity equation is" +brighter (han this contribute to the whole-skv NRB and they conclude that the true resolved fraction may be 10 to higher.,brighter than this contribute to the whole-sky XRB and they conclude that the true resolved fraction may be 10 to higher. + Even though only ~20% of the counts in the HIEAO passband comes from photons with energies above 7hel. an unresolved component can still significantly affect the estimate of the bias.," Even though only $\sim 20\%$ of the counts in the HEAO passband comes from photons with energies above $7~keV$, an unresolved component can still significantly affect the estimate of the bias." + As a pessimistic case. we ignore the bright source correction and assume a 30%( unresolved component below 5hel.," As a pessimistic case, we ignore the bright source correction and assume a $30\%$ unresolved component below $5~keV$." + In this case roughly 1/3 of the 2-10 ΛΕΣ ARB is unresolved., In this case roughly $1/3$ of the 2-10 $keV$ XRB is unresolved. + If this unresolved component is distributed in reclshilt like the resolved component. then there is no change in the implied bias.," If this unresolved component is distributed in redshift like the resolved component, then there is no change in the implied bias." + On the other hand. if the unresolved component is entirely due to sources αἱ high redshift where it does nol contribute to the AC'F signal. then the implied bias will be 50% higher than our canonical value.," On the other hand, if the unresolved component is entirely due to sources at high redshift where it does not contribute to the ACF signal, then the implied bias will be $50\%$ higher than our canonical value." + If instead (he unresolved component is due to sources al low redshift. 2«I. then the implied bias will be 20% lower than our canonical value.," If instead the unresolved component is due to sources at low redshift, $z < 1$, then the implied bias will be $20\%$ lower than our canonical value." +" These fall somewhat outside our two ""extreme"" values in Table 1 and so provide a caveat to those estimates of the limits of svslenmatic error.", These fall somewhat outside our two “extreme” values in Table 1 and so provide a caveat to those estimates of the limits of systematic error. + Llowever. if only hall of the unresolved component is located at high (low) redshifts and the other half is distributed like the resolved component. then (he implied bias is only 20% (11%) higher (lower) than our canonical value. well within the limits of Table 1.," However, if only half of the unresolved component is located at high (low) redshifts and the other half is distributed like the resolved component, then the implied bias is only $20\%$ $11\%$ ) higher (lower) than our canonical value, well within the limits of Table 1." +" It is difficult to quantily all possible systematic errors: however. considering that the above ""extremes result in errors of the same order as the statistical error in the fit. we conclude (hat the total svstematic error 15 no larger than the statistical error quoted."," It is difficult to quantify all possible systematic errors; however, considering that the above “extremes” result in errors of the same order as the statistical error in the fit, we conclude that the total systematic error is no larger than the statistical error quoted." + We have determined the X-ray bias of the hard NIB assuming it is time (i.e.. reclshilt) and scale independent.," We have determined the X-ray bias of the hard XRB assuming it is time (i.e., redshift) and scale independent." + These assumptions are probably equite reasonable since the mean redshift weighting of the X-ray ACF is quite low. z& 0.1. and the linear scales probed. by the ACF are quite large (LOApe to 200M pe).," These assumptions are probably quite reasonable since the mean redshift weighting of the X-ray ACF is quite low, $z \sim 0.1$ , and the linear scales probed by the ACF are quite large $10~Mpc$ to $200~Mpc$ )." +" Even if these assumptions are violated to some extent. 6, can still be interpreted as an ‘average N-ray. bias."," Even if these assumptions are violated to some extent, $b_x$ can still be interpreted as an `average' X-ray bias." + There are several (vpes of sources (hat contribute to the NRB. including quasars. Sevlert ealaxies. LINERS. and clusters of galaxies. and the implied value of the bias must be considered to be an average over all these sources.," There are several types of sources that contribute to the XRB, including quasars, Seyfert galaxies, LINERS, and clusters of galaxies, and the implied value of the bias must be considered to be an average over all these sources." + However. the dominant contribution to the XRD is most likely to be moderately active AGN (Cowie et al.," However, the dominant contribution to the XRB is most likely to be moderately active AGN (Cowie et al." +" 2003). so 6, should be representative of the bulk of the sources of (he XRB."," 2003), so $b_x$ should be representative of the bulk of the sources of the XRB." +" With these caveats in mind. we find an X-ray bias of bP=1.120.338. i.e.. b,=10640.16 (statistical error only)."," With these caveats in mind, we find an X-ray bias of $b_x^2 = 1.12 \pm 0.33$, i.e., $b_x = 1.06 \pm 0.16$ (statistical error only)." + This error includes photon shot noise. fluctuations in the NRB [from beam smearing. and the clustering of the XRD itself.," This error includes photon shot noise, fluctuations in the XRB from beam smearing, and the clustering of the XRB itself." +" The fits of 6, for two extreme models ol dI/dz indicate that the uncertainty due to our ignorance of (he X-ray luminosity function is likely less (han the statistical error.", The fits of $b_x$ for two extreme models of $dI/dz$ indicate that the uncertainty due to our ignorance of the X-ray luminosity function is likely less than the statistical error. + Otherpossible sources of svstematic error also seem, Otherpossible sources of systematic error also seem +1n acidiion to obvious changes in the swing. it is remarkae hat it also changes in absolute PA value.,"In addition to obvious changes in the swing, it is remarkable that it also changes in absolute PA value." + This is notae Ν΄ conixuwing the separation of the PA values measured al cilleren davs and relating this to the fixed offset introcuced o the N curves and. visible in the ALP plots., This is notable by comparing the separation of the PA values measured at different days and relating this to the fixed offset introduced to the PA curves and visible in the MP plots. + As the SX swings in the MP? components agree perfectly as shown above. his variation in absolute PA is clearly intrinsic lo he source.," As the PA swings in the MP components agree perfectly as shown above, this variation in absolute PA is clearly intrinsic to the source." + A possible explanation for this effect is obtained when οςnsidering the existence of polarization modes., A possible explanation for this effect is obtained when considering the existence of polarization modes. + τι radio pulsars are known to exhibi linear »olarisation moces which are typically orthogonal to each other., Normal radio pulsars are known to exhibit linear polarisation modes which are typically orthogonal to each other. + The origin of these so-called: orthogona modes (c.g. Backer ct al., The origin of these so-called orthogonal modes (e.g. Backer et al. + is »olieved to be related to moce-separating birefringence effects in the pulsar magnetosphere (Mcelxinnon 1997. Petrova Simultaneous multi- observations found (Ixarastergiou et al.," \nocite{brc76} is believed to be related to mode-separating birefringence effects in the pulsar magnetosphere (McKinnon 1997, Petrova \nocite{mck97,pet01} Simultaneous multi-frequency observations found (Karastergiou et al." + that here is a high degree of correlation between the polarization mocles at two cillerent [recuencies., \nocite{kkj+02} that there is a high degree of correlation between the polarization modes at two different frequencies. + Thev also found. that ho moles occur more equally. towards higher freuencies. orovidirig some explanation or the de-polarization of pulsar emission al hich [recuencies. as overlapping orthogonal mocles |ead to a lower average degree of polarization.," They also found that the modes occur more equally towards higher frequencies, providing some explanation for the de-polarization of pulsar emission at high frequencies, as overlapping orthogonal modes lead to a lower average degree of polarization." + The extremely high. degree of polarization seen at all pecquencies for would suggest that cillerent orthogonal modes. should. not be present as thev often cack to a de-polarization of the average pulse. profiles (Mcelxinnon 1997. ]xarastergiou et al.," The extremely high degree of polarization seen at all frequencies for would suggest that different orthogonal modes should not be present as they often lead to a de-polarization of the average pulse profiles (McKinnon 1997, Karastergiou et al." + 2002)., 2002). + In. order to verily this «xpectation. we studied the disribution of PAs or each phise bin.," In order to verify this expectation, we studied the distribution of PAs for each phase bin." + To avoid spurious contributions. we onlv registered. those signals where both the total and linear intensity Wweve 6 times stronger than the corresponding oll-»ulse RAIS.," To avoid spurious contributions, we only registered those signals where both the total and linear intensity were 6 times stronger than the corresponding off-pulse RMS." + The resultant PA histograms for three e»ochs are plotted in Figure 9 where we concentrate on the highest S/N data. ie. frequencies of 4.9 Gllz and 8.4 Giz.," The resultant PA histograms for three epochs are plotted in Figure \ref{fig:pahist} + where we concentrate on the highest S/N data, i.e. frequencies of 4.9 GHz and 8.4 GHz." + For each epoch and frequency. we show two PA ots.," For each epoch and frequency, we show two PA plots." + The bottom. plot. shows a scatter. plot. indicating simply the measured. PA values. irrespective of the frequeney of OCCUurrence.," The bottom plot shows a scatter plot, indicating simply the measured PA values, irrespective of the frequency of occurrence." + The middle plot. shows instead. how ofiCh et particular A value was measured. per phase bin. using a grav-scalc| plot.," The middle plot shows instead how often a particular PA value was measured per phase bin, using a gray-scale plot." + The darkest regions mark the highest OCCUrPrences of PA., The darkest regions mark the highest occurrences of PA. + The AIP and HP regions were scaled independenIv. so that the darkest shades of &ray correspond lo the niosU frequently measured PAs in. cach region respectively.," The MP and IP regions were scaled independently, so that the darkest shades of gray correspond to the most frequently measured PAs in each region respectively." + 1n the ustogram for session 1 at 8.4 Cillz. one can see two well sexwaled. regions of highly. populated. PA values indicating he existence. of two polarization modes.," In the histogram for session 1 at 8.4 GHz, one can see two well separated regions of highly populated PA values indicating the existence of two polarization modes." + “The, The +mean relation towards redder colours and/or fainter brightnesses (seetig.2inPriceetal.2009).,"mean relation towards redder colours and/or fainter brightnesses \citep[see fig.\,2 in][]{P09}." +. Coma's cEs have age and abundances estimations., Coma's cEs have age and abundances estimations. + All three galaxies are coeval within the age estimation errors., All three galaxies are coeval within the age estimation errors. + CeGV9a and CeGV|I9b present similar. (7I) colours. and. similar [Fe/H] and [Mg/Fe] abundances. while CeGVI9a is the reddest cE galaxy in the association. with the highest [Fe/H] and [Mg/Fe] values.," CcGV9a and CcGV19b present similar $(B-I)$ colours, and similar [Fe/H] and [Mg/Fe] abundances, while CcGV19a is the reddest cE galaxy in the association, with the highest [Fe/H] and [Mg/Fe] values." + Therefore. the different locations of these three cEs in the colour-magnitude diagram can be explained through abundance differences and/or luminosity fading.," Therefore, the different locations of these three cEs in the colour–magnitude diagram can be explained through abundance differences and/or luminosity fading." + In this context it is interesting to point out that Faber(1973) noticed that and that these objectsellipticals., In this context it is interesting to point out that \citet{Faber73} noticed that and that these objects. + Moreover. Faber considered that these systemsgalaxies.," Moreover, Faber considered that these systems." + Given the universality of the CMR in clusters of galaxies. if the increase in the scatter at low luminosities has a physical origin. it should be observed at the same absolute magnitude in all cases.," Given the universality of the CMR in clusters of galaxies, if the increase in the scatter at low luminosities has a physical origin, it should be observed at the same absolute magnitude in all cases." + Seckeretal.(1997) have obtained a CMR for the Coma cluster with a scatter that increases faintwards from /?7-—19.5 mag. corresponding to Mj;=—15.5 mmag with a distance modulus (mAl)=35.," \citet{S97} have obtained a CMR for the Coma cluster with a scatter that increases faintwards from $R\simeq 19.5$ mag, corresponding to $M_R=-15.5$ mag with a distance modulus $(m-M)=35$." + In the Perseus cluster. the scatter increases significantly at Ale=—15 mag (seefig.3inPenny 2008).," In the Perseus cluster, the scatter increases significantly at $M_B=-15$ mag \citep[see fig. 3 in][]{PC08}." +. By meansof the transformations given by Fukugita (1995). this is equivalent to 3j;=—16.6 mag.," By meansof the transformations given by \citet{F95}, this is equivalent to $M_R=-16.6$ mag." + In Fornax. Hilkeretal.(2003). and Mieskeetal.(2007) have found an increase of the CMR scatter at Aio12.5 mag or Ady=13.1 mag.," In Fornax, \citet{H03} and \citet{M07} have found an increase of the CMR scatter at $M_V\simeq-12.5$ mag or $M_R\simeq-13.1$ mag." + In Hydra. the increase in the scatter is significant from Ady—14 mag (fig.10inMisgeldetal.2008) or Adyc14.60 mag.," In Hydra, the increase in the scatter is significant from $M_V\simeq-14$ mag \citep[fig. 10 in][]{M08} or $M_R\simeq-14.6$ mag." + In Centaurus. from Adyo.13 mag or My&3.6 mag (fig.3inMisgeldetal. 2009).," In Centaurus, from $M_V\simeq-13$ mag or $M_R\simeq-13.6$ mag \citep[fig. 3 in][]{M09}." +". In Virgo. the peak of the dispersion is found at A,=lY mag which is equivalent to Aly;~17.5 mag."," In Virgo, the peak of the dispersion is found at $M_r=-17$ mag which is equivalent to $M_R\sim-17.3$ mag." + In our case. the faintest Antlia confirmed members and candidates introduce a detectable dispersion increase starting from 15 mag.," In our case, the faintest Antlia confirmed members and candidates introduce a detectable dispersion increase starting from $M_R\sim-15$ mag." + Therefore. in all these clusters. the increase of the scatter starts different absolute magnitudes. which tend to be brighter for more distant clusters. if Virgo is excluded from the sample.," Therefore, in all these clusters, the increase of the scatter starts at different absolute magnitudes, which tend to be brighter for more distant clusters, if Virgo is excluded from the sample." + This rend could be interpreted as a diminishing of the precision of the johotometrie data and a more uncertain morphological/membership classification as we go to more distant clusters., This trend could be interpreted as a diminishing of the precision of the photometric data and a more uncertain morphological/membership classification as we go to more distant clusters. +" From the analysis performed in 5.1.3... it might be inferred hat. once photometric errors are discounted. different CMRs obtained using metallicity sensitive colours. like (οἱ74) and (D2). display fairly low intrinsic dispersions ἔσιο4,<08 mmag)."," From the analysis performed in \ref{s.CMRA}, it might be inferred that, once photometric errors are discounted, different CMRs obtained using metallicity sensitive colours, like $(C-T_1)$ and $(B-R)$, display fairly low intrinsic dispersions $\sigma_{(C-T_1)}<0.08$ mag)." + Several processes have been proposed as responsible for the intrinsic scatter of the relation (e.g. differences in ages. Terlevichetal. 1999.. Ferreras&Silk 2003.. Romeoetal. 2008: minor mergers. Kavirajetal.2009:: accretion of small amounts of gas at high redshifts. Pipino&Matteucci 2006)).," Several processes have been proposed as responsible for the intrinsic scatter of the relation (e.g., differences in ages, \citealp{TK99}, \citealp{F03}, \citealp{R08}; minor mergers, \citealp{K09}; accretion of small amounts of gas at high redshifts, \citealp{PM06}) )." + Whatever the process dominating the intrinsic scatter is. from our comparison we could say that it arises with similar strength in different clusters.," Whatever the process dominating the intrinsic scatter is, from our comparison we could say that it arises with similar strength in different clusters." + In this sense. Jafféetal.(2011). have found a colour scatter with no evolution with redshift or correlation with the velocity dispersions of the clusters included in their analysis.," In this sense, \citet{J11} have found a colour scatter with no evolution with redshift or correlation with the velocity dispersions of the clusters included in their analysis." + As it was shown in refmueff.. in a plot of 7) magnitude versus(ruc). FS9O early-type dwarf members of Antlia follow the locus of constant effective radius of| kpe down to 7)~18 mag.," As it was shown in \\ref{mueff}, in a plot of $T_1$ magnitude versus$\langle\mu_{\rm eff}\rangle$, FS90 early-type dwarf members of Antlia follow the locus of constant effective radius of1 kpc down to $T_1 \sim 18$ mag." + Fainter F590 members tend to deviate from this locus towards smaller radii., Fainter FS90 members tend to deviate from this locus towards smaller radii. +" All of the new dwarf galaxy members. which have luminosities fainter than Ti,=IS mag. show the same behaviour."," All of the new dwarf galaxy members, which have luminosities fainter than $T_1=18$ mag, show the same behaviour." + The mean effective radius of the contirmed members with 7;o>LS mag is (rac)=0.58 (rms 0.26) kpe., The mean effective radius of the confirmed members with $T_1>18$ mag is $\langle r_{\rm eff}\rangle=0.58$ (rms 0.26) kpc. + Therefore. there seems to be a faint limit in magnitude for the constant effective radius relation followed by dEs.," Therefore, there seems to be a faint limit in magnitude for the constant effective radius relation followed by dEs." + We have already mentioned that this could be due to the isophotal limit of our photometry., We have already mentioned that this could be due to the isophotal limit of our photometry. + It is possible that we are not reaching the most external regions of the galaxies as they are embedded in the background., It is possible that we are not reaching the most external regions of the galaxies as they are embedded in the background. + Many of these faint objects are located near brighter galaxies as well., Many of these faint objects are located near brighter galaxies as well. +" In this way. our effective radius could be underestimated for galaxies fainter than 71.~15 mag (AA~14.1 mag. Fukugitaetal.19959). leading to the apparent discontinuity or ""break"" in this relation."," In this way, our effective radius could be underestimated for galaxies fainter than $T_1\sim18$ mag $M_V\sim-14.1$ mag, \citealp{F95}) ), leading to the apparent discontinuity or “break” in this relation." + However. Chiboucas.Karachentsev&Tully(2009). have ound that newly discovered dwarf galaxies in the M8! Group (D=3.6 Mpc). have effective radii in agreement to those found or the new dwarf galaxies in Antlia. Le. 74r0.5 kpe (see heir table 3).," However, \citet*{Chi09} have found that newly discovered dwarf galaxies in the M81 Group $D=3.6$ Mpc), have effective radii in agreement to those found for the new dwarf galaxies in Antlia, i.e. $r_{\rm eff}\lesssim 0.5$ kpc (see their table 3)." + Local Group dSphs have rap&0.5 Kpe. as well (Zaritsky.González&Zabludoff2006.. and references therein).," Local Group dSphs have $r_{\rm eff}\lesssim 0.5$ kpc, as well \citealp*{Za06}, and references therein)." + Cellone&Buzzoni(2005) as well as DeRijckeetal.(2009) ound a similar trend to our faint break. in their respective samples of dwarf galaxies.," \citet{CB05} as well as \citet{deRij09} found a similar trend to our faint break, in their respective samples of dwarf galaxies." + Therefore. we cannot rule out the possibility that he luminosity vs. (feu) relation. corresponding to a mean constant effective radius of ~1 kpc. presents two physical breaks: one at magnitudes brighter than Aj;~20 mag. and another at its faint end. at magnitudes fainter than Aj;—1H mag.," Therefore, we cannot rule out the possibility that the luminosity vs. $\langle\mu_{\rm eff}\rangle$ relation, corresponding to a mean constant effective radius of $\sim 1$ kpc, presents two physical breaks: one at magnitudes brighter than $M_R\sim-20$ mag, and another at its faint end, at magnitudes fainter than $M_R\sim-14$ mag." + We recall that the correlation between luminosity and μοι)— for magnitudes brighter han Ady~30 mag corresponds to the Kormendy(1977b) scaling relation detined by bright Es and bulges of S galaxies on he rjr vs. feu diagram., We recall that the correlation between luminosity and $\langle\mu_{\rm eff}\rangle$ for magnitudes brighter than $M_R\sim-20$ mag corresponds to the \citet{K77b} scaling relation defined by bright Es and bulges of S galaxies on the $\rm r_{eff}$ vs. $\mu_{\rm eff}$ diagram. + This is a projection of the Fundamental Plane of E galaxies., This is a projection of the Fundamental Plane of E galaxies. + As mentioned above in this section. most of the galaxies “unter than the low luminosity break are located near brighter ones.," As mentioned above in this section, most of the galaxies fainter than the low luminosity break are located near brighter ones." + The smaller reir found in our faint candidates might then be related with tidal effects., The smaller $r_{\rm eff}$ found in our faint candidates might then be related with tidal effects. + The newly confirmed cE galaxies deviate from the locus followed by the rest of early-type dwarfs of similar luminosities towards smaller effective radii. as well.," The newly confirmed cE galaxies deviate from the locus followed by the rest of early-type dwarfs of similar luminosities towards smaller effective radii, as well." + They are companions of the giant ellipticals that dominate the central region of the cluster., They are companions of the giant ellipticals that dominate the central region of the cluster. + In PaperIN we showed that one of them. 1110. displays a low surface brightness bridge that links it with 33258. confirming the existence of an interaction between both galaxies.," In II we showed that one of them, 110, displays a low surface brightness bridge that links it with 3258, confirming the existence of an interaction between both galaxies." + Surface brightness profiles displaying a break. as is the case of 1110 (see ITI) would favour this interpretation (Choietal.2002:Mieske ," Surface brightness profiles displaying a break, as is the case of 110 (see II) would favour this interpretation \citep{choi02,MJ06}. ." +"2006).. Graham&Guzmán(2003) have argued that. with the exception of the very bright galaxies CM 20.5. AA 21.5. Le. ""core"" E). the break at the bright end of the luminosity versus (feu relation is not due to different formation mechanisms among dwarf and bright E galaxies."," \citet{Graham03} have argued that, with the exception of the very bright galaxies $M_B\lesssim-20.5$ , $M_V\lesssim-21.5$ , i.e. “core” E), the break at the bright end of the luminosity versus $\langle\mu_{\rm eff}\rangle$ relation is not due to different formation mechanisms among dwarf and bright E galaxies." + They emphasize that both type of galaxies display continuous trends in the central surface brightness (75) versus luminosity plot. and in the Sérrsic index (Sérsic1968) ," They emphasize that both type of galaxies display continuous trends in the central surface brightness $\mu_0$ ) versus luminosity plot, and in the $n$ Sérrsic index \citep{S68} " +Alaking use of Eqs. (25)). (26)),"Making use of Eqs. \ref{eq:polo}) ), \ref{eq:rez}) )" + ancl (30)). we obtain Next. we write the particle specific energy. (leq. 13))," and \ref{eq:cont}) ), we obtain Next, we write the particle specific energy (Eq. \ref{eq:spenergy}) )" + using the cdimensionless radius and the spin parameter., using the dimensionless radius and the spin parameter. +" Then. we substitute this equation. (evaluated at ry, and Fas, respectively) together with (18)) (27)). (30)) and (31)) for Eq. (172)."," Then, we substitute this equation (evaluated at $r_{\mathrm{sl}_*}$ and $r_{\mathrm{ms}_*}$ , respectively) together with \ref{eq:omegaH}) ) – \ref{eq:magn}) ), \ref{eq:cont}) ) and \ref{dRdr}) ) for Eq. \ref{eq:jetspow}) )." + So. the launching power of the jets becomes where consider the strength. of the magnetic field in Eq. (82))," So, the launching power of the jets becomes where For the following calculations, we consider the strength of the magnetic field in Eq. \ref{eq:jets}) )" + to be as high as its maximum value By~Dg., to be as high as its maximum value $B_{H} \sim B_{\mathrm{H}}^{\mathrm{max}}$. + On the right-hand. side. the first term represents the accretion. power of the dise inside the DII ergosphere and the second. term represents the 111 spin-down powertransferred to the disc by magnetic connection.," On the right-hand side, the first term represents the accretion power of the disc inside the BH ergosphere and the second term represents the BH spin-down powertransferred to the disc by magnetic connection." + So. Eq. (32))," So, Eq. \ref{eq:jets}) )" + can also reac: In Fig. 4.0," can also read: In Fig. \ref{PjetsVsMdot}," + we plot the launching power of the jets as a [function of the mass accretion rate., we plot the launching power of the jets as a function of the mass accretion rate. + The plot shows that a transition from an accretion power regime to a spin-down power regime is produced for mz10*, The plot shows that a transition from an accretion power regime to a spin-down power regime is produced for $\dot{m} \simeq 10^{-1.8}$. + So. we have: (1) an accretion. power regime. in. which. case m.10LN and the dominating term in the launching power of the jets is PAL. and (2) a spin-down power regime in which case ii«10.7 and the dominating term in the launching power of the jets is DET.," So, we have: (1) an accretion power regime in which case $\dot{m} > 10^{-1.8}$ and the dominating term in the launching power of the jets is $P_{\mathrm{jets}}^{\mathrm{acc}}$, and (2) a spin-down power regime in which case $\dot{m} < 10^{-1.8}$ and the dominating term in the launching power of the jets is $P_{\mathrm{jets}}^{\mathrm{rot}}$ ." + In Eq. (32)).," In Eq. \ref{eq:jets}) )," + the launching power of the jets depends on: (i) the mass accretion rate m. Gi) the DII mass AM. (iil) the DII spin parameter αν. (iv) the power-law index n. and (v) the ratio of the magnetic field strengths ο.," the launching power of the jets depends on: (i) the mass accretion rate $\dot{m}$, (ii) the BH mass $M$, (iii) the BH spin parameter $a_*$, (iv) the power-law index n, and (v) the ratio of the magnetic field strengths $\zeta$." + We chose the last two parameters as follows: the power-law index η is taken to be 72 as for a frozen magnetic field (?).. and & is set by taking its value corresponding to the maximum of the launching power of the jet. which is one.," We chose the last two parameters as follows: the power-law index $n$ is taken to be `2' as for a frozen magnetic field \citep{alfven}, , and $\zeta$ is set by taking its value corresponding to the maximum of the launching power of the jet, which is one." + Fherefore. for the following calculations. we consider η=2ancd¢1.," Therefore, for the following calculations, we consider $n = 2 \: \textrm{and} \,\zeta=1$." + In Fig. 5..," In Fig. \ref{fig:Pjets}," + we plot the launching power of the jets as à function of the DII spin parameter. for a BIL mass of 10A7.. given four values of the mass aceretion rate (ini=1.0.5.0.1and0.01). as well as the DEI spin-down power contribution to the jets power (bottom curve).," we plot the launching power of the jets as a function of the BH spin parameter, for a BH mass of $10^{9} M_{\odot}$, given four values of the mass accretion rate $(\dot{m}=1, 0.5, 0.1\,\textrm{and}\, 0.01)$, as well as the BH spin-down power contribution to the jets power (bottom curve)." + Since the area of the disc inside the ergosphere increases with an increase of (ets. there is à dominating trend of the jet power to increase as well. except for αν close to the maximal value and 5j20.1 where the turn-over of the curve is. produced. due to the general relativistic factor that appears in the term (1.—d.) of the accretion power.," Since the area of the disc inside the ergosphere increases with an increase of $a_*$, there is a dominating trend of the jet power to increase as well, except for $a_*$ close to the maximal value and $\dot{m} > 0.1$ where the turn-over of the curve is produced due to the general relativistic factor that appears in the term $(1-q_{\mathrm{jets}})$ of the accretion power." + In the case of the spin-downpower regime. the jet power is ~107 erg to which is only LO7 of the Eddington luminosity of a 10 solar mass DIL.," In the case of the spin-downpower regime, the jet power is $\sim 10^{45}$ erg $^{-1}$, which is only $10^{-2}$ of the Eddington luminosity of a $10^{9}$ solar mass BH." +" ‘This value of P7 is comparable to the maximum rate of energy extraction by the Blandford.Znajek mechanism. which is ~107 eres 1 fora Bll mass of 10AZ. and a, close to the maximal value Eq."," This value of $P_{\mathrm{jets}}^{\mathrm{rot}}$ is comparable to the maximum rate of energy extraction by the Blandford–Znajek mechanism, which is $\sim 10^{45}$ erg $^{-1}$ for a BH mass of $10^{9} M_{\odot}$ and $a_*$ close to the maximal value [Eq." + 4.50 of ?]]., 4.50 of \citet{membrane}] ]. + For a lower mass of the BIL. the jet power decreases. as the launching power of the jets is proportional to the DII mass.," For a lower mass of the BH, the jet power decreases, as the launching power of the jets is proportional to the BH mass." + On sub-parsec scales. the jets are. likely to. be ominated by electromagnetic: processes. (MIID. or. pure lectrodynamic). where the energv is. transported. along thejets via. Povnting flux. andare potentially unstable if significant thermal mass load is present. (?)..," On sub-parsec scales, the jets are likely to be dominated by electromagnetic processes (MHD or pure electrodynamic), where the energy is transported along thejets via Poynting flux, andare potentially unstable if significant thermal mass load is present \citep{meier03}. ." + Next. we stimate the magnetization parameter of the jet. plasmaat 1¢ launching points. o. which reflects the effect ofà rotating," Next, we estimate the magnetization parameter of the jet plasmaat the launching points, $\sigma$ , which reflects the effect of a rotating" +scalines show that the Mach umber of the flow iucreases as the radius decreases.,scalings show that the Mach number of the flow increases as the radius decreases. + At p. the Mach iuuber is Therefore. there is a critical radius at which the flow would make a sonic transition: FT1H The key phyvsies which determines the nature of the cooling flow to accretion flow transition is whetherFuZod'nur OY MySSgage ," At $r_o$, the Mach number is Therefore, there is a critical radius at which the flow would make a sonic transition: r. The key physics which determines the nature of the cooling flow to accretion flow transition is whether$\rt \gsim \rc$ or $\rt \lsim + \rc$." +That is. is the radius where the gravitational influence of the black hole becomes iuportant inside or outside of the radius where. in the absence of the point mass. the cooling flow would have its sonic point?," That is, is the radius where the gravitational influence of the black hole becomes important inside or outside of the radius where, in the absence of the point mass, the cooling flow would have its sonic point?" + [frySrear the cooling flow is oblivious to the existence of the point amass., If $\rt \lsim \rc$ the cooling flow is oblivious to the existence of the point mass. + It undergocs its sonic transition with little modification because of the black hole., It undergoes its sonic transition with little modification because of the black hole. + Iuside of the sonic poiut. the gas quickly cools towards zero temperature.," Inside of the sonic point, the gas quickly cools towards zero temperature." + The reason is that in the supersonic zoue a cooling flow ina logarithuiuc potential has οx[luisTE2 idl poxortet—p7.," The reason is that in the supersonic zone a cooling flow ina logarithmic potential has $v \propto [\ln(r_s/r)]^{1/2}$ and $\rho \propto r^{-2} v^{-1} \sim + r^{-2}$." + The velocity (density) therefore rises more slowly (quickly) with decreasing radius than iu the subsonic zone. where the cooliug time was of order the inflow time.," The velocity (density) therefore rises more slowly (quickly) with decreasing radius than in the subsonic zone, where the cooling time was of order the inflow time." + Consequently. in the supersonic zone the cooling time becomes much shorter than the inflow time and the gas cools rapidly (sec. e.g.. Fig.," Consequently, in the supersonic zone the cooling time becomes much shorter than the inflow time and the gas cools rapidly (see, e.g., Fig." + 1 of Sarazin White 1987)., 4 of Sarazin White 1987). + In this case. a simple cooling flow to accretion How transition is not possible.," In this case, a simple cooling flow to accretion flow transition is not possible." + Whether such a cooling How is an miportaut source of mass for an accretion flow depends critically on the fate of the rapidly cooling matter inside the sonic point (e.e.. does it forma stars which lose nass to feed the ceutral black hole?).," Whether such a cooling flow is an important source of mass for an accretion flow depends critically on the fate of the rapidly cooling matter inside the sonic point (e.g., does it form stars which lose mass to feed the central black hole?)." +" For M87. rg,20.15 kpe: this is comparable to reir if q=0."," For M87, $\rt \approx 0.15$ kpc; this is comparable to $\rc$ if $q = + 0$." +" Many other observed cooling flows have AL,xm10AM.vr (AISTs value) aud would have rig29rng d q were equal to 0.", Many other observed cooling flows have $\md \ \gg 10 \ \mpy$ (M87's value) and would have $\rc \gg \rt$ if $q$ were equal to $0$. + Significant mass drop out is. however. eoncrally interred iu such cooling flows (for MBST. q220.6 is appropriate: see low).," Significant mass drop out is, however, generally inferred in such cooling flows (for M87, $q \approx 0.6$ is appropriate; see below)." + From equation (3)) it follows that ifg~1 the Mach πο of the cooling flow is roughly constant., From equation \ref{scaling}) ) it follows that if $q \sim 1$ the Mach number of the cooling flow is roughly constant. + This insures that the eas remains subsonic down o the radius where the poteutial of the black hole beeius ο dominate the potential of the galaxy (16. ryeE reg).," This insures that the gas remains subsonic down to the radius where the potential of the black hole begins to dominate the potential of the galaxy (i.e., $\rt \gsim \rc$ )." + We now turn our attention to this reeime., We now turn our attention to this regime. +" There is one conceptual complication iu wuderstanding he cooling flow to accretion flow structure in the reeime where my,Ereir.", There is one conceptual complication in understanding the cooling flow to accretion flow structure in the regime where $\rt \gsim \rc$. +" Natucly, in the point mass potential (Le. for rr« rg). there are two viable analytical solutions o equations (2))-(2))."," Namely, in the point mass potential (i.e., for $r \ll \rt$ ), there are two viable analytical solutions to equations \ref{mdot}) \ref{energy}) )." + Oue is Dondi's adiabatic spherical accretion solution (Boudi 1952)., One is Bondi's adiabatic spherical accretion solution (Bondi 1952). + The other (valid ouly for ~c 11/7) is a cooliug flow solution (cf Fabian Nulsen ---1977) which: has e22ν topxrm aud coxor1," The other (valid only for $\gamma > + 11/7$ ) is a cooling flow solution (cf Fabian Nulsen 1977) which has $c_s^2 \propto r^{-1}$, $\rho \propto r^{-7/4}$ and $v \propto + r^{-1/4}$." + Tt is. not obvious which of these solutions the cooling flow at large radii (iu the ealaxys logaxitlhuuie potential) will match onto at small radii., It is not obvious which of these solutions the cooling flow at large radii (in the galaxy's logarithmic potential) will match onto at small radii. + Oue melt iu fact suspect. ou the basis of “continuity” arguneuts. that the cooling flow at large radii would match outo a cooling flow at snall radi.," One might in fact suspect, on the basis of “continuity” arguments, that the cooling flow at large radii would match onto a cooling flow at small radii." + Our caleulatious indicate. however. that this is not so.," Our calculations indicate, however, that this is not so." + The reason is simply that there is nofremsomic cooling flow solution in the r.1 poteutial, The reason is simply that there is no cooling flow solution in the $r^{-1}$ potential. +" The Mach umuber of tle cooling flow solution in a poiut mass potential decreases with decreasing radius as rt/t: this solution cannot be matched to a sonic transition even with the introduction of a singularity iuto the poiut mass problem via the 1/(r.—ry) We have checked this carefully by απλοήσαν searching the AT, and rs. space: we find that there is no ταδολ] cooling flow solution for r«rg.", The Mach number of the cooling flow solution in a point mass potential decreases with decreasing radius as $r^{1/4}$; this solution cannot be matched to a sonic transition even with the introduction of a singularity into the point mass problem via the $1/(r-r_g)$ We have checked this carefully by numerically searching the $\md$ and $r_s$ space; we find that there is no transonic cooling flow solution for $r < \rt$. + The upshot of this analysis is that the cooling flow makes a smooth transition to a nearly adiabatie Doudi flow iu the vicinity of πε., The upshot of this analysis is that the cooling flow makes a smooth transition to a nearly adiabatic Bondi flow in the vicinity of $\rt$. + This provides a direct. dynamical link between the cooling flow aud the accretion flow outo the central black hole., This provides a direct dynamical link between the cooling flow and the accretion flow onto the central black hole. + The details of the flow structure near rg are shown iu Figure 1l. where we plot the temperature. deusitv. Mach iuuber. aud the ratio of the cooling time to the inflow ine for models with 4=0.2.0.6. and 1.," The details of the flow structure near $\rt$ are shown in Figure 1, where we plot the temperature, density, Mach number, and the ratio of the cooling time to the inflow time for models with $q = 0.2,\, 0.6$ , and $1$." + Figure 2 shows he accretion rate as a function of radius for these models., Figure 2 shows the accretion rate as a function of radius for these models. + The boundary conditions at ο=LOO pe are those appropriate for AIST., The boundary conditions at $\ro = 100$ kpc are those appropriate for M87. + Tn ALs7. AT is inferred. to decrease yours 10M.vr bat =TÜ kpe to XLAL.wrfata few slo-parsecs (Stewart ct al.," In M87, $\dot M$ is inferred to decrease from $\approx \, 10 \, \mpy$ at $\approx 70$ kpc to $\lsim \, 1 \, + \mpy$ at a few kilo-parsecs (Stewart et al." + 198D)., 1984). + This is reasonably well captured by our g=0.6 model., This is reasonably well captured by our $q = 0.6$ model. + The additional values of q are shown to indicate the range of expected behavior., The additional values of $q$ are shown to indicate the range of expected behavior. + Note hat the models iu Figures l aud 2 assume that rj=0. ic. that the ealaxy potential is logaritlinic evervwhere.," Note that the models in Figures 1 and 2 assume that $r_b = 0$, i.e., that the galaxy's potential is logarithmic everywhere." + Modifications due tos alternative potentials are discussed πι 833.1., Modifications due to alternative potentials are discussed in 3.1. + The conceptually most important result in Figure 1 is he ratio of the cooling time to the inflow time., The conceptually most important result in Figure 1 is the ratio of the cooling time to the inflow time. + This is Lat large radiwhere the accreting matter is mdeed a cooling flow but it increases rapidly at inaller radii as the How undergoes the transition to nearly adiabatic (DBoucdi) accretion., This is $\sim 1$ at large radiiwhere the accreting matter is indeed a cooling flow but it increases rapidly at smaller radii as the flow undergoes the transition to nearly adiabatic (Bondi) accretion. + Associated with this transition is a decrease in he imuportance of mass drop out., Associated with this transition is a decrease in the importance of mass drop out. + Iu the Dondi regime. fogDfug and so overdense regions do not have time ο condense out of the flow.," In the Bondi regime, $\tc \gg \ti$ and so overdense regions do not have time to condense out of the flow." + This accounts for the nearly constant accretion rate forkrzi300 pc in Figure 2., This accounts for the nearly constant accretion rate for$r \lsim 300$ pc in Figure 2. +" To illustrate the nupact of the underlving potcutial of the host galaxy on the structure of the cooling flow. consider the analytical solution to equations (2))-(2)) in he region where the ealaxws mass profile flattens (.c.. Ol regmorSry, and 3< 1): eXrSH pxrofl L aud ocoxs91071 (for simplicity. we have taken q= )."," To illustrate the impact of the underlying potential of the host galaxy on the structure of the cooling flow, consider the analytical solution to equations \ref{mdot}) \ref{energy}) ) in the region where the galaxy's mass profile flattens (i.e., for $\rt \lsim r \lsim r_b$ and $\beta < 1$ ): $c_s^2 \propto r^{-\beta + 1}$ , $\rho \propto +r^{-5/4 - \beta/4}$ , and $v \propto r^{-3/4 + \beta/4}$ (for simplicity, we have taken $q = 0$ )." + Because the cooliug flow is roughlv virial. the eas cluperature decreases mweard.," Because the cooling flow is roughly virial, the gas temperature decreases inward." + The Mach unmber of the resulting solution thereforeincreases rapidly inwards. as CUAL 361 ," The Mach number of the resulting solution thereforeincreases rapidly inwards, as $r^{3\beta/4 - 5/4}$ ." +For observed values of Jz 0.25. the Mach number increases roughly as 71 anmeli more rapidly than," For observed values of $\beta \approx 0.25$ , the Mach number increases roughly as $r^{-1}$, much more rapidly than" +temperatures. while their Ix-shell counterparts are generated in higher temperature regions.,"temperatures, while their K-shell counterparts are generated in higher temperature regions." + Assuming that the same elements in different regions have the same abundances. (he presence of both L-shell ancl Ix-shell lines in the spectrum provides important constraints on the enission measure of low and high temperature regions.," Assuming that the same elements in different regions have the same abundances, the presence of both L-shell and K-shell lines in the spectrum provides important constraints on the emission measure of low and high temperature regions." + Without these L-shell lines. the lower temperature DEM is primarily constrained by Ix-shell lines of low-Z elements. while hieher temperature DEM is constrained by L-shell lines of Fe.," Without these L-shell lines, the lower temperature DEM is primarily constrained by K-shell lines of low-Z elements, while higher temperature DEM is constrained by L-shell lines of Fe." + IC would therefore be more difficult. to determine the ratio of low and hieh temperature DEMSs. without. knowing the abundance ratios of low-Z elements and Fe., It would therefore be more difficult to determine the ratio of low and high temperature DEMs without knowing the abundance ratios of low-Z elements and Fe. + Moreover. for some elements. such as 9. Ar. and Ca. (he Ix-shell lines are not detected by RGS. aud their abundances are only. constrained by ihe L-shell lines.," Moreover, for some elements, such as S, Ar, and Ca, the K-shell lines are not detected by RGS, and their abundances are only constrained by the L-shell lines." + To illustrate the effects of these L-shell lines. we carried out two fits.," To illustrate the effects of these L-shell lines, we carried out two fits." + One includes the entire spectral region from 6 to 38A. and the other excludes some regions where strong L-shell lines of $i. S. Ar. and Ca are identified. primarily above ~20A.," One includes the entire spectral region from 6 to 38, and the other excludes some regions where strong L-shell lines of Si, S, Ar, and Ca are identified, primarily above $\sim 20$." + The resulting DEM reconstructions are shown as the green and blue lines in Figure 6.. respectively.," The resulting DEM reconstructions are shown as the green and blue lines in Figure \ref{fig:dem}, respectively." + The abundance measurements are shown as green and blue svmbols in Figure 7.., The abundance measurements are shown as green and blue symbols in Figure \ref{fig:ab}. + The summed RGSIL and RGS2 spectrum and the best-fit model are shown in Figure 9.., The summed RGS1 and RGS2 spectrum and the best-fit model are shown in Figure \ref{fig:rgssp}. + The reconstructed DESMSs are dominated by a broad peak near log(7)=6.8 and a smaller secondary peak near log(7)=6.4., The reconstructed DEMs are dominated by a broad peak near $\log(T)=6.8$ and a smaller secondary peak near $\log(T)=6.4$. + It is seen that the main differences between the (wo DEMSs are the secondary peak in the temperature region of log(7) between 6.3 and 6.6. which is where most L-shell ions of intermediate-Z elements are formed.," It is seen that the main differences between the two DEMs are the secondary peak in the temperature region of $\log(T)$ between 6.3 and 6.6, which is where most L-shell ions of intermediate-Z elements are formed." + The abundance measurements in the two fits are eenerallv consistent with each other. except for S. Ar. and Ca.," The abundance measurements in the two fits are generally consistent with each other, except for S, Ar, and Ca." + The uncertainties of these abundances in the fit with intermediate-Z L-shell regions exeluded are very. large. and (heir values are practically unconstrained.," The uncertainties of these abundances in the fit with intermediate-Z L-shell regions excluded are very large, and their values are practically unconstrained." + The $i abundance is süll well determined because its lines fall within the RGS wavelength band., The Si abundance is still well determined because its K-shell lines fall within the RGS wavelength band. + However. the RGS elective area calibration al (he Si Ix-shell region is quite uncertain. making the derived $i abundances unreliable.," However, the RGS effective area calibration at the Si K-shell region is quite uncertain, making the derived Si abundances unreliable." + In Figure 7.. (he abundances are plotted against the first ionization potential (FL?) order of the elements to examine whether the well known FIP or inverse FIP effect is present in Capella.," In Figure \ref{fig:ab}, the abundances are plotted against the first ionization potential (FIP) order of the elements to examine whether the well known FIP or inverse FIP effect is present in Capella." + Based on the RGS fit. one may tentatively conclude that the Capella abundances appear io manifest the solar-like FIP effect.," Based on the RGS fit, one may tentatively conclude that the Capella abundances appear to manifest the solar-like FIP effect." + IIowever. we note that our derived abundances are significantly different [rom earlier measurement of Auclarcdοἱal.(2003) using the same RCS data ancl a four-temperature fitting model.," However, we note that our derived abundances are significantly different from earlier measurement of \citet{audard03} using the same RGS data and a four-temperature fitting model." + Moreover. (here are a lew problems in the DEM and abundaice determinations using the RGS data alone. especially due to the calibration uncertainties in the short wavelength region. which may bias the results.," Moreover, there are a few problems in the DEM and abundance determinations using the RGS data alone, especially due to the calibration uncertainties in the short wavelength region, which may bias the results." + In our analvsis of EPIC and RGS spectra of some strong sources. we discovered that the RGS effective area below 8 is underestimated by ~20% relative to EPIC.," In our analysis of EPIC and RGS spectra of some strong sources, we discovered that the RGS effective area below 8 is underestimated by $\sim 20$ relative to EPIC." + To make up this loss of μας. the DEM derived [rom RGS data show a significant hieh temperature tail. and the derived Si abundance may. have also been overestimatecd.," To make up this loss of flux, the DEM derived from RGS data show a significant high temperature tail, and the derived Si abundance may have also been overestimated." +the profile for the observed deviations.,the profile for the observed deviations. + We have measured the galaxy's half light radius: Τεάεεοπυ=0.42+0.14 kpc.," We have measured the galaxy's half light radius: $r_{e, deconv} = 0.42 +\pm 0.14$ kpc." + This result is robust to changes in the imposed Sérrsic profile., This result is robust to changes in the imposed Sérrsic profile. + As a check of our data's sensitivity to a low surface brightness component we have constructed simulated galaxy images which include a faint extended component., As a check of our data's sensitivity to a low surface brightness component we have constructed simulated galaxy images which include a faint extended component. + We can reproduce the effective radii to using our technique., We can reproduce the effective radii to using our technique. + A possible cause for concern is that the galaxy might deviate strongly from a Sérrsic profile., A possible cause for concern is that the galaxy might deviate strongly from a Sérrsic profile. +" We have incorporated the residuals in our fit to compensate for such errors, and we note that the residuals from our best Sérrsic model fit are quite low (< 10%)."," We have incorporated the residuals in our fit to compensate for such errors, and we note that the residuals from our best Sérrsic model fit are quite low $<10\%$ )." + This implies that our model profile is close to the real profile., This implies that our model profile is close to the real profile. +" This, and the fact that varying n has little influence on the derived half-light radius, suggests that our results are not strongly affected by this source of error."," This, and the fact that varying $n$ has little influence on the derived half-light radius, suggests that our results are not strongly affected by this source of error." +" Thus, our findings indicate that the small effective radius that has been found is not due to oversimplified modeling or a lack of S/N, and gives additional evidence that a strong evolution in size occurs from ze2 to z=0."," Thus, our findings indicate that the small effective radius that has been found is not due to oversimplified modeling or a lack of S/N, and gives additional evidence that a strong evolution in size occurs from $z\approx 2$ to $z=0$." + It should be noted that our derived effective radius is 1.6 times smaller than the radii derived by Daddi(2005) in the i andz bands.," It should be noted that our derived effective radius is $1.6$ times smaller than the radii derived by \cite{dad05} + in the $i$ and$z$ bands." +" When we repeat our analysis on the ACS z-band data we obtain a slightly different value, re,4econe©0.65 kpc closer to the deep H-band imaging, and somewhat (uncircularized),smaller than the value derived by Daddietal.(2005) (but consistent within the errors)."," When we repeat our analysis on the ACS $z$ -band data we obtain a slightly different value, $r_{e, deconv} +\approx 0.65$ kpc (uncircularized), closer to the deep $H$ -band imaging, and somewhat smaller than the value derived by \cite{dad05} + (but consistent within the errors)." + Hence all bands indicate a very small size., Hence all bands indicate a very small size. +" Figure 4 illustrates the difference in size and mass between our galaxy and the z—0 elliptical population; plotted in the first two panels are the compact galaxy we have studied and a sample of low-redshift central galaxies from groups and clusters in the Sloan Digital Sky Survey, analyzed by Guoetal.(2009)."," Figure \ref{fig:rel} illustrates the difference in size and mass between our galaxy and the $z=0$ elliptical population; plotted in the first two panels are the compact galaxy we have studied and a sample of low-redshift central galaxies from groups and clusters in the Sloan Digital Sky Survey, analyzed by \cite{guo09}." +. The compact 2z galaxy lies far off from the z—0 mass-size relation., The compact $z\approx 2$ galaxy lies far off from the $z=0$ mass-size relation. + The middle panel shows the galaxy on the mass-luminosity relation., The middle panel shows the galaxy on the mass-luminosity relation. + We estimated the luminosity evolution of the compact galaxy from z—1.91 to z—0 in two ways: we first used the rest-frame B—I color difference between low and high redshift to estimate the difference in mass-to-light ratio., We estimated the luminosity evolution of the compact galaxy from $z=1.91$ to $z=0$ in two ways: we first used the rest-frame $B-I$ color difference between low and high redshift to estimate the difference in mass-to-light ratio. +" Second we used the Fundamental Plane to estimate the evolution from z—0 to z—1 from vanderWeletal. (2005),, and used the average evolution of the mass-to-light ratios of early-types in the CDFS at z=1 and the z=1.91 galaxy, both from Forrster Schreiber et al. ("," Second we used the Fundamental Plane to estimate the evolution from $z=0$ to $z=1$ from \cite{wel05}, and used the average evolution of the mass-to-light ratios of early-types in the CDFS at $z=1$ and the $z=1.91$ galaxy, both from Förrster Schreiber et al. (" +in preparation).,in preparation). + The resulting evolution is 1.8-2.2 magnitudes., The resulting evolution is 1.8-2.2 magnitudes. +" As a result, the galaxy still lies off from the size-magnitude relation after correcting for evolution."," As a result, the galaxy still lies off from the size-magnitude relation after correcting for evolution." + In the third panel of Figure 4 we compare the surface brightness profile of this galaxy to those of elliptical galaxies in the Virgo cluster., In the third panel of Figure \ref{fig:rel} we compare the surface brightness profile of this galaxy to those of elliptical galaxies in the Virgo cluster. + The profile shown has been corrected for cosmological surface brightness dimming and passive luminosity evolution from z—1.91 to z—0., The profile shown has been corrected for cosmological surface brightness dimming and passive luminosity evolution from $z=1.91$ to $z=0$. + The total correction is —3.5+2z—1.5 magnitudes.," The total correction is $-3.5 + 2 +\approx -1.5$ magnitudes." +" Even though the galaxy has an average density >100 times larger than the average z=0 elliptical of the same mass, its surface brightness profile in the central kpc is actually rather similar to those of the most massive galaxies at z=0 - the average density measured at fixed physical radius is not that different."," Even though the galaxy has an average density $>100$ times larger than the average $z=0$ elliptical of the same mass, its surface brightness profile in the central kpc is actually rather similar to those of the most massive galaxies at $z=0$ - the average density measured at fixed physical radius is not that different." +" This is consistent with results obtained by other authors Bezansonetal.2009;; Hopkinsetal. 2009a;; Feldmann(e.g.,etal. 2009;; vanDokkumetal. 2010))."," This is consistent with results obtained by other authors (e.g., \citealt{bez09}; \citealt{hop09a}; \citealt{fel09}; \citealt{dok10}) )." +" Thus, the main difference between z—0 and this z+2 galaxy is at larger radii where the ze2 galaxy has much lower surface brightness."," Thus, the main difference between $z=0$ and this $z\approx 2$ galaxy is at larger radii where the $z\approx 2$ galaxy has much lower surface brightness." + Such a result could be explained by inside-out growth., Such a result could be explained by inside-out growth. +" We also note that there may be significant errors in the mass determination of z+2 compact galaxies, due to iincorrect assumptions about the IMF."," We also note that there may be significant errors in the mass determination of $z\approx 2$ compact galaxies, due to incorrect assumptions about the IMF." +" Changes in the low mass end of the IMF affect both the masses of the high redshift and low redshift galaxies, and are nearly irrelevant."," Changes in the low mass end of the IMF affect both the masses of the high redshift and low redshift galaxies, and are nearly irrelevant." +" However, changes in the slope of the IMF will affect the derived passive evolution between z=2 and z= 0, and will increase or decrease the size evolution."," However, changes in the slope of the IMF will affect the derived passive evolution between $z=2$ and $z=0$ , and will increase or decrease the size evolution." + Changes in the IMF could thus have important consequences for evolution., Changes in the IMF could thus have important consequences for evolution. + Future deep NIR spectroscopic data should provide direct information on the kinematics of these objects and will allow us to, Future deep NIR spectroscopic data should provide direct information on the kinematics of these objects and will allow us to +Ligh time resolution spectroscopic observations were carried out at the European Southern Observatory (ESO) using the Ultraviolet and. Visual Echelle Spectrograph (UVES) installed at Unit. Telescope 2 (UT2) of the Verv Large Telescope (VEL).,High time resolution spectroscopic observations were carried out at the European Southern Observatory (ESO) using the Ultraviolet and Visual Echelle Spectrograph (UVES) installed at Unit Telescope 2 (UT2) of the Very Large Telescope (VLT). + For 669013. data were obtained during two high time resolution observing runs on 2008. January 17 and February 6.," For 69013, data were obtained during two high time resolution observing runs on 2008 January 17 and February 6." + For each run 34 spectra were obtained with exposure times of SOss and readout and overhead times of ~ 21ss. corresponding to a time resolution of ss. For 996237. we obtained 34 spectra on 2008. March. 15 with the same exposure and readout times.," For each run 34 spectra were obtained with exposure times of s and readout and overhead times of $\sim21$ s, corresponding to a time resolution of $\sim$ s. For 96237 we obtained 34 spectra on 2008 March 15 with the same exposure and readout times." + The wavelength region observed is AA4970.—1010AA.. with a small eap in the region around. ecaused by the space between the two CCDs.," The wavelength region observed is $\lambda\lambda\,4970 - 7010$, with a small gap in the region around caused by the space between the two CCDs." + The average spectral resolution is about 42—107., The average spectral resolution is about $R = 10^5$. + Phe CCD frames were processed using the UVES pipeline to extract. ancl merge the echelle orders to 1D spectra that were normalised to the continuum., The CCD frames were processed using the UVES pipeline to extract and merge the echelle orders to 1D spectra that were normalised to the continuum. + We also. obtained. photometric observations οἱ 669013. and 996237. in January. February and Alay 2010.," We also obtained photometric observations of 69013 and 96237 in January, February and May 2010." + These observations were obtained at the South African Astronomical Observatory (SAAO) in. Johnson D filter with the lem telescope and SAAO CCD and STE detector and with the modular. photometer at. the 0.5-m telescope., These observations were obtained at the South African Astronomical Observatory (SAAO) in Johnson $B$ filter with the 1-m telescope and SAAO CCD and STE4 detector and with the modular photometer at the 0.5-m telescope. + The reduction of photometric observations was done with software and with software developed at SAAO., The reduction of photometric observations was done with software and with software developed at SAAO. + The lists of the observations are shown in 11 and 2., The lists of the observations are shown in 1 and 2. + For roAp stars lines of rare earth. elements show higher pulsation amplitudes. while the lines of other chemical species. including light. elements and iron. peak elements. show much smaller. pulsation amplitude. or show none at all (see. c.g. Malanushenko.Savanov&Itvabchikova1998:: ]|xurtz.Elkin&Alathyvs2007)).," For roAp stars lines of rare earth elements show higher pulsation amplitudes, while the lines of other chemical species, including light elements and iron peak elements, show much smaller pulsation amplitude, or show none at all (see, e.g., \citealt{Malanushenko98}; \citealt{Kurtz07}) )." + This strange. behaviour is explained. by stratification where rare earth. elements concentrate in the upper Layers of the stellar atmosphere where oscillation amplitudes reach a maximum. while most other chemical elements tend to concentrate in deeper Iavers where the pulsation amplitude is lower.," This strange behaviour is explained by stratification where rare earth elements concentrate in the upper layers of the stellar atmosphere where oscillation amplitudes reach a maximum, while most other chemical elements tend to concentrate in deeper layers where the pulsation amplitude is lower." + Lines of iron peak elements in roXp stars show very low pulsation amplitude or none at all (IxXochukhoy&Ryabchikova2001.. Elkin.Kurtz&Mathys2008) ).," Lines of iron peak elements in roAp stars show very low pulsation amplitude or none at all \citealt{Koch01}, \citealt{Elkin08}) )." + To search for rapid. radial velocity variability we performed cross-correlation of sections. of the spectrum using software., To search for rapid radial velocity variability we performed cross-correlation of sections of the spectrum using software. + We also measured the central positions for profiles of individual spectral lines by the centre of gravity method., We also measured the central positions for profiles of individual spectral lines by the centre of gravity method. + Frequency analyses of racial velocity and photometric time series were performed using ESO-MIDAS’s Time Series Analysis ancl a discrete Fourier transform programme by Ixurtz(1985)., Frequency analyses of radial velocity and photometric time series were performed using 's Time Series Analysis and a discrete Fourier transform programme by \citet{kurtz85}. +. Cross correlation for the spectral band 50005800 wwith an average spectrum taken as a template shows obvious rapid oscillations for 669013. as can be seen in rof69013:freq1..," Cross correlation for the spectral band $5000 - 5800$ with an average spectrum taken as a template shows obvious rapid oscillations for 69013, as can be seen in \\ref{69013:freq1}." + For the two independent observing data sets hat we obtained with the ESO VLT telescope we find in he amplitude spectra highest peaks at v=—L46munllz and 5=142 mmllz. correspondinglv. with a fullewidth-willimaximum uncertainty of mamllz.," For the two independent observing data sets that we obtained with the ESO VLT telescope we find in the amplitude spectra highest peaks at $\nu = 1.46$ mHz and $\nu = 1.42$ mHz, correspondingly, with a full-width-half-maximum uncertainty of mHz." + Hence these two independent peaks are at the same frequency within the LeEQUCHEY error., Hence these two independent peaks are at the same frequency within the frequency error. + The spectral lines of the rare earth elements also show αιπαος with cdillerent amplitudes., The spectral lines of the rare earth elements also show pulsation with different amplitudes. + The highest amplitude we detected was obtained for lines ofextsciii.. shown in rof69013:prii.. while lines of reveal a smaller zumplitude as shown in ret69013:ndii..," The highest amplitude we detected was obtained for lines of, shown in \\ref{69013:priii}, while lines of reveal a smaller amplitude as shown in \\ref{69013:ndiii}." + Phe other lines which belong toexiscii..exiscii.. also show pulsations with significant peaks in the amplitude spectra.," The other lines which belong to, also show pulsations with significant peaks in the amplitude spectra." + The pulsation amplitude is smaller. for. the. second observing run. which suggests either rotational modulation or multiperiodicitv.," The pulsation amplitude is smaller for the second observing run, which suggests either rotational modulation or multiperiodicity." + While many Ap stars show rotational light) variations caused by abundance spots usually associated with their magnetic poles. there is no such evidence vet found for 669013 (Ereshammeretal.2008)..," While many Ap stars show rotational light variations caused by abundance spots usually associated with their magnetic poles, there is no such evidence yet found for 69013 \citep{Freyhammer08b}." + This constraint is weak and does not rule out rotational moculation pulsation amplitudes., This constraint is weak and does not rule out rotational modulation pulsation amplitudes. + Further observations are needed to study this question., Further observations are needed to study this question. + The photometric observations of this star obtained. at SAAO also show rapid oscillations. as can be seen in rof69013:saao..," The photometric observations of this star obtained at SAAO also show rapid oscillations, as can be seen in \\ref{69013:saao}." + Previous photometric observations by Nelson&Ixreidl(1993). and Martinez&Ixurtz(1994) did not detect. variations in this star., Previous photometric observations by \cite{Nelson93} and \cite{Martinez94} did not detect variations in this star. + The amplitude spectra of our SAAO photometric observations are shown in 44., The amplitude spectra of our SAAO photometric observations are shown in 4. + We obtained data on two nights., We obtained data on two nights. + The first data sets shows a, The first data sets shows a +equation of state.,equation of state. + The only other neutron stars whose thermal component is better described bv an aüimospheric model. ancl for which this interpretation resolves all the inconsistencies which follow from the blackbody interpretation. are (he raclio-silent neutron stars LE 1207-52 (Zavlinetal. 1998)) and RX. JOS22-4300 (Zavlinetal.1999)).," The only other neutron stars whose thermal component is better described by an atmospheric model, and for which this interpretation resolves all the inconsistencies which follow from the blackbody interpretation, are the radio-silent neutron stars 1E 1207-52 \citealt{za98}) ) and RX J0822-4300 \citealt{za99}) )." + The oobservation reported here allows us to add. another entry (ο the list., The observation reported here allows us to add another entry to the list. + If indeed (the X-ray emission detected [rom iis originating in (he cooling atmosphere of the neutron star. our estimate of the effective temperature allows us to localize the object in the neulrvon stars thermal evolutionary cliagranm.," If indeed the X-ray emission detected from is originating in the cooling atmosphere of the neutron star, our estimate of the effective temperature allows us to localize the object in the neutron stars thermal evolutionary diagram." + Our knowledge of neutron star interiors is still uncertain and accurate measurements of ihe neutron star surface temperature are particularly important to constrain the cooling models and provide information on the physics of the neutron star., Our knowledge of neutron star interiors is still uncertain and accurate measurements of the neutron star surface temperature are particularly important to constrain the cooling models and provide information on the physics of the neutron star. + Roughly speaking. theoretical models preclict a (wo-Iold behavior of the cooling curves depending on (he star mass.," Roughly speaking, theoretical models predict a two-fold behavior of the cooling curves depending on the star mass." + In low-mass neutron stars neut(rino emission is mainly due to a modified Urea process and nucleon-nucleon bremsstrahlung., In low-mass neutron stars neutrino emission is mainly due to a modified Urca process and nucleon-nucleon bremsstrahlung. + These are relatively weak mechanisms and producecooling., These are relatively weak mechanisms and produce. + In stus of higher mass (he neutrino emission is enhanced by a direct. Urea process (or other mechanisms in exotic matter). therefore these stars cool down much faster regime).," In stars of higher mass the neutrino emission is enhanced by a direct Urca process (or other mechanisms in exotic matter), therefore these stars cool down much faster regime)." + To date (see Yakovlevetal.2002. for a discussion) it has been realized that simple models which do not account for proton and neutron supertlIuidity fail in explaining the surface temperatures observed in many sources. unless objects such as e.g. Vela. Geminga. IX. J1356-31754 do have exactly the critical mass that bounds the transition between (he verv differentcooling aud regimes.," To date (see \citealt{ya02} for a discussion) it has been realized that simple models which do not account for proton and neutron superfluidity fail in explaining the surface temperatures observed in many sources, unless objects such as e.g. Vela, Geminga, RX J1856-3754 do have exactly the critical mass that bounds the transition between the very different and regimes." + This unlikely is not required if the effects of nucleon superfluiditv are accounted Lor., This unlikely fine-tuning is not required if the effects of nucleon superfluidity are accounted for. + la particular. nodels wilh proton superfluiditv included predict an intermediate region between fast cooling and slow cooling curves. which is expected to be populated by medium mass neutron stars (roughly with AZ between 1.4 and 1.65 M. ).," In particular, models with proton superfluidity included predict an intermediate region between fast cooling and slow cooling curves, which is expected to be populated by medium mass neutron stars (roughly with $M$ between 1.4 and 1.65 $M_\sun$ )." +" Although the fill picture only holds if. at the same lime, neutron superfluiditv is assumed to be rather weak. it is sill interesting (hat nanv neutron stars (as 1E 1207-52. Vela. RX J1856-3754. PSR 0656+14) have a surface temperature which falls in such a (vansition region (Yakovlevetal.2002)."," Although the full picture only holds if, at the same time, neutron superfluidity is assumed to be rather weak, it is still interesting that many neutron stars (as 1E 1207-52, Vela, RX J1856-3754, PSR 0656+14) have a surface temperature which falls in such a transition region \citep{ya02}." +. In turn. this neans (hat measuring (he surface temperature allows us to “weigh” neutron stars 2001).," In turn, this means that measuring the surface temperature allows us to “weigh” neutron stars \citep{ka01}." +. As we can see from the first (wo panels of Figure 2 in Yakovlevetal.(2002).. assumine an age of log7=4.6. the surface temperature of dderived from the blackbody fit is even higher than the upper cooling curves ie. Chose corresponding to the slow cooling regime.," As we can see from the first two panels of Figure 2 in \cite{ya02}, assuming an age of $\log \tau = 4.6$, the surface temperature of derived from the blackbody fit is even higher than the upper cooling curves i.e. those corresponding to the slow cooling regime." + However. (he surface temperature logZ7=5.9 obtained by fitting with the magnetized model and 2=13 km falls well within the above mentioned transition region of medium mass neutron stars.," However, the surface temperature $\log T^\infty = 5.9$ obtained by fitting with the magnetized model and $R=13$ km falls well within the above mentioned transition region of medium mass neutron stars." + The mass of, The mass of +abrupt period jumps (Srivastava1991).,abrupt period jumps \citep{Srivastava1991}. +. With the new set of up-to-date times of nüniua. counting altogether 113 data points. one is able to identity the long-term variation to be periodic mstead of the steady increase caused by a lass transfer.," With the new set of up-to-date times of minima, counting altogether 143 data points, one is able to identify the long-term variation to be periodic instead of the steady increase caused by a mass transfer." + Especially. the new data points after the vear 2000 evideutly deviate frou the quadratic ephemeris (sce tj).," Especially, the new data points after the year 2000 evidently deviate from the quadratic ephemeris (see \ref{FigDFHya}) )." + The parameters of the LITE are eiven in Table 3.. the final ft is given in Fie. and the predicte third-hodw’s minimal mass results in 0.8," The parameters of the LITE are given in Table \ref{TableBig2}, the final fit is given in \ref{FigDFHya} and the predicted third-body's minimal mass results in 0.84." +LAD... πο the componcut to be a maiu-sequence star. then it shouk be of IK1 spectral type aud therefore a third light shoul be considered in the elt curve solution.," Assuming the component to be a main-sequence star, then it should be of K1 spectral type and therefore a third light should be considered in the light curve solution." + Such a thin light was not included in the light curve solution of Miarchosetal.(1992).., Such a third light was not included in the light curve solution of \cite{1992DFHya}. + Usine the same method as iu the case of Vso3 Αα. one could also estimate the value of the photometric distance of the additional componeu resulting in 190 pc. which vields the predicted augular separation of 135 mas and a magnitude difference frou the EB of about 1.3 mag.," Using the same method as in the case of V803 Aql, one could also estimate the value of the photometric distance of the additional component resulting in 190 pc, which yields the predicted angular separation of 135 mas and a magnitude difference from the EB of about 1.3 mag." + Such a star could be easily detectable with the modern stellar interferometers., Such a star could be easily detectable with the modern stellar interferometers. + The eclipsing binary system PY Lar (GSC 02136-3365) is of W λαπρο aud its magnitude is about 12.5 in B filter., The eclipsing binary system PY Lyr (GSC 02136-03365) is of W UMa-type and its magnitude is about 12.5 in $B$ filter. + Both primary aud secondary χα are about 0.6 mae deep aud the orbital period is about O.L d. Its spectral type was classified as FO al. 2006).. but it is only a preliminary one.," Both primary and secondary minima are about 0.6 mag deep and the orbital period is about 0.4 d. Its spectral type was classified as F0 \citep{2006Malkov}, but it is only a preliminary one." + Precise CCD observations were carried out by Manimamsetal.(2006).. but they didut iuchule the hird Leht iuto their aualvsis.," Precise CCD observations were carried out by \cite{PYLyr2006}, but they didn't include the third light into their analysis." + The radial velocities jiwe not been measured. but many papers have been mblished with times of nünimna.," The radial velocities have not been measured, but many papers have been published with times of minima." + Information about a »ossible period change is given by Pribullaetal.(2003). who noticed some modulation of its orbital period. but hey concluded that this variation is uncertain.," Information about a possible period change is given by \cite{2003Pribulla}, who noticed some modulation of its orbital period, but they concluded that this variation is uncertain." + Ou the other haud. Brat(2001) published a paper on PY Lyr. where the period changes were described bv two period juups near 1967 and 1987.," On the other hand, \cite{Brat2001} published a paper on PY Lyr, where the period changes were described by two period jumps – near 1967 and 1987." + Collecting all the minima times. one gets a set of 123 data points.," Collecting all the minima times, one gets a set of 123 data points." + Fie.5 represents the ο6 diagram of all hese measurements. where the period variation is clearly visible.," \ref{FigPYLyr} represents the $O-C$ diagram of all these measurements, where the period variation is clearly visible." + A period of about 50 vears is now well covered and the resulting parameters of the predicted LITE variation are given m Table 2.., A period of about 50 years is now well covered and the resulting parameters of the predicted LITE variation are given in Table \ref{TableBig1}. + Assimine that tle mass of the eclipsing pair is about 2.5 (according to its spectral type). the miuinual mass of the predicted third conrponeut results iu 1.17AL... which is approximately the same value of mass as the primary and secondary component.," Assuming that the mass of the eclipsing pair is about 2.5 (according to its spectral type), the minimal mass of the predicted third component results in 1.17, which is approximately the same value of mass as the primary and secondary component." + Therefore. the third light cau be easily detectable iu the elt curve solution.," Therefore, the third light can be easily detectable in the light curve solution." + Regrettably. the parallax and the distance to this system is uot known. but it could be estimated using the same method as in the previous case.," Regrettably, the parallax and the distance to this system is not known, but it could be estimated using the same method as in the previous case." + The value of the system's photometric distance results in 750 pc. therefore the predicted angular separation of the third coniponeut is about 29 ias and its maenitude difference from the ED is about 1.3 mae.," The value of the system's photometric distance results in 750 pc, therefore the predicted angular separation of the third component is about 29 mas and its magnitude difference from the EB is about 1.3 mag." + Such a component would be hardly observable interterometrically., Such a component would be hardly observable interferometrically. + The photometric data obtained. by oue of us (VAL). we reanalysed again by taking iuto cousideration the third )odys contribution to the total light of the system.," The photometric data obtained by one of us (V.M.), we reanalysed again by taking into consideration the third body's contribution to the total light of the system." + The software PITOEBE 0.294. which is based ou the Wilsou- code. was used in order to extract the new nodel of the system. B. V. R.," The software PHOEBE 0.29d, which is based on the Wilson-Devinney code, was used in order to extract the new model of the system. $B$, $V$, $R$," + aud £ observations of lis system were analyzed (see Fig.6)). vieldiug a new set of plivsical paraiucters eiven in Table L. where {πι L;. O;. aud ue; denote the temperature. the Iuninosity. he modifed Lopal poteutial. aud the linb-darkenuius cocfiicicuts for primary aud secondary. respectively.," and $I$ observations of this system were analyzed (see \ref{FigPYLyrLC}) ), yielding a new set of physical parameters given in Table \ref{Table3}, where $T_i$, $L_i$, $\Omega_i$, and $x_i$ denote the temperature, the luminosity, the modified Kopal potential, and the limb-darkening coefficients for primary and secondary, respectively." + The “anode 3° was used for computing (hence O4 = 05) aud he ceceutricity was set to 0 (circular orbit).," The ""mode 3"" was used for computing (hence $\Omega_1$ = $\Omega_2$ ) and the eccentricity was set to 0 (circular orbit)." + The value, The value +"and are rewritten as where f(x,p) is the distribution function containing only cosmic ray contribution in the sense of the above definition.","and \ref{eflux} are rewritten as where $f(x,{\bf p})$ is the distribution function containing only cosmic ray contribution in the sense of the above definition." +" At x>x4, where anisotropies of thermal particle distribution are important, Eqs."," At $x>\xFP$, where anisotropies of thermal particle distribution are important, Eqs." + [8] and [9] are used., \ref{pflux} and \ref{eflux} are used. +" As one can see, between the location z4 and the subshock, thermal particles are only heated by compression, but if this compression is rapid, like at the subshock, this compressive heating is non-adiabatic."," As one can see, between the location $\xFP$ and the subshock, thermal particles are only heated by compression, but if this compression is rapid, like at the subshock, this compressive heating is non-adiabatic." +" In fact, it turns out that the solutions provided by the model contain a region of finite thickness 0r>Zeit, in which this non-adiabatic compressive heating takes place: this region is interpreted as the subshock."," In fact, it turns out that the solutions provided by the model contain a region of finite thickness $0 > x > x_\mathrm{crit}$, in which this non-adiabatic compressive heating takes place: this region is interpreted as the subshock." +" The semi-analytic formalism for the NLDSA problem developed by Caprioli, Amato and Blasi (hereafter CAB) couples the conservation of mass, momentum and energy flux with an analytical solution of the stationary diffusion-convection equation for the isotropic part of the CR distribution function ∙∙"," The semi-analytic formalism for the NLDSA problem developed by Caprioli, Amato and Blasi (hereafter CAB) couples the conservation of mass, momentum and energy flux with an analytical solution of the stationary diffusion-convection equation for the isotropic part of the CR distribution function \citep{cab09}." +" More precisely, the transport equation is taken as in Eq. Dl,"," More precisely, the transport equation is taken as in Eq. \ref{diffcon}," +" with the velocity of the scattering centres u,, neglected with respect to the fluid one, their ratio being typically of order of v4/u<1: The injection term Q(z,p) is written following Blasi,Gabici&Vannoni|(2005) as where 7) is the fraction of particles crossing the shock and injected in the acceleration process and pj;,; is the injection momentum (see refCAB:inj for further details)."," with the velocity of the scattering centres $u_{w}$ neglected with respect to the fluid one, their ratio being typically of order of $v_{A}/u\ll 1$: The injection term $\mathcal{Q}(x,p)$ is written following \cite{bgv05} as where $\eta$ is the fraction of particles crossing the shock and injected in the acceleration process and $\pj$ is the injection momentum (see \\ref{CAB:inj} for further details)." + Eq., Eq. +" is solved imposing the upstream boundary condition f(xo,p)—0 as in KJ model, which mimics the presence of a free-escape boundary at a distance ro upstream of the shock."," \ref{diffconvstat} is solved imposing the upstream boundary condition $f(x_{0},p)=0$ as in KJ model, which mimics the presence of a free-escape boundary at a distance $x_{0}$ upstream of the shock." +tud spiral galaxies.,and spiral galaxies. + The total rate also agrees with our rate in equation (5))., The total rate also agrees with our rate in equation \ref{eq:volsnr}) ). + The detailed numbers t'e preseuted in Table [. Sullivane, The detailed numbers are presented in Table \ref{tbl:rate}. +tal.(2006) modelled SN Ia rate as a function of stellar masses aud mean SFRs ol host galaxies., \citet{Sullivan06} modelled SN Ia rate as a function of stellar masses and mean SFRs of host galaxies. + We use the morphology clepeudent luminosity density of Nakamura aud the morphologically depeudeut star formation rate calculated from the star formation rate of the bugle aud cisk components given in Nagamineetal.(2006)., We use the morphology dependent luminosity density of \citet{Nakamura03} and the morphologically dependent star formation rate calculated from the star formation rate of the bugle and disk components given in \citet{Nagamine06}. +. The predicted SN Ia rate is rp=2.6«10°?Mpevr.|. of which are prompt: see also Table L.," The predicted SN Ia rate is $r_V=2.6\times10^{-5}\;{\rm Mpc}^{-3}\;{\rm yr}^{-1}$, of which are prompt: see also Table \ref{tbl:rate}." + The predicted numbers ol SNe Ia are plotted in Figure LL as dotted (Naunuccei et al, The predicted numbers of SNe Ia are plotted in Figure \ref{fig:hostcf} as dotted (Mannucci et al. +s model) aud cashed (Sullivan et al,'s model) and dashed (Sullivan et al. +s model) curves taking the colour cistributiou of each morphological type as a Gaussian with mean aud dispersion.⋅ given⋅ by Fukugita4⋅etal.∣⋅∣−⋅(2007).,'s model) curves taking the colour distribution of each morphological type as a Gaussian with mean and dispersion given by \citet{Fukugita07}. +. The 47Dp for the two models are 4-315.1 aud 01)23.67 for 11 degrees of freedom using data for 0.1«g—r1.0., The $\chi^2$ for the two models are 15.1 and 23.6 for 11 degrees of freedom using data for $0.1 1$ assuming $S_{\nu} +\propto \nu^{-\alpha}$ ) and are linearly polarized \citep{gf04}." +. The X-rav surface brightuess around most radio relies is low. uakiug it difficult to study the relationship between the A-ray gas and radio enuüssion.," The X-ray surface brightness around most radio relics is low, making it difficult to study the relationship between the X-ray gas and radio emission." + Αα radio relics. including some of the best known and studied (e.9..heComaclusterrelic125:53|275aud 1997).. are located fav from the cluster ceuter. ou the order of Mpes.," Many radio relics, including some of the best known and studied \citep[e.g., the Coma cluster relic 1253$+$275 and Abell +3667;][]{gfs91,rwh+97}, are located far from the cluster center, on the order of Mpcs." + However. there exists a subclass of radio relics which are located significautly closer to the cluster center. ~50 to 350 kpe.," However, there exists a subclass of radio relics which are located significantly closer to the cluster center, $\sim$ 50 to 350 kpc." + Cüovauniui&Feretti(2001) classify these as relic sources near the first ranked galaxy., \citet{gf04} classify these as relic sources near the first ranked galaxy. + These radio sources share many of the same properties of classical racio relies mcelucdiug steep spectra. flamenutary structure. and polarization (Sleeetal.2001).," These radio sources share many of the same properties of classical radio relics including steep spectra, filamentary structure, and polarization \citep{srm+01}." +. Abell 133 is one of the class of radio relics near the first rane: ealaxv., Abell 133 is one of the class of radio relics near the first ranked galaxy. + A observation. revealed a tongue-Iike feature in the X-rav ciuission comprised of cool gas (AEzm1.3 keV) which extended from the cD galaxy to the radio relic (Fujitactal.2002)., A observation revealed a tongue-like feature in the X-ray emission comprised of cool gas $kT \approx 1.3$ keV) which extended from the cD galaxy to the radio relic \citep{fsk+02}. +.. À number of possible origius for the tongue were explored iucludiug the sugeestion that the cool gas in the tongue was uplitted from the cluster core by the buovautlv rising radio relic., A number of possible origins for the tongue were explored including the suggestion that the cool gas in the tongue was uplifted from the cluster core by the buoyantly rising radio relic. + A followup observation with is consistent with the uplifted bubble scenario (Fujitaetal. 2001)., A followup observation with is consistent with the uplifted bubble scenario \citep{fsr+04}. +. However the detection of a cold front. southeast of the cluster core aud a weak shock in the core suggests that an unequal mass 1ierger is responsible for the tongue feature., However the detection of a cold front southeast of the cluster core and a weak shock in the core suggests that an unequal mass merger is responsible for the tongue feature. + Ta either model the radio plasma appears to," In either model, the radio plasma appears to" +a really complex galaxy.,a really complex galaxy. + On the other hand. the study of the stellar populations provides surprisingly homogeneus results and sheds light on the most probable assembly process [or our galaxy.," On the other hand, the study of the stellar populations provides surprisingly homogeneus results and sheds light on the most probable assembly process for our galaxy." + For the sake of clarity. we split the Discussion in two Sections. devoted to each of these questions.," For the sake of clarity, we split the Discussion in two Sections, devoted to each of these questions." + Photometrical studies have confirmed that 3357. is composed. of. at least. four structures. namely bulge. inner bar. outer bar and cise (erwin2004:Xguerriοἱal.2005)..," Photometrical studies have confirmed that 357 is composed of, at least, four structures, namely bulge, inner bar, outer bar and disc \citep{2004A&A...415..941E,2005A&A...434..109A}." + The presence of the inner bar is also supported by the photometrical and. kinematical analysis performed. in this work., The presence of the inner bar is also supported by the photometrical and kinematical analysis performed in this work. + In fact. the cllipticity and PA profiles presented. in Figure 2.. and the velocity and. velocity. dispersion profiles along the inner bar direction presented in Figure 3.. show clear signatures of this small. secondary bar. as explained in Sections 77. and ?7..," In fact, the ellipticity and PA profiles presented in Figure \ref{fig:mor}, and the velocity and velocity dispersion profiles along the inner bar direction presented in Figure \ref{fig:kin}, show clear signatures of this small, secondary bar, as explained in Sections \ref{sec:mor} and \ref{sec:kin}." + Interestingly. the analysis of the kinematics also shows evidence of an additional. inner component: a kinematically decoupled structure appears at the centre of 3357. rotating Laster than its surroundings.," Interestingly, the analysis of the kinematics also shows evidence of an additional, inner component: a kinematically decoupled structure appears at the centre of 357, rotating faster than its surroundings." + This decoupling spans approximately +2 aresec and matches in size with the observed central e-drop., This decoupling spans approximately $\pm$ 2 arcsec and matches in size with the observed central $\sigma$ -drop. + The different structures that shape 3357 have to account for all the signatures present in the kinematical profiles., The different structures that shape 357 have to account for all the signatures present in the kinematical profiles. + In this Section we state the two possibilities that match with the results obtained in this work., In this Section we state the two possibilities that match with the results obtained in this work. + The presence of a central velocity dispersion minimum in à spiral galaxy was first reported by Bottema(1989)..Since then. the number of galaxies showing a e-drop has increased significantly.," The presence of a central velocity dispersion minimum in a spiral galaxy was first reported by \citet{1989A&A...221..236B}.Since then, the number of galaxies showing a $\sigma$ -drop has increased significantly." + In fact. Falcón-Darrosoetal.(2006) find this signature in at least of a sample of 48 early-type spirals. although other cases have been noticed in smaller samples (e.g...Márquezetal.2003)... particularly in barred. galaxies and even including late-type spirals (Ciandaetal.2006) and double-barred. objects. (IEámsellenietal.2001)...," In fact, \citet{2006MNRAS.369..529F} find this signature in at least of a sample of 48 early-type spirals, although other cases have been noticed in smaller samples \citep[e.g.,][]{2003A&A...409..459M}, particularly in barred galaxies and even including late-type spirals \citep{2006MNRAS.367...46G} + and double-barred objects \citep{2001A&A...368...52E}." + Phe most accepted explanation for the formation of e-drops in disc galaxies is the star formation at their central regions: the new stars acquire the kinematical properties ofthe gas they ave formed from: the clissipative nature of that gas is more ellicient in the central regions because of the higher density and converts the gas into a cold. stellar component. such as an inner disc. with a lower velocity dispersion than the surrouncings.," The most accepted explanation for the formation of $\sigma$ -drops in disc galaxies is the star formation at their central regions: the new stars acquire the kinematical properties of the gas they are formed from; the dissipative nature of that gas is more efficient in the central regions because of the higher density and converts the gas into a cold stellar component, such as an inner disc, with a lower velocity dispersion than the surroundings." + This scenario is in agreement with the N-bodvy simulations of Wozniaketal.(2003). and Wozniak&Cham-pavert (2006).. who mace use of bars to transport gas to the central regions.," This scenario is in agreement with the N-body simulations of \citet{2003A&A...409..469W} and \citet{2006MNRAS.369..853W}, who made use of bars to transport gas to the central regions." + The case of 3357 seems to support that hypothesis since the central decoupling in velocity might be due to an inner disc whose low velocity dispersion would be the cause of the e-drop., The case of 357 seems to support that hypothesis since the central decoupling in velocity might be due to an inner disc whose low velocity dispersion would be the cause of the $\sigma$ -drop. + Therefore. 3357 is composed of at Least live structures: bulge. inner disc. inner bar. outer bar and disc.," Therefore, 357 is composed of at least five structures: bulge, inner disc, inner bar, outer bar and disc." + The e-drop means a local minimum in the velocity dispersion with respect to the corresponding value for the bulge. which reaches σ —180 + or higher (the velocity dispersion. profile should. peak at the centre. where the σ-drop masks the velocity dispersion of the bulge).," The $\sigma$ -drop means a local minimum in the velocity dispersion with respect to the corresponding value for the bulge, which reaches $\sigma\sim$ 180 $^{-1}$ or higher (the velocity dispersion profile should peak at the centre, where the $\sigma$ -drop masks the velocity dispersion of the bulge)." + This high velocity dispersion value for the bulge implies it is pressure supported: and. classical., This high velocity dispersion value for the bulge implies it is pressure supported and classical. + Επι result. is supported by the work of Aguerrietal.(2005).. who find that the bulge of 3357. follows the same fundamental plane as the ellipticals or classical bulges of other carly-type objects.," This result is supported by the work of \citet{2005A&A...434..109A}, who find that the bulge of 357 follows the same fundamental plane as the ellipticals or classical bulges of other early-type objects." + Within this context. the appearance of the e-hollows at the edges of the inner bar in the velocity dispersion profile is also well understood.," Within this context, the appearance of the $\sigma$ -hollows at the edges of the inner bar in the velocity dispersion profile is also well understood." + The c-hollows were first seen in a sample of four couble-harred galaxies analysed: through inteeral-field spectroscopy (deLorenzo-C'áceresetal.2008)., The $\sigma$ -hollows were first seen in a sample of four double-barred galaxies analysed through integral-field spectroscopy \citep{2008ApJ...684L..83D}. +. Dv means of N-bocky simulations. they tested the possible scenarios that might eive rise to these hollows. showing that weir size and amplitude depend on two parameters: the relative contribution of the flux of the bulge to the total uminosity and the difference in the velocity. clispersion of 10 two components.," By means of N-body simulations, they tested the possible scenarios that might give rise to these hollows, showing that their size and amplitude depend on two parameters: the relative contribution of the flux of the bulge to the total luminosity and the difference in the velocity dispersion of the two components." + Therefore. a galaxy hosting a classical oige with a high velocity dispersion. and a colder. inner xw which dominates the total luminosity at its ends (where 1e light. profile of the bulge has already cecavecl) will ‘learly show the two e-hollows at the bar edges. as for 1ο case of 3357.," Therefore, a galaxy hosting a classical bulge with a high velocity dispersion and a colder, inner bar which dominates the total luminosity at its ends (where the light profile of the bulge has already decayed) will clearly show the two $\sigma$ -hollows at the bar edges, as for the case of 357." + In this scenario. the bulge is the jobτον structural component of 3357 and the velocity dispersion decreases for the outer structures.," In this scenario, the bulge is the hottest structural component of 357 and the velocity dispersion decreases for the outer structures." + Table. 3 indicate the velocity dispersion. values for cach component., Table \ref{tab:sigmas} indicate the velocity dispersion values for each component. + Lt is important to note that the actual velocity. dispersion of the inner dise is probably lower than the value given in ‘Table 3.. since the measured. value includes the contribution of the bulge within the inner disc region.," It is important to note that the actual velocity dispersion of the inner disc is probably lower than the value given in Table \ref{tab:sigmas}, since the measured value includes the contribution of the bulge within the inner disc region." + There are two important. drawbacks for this possible structural. composition of 3357., There are two important drawbacks for this possible structural composition of 357. + First. the αι70 signature of the inner disc should be detected. in the photometrical analysis presented in Section ??..," First, the $a_4>0$ signature of the inner disc should be detected in the photometrical analysis presented in Section \ref{sec:mor}." + Εις is the case of the nuclear stellar dises observed. in the centre of ellipticals and. bulges (Morelliet.al.2010.anclreferences therein).., This is the case of the nuclear stellar discs observed in the centre of ellipticals and bulges \citep[][and references therein]{2010A&A...518A..32M}. +" A careful inspection to the inner c2 aresee in =""eure 2. shows no evidence of clisey isophotes.", A careful inspection to the inner $\pm$ 2 arcsec in Figure \ref{fig:mor} shows no evidence of discy isophotes. + Second. the formation of the inner disc is usually related to a recent star formation in the centre. but the analysis of the stellar populations for 3357 shows old. ages lor the 'entral components: a significant voung population such as wt of an inner dise should be noticed when studsing the mean Iuminositv-weighted age. even i£ it is mixed with an older. more massive component.," Second, the formation of the inner disc is usually related to a recent star formation in the centre, but the analysis of the stellar populations for 357 shows old ages for the central components; a significant young population such as that of an inner disc should be noticed when studying the mean luminosity-weighted age, even if it is mixed with an older, more massive component." + Therefore. although this hypothesis seems promising. it does not explain all the properties found in this work.," Therefore, although this hypothesis seems promising, it does not explain all the properties found in this work." + The second. possibility. for. the structure of 3357 is that there is no inner disc., The second possibility for the structure of 357 is that there is no inner disc. + Lf this is the case. the central kinematical decoupling and the e-drop have to be caused by the bulge itself. which therefore shows clise-like properties that indicate it is a pseucdobulec rather than a classical one.," If this is the case, the central kinematical decoupling and the $\sigma$ -drop have to be caused by the bulge itself, which therefore shows disc-like properties that indicate it is a pseudobulge rather than a classical one." + This hypothesis is strongly supported. by the Sérrsic index (SersicLOGS) measured for the bulge of NGCS3357 by XAguerriοἱal. (2005): they performeci a photometric decomposition of an /--band image and obtained n2-—1.40-0.08. which is compatible with a pseudobulge.," This hypothesis is strongly supported by the Sérrsic index \citep{1968adga.book.....S} measured for the bulge of 357 by \citet{2005A&A...434..109A}; ; they performed a photometric decomposition of an -band image and obtained $\pm$ 0.08, which is compatible with a pseudobulge." + Indeed. Fisher&Drory(2008). study a sample of TT galaxies and find that ~90% of pseudobulges have n«2. whereasclassicalbulgeshacenzs2.," Indeed, \citet{2008AJ....136..773F} study a sample of 77 galaxies and find that $\sim$ of pseudobulges have $\textless$ 2, whereas classical bulges have $\textgreater$ 2." +cosmological model via the growth of density perturbations and the distance-redshift/ relation.,cosmological model via the growth of density perturbations and the distance-redshift relation. +" Results for CDAI-Like power spectra for different values ol O,, and Ox are presented in Section 3.", Results for CDM-like power spectra for different values of $\Omega_m$ and $\Omega_{\Lambda}$ are presented in Section 3. + We explore ways to isolate the elfect of the lensing contribution to «(8) in Section 4 and conclude in Section 5., We explore ways to isolate the effect of the lensing contribution to $\wth$ in Section 4 and conclude in Section 5. + The cllect of magnification bias due to weak gravitatinal lensing on the galaxyangular correlation function w(8) has been derived in Villumsen (1996)., The effect of magnification bias due to weak gravitatinal lensing on the galaxyangular correlation function $\wth$ has been derived in Villumsen (1996). + Written in terms of the time-dependent power spectrum instead of the present clay one. which makes it applicable to nonlinear power spectra. w(8) is given by In this section the physical meaning of the various ternis in the above equation and the notation used will be clarified.," Written in terms of the time-dependent power spectrum instead of the present day one, which makes it applicable to nonlinear power spectra, $\wth$ is given by In this section the physical meaning of the various terms in the above equation and the notation used will be clarified." + We have used the notation of Jain Seljak (1997). where x is the radial comoving distance. yg that to the horizon. r(x) is the comoving angular diameter distance. Wy) the normalized. racial clistribution of galaxies in the sample. and From the expression for the unperturbecl line element Tr being conformal time. it follows that where A is the spatial curvature.," We have used the notation of Jain Seljak (1997), where $\chi$ is the radial comoving distance, $\chi_H$ that to the horizon, $r(\chi)$ is the comoving angular diameter distance, $W(\chi)$ the normalized radial distribution of galaxies in the sample, and From the expression for the unperturbed line element $\tau$ being conformal time, it follows that where $K$ is the spatial curvature." + Note that for a delta-function distribution of galaxies. V(X)=δεν)Vo: qi] reduces to gy)=r(x)r(xsr(xs).," Note that for a delta-function distribution of galaxies, $W(\chi')=\delta(\chi'-\chi_S)$, $g(\chi)$ reduces to $g(\chi)=r(\chi)r(\chi_S-\chi)/r(\chi_S)$." + This notation is related to the one of Villumsen (1996) through X=ore yor}. Way)my)—Sr) and g(x)/r(x)=wr).," This notation is related to the one of Villumsen (1996) through $\chi=x$, $r(\chi)=y(x)$ , $W(\chi)/r^2(\chi)=S(x)$ and $g(\chi)/r(\chi)=w(x)$." + First we shall brielly describe the effect of magnification bias on wl)., First we shall briefly describe the effect of magnification bias on $\wth$. + Gravitational lensing of a galaxy by dark matter concentrations between us and the galaxy increases the area of the galaxv image while conserving surface brightness., Gravitational lensing of a galaxy by dark matter concentrations between us and the galaxy increases the area of the galaxy image while conserving surface brightness. + This results in a magnification // which is given by the ratio of lensed to unlensed area of the image., This results in a magnification $\mu$ which is given by the ratio of lensed to unlensed area of the image. + The amplitude of (p depends on the convergence s. which is the surface mass density divided by the critical density. and the shear 5 through (Young 1981) In the limit of weak lensing. Hh1. applicable to lensing by large-scale structure. the above expression reduces to This magnification has two elfects.," The amplitude of $\mu$ depends on the convergence $\kappa$ , which is the surface mass density divided by the critical density, and the shear $\gamma$ through (Young 1981) In the limit of weak lensing, $|\kappa|, |\gamma| \ll 1$, applicable to lensing by large-scale structure, the above expression reduces to This magnification has two effects." + Since the [ense area is increased due to deflection. of the light rays. the number density of galaxies decreases inversely. proportiona to (i.," Since the lensed area is increased due to deflection of the light rays, the number density of galaxies decreases inversely proportional to $\mu$." + There is a competing ellect. however.," There is a competing effect, however." + In a fux Limite: survev. magnification brings some faint. galaxies above the ας limit. which would not otherwise have been detectable. thus increasing the number density of galaxies.," In a flux limited survey, magnification brings some faint galaxies above the flux limit, which would not otherwise have been detectable, thus increasing the number density of galaxies." + Which. of the effects wins depends on the reservoir of faint galaxies available. which can be quantified by the slope s of the true number counts No) for a magnitude limit m. s—πο The two cllects change the galaxy numbers by (c.g. Broadhurst. Tavlor Peacock 1995) NoGn)pg which reduces to in the weak lensing limit.," Which of the effects wins depends on the reservoir of faint galaxies available, which can be quantified by the slope $s$ of the true number counts $N_0(m)$ for a magnitude limit $m$, s=. The two effects change the galaxy numbers by (e.g. Broadhurst, Taylor Peacock 1995) (m)=N_0(m) which reduces to in the weak lensing limit." + In addition. the number density. of galaxies is changed by On» due to intrinsic clustering.," In addition, the number density of galaxies is changed by $\delta n$ due to intrinsic clustering." + Let » denote the average number censity of ealaxies., Let $\bar{n}$ denote the average number density of galaxies. + At a given position in the sky 6. the number density is thus changed to ΠΠ| n(60)) 0-5(00))) ).," At a given position in the sky $\hth$, the number density is thus changed to ( 1+ ) ) )." + Now we further assume that galaxies trace the underlying dark matter distribution so that the 3- galaxy overdensity is. Grim t where à6£7) is the dark matter overdensitv ane the bias bis the proportionality factor.," Now we further assume that galaxies trace the underlying dark matter distribution so that the 3-dimensional galaxy overdensity is, x) = b x) , where $\delta(\vec x)$ is the dark matter overdensity and the bias $b$ is the proportionality factor." + In this linear biasmodel. the perturbed. projected number density is given by (Villumsen 1996) righty).," In this linear biasmodel, the perturbed, projected number density is given by (Villumsen 1996) )= b d ) ) ) ." +systematically higher Ty for the outer disk GAICs. which we interpreted above as higher kinetic gas temperatures due to elevated. radiation levels from nearby star formation.,"systematically higher ${\rm T_{B}}$ for the outer disk GMCs, which we interpreted above as higher kinetic gas temperatures due to elevated radiation levels from nearby star formation." + The higher tempcratures could lead to higher excitation of the CO molecules2001).. thus lowering the measuredoc9.," The higher temperatures could lead to higher excitation of the CO molecules, thus lowering the measured." +. With the resolution and seusitivitv of CARALA we are able to measure the properties of 8 GMCS in the heavily l--douunated outer part of M23., With the resolution and sensitivity of CARMA we are able to measure the properties of 8 GMCs in the heavily -dominated outer part of M33. + Despite an chviromment very distinct from a normal spiral galaxy (low inolecular gas fraction. stellar surface density aud dust-to-gas ratio). the clouds we observe show eenerallv simular properties compared to GMCSsS in the Milkv Wax or other nearby galaxies.," Despite an environment very distinct from a normal spiral galaxy (low molecular gas fraction, stellar surface density and dust-to-gas ratio), the clouds we observe show generally similar properties compared to GMCs in the Milky Way or other nearby galaxies." + The main differcuce is that the eas appears to be hotter. with excitation temperatures between 6 IEI&K. which is likely to be the responsible mechanisui for a lower inferred. cconversion factor.," The main difference is that the gas appears to be hotter, with excitation temperatures between $\sim6-11$ K, which is likely to be the responsible mechanism for a lower inferred conversion factor." + This difference appears mostly attributable to heating bw massive star formation coincident or adjacent to the CMCsS, This difference appears mostly attributable to heating by massive star formation coincident or adjacent to the GMCs. +", F.D. acknowledges support frou NSF eraut AST-0838258.", F.B. acknowledges support from NSF grant AST-0838258. + A.B. acknowledges partial support frou: NSF erant AST-0sS38178., A.B. acknowledges partial support from NSF grant AST-0838178. + Support for A.L. was provided bv NASA through Hubble Fellowship eraut. HST-IIE-51258.01-À awarded by the Space Telescope Science Iustitute. which is operated by the Association of Universities for Research in Astrououiv. Iuc.. for NASA. under contract NAS 5-26555.," Support for A.L. was provided by NASA through Hubble Fellowship grant HST-HF-51258.01-A awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS 5-26555." + E.R. is supported by a Discovery Caaut Πο NSERC of Canauda., E.R. is supported by a Discovery Grant from NSERC of Cananda. + Support for CARMA construction was derived. from the states of California. DHlinois. and Maryland. the James S. MeDouuell Foundation. the Cordon aud Betty Moore Foundation. the Isenneth T. aud Eileen L. Norris Foundation. the University of Chicago. the Associates of the California Institute of Technology. aud the National Science Foundation.," Support for CARMA construction was derived from the states of California, Illinois, and Maryland, the James S. McDonnell Foundation, the Gordon and Betty Moore Foundation, the Kenneth T. and Eileen L. Norris Foundation, the University of Chicago, the Associates of the California Institute of Technology, and the National Science Foundation." + Ougoine CARMA development and operations are supported bv the National Science Foundation under a cooperative aerecment. aud by the CARMA partner universities.," Ongoing CARMA development and operations are supported by the National Science Foundation under a cooperative agreement, and by the CARMA partner universities." + We have made use of tle NASA/IPAC Extragalactic Database (NED). which is operated by the Jet Propulsion Laboratory. California Tustitute of Technology. uncer contract with the National Acronantics aud Space Acimiuistratiou.," We have made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration." + This research has made use of NASA's Astroplivsies Data System (ADS)., This research has made use of NASA's Astrophysics Data System (ADS). +"settings are as follows: the stellar temperature T.=3,000 K, the stellar radius RF,=2.0 Ro, the distance from the star R=1 AU, the grazing angle a=0.05, the visible fraction of the stellar photosphere fyis=0.5, the total visual optical depth of the disc To.55um=104 (i.e. To.55um=5X10° at the equatorial plane), and no scattering.","settings are as follows: the stellar temperature $T_*=3,000$ K, the stellar radius $R_*=2.0$ $R_\odot$, the distance from the star $R=1$ AU, the grazing angle $\alpha=0.05$, the visible fraction of the stellar photosphere $f_{\rm vis}=0.5$, the total visual optical depth of the disc $\tau_{0.55\micron}=10^4$ (i.e. $\tau_{0.55\micron}=5\times10^3$ at the equatorial plane), and no scattering." + We used the dust opacity model downloaded from the web page which is the same as that assumed in the calculation by C. P. Dullemond., We used the dust opacity model downloaded from the web page which is the same as that assumed in the calculation by C. P. Dullemond. + The figure shows an excellent agreement between both results., The figure shows an excellent agreement between both results. +" Here, we derive an analytic expression of the radiation field in an isothermal medium with absorption and isotropic scattering."," Here, we derive an analytic expression of the radiation field in an isothermal medium with absorption and isotropic scattering." +" In the derivation, we adopt the Eddington approximation with two-stream lines (e.g.,Rybicki&man 1979)."," In the derivation, we adopt the Eddington approximation with two-stream lines \citep[e.g.,][]{ryb79}." +. We consider a diffuse incident radiation., We consider a diffuse incident radiation. + Suppose a plane-parallel medium (see Figure B1)., Suppose a plane-parallel medium (see Figure B1). + We set the extinction (absorption+scattering) optical depth coordinate 7 along the normal of the medium., We set the extinction (absorption+scattering) optical depth coordinate $\tau$ along the normal of the medium. + The total extinction optical depth of the medium is set to be 7., The total extinction optical depth of the medium is set to be $\tau_{\rm L}$ . +" Then, suppose that the single scattering albedo in this medium is w and this medium is isothermal and in the thermal equilibrium."," Then, suppose that the single scattering albedo in this medium is $\omega$ and this medium is isothermal and in the thermal equilibrium." + The thermal radiation is denoted as B., The thermal radiation is denoted as $B$. +" Let us consider two-stream lines with the direction of p=+1/V3, where µ is the cosine of the angle between the rayand the 7 coordinate."," Let us consider two-stream lines with the direction of $\mu=\pm1/\sqrt{3}$, where $\mu$ is the cosine of the angle between the rayand the $\tau$ coordinate." +" When the direction of the rays is denoted by the subscript of + or —, the equation of the radiation transfer becomes 'The source function can be expressed as where J is the mean intensity."," When the direction of the rays is denoted by the subscript of $+$ or $-$, the equation of the radiation transfer becomes The source function can be expressed as where $J$ is the mean intensity." +" In the two-stream approximation, we can define the mean intensity J, the mean flux H, and the mean radiation pressure K as and The first and second moments of (B1) with the source function (B2) are and Withan effective optical depth το=7r4/3(1— w), we have from equations (B6) and (B7)."," In the two-stream approximation, we can define the mean intensity $J$, the mean flux $H$, and the mean radiation pressure $K$ as and The first and second moments of (B1) with the source function (B2) are and Withan effective optical depth $\tau_{\rm e}\equiv \tau\sqrt{3(1-\omega)}$ , we have from equations (B6) and (B7)." +present and directly visible. bu most of its accretion power ls exracted Via nonradiative procpresses. Such as inechanical outflows or Povutine flux (Iuucic aud Dickuell. 20M.,"present and directly visible, but most of its accretion power is extracted via non-radiative processes, such as mechanical outflows or Poynting flux (Kuncic and Bicknell, 2004)." +" In this case, he peak temperature occurs inch further away from the inner disk οσο,"," In this case, the peak temperature occurs much further away from the inner disk edge." + Some of the power τοeased hrough non-radiative channels wotId then be couverte to power-law photous., Some of the power released through non-radiative channels would then be converted to power-law photons. +§f We leave a muore detailed discussion of t15 physical interpretatio1 of the traition radius to firther work (Soria and Ivunucie. 20071).," We leave a more detailed discussion of the physical interpretation of the transition radius to further work (Soria and Kuncic, 2007b)." + Au important question to ask is whether t1¢ ultraluminoudi xanch corresponds to a jeher or lower accretion state han the classical very high state., An important question to ask is whether the ultraluminous branch corresponds to a higher or lower accretion state than the classical very high state. + The «etected 2 20 keV flux(RATE data. Sobczak ct al.," The detected $2$ $20$ keV flux data, Sobczak et al.," + 20003 was üeher in the τον hieji state., 2000) was higher in the very high state. + Towever. hat is uot jecessarilv a eood indicator of the total huninosity. especially when the disk Cluission is very soft. nor of he accretion rate.," However, that is not necessarily a good indicator of the total luminosity, especially when the disk emission is very soft, nor of the accretion rate." +" For example, the total huuinosity at the top of the thernal track is 7Lag. with a radiative efücieney 20.1."," For example, the total luminosity at the top of the thermal track is $\approx L_{\rm Edd}$, with a radiative efficiency $\ga 0.1$." + The non-thermal processes responsible for the doilant power-law enmission in the very lieh aud ultraluninous states are expected to have ower radiative efficicuey., The non-thermal processes responsible for the dominant power-law emission in the very high and ultraluminous states are expected to have lower radiative efficiency. +" So; the total luuinosity nav still be zLada. jst cliffercutly redistributed between hermal and nou-theniual components, even if ijj2 a ew."," So, the total luminosity may still be $\approx L_{\rm Edd}$, just differently redistributed between thermal and non-thermal components, even if $\dot{m} \ga$ a few." +" In the case of NTE 561. the total disk plus vower-law flux is a least as high. aud probably sligitly uigher, along the ultraluiminous branch (Soria and Ikunucie; 2007b)."," In the case of XTE $-$ 564, the total disk plus power-law flux is at least as high, and probably slightly higher, along the ultraluminous branch (Soria and Kuncic, 2007b)." + More inurportantly. the disk huninosity is slightly increasiis along the ultraluiniinous branch. or an increasing mner-«disk racius.," More importantly, the disk luminosity is slightly increasing along the ultraluminous branch, for an increasing inner-disk radius." + This can happen (recall Eq., This can happen (recall Eq. + 2) only if the accretion rates also inereases along the ultraluninot1S branch (even if the total muinositv did noV, 2) only if the accretion rates also increases along the ultraluminous branch (even if the total luminosity did not). +" The fact hat NTE J1550 πο reached both he very high state and he ultraliiiinous xanch in the first. riore energetic phase of itx outburst, and only (briefiv) the very high stae in the second. weaker phase (Sohezals et al."," The fact that XTE $-$ 564 reached both the very high state and the ultraluminous branch in the first, more energetic phase of its outburst, and only (briefly) the very high state in the second, weaker phase (Sobczak et al.," + 2000) also sugeests hat the ulramnaunuous brauch corres»onds to a higher activity state., 2000) also suggests that the ultraluminous branch corresponds to a higher activity state. +" As the source started to decline, it wet roni very hig) state to hieh/soft state, aud finally to owματα sate, consistent with this iiterpretation."," As the source started to decline, it went from very high state to high/soft state, and finally to low/hard state, consistent with this interpretation." +" A plausible phenomenological way to 1nodel the disk paralcters on the ultraluminous branch is to assume a transition radius FR,>Rico.", A plausible phenomenological way to model the disk parameters on the ultraluminous branch is to assume a transition radius $R_{\rm c} \gg R_{\rm ISCO}$. + For RoΠο the inflow can be approximated by a standard disk. such that," For $R > R_{\rm c}$, the inflow can be approximated by a standard disk, such that" +"be studied in statistically significant fashion modeling the SED of the sources found in correspondence of the multitude ofHn-driven bubble-like structures found in the images, as shown for the bubble N49 by Zavagnoetal.(2010).","be studied in statistically significant fashion modeling the SED of the sources found in correspondence of the multitude of}-driven bubble-like structures found in the images, as shown for the bubble N49 by \citet{zavagno10}." +". Feedbacks from massive star formation, together with the intricate relationship between the interstellar radiation field and molecular clouds, are at the origin of the observed complexity of the ISM emission structure, where temperature ranges from ~10K of pre-stellar cores to the —40-50K of the photodissociation regions (Bernardetal.,2010)."," Feedbacks from massive star formation, together with the intricate relationship between the interstellar radiation field and molecular clouds, are at the origin of the observed complexity of the ISM emission structure, where temperature ranges from $\sim$ 10K of pre-stellar cores to the $\sim$ 40-50K of the photodissociation regions \citep{bernard10}." +". The extraction of compact sources is quite a challenging task in these fields, which we faced using a novel approach based on the study of the multidirectional second derivatives in the image to aid in source detection and size estimate, and subsequent constrained multi-Gaussian fitting."," The extraction of compact sources is quite a challenging task in these fields, which we faced using a novel approach based on the study of the multidirectional second derivatives in the image to aid in source detection and size estimate, and subsequent constrained multi-Gaussian fitting." +" This approach greatly increases the dynamical range between compact sources and diffuse emission, irrespective of the local absolute value of the emission."," This approach greatly increases the dynamical range between compact sources and diffuse emission, irrespective of the local absolute value of the emission." +" The method is fully described elsewhere (Molinarietal.,2010a) and has been applied for this first attempt to generate source catalogs.", The method is fully described elsewhere \citep{moli10b} and has been applied for this first attempt to generate source catalogs. +" As the thresholding for source detection is done on the image (Molinarietal., 2010a),, the S/N of the detected sources is determined measuring the ratio of the source peak flux over the rms of the residuals after the Gaussian fit."," As the thresholding for source detection is done on the image \citep{moli10b}, the S/N of the detected sources is determined measuring the ratio of the source peak flux over the $rms$ of the residuals after the Gaussian fit." + Source catalogs were generated for the two fields and for the 5 bands and are made available in tabular form in the online version of the paper., Source catalogs were generated for the two fields and for the 5 bands and are made available in tabular form in the online version of the paper. +" Catalogs completeness was estimated with artificial source injection experiments, and the peak flux levels for completeness for the 70, 160, 250, 350 and pphotometry are [0.5, 4.1, 4.1, 3.2, 2.5] Jy/beam for the /=30° ffield, and [0.06, 0.9, 0.7, 0.7, 0.8] Jy/beam for the /=59° ffield."," Catalogs completeness was estimated with artificial source injection experiments, and the peak flux levels for completeness for the 70, 160, 250, 350 and photometry are [0.5, 4.1, 4.1, 3.2, 2.5] Jy/beam for the $l$ field, and [0.06, 0.9, 0.7, 0.7, 0.8] Jy/beam for the $l$ field." + The difference is entirely compatible with the very different intensity regimes of the underlying diffuse emission in the two fields., The difference is entirely compatible with the very different intensity regimes of the underlying diffuse emission in the two fields. +" Estimating the source's physical properties requires that detection in the various band catalogs are merged in coherent SEDs, a process that can only be done coarsely in this early stage, but which is nonetheless useful for isolating 528 sources in the /=30° ffield and 444 sources in the /=59° ffield (see Eliaetal. 2010))."," Estimating the source's physical properties requires that detection in the various band catalogs are merged in coherent SEDs, a process that can only be done coarsely in this early stage, but which is nonetheless useful for isolating 528 sources in the $l$ field and 444 sources in the $l$ field (see \citealt{elia10}) )." + The two observed fields encompass emission from regions at very different distances., The two observed fields encompass emission from regions at very different distances. +" In a considerable effort, which involved a critical re-evaluation of available data and evidence, and the collection of additional data for hundreds of previously unknown objects, Russeiletal.(2010) provide recommended distances for a fraction of the detected sources (312 out of 528, and 91 out of 444 sources for the two fields, respectively) for which the derivation of masses and luminosities is possible."," In a considerable effort, which involved a critical re-evaluation of available data and evidence, and the collection of additional data for hundreds of previously unknown objects, \citet{russeil10} provide recommended distances for a fraction of the detected sources (312 out of 528, and 91 out of 444 sources for the two fields, respectively) for which the derivation of masses and luminosities is possible." +" Adopting standard prescriptions for Class 0 classification (L;235045/Loo;= 0.005, Andréetal. 2000)) results in almost the totality of sources being Class 0 (90 out of 91 sources in /259? aand 306 out of 312 in /=30°,, see Eliaetal. 2010))."," Adopting standard prescriptions for Class 0 classification $L_{\lambda \geq 350\mu m}/L_{bol}\geq 0.005$ , \citealt{andre00}) ) results in almost the totality of sources being Class 0 (90 out of 91 sources in $l$ and 306 out of 312 in $l$, see \citealt{elia10}) )." + The most extraordinary feature exhibited by the maps is the pattern of filaments in the ISM structure., The most extraordinary feature exhibited by the maps is the pattern of filaments in the ISM structure. + This is more apparent when we enhance the contrast of the filaments using the same method (see refcensus)) as used for the source detection 2010a)., This is more apparent when we enhance the contrast of the filaments using the same method (see \\ref{census}) ) as used for the source detection \citep{moli10b}. +". Here we start from the dderivatives carried out in four directions (x, y, and the two diagonals), as for the standard detection method, and then create another image F of the same size so that the maximum curvature is selected for each pixel: F;;=max|O?x;;,0y;j,9?Dj;;, ?D»;;]."," Here we start from the derivatives carried out in four directions (x, y, and the two diagonals), as for the standard detection method, and then create another image F of the same size so that the maximum curvature is selected for each pixel: $F_{ij} = max [ \partial ^2 {\rm{x}} _{ij}, \partial ^2 {\rm{y}} _{ij}, \partial ^2 {\rm{D_{1}}} _{ij}, \partial ^2 {\rm{D_{2}}} _{ij} ]$ ." + In this way we are following the direction of maximum curvature pixel-by-pixel for all compact features in the image., In this way we are following the direction of maximum curvature pixel-by-pixel for all compact features in the image. + We show in fig.3 the result of this processing on the /=59° ffield at250um., We show in \ref{l59_filaments} the result of this processing on the $l$ field at. +". The maps clearly show an interconnected maze of filaments at different levels of brightness (e.g. different levels of emission intensity and curvature), and the striking aspect is that the compact sources detected at aare distributed for the most part along the brightest filaments."," The maps clearly show an interconnected maze of filaments at different levels of brightness (e.g. different levels of emission intensity and curvature), and the striking aspect is that the compact sources detected at are distributed for the most part along the brightest filaments." +" Interestingly, a similar scenario was also reported for Taurus by Goldsmithetal.(2008) where the physical conditions and spatial scales involved are radically different."," Interestingly, a similar scenario was also reported for Taurus by \citet{gold08} where the physical conditions and spatial scales involved are radically different." +" Since the source integrated fluxes are estimated by fitting Gaussians on top of planar plateaus, the values of the local background at every wavelength are a by-product of our source extraction and, after applying the absolute correction factors asrecommended by Bernardetal.(2010) and subtracting the foreground contribution estimated using Bohlin (1975),, can be used to estimate the local beam-averaged column density in the hosting"," Since the source integrated fluxes are estimated by fitting Gaussians on top of planar plateaus, the values of the local background at every wavelength are a by-product of our source extraction and, after applying the absolute correction factors asrecommended by \citet{bernard10} and subtracting the foreground contribution estimated using \citet{bohlin75}, , can be used to estimate the local beam-averaged column density in the hosting" +The universe is assumed to be covered by simulation boxes and. consequenthy. it is periodic.,"The universe is assumed to be covered by simulation boxes and, consequently, it is periodic." + As it was pointed out bv Cerdaé-Durdn.Quilis&Sáez(2004) and Antonοἱal. (2005).. periodicity effects. magnify lens deformations and. in general. gravitational anisotropies as the RS cllect.," As it was pointed out by \citet{cer04} and \citet{ant05}, periodicity effects magnify lens deformations and, in general, gravitational anisotropies as the RS effect." +" Various techniques (rav-tracing methods) have been used o avoid this magnification. lor example. Πίο,Laguna&Anninos(1096) averaged the temperature contrasts of many ravs. but then. they found a map with too large Pixels. from which. the multipoles corresponding to f=TOO could not be obtained."," Various techniques (ray-tracing methods) have been used to avoid this magnification, for example, \citet{tul96} averaged the temperature contrasts of many rays, but then, they found a map with too large pixels, from which, the multipoles corresponding to $\ell > 700$ could not be obtained." + Another method based on multiple ane projections was proposed and applied to study week ensing by cosmological structures (see Jain.Seljak(2000) for a detailed: description), Another method based on multiple plane projections was proposed and applied to study week lensing by cosmological structures (see \citet{jai00} for a detailed description). +" Afterwards. White&llu(2001) designed the ""tiling"" ray tracing procedure. in which. independent. simulations with appropriate boxes and resolutions tile the photon trajectories."," Afterwards, \citet{whi01} designed the ""tiling"" ray tracing procedure, in which, independent simulations with appropriate boxes and resolutions tile the photon trajectories." + Finally. another method based. on the existence of preferred directions and on the use of an appropriate cutolf was. recently proposed and applied (Cerdá-Durán.Quilis&Sáez(2004):: Antónetal. (2005))).," Finally, another method based on the existence of preferred directions and on the use of an appropriate cutoff was recently proposed and applied \citet{cer04}; \citet{ant05}) )." +" In the required. eutolf. the Fourier modes corresponding to spatial scales larger than a given one (L,,,,) are eliminated. from the peculiar gravitational »otential."," In the required cutoff, the Fourier modes corresponding to spatial scales larger than a given one $L_{max}$ ) are eliminated from the peculiar gravitational potential." + Phe Ly... value is chosen in such a wav that: (a) he cutoll eliminates all the spatial scales which are too large o be well described in the simulation box. and (b) after the cutolf is performed. CALB photons cross neighbouring boxes hrough statistically independent regions.," The $L_{max}$ value is chosen in such a way that: (a) the cutoff eliminates all the spatial scales which are too large to be well described in the simulation box, and (b) after the cutoff is performed, CMB photons cross neighbouring boxes through statistically independent regions." + This cutolf is only »erformed. in the output. peculiar gravitational potential with the essential aim of calculating the integral in Eq. (1):, This cutoff is only performed in the output peculiar gravitational potential with the essential aim of calculating the integral in Eq. \ref{rtp}) ); + however. all the spatial scales. allowed by the box size are taken into account in the N-bocly simulation.," however, all the spatial scales allowed by the box size are taken into account in the N-body simulation." + Our rav-tracing method is a very goocl choice presenting some advantages with respect to other techniques (sce Antonetal. (200523). e.&.. there are no discontinuities at the crossing points between successive boxes. the computational cost is niocderated. and so on.," Our ray-tracing method is a very good choice presenting some advantages with respect to other techniques (see \citet{ant05}) ), e.g., there are no discontinuities at the crossing points between successive boxes, the computational cost is moderated, and so on." + In order to study the RS effect. we develop the same tvpe of N-body simulations which were used. in Antonal. (2005).. to deal with lensecl maps of the CALB.," In order to study the RS effect, we develop the same type of N-body simulations which were used, in \citet{ant05}, to deal with lensed maps of the CMB." + In this way. various maps of the relative temperature variations due to the RS elfect are created and. analvzed. and the dependence of the results on various parameters involved in the simulations and also in their statistical analysis is then discussed.," In this way, various maps of the relative temperature variations due to the RS effect are created and analyzed, and the dependence of the results on various parameters involved in the simulations and also in their statistical analysis is then discussed." + Most maps are regularly. pixelised. but some maps based on LIEALPLsSphere. see Gorski.Hivon&Wan-ο (1999))) are also considered.," Most maps are regularly pixelised, but some maps based on HEALPIx, see \citet{gor99}) ) are also considered." + Taking into account that the box size used in the mentioned N-body simulations (see Antónetal.(2005). for details) is £=256Alpe. and also that the main part of the RS elfect is assumed to be produced: at. redshift ο<5.2 (see below). the size of the resulting RS maps appears to be close to 27.," Taking into account that the box size used in the mentioned N-body simulations (see \citet{ant05} for details) is $L= 256 \ Mpc$, and also that the main part of the RS effect is assumed to be produced at redshift $z < 5.2$ (see below), the size of the resulting RS maps appears to be close to $2^{\circ}$." + Simulation boxes cover a periodic universe and. for the direction 6=11.27 and ó=12.67 (where 6 and © are spherical coordinates defined with respect to the box edges). the CALB photons cross around 30 boxes before passing through the region where they were initially located. (in the first box).," Simulation boxes cover a periodic universe and, for the direction $\theta=77.2^\circ $ and $\phi = 12.6^\circ$ (where $\theta$ and $\phi$ are spherical coordinates defined with respect to the box edges), the CMB photons cross around $30$ boxes before passing through the region where they were initially located (in the first box)." +" 1t can be verified that these boxes cover the trajectory of the CXMD photons from the redshift 2),%5.2 to present. timo. and. also that these photons cross successive boxes through independent regions separated by a distance close to 52Mpe."," It can be verified that these boxes cover the trajectory of the CMB photons from the redshift $z_{in} \simeq 5.2$ to present time, and also that these photons cross successive boxes through independent regions separated by a distance close to $52 \ Mpc$." + The cutolf is performed at the scale Aisin=tfLane with Las=GOAlpe (in agreement with previous comments about the scales involved in our simulations)., The cutoff is performed at the scale $k_{min} =2 \pi / L_{max}$ with $L_{max} = 60 \ Mpc$ (in agreement with previous comments about the scales involved in our simulations). + Along the paper we develop three types of N-body simulations in boxes of LMpe (integer and even L): Low Resolution (LR) simulations involving £/2 cells per edge and (L/2)? particles (2Mpe cell size and ~380 time steps). Intermediate Resolution (LR) simulations using L cells per edge and L? particles (1Adpe cell size ad ~410 time steps). and High Resolution (HIU) simulations with 2£ cells per edge and (2L)°% particles (0.5Adpe cell size and ~500 time steps)," Along the paper we develop three types of N-body simulations in boxes of $L \ Mpc$ (integer and even L): Low Resolution (LR) simulations involving $L/2$ cells per edge and $(L/2)^{3}$ particles $2 \ Mpc$ cell size and $\sim 380$ time steps), Intermediate Resolution (IR) simulations using L cells per edge and $L^{3}$ particles $1 \ Mpc$ cell size and $\sim 410$ time steps), and High Resolution (HR) simulations with $2L$ cells per edge and $(2L)^{3}$ particles $0.5 \ Mpc$ cell size and $\sim 500$ time steps)." + Figure (4)) shows a RS map which has been obtained with our rav-tracing method and a LR simulation of structure., Figure \ref{figucolour}) ) shows a RS map which has been obtained with our ray-tracing method and a HR simulation of structure. + Lis look is promising. but the correlations appearing in this vpe of maps must be estimated to get objective conclusions.," Its look is promising, but the correlations appearing in this type of maps must be estimated to get objective conclusions." + Lt is done in next sections., It is done in next sections. + For any observation direction 7. function Ooó/0i] must » calculated. in à set of points to estimate the integral in Eq (1)).," For any observation direction $\vec {n}$, function $\partial \phi / \partial \eta $ must be calculated in a set of points to estimate the integral in Eq. \ref{rtp}) )." + We have chosen equidistant points (on he corresponding background. σουοσο) separated bv a comoving distance equal to the cell size., We have chosen equidistant points (on the corresponding background geodesic) separated by a comoving distance equal to the cell size. + Each of these »oints has a comoving position vector τρ.p and the photon oxwsses by this position at time Γρ.," Each of these points has a comoving position vector $\vec{x}_{_{P}}$, and the photon passes by this position at time $\eta_{_{P}} $." +" Point £2 is placed inside a certain. P-cell of the computational grid and time 4), xlongs to some interval ane aj. where ap and nii are wo successive times of the N-bocly simulation. at. which. he peculiar potential ó is found at any erill node."," Point $P$ is placed inside a certain $P$ -cell of the computational grid and time $\eta_{_{P}} $ belongs to some interval $\eta_{i}, \eta_{i+1} $ ], where $\eta_{i} $ and $\eta_{i+1} $ are two successive times of the N-body simulation, at which, the peculiar potential $\phi $ is found at any grill node." + The »»ential at point £2? is calculated at times aol. m. i and 5j;2.," The potential at point $P$ is calculated at times $\eta_{i-1} $, $\eta_{i} $, $\eta_{i+1} $, and $\eta_{i+2} $." + Phe calculation at any of these times is performed ww means of a suitable 3D. interpolation. which uses the »»ential in the vertices of the P-cell and in those of the neighbouring ones.," The calculation at any of these times is performed by means of a suitable 3D interpolation, which uses the potential in the vertices of the $P$ -cell and in those of the neighbouring ones." + From the resulting potential at the above our times. the partial derivative 00/09 is finally caleulated with an appropriatecl numerical method.," From the resulting potential at the above four times, the partial derivative $\partial \phi / \partial \eta $ is finally calculated with an appropriated numerical method." + For cach type of ροςν simulations (LR. LR or LUR). various methods for spatial interpolation and also for the numerical calculation of time derivatives have been tried.," For each type of N-body simulations (LR, IR or HR), various methods for spatial interpolation and also for the numerical calculation of time derivatives have been tried." + “Phe final results do not significantly depend on the chosen methods because these, The final results do not significantly depend on the chosen methods because these +data. at an elfective wavelength of6165À. (,"data, at an effective wavelength of. (" +We also repeated our analvsis at g and 7. the other two bands with high signal-to-noise. and did not find significantly different results from our r band analvsis.),"We also repeated our analysis at $g$ and $i$, the other two bands with high signal-to-noise, and did not find significantly different results from our $r$ band analysis.)" +" Two measures of the apparent axis ratio are given bv thebest-fitting axis τα1ος q,, for the de Vaucouleurs and exponential models.", Two measures of the apparent axis ratio are given by thebest-fitting axis ratios $q_m$ for the de Vaucouleurs and exponential models. +" However. the algorithm for fitting the models introduces «quantization in the distribution of q,,"""," However, the algorithm for fitting the models introduces quantization in the distribution of $q_m$." + Because of this artificial «quantization. we do not use the model axis ratios as estimates of (he (rue apparent shapes ol galaxies.," Because of this artificial quantization, we do not use the model axis ratios as estimates of the true apparent shapes of galaxies." + A useful measure of the apparent shape in the outer regions of galaxies is the axisratio of the 25 mag 7 isophote., A useful measure of the apparent shape in the outer regions of galaxies is the axisratio of the 25 mag $^{-2}$ isophote. + The SDSS DR3 data pipeline finds the best fitting ellipse io the 25 mag 7 isophote in each band: the semimajor axis and semiminoraxis of (his isophotal ellipse are slo; and ος., The SDSS DR3 data pipeline finds the best fitting ellipse to the 25 mag $^{-2}$ isophote in each band; the semimajor axis and semiminoraxis of this isophotal ellipse are $A_{25}$ and $B_{25}$. + The isophotal axis ratio qo;=Bo;/lo5 then provides a measure of (he apparent galaxy shape al a few times the effective radius., The isophotal axis ratio $q_{25} \equiv B_{25}/A_{25}$ then provides a measure of the apparent galaxy shape at a few times the effective radius. + For galaxies in our saniple with fracDeV=1. the mean aud standard deviation of As;/H4. are 3.12c1.00: for galaxies wilh fracDeV=0. the mean and standard deviation are ος=2.40+0.36.," For galaxies in our sample with $\texttt{fracDeV} = 1$, the mean and standard deviation of $A_{25}/R_e$ are $3.12 \pm 1.00$; for galaxies with $\texttt{fracDeV} += 0$, the mean and standard deviation are $A_{25}/R_e = 2.40 \pm 0.36$." + Another measure of the apparent shape is qa. the axis ratio determined by the use of adaptive moments of the galaxys lisht.," Another measure of the apparent shape is $q_{\rm am}$, the axis ratio determined by the use of adaptive moments of the galaxy's light." + The method of adaptive moments determines the nth order moments of a galaxy image. using an elliptical weight Iunction whose shape matches that of the image (Bernstein&Jarvis2002:HirataSeljak2003).," The method of adaptive moments determines the $n$ th order moments of a galaxy image, using an elliptical weight function whose shape matches that of the image \citep{bj02,hs03}." +. The SDSS DR3 adaptive momentis use a weight function wir.y) Chat is a Gaussian matched to the size ancl ellipticit of (he galaxy image ZCr.y).," The SDSS DR3 adaptive moments use a weight function $w (x,y)$ that is a Gaussian matched to the size and ellipticity of the galaxy image $I(x,y)$." +" The adaptive first order moments. ancl tell us the ‘center of light, of the galaxys image."," The adaptive first order moments, and tell us the `center of light' of the galaxy's image." + With (his knowledge. we can compute the adaptive second order moments: and so forth.," With this knowledge, we can compute the adaptive second order moments: and so forth." +" The SDSS DIBA3 provides for each image the values of (he parameters T=Ay+ λέω 6=04,— My)/r. and e,= 2AL.,/7."," The SDSS DR3 provides for each image the values of the parameters $\tau = M_{xx} + M_{yy}$ , $e_+ = (M_{xx}-M_{yy})/\tau$ , and $e_\times = 2 M_{xy} / \tau$ ." + The adaptive second moments can be converted into an axis ratio using the relation, The adaptive second moments can be converted into an axis ratio using the relation + SEP(Pr) wherethe polynomialsP(r),"the central charge is and the ADM mass takes the form: Note that when taking the limit $\mu\gg k$ in the above expressions, our approximation requires that $\abs{\frac{E\mu}{\mathcal{D}k}}\ll1$." + are g, In the following we assume $\mathcal{D}$ and $E$ have the same sign. +ivenin the appendix. For δες =Dai a," The higher curvature corrections increase the entropy, decrease the temperature (for $\mu>0$ ), decrease the mass for small $\mu$ and increase the mass for large $\mu$." +nd Dy =Dy: &x(r) 4h (—-6(r +h," In the extremal limit $\mu=0$ , this agrees with the mass-charge ratio conjecture of \cite{mass_charge}." + (2k+4 po? *(2rh + rp —bu)," The maximum temperature, where the specific heat diverges, is at lower $\mu$." + 542-- Shy= Isp?) ln —, I would like to thank Yaron Oz for his support and guidance. + +hth +OP) 45DI?(re+ Ee4 (e+qu) AE ο. ουσ. ο + hp yk? Skye+ 2607) UE min) ISDh?(r bythe+ pr(2hk+gn) + (34)," This work is supported in part by the Israeli Science Foundation center of excellence, by the Deutsch-Israelische Projektkooperation (DIP), by the US-Israel Binational Science Foundation (BSF), and by the German-IsraeliFoundation (GIF)." +1993).. the high-resolution. IR spectrograph at the NASA IRTF 3-1 telescope.,", the high-resolution, IR spectrograph at the NASA IRTF 3-m telescope." + The secius was 0.1 0.8., The seeing was $-$ $''$. + Each object was observed ou & nielts., Each object was observed on $-$ 8 nights. +" The 0.5"" shit vielded R~ 16.000."," The $''$ slit yielded $\sim$ 46,000." +" We obtained data im 10"" nodded pairs.", We obtained data in $''$ nodded pairs. + Spectra were ceutered at 2.298 ju (vacuma)., Spectra were centered at 2.298 $\mu$ m (vacuum). + Iutegration times were 1 hour for the T Tauri stars and 8 minutes for the standards., Integration times were $\sim$ 1 hour for the T Tauri stars and $\sim$ 8 minutes for the standards. + The signal to noise ratio (SNB) was — 120., The signal to noise ratio (SNR) was $\sim$ $-$ 120. + Data were reduced as described in JohusIE&rulletal.(1999)., Data were reduced as described in \citet{joh99}. +. Relative RVs were determined by cross correlating a lieh SNR. fiducial spectrmu against all other spectra for the same target.," Relative RVs were determined by cross correlating a high SNR, fiducial spectrum against all other spectra for the same target." + We used six orders spanning ~5700 Πο σοςA., We used six orders spanning $\sim$ 5700 to 6800. + Uncertaiuties were estimated from the standard deviation of the mean for the 6 orders. added in quadrature with the 110 i | uncertainty derived froin the RV standards (82:Huertaetal.2008).," Uncertainties were estimated from the standard deviation of the mean for the 6 orders, added in quadrature with the 140 m $^{-1}$ uncertainty derived from the RV standards \citep[\S 2;][]{hue08}." +. RVs were corrected for the Eartl’s harveeutric motion., RVs were corrected for the Earth's barycentric motion. + Optinimui periods aud uncertaiuties for pliasiug the RV data were selected based on power spectra (ITuerta 2008)., Optimum periods and uncertainties for phasing the RV data were selected based on power spectra \citep{hue08}. +. For DN Tau we found P=6.33 40.20 davs aud a alse «απ probability (FAP) of «0.001. for V836 Tan. p-2.18 £0.19 davs and FAP=0.10. aud for Vs27 Tan. P=3.76 £0.06 davs aud FAP<0.001.," For DN Tau we found $=$ 6.33 $\pm$ 0.20 days and a false alarm probability (FAP) of $< $ 0.001, for V836 Tau, $=$ 2.48 $\pm$ 0.49 days and $=$ 0.10, and for V827 Tau, $=$ 3.76 $\pm$ 0.06 days and $<$ 0.001." + We also checked or periodicity using the discrete Fourier transform plus CLEAN method of Roberts et al. (, We also checked for periodicity using the discrete Fourier transform plus CLEAN method of Roberts et al. ( +1987).,1987). + The strongest power spectruii peaks for DN Tau aud. V836 Tau occur at he same periods., The strongest power spectrum peaks for DN Tau and V836 Tau occur at the same periods. + The CLEAN method recovered a best seriod of 3.61 d for Va27 Tau. within ~2 0 of the above estimate.," The CLEAN method recovered a best period of 3.61 d for V827 Tau, within $\sim$ 2 $\sigma$ of the above estimate." + The phased RV data are shown in Figures 13., The phased RV data are shown in Figures $-$ 3. + The presence of a starspot will distort the line profile at the RV that corresponds to the stellar velocity at he location of the spot., The presence of a starspot will distort the line profile at the RV that corresponds to the stellar velocity at the location of the spot. +" This distortion is iu proportion o the ratio of quiescent plotosphere surface brightuess and surface brightness within the spot. at the observing wavelength. aud the fraction of stellar surface covered by he spot οιο,,Quelozetal.2001)."," This distortion is in proportion to the ratio of quiescent photosphere surface brightness and surface brightness within the spot, at the observing wavelength, and the fraction of stellar surface covered by the spot \citep[e.g.,][]{que01}." +. Thus. asviunetries in the line profiles originatiug from) spots will be present or all lues in the spectimm of a voung star and are vpically correlated with the RV iecasured from the same spectrum.," Thus, asymmetries in the line profiles originating from spots will be present for all lines in the spectrum of a young star and are typically correlated with the RV measured from the same spectrum." +" These asvuuuetries have become the standard criterion for rejecting starspots as the cause of false RV. signals (ο,ο,,Quelozetal.2001:Bouvier2007:IIuertaetal.2008:Setiawan 2008)."," These asymmetries have become the standard criterion for rejecting starspots as the cause of false RV signals \citep[e.g.,][]{que01, bou07, hue08, set08}." +. For each of the six orders used to determine the RVs. woe cross-correlated all absorption lines and measured the cross-correlation function (CCE) for that order.," For each of the six orders used to determine the RVs, we cross-correlated all absorption lines and measured the cross-correlation function (CCF) for that order." + The average of these six οςΕμ was used to measure the bisector spans (lower panels of Figures 3), The average of these six CCFs was used to measure the bisector spans (lower panels of Figures $-$ 3). + The linear correlation cocficient and associated FAP (Bevineton&Robinson1992) 1 listed iu the captions., The linear correlation coefficient and associated FAP \citep{bev92} is listed in the captions. + As expected for a spotted star. a clear correlation between bisector span aud RV is observed for VSN27 Tau.," As expected for a spotted star, a clear correlation between bisector span and RV is observed for V827 Tau." + DN Tau aud. V836 Tau show no correlation. sugecsting that the variability is uot the result of spots.," DN Tau and V836 Tau show no correlation, suggesting that the variability is not the result of spots." + The contrast between a 1000 ER photosphere aud a 3000 I& spot (Bouvier&BertoutL989) is ercater in visible han in IR light because flux scales as a steeper function of cluperature at waveleugths shorter than the black body oeak (e...Carpenteretal.2001).," The contrast between a 4000 K photosphere and a 3000 K spot \citep{bou89} is greater in visible than in IR light because flux scales as a steeper function of temperature at wavelengths shorter than the black body peak \citep[e.g.,][]{car01}." +. Given the decreased spot to photosplere contrast in the near-IR. the amplitude of the RV modulation will be smaller.," Given the decreased spot to photosphere contrast in the near-IR, the amplitude of the RV modulation will be smaller." + Couversely. if a anet drives the RV iodulation. the aniplitude should o the same in visible aud IR light.," Conversely, if a planet drives the RV modulation, the amplitude should be the same in visible and IR light." + Blakeetal.(2007.2008) used. near-IBR. observatious o search for coimipanions τω lowanass objects. exploiting tellure absorption lines for high-precisioun RV ueasureineuts.," \citet{bla07, bla08} used near-IR observations to search for companions to low-mass objects, exploiting telluric absorption lines for high-precision RV measurements." + Figure [| shows an exiunple of a GJ 281 Is-band spectrum and illustrates oursimular approach., Figure 4 shows an example of a GJ 281 K-band spectrum and illustrates oursimilar approach. +" We created models by combining high resolution telluric isorption (Livingston&Wallace1991) aud cool stellar spectra (tle sunspot atlas of Wallace Livinestou 1992). LIραπιο a rauge of velocity shifts relative to the telluric aes,"," We created models by combining high resolution telluric absorption \citep{liv91} and cool stellar spectra (the sunspot atlas of Wallace Livingston 1992), applying a range of velocity shifts relative to the telluric lines." + Other free parameters ave esinz a Caussiauu EWIIM or the spectrometer Lue spread function. scale factors or line depths. aud a first order continu normalization Muction.," Other free parameters are $v$ $i$, a Gaussian FWHM for the spectrometer line spread function, scale factors for line depths, and a first order continuum normalization function." + We enploved the Marquardt method for LBrear least squares fitting (Bevington&Robinson1992) of each model to an observed spectrum., We employed the Marquardt method for non-linear least squares fitting \citep{bev92} of each model to an observed spectrum. + The difference οπου the stellar and telluric velocities in the best fit uodel spectrum vields the BV. which was then corrected or barvcentrie motion.," The difference between the stellar and telluric velocities in the best fit model spectrum yields the RV, which was then corrected for barycentric motion." + Figures 3 show the IB-derived relative RVs., Figures $-$ 3 show the IR-derived relative RVs. + The data are phased to the periods given in 833.1., The data are phased to the periods given in 3.1. + The RV staucdare. deviation in the IR data for ΠΟ 65277 is 127 ws 3 aud for CE 281 is O8 αν +., The RV standard deviation in the IR data for HD 65277 is 127 m $^{-1}$ and for GJ 281 is 98 m $^{-1}$. + Tuternal errors. incasured from the least squares fitting. are ~ 40 ni + for both standards.," Internal errors, measured from the least squares fitting, are $\sim$ 40 m $^{-1}$ for both standards." + For the vouug stars. iuterual errors were 300 12 l depending ou the SNR achieved.," For the young stars, internal errors were $-$ 300 m $^{-1}$, depending on the SNR achieved." + Random errors. which we asstme add in quadrature with our iternal errors to give the overall scatter in velocities. are 120 imi |! for IID 65277 aud 90 mi + for CI 281.," Random errors, which we assume add in quadrature with our internal errors to give the overall scatter in velocities, are 120 m $^{-1}$ for HD 65277 and 90 m $^{-1}$ for GJ 281." + Wo 1se dlOnns bas our final value for the raudoni errors., We use 110 m $^{-1}$ as our final value for the random errors. + The uncertaimties shown for the IR data in Figures 23 represent the sun. in quadrature. of the individual internal error aud the 110 ms 1 random error.," The uncertainties shown for the IR data in Figures $-$ 3 represent the sum, in quadrature, of the individual internal error and the 110 m $^{-1}$ random error." + Within our measurement precision. we are unable to detect auy IR RV variability iu DN Tau and V836 Tau.," Within our measurement precision, we are unable to detect any IR RV variability in DN Tau and V836 Tau." + V827 Tau shows significant IR RV variatious but at a reduced amplitude from those observed iu visible light., V827 Tau shows significant IR RV variations but at a reduced amplitude from those observed in visible light. + Figures l and 2 show the visible light RV. modulation for DN Tau and Vs3o Tau. with full amplitudes of ~1500 and ~2700 in ft. respectively.," Figures 1 and 2 show the visible light RV modulation for DN Tau and V836 Tau, with full amplitudes of $\sim 1500$ and $\sim 2700$ m $^{-1}$, respectively." + Within the 1 6 uncertainties. all but one poiut iu the IR RVs of DN Tau are cousisteut with zero: all six IR RVs of V836 Tau also show no variation.," Within the 1 $\sigma$ uncertainties, all but one point in the IR RVs of DN Tau are consistent with zero; all six IR RVs of V836 Tau also show no variation." + These results indicate that uo plaucts are present around DN Tau or V836 Tau with masses greater than a few Ανν at «0.5 AU or ~10 Mj at l AU. despite the absence of a correlation between the visible ποτ RVs aud bisector spans.," These results indicate that no planets are present around DN Tau or V836 Tau with masses greater than a few $_{Jup}$ at $<$ 0.5 AU or $\sim$ 10 $_{Jup}$ at $\sim$ 1 AU, despite the absence of a correlation between the visible light RVs and bisector spans." + Mathieuetal.(1989) identify V836 Tau aud V8S27 Tiu as RV variables with peak-to-peak amplitudes of ὅ kins +., \citet{mat89} identify V836 Tau and V827 Tau as RV variables with peak-to-peak amplitudes of $-$ 8 km $^{-1}$ . + Apparently the density aud size of spots on V836 Tau vary: historical data may serve as an additional criterion for heavily spotted young stars., Apparently the density and size of spots on V836 Tau vary; historical data may serve as an additional criterion for heavily spotted young stars. + The primary conclusion from our visible light data is that the lack of a correlation between the line bisector, The primary conclusion from our visible light data is that the lack of a correlation between the line bisector +Finally. for (he purpose of checking the impact of a ‘peculiar heavy element distribution on relative age-daling methods. we have also adopted the set of stellar models presented in accounting for an extreme CNONa chemical patterns.,"Finally, for the purpose of checking the impact of a peculiar heavy element distribution on relative age-dating methods, we have also adopted the set of stellar models presented in accounting for an extreme CNONa chemical patterns." + In order to cover the whole metallicity range sampled by GGCs properly. we have extended (he original set of models to lower metallicities. so the final database of stellar models adopted in the presen( analvsis covers an iron content range [from —2.39 to —0.56.," In order to cover the whole metallicity range sampled by GGCs properly, we have extended the original set of models to lower metallicities, so the final database of stellar models adopted in the present analysis covers an iron content range from $-2.89$ to $-0.56$." + For a detailed description of the assumed heavy element distribution and more details on (hese stellar models and isochrones we refer (he reader to (he quoted reference., For a detailed description of the assumed heavy element distribution and more details on these stellar models and isochrones we refer the reader to the quoted reference. + However. il is important to remark that the adopted heavy element clistvibution corresponds (o a mixture in which the sum (C'+N+Q) is enhanced by a factor of approximately 2 with respect to thereference mixture.," However, it is important to remark that the adopted heavy element distribution corresponds to a mixture in which the sum $+$ $+$ O) is enhanced by a factor of approximately 2 with respect to the mixture." + This value is consistent - although it represents an upper limit - with the results of the spectroscopic analvsis performed by for the extreme values of the chemical anti-correlations observed in GGCs., This value is consistent - although it represents an upper limit - with the results of the spectroscopic analysis performed by for the extreme values of the chemical anti-correlations observed in GGCs. + ]t is worth noting that the stellar models for (he various chemical compositions adopted in the present work are based on (he most up-to-date physics currently available and. more importantly for our aim. all evolutionary predictions are fully homogeneous ancl being based exactly on the same physical framework.," It is worth noting that the stellar models for the various chemical compositions adopted in the present work are based on the most up-to-date physics currently available and, more importantly for our aim, all evolutionary predictions are fully homogeneous and self-consistent, being based exactly on the same physical framework." +" Belore closing this section. we wish to note that it is quite important to perform the comparison between isochrones and those corresponding to the""peculiar chemical patterns at fixed iron content."," Before closing this section, we wish to note that it is quite important to perform the comparison between isochrones and those corresponding to the chemical patterns at fixed iron content." + The main reasons for this choice are the following: when performing relative GGC age measurements the commonly adopted procedure is to divide the whole cluster sample into sub-samples on the basis of their |Fe/IIl] value (that is. the parameter provided by spectroscopical measurements) and (hen to apply the adopted relative age dating method to each selected sub-sample: at fixed global metallicity Z. and hence MT]. a change in the helium content (see above) and/or in the heavy element distribution (see the discussion im. implies a change in the corresponding |Fe/1l) value.," The main reasons for this choice are the following: when performing relative GGC age measurements the commonly adopted procedure is to divide the whole cluster sample into sub-samples on the basis of their [Fe/H] value (that is, the parameter provided by spectroscopical measurements) and then to apply the adopted relative age dating method to each selected sub-sample; at fixed global metallicity Z, and hence [M/H], a change in the helium content (see above) and/or in the heavy element distribution [see the discussion in implies a change in the corresponding [Fe/H] value." + Therefore. in order to obtain reliable results. we need to use the same approach that is adopted when managing real stellar svstems: (hal means investigating the impact of changing the helium content or the heavy element distribution at fixed |Fe/1l].," Therefore, in order to obtain reliable results, we need to use the same approach that is adopted when managing real stellar systems; that means investigating the impact of changing the helium content or the heavy element distribution at fixed [Fe/H]." + In this section. the most widely used relative age-dating methods are described.," In this section, the most widely used relative age-dating methods are described." + Figure illustrates the horizontal. vertical and rMSE (techniques. applied to 8. 10. 12. and 14 Gyr," Figure illustrates the horizontal, vertical and rMSF techniques, applied to 8, 10, 12, and 14 Gyr" +"This result suggests that the aabundance in the different velocity components. defined as X(HCO)=N(HCO™)/Ny. ranges between 5x107'"" and 5x10? toward both W49N and W451.","This result suggests that the abundance in the different velocity components, defined as $X({\rm HCO}^{+}) = N({\rm HCO}^{+})/N_{\rm H}$, ranges between $\times 10^{-10}$ and $\times 10^{-9}$ toward both W49N and W51." + For HCN. the scatter of abundances is also an order of magnitude among the components. with values ranging between 2x107? and 3x10 for W49N. A similar scatter is also found for HNC with abundances ~10 times smaller.," For HCN, the scatter of abundances is also an order of magnitude among the components, with values ranging between $\times 10^{-9}$ and $\times 10^{-8}$ for W49N. A similar scatter is also found for HNC with abundances $\sim 10$ times smaller." + In summary. since the column densities of the Gaussian components span less than two orders of magnitude while their linewidths span only a factor ~10 (between 0.3 and 3.4 )). actual fluctuations of molecular abundances are therefore observed among the components.," In summary, since the column densities of the Gaussian components span less than two orders of magnitude while their linewidths span only a factor $\sim +10$ (between 0.3 and 3.4 ), actual fluctuations of molecular abundances are therefore observed among the components." + The above average description 1s crude and is only meant to ascribe an average column density to a velocity interval. ignoring velocity crowdings: the lines of sight toward distant star-forming regions sample gas components with a broad distribution of densities. velocity dispersions. and column densities.," The above average description is crude and is only meant to ascribe an average column density to a velocity interval, ignoring velocity crowdings: the lines of sight toward distant star-forming regions sample gas components with a broad distribution of densities, velocity dispersions, and column densities." + We have shown that the upper limit on the gas density is ng«5x107 ((cf., We have shown that the upper limit on the gas density is $n_{\rm H} < 5 \times 10^{3}$ (cf. + Sect. 3.1) , Sect. \ref{SectTemp}) ) +and that the total column densities per velocity components Ny are at most of the order of a few magnitudes. similar to those obtained along the high latitude lines of sight observed by Liszt Lucas (2001).," and that the total column densities per velocity components $N_{\rm H}$ are at most of the order of a few magnitudes, similar to those obtained along the high latitude lines of sight observed by Liszt Lucas (2001)." + According to the definitions of Snow MeCall (2006). the gas sampled by these lines of sight is a mixture of diffuse Gay«500 em? with a shielding from the UV field Ay«1) and translucent gas ( 500 i 10 Τον energies.,shock is actively accelerating particles to $>10$ TeV energies. + Moreover. ROW 86 is detected by ILE.S.S. as a TeV eanuna-ray source (Aharonianetal.2008)..," Moreover, RCW 86 is detected by H.E.S.S. as a TeV gamma-ray source \citep{aharonian08}. ." + DIudecd elderetal.(2009). found that the plasima temperature isa factor of at least three lower than expected given the neasuredl sliock velocity., Indeed \citet{helder09} found that the plasma temperature is a factor of at least three lower than expected given the measured shock velocity. + Towever. this value could not be directly translated iuto a fractional cosmic-ray pressure dud the shock. but was translated iuto a lower Πιτ of fractional cosmic-ray pressure of 25056.," However, this value could not be directly translated into a fractional cosmic-ray pressure behind the shock, but was translated into a lower limit of fractional cosmic-ray pressure of $\geq 50$." + This lower iuit was derived using the Raukine-Unegouiot relatious or a two-fluid shock (seealsoVink2008).., This lower limit was derived using the Rankine-Hugoniot relations for a two-fluid shock \citep[see also][]{vink08d}. + Here we explore the Raukinc-IHueconiot relations for a two-fluid shock further., Here we explore the Rankine-Hugoniot relations for a two-fluid shock further. + We show that for a eiven ractional cosmic-ray pressure «(=PoPor). there js a unique cosmic-ray chcrey escape f/flux. eel=Fu.fApy V2). associated with it that ouly depends ou the overall Mach umber of the shock.," We show that for a given fractional cosmic-ray pressure $w(\equiv P_{\rm cr}/P_{\rm tot})$, there is a unique cosmic-ray energy escape flux, $\epsilon_{\rm esc} (= F_{\rm cr}/\frac{1}{2}\rho_0 V_s^3)$ , associated with it that only depends on the overall Mach number of the shock." + Iu the next section we present the derivation of the relation between a. ες and post-shock plasma temperature.," In the next section we present the derivation of the relation between $w$, $\epsilon_{\rm esc}$ and post-shock plasma temperature." + Iu Sect., In Sect. + 3. we discuss this relation aud its limitations im the context of two-fluid models. ando cosmic-ray acceleration inodels and we use the relatious to derive the /cosnüc-cray pressure content for the northeastern region of ROW 56 aud for the newly measured plasiua temperature of the voung Large Magellanic Cloud SNR 0509-67.5 (elderetal.2010).," \ref{discussion} we discuss this relation and its limitations in the context of two-fluid models, and cosmic-ray acceleration models, and we use the relations to derive the cosmic-ray pressure content for the northeastern region of RCW 86 and for the newly measured plasma temperature of the young Large Magellanic Cloud SNR 0509-67.5 \citep{helder10}." +". Efficient particle acc‘cleration by shocx frouts loads to a shock structure that «eviates sienificauIv from a normal ""oue fluid” shock (c.g.Drury&Voclk|951:BerezhkoDruryetal.2009:IKaug;Reville 20093: the particles diffusing ahead (=upstream) of the shock. forma a shock precursor that pre-compresses and slows down the gas flowing iuto the shock."," Efficient particle acceleration by shock fronts leads to a shock structure that deviates significantly from a normal “one fluid” shock \citep[e.g.][]{drury81,berezhko99,blasi05,vladimirov08,drury09,kang09,reville09}: the particles diffusing ahead (=upstream) of the shock, form a shock precursor that pre-compresses and slows down the gas flowing into the shock." + The pre-compressiou caused by the precursor adiabatically heats the gas., The pre-compression caused by the precursor adiabatically heats the gas. + The Mach nunber at the shock is. therefore. reduced with respect to the overall Mach umber. as the shock velocity is reduced aud the gas pressure upstream of the shock is increased with respect to a shock without a precursor.," The Mach number at the shock is, therefore, reduced with respect to the overall Mach number, as the shock velocity is reduced and the gas pressure upstream of the shock is increased with respect to a shock without a precursor." + Additional heating of the eas may occur in the precursor due to non-adiabatie processes such as Alfvéóunie heating (0.8.Vladinirovetal.2008:Capriol2008).," Additional heating of the gas may occur in the precursor due to non-adiabatic processes such as Alfvénnic heating \citep[e.g.][]{vladimirov08,caprioli08}." +. Iu sich a multi-Huid system. the shock that heats the plasma is called the subshock.," In such a multi-fluid system, the shock that heats the plasma is called the subshock." + Tn the limit of a one fluid gas the subshock is identical to the shock., In the limit of a one fluid gas the subshock is identical to the shock. + Tere we follow a different approach then Blasietal.villeetal.(2009) in that we treat the whole svstem oulv thermodvuamically. using a two-fluid approach. with the two components represcuting the thermal gas aud a eas of accelerated particles (cosmic ravs).," Here we follow a different approach then \citet{blasi05,vladimirov08,kang09,reville09} + in that we treat the whole system only thermodynamically, using a two-fluid approach, with the two components representing the thermal gas and a gas of accelerated particles (cosmic rays)." + For the moment we ueelect the possible influence of nou-adiabatic heating iu the shock precursor due to interactions between the gas and accelerated particles., For the moment we neglect the possible influence of non-adiabatic heating in the shock precursor due to interactions between the gas and accelerated particles. + Our approach is reminiscent of the work by Drury&Vocls(1981). (seealsoAchterbereetal.1051Voelk198:Drury2009) ancl is an exteusiou of the work presented by Vink(2008). aud IIelderetal.(2009).," Our approach is reminiscent of the work by \citet{drury81} + \citep[see also][]{achterberg84,voelk84,drury09} + and is an extension of the work presented by \citet{vink08d} and \citet{helder09}." +. Our starting point is the basic Equations expressing conservation of nass. momentum aud οποίον flux.," Our starting point is the basic Equations expressing conservation of mass, momentum and energy flux." + We evaluate these expressions for three distinct regious: (0) far upstream. where the presence of accelerated particles can be neglected. (1) in the shock precursor. just upstream of the subshock. aud (2) behind (downstream of) the shock.," We evaluate these expressions for three distinct regions: (0) far upstream, where the presence of accelerated particles can be neglected, (1) in the shock precursor, just upstream of the subshock, and (2) behind (downstream of) the shock." + Mass fiux couservation gives: with e the velocity of the gas with respect to the shock., Mass flux conservation gives: with $v$ the velocity of the gas with respect to the shock. + Note that ey=Vy. the shock velocity in the observers fraane of reference.," Note that $v_0=V_s$, the shock velocity in the observer's frame of reference." + Momentum flix conservation can be expressed as: with P the pressure., Momentum flux conservation can be expressed as: with $P$ the pressure. +" At this point it is convenient to introduce the Mach uunuber My for the shock structure far upstream. with >, the adiabatic iudex of the thermal particles."," At this point it is convenient to introduce the Mach number $M_0$ for the shock structure far upstream, with $\gamma_g$ the adiabatic index of the thermal particles." +" Iu addition we introduce the compression ratios across the different regions 0.1. aud 2: We now use the assiuuption that the thermal pressure in the precursor is only due to adiabatic heating iu the precursor. 1.0. Py4,=Poy"" (c.f.Druryetal.2009).. anc that across the subshock the pressure associated with the accelerated particles does not chanee (seeDrury&Voclk1981:Achterbere 2001)."," In addition we introduce the compression ratios across the different regions 0,1, and 2: We now use the assumption that the thermal pressure in the precursor is only due to adiabatic heating in the precursor, i.e. $P_{1,th}= P_0 \chi_1^{\gamma_g}$ \citep[c.f.][]{drury09}, and that across the subshock the pressure associated with the accelerated particles does not change \citep[see][]{drury81,achterberg04}." +. The cosmic-ray terius therefore cancel each other iu Equation (2)). when considering the 1iomienutuni flux from region 1 to 2.," The cosmic-ray terms therefore cancel each other in Equation \ref{eq:momentum}) ), when considering the momentum flux from region 1 to 2." + In other words the non-thermal particle pressure at the subshock isoulv relevaut for reducing the Mach umuber. but leads otherwise again to the standard. oue fluid. relation for shock compression with a reduced Mach number given by: Combining Equatious (2)). (3)). aud (1)) one finds for the total downstream pressure 75 aud the thermal pressure P: with the subscript er referring to the cosmüc ravs.," In other words the non-thermal particle pressure at the subshock isonly relevant for reducing the Mach number, but leads otherwise again to the standard, one fluid, relation for shock compression with a reduced Mach number given by: Combining Equations \ref{eq:momentum}) ), \ref{eq:mach}) ), and \ref{eq:chi}) ) one finds for the total downstream pressure $P_2$ and the thermal pressure $P_{th}$: with the subscript $cr$ referring to the cosmic rays." + We have introduced here the syaibol a describing the fraction of the dowustream pressure contributed bv cosunic ravs (c.f.Vink2008:elderetal. 2009):: Usinga prep9=poVl/xvQ-we can now derive. an expression for the fractional cosmic-ray pressure for a even Mach umber My:," We have introduced here the symbol $w$ describing the fraction of the downstream pressure contributed by cosmic rays \citep[c.f.][]{vink08d,helder09}: : Using $\rho_1v_1^2=\rho_0V_s^2/\chi_1$we can now derive an expression for the fractional cosmic-ray pressure for a given Mach number $M_0$ :" +"the galaxy, contain a small RGB population and are presumed to represent an underlying halo population in this galaxy.","the galaxy, contain a small RGB population and are presumed to represent an underlying halo population in this galaxy." +" The origin of the large stellar feature around M33 is discussed in ??),, and we refer the reader to those papers for more details."," The origin of the large stellar feature around M33 is discussed in \citet{2009Natur.461...66M,2010ApJ...723.1038M}, and we refer the reader to those papers for more details." + Here we summarise the main conclusions of these authors in light of our additional results., Here we summarise the main conclusions of these authors in light of our additional results. + Their favoured scenario assumes that the structure is the result of a tidal disturbance caused by the motion of M33 around M31., Their favoured scenario assumes that the structure is the result of a tidal disturbance caused by the motion of M33 around M31. +" The northwest - southeast symmetry of the ""S-shaped"" structure, and the rough alignment with the warp, are the main pieces of evidence supporting this interpretation."," The northwest - southeast symmetry of the ""S-shaped"" structure, and the rough alignment with the warp, are the main pieces of evidence supporting this interpretation." + Simulations of the M31-M33 system have showed that a close encounter at a pericentre distance of about 40 kpc would excite tidal tails in M33 without severely distorting or disrupting the disc., Simulations of the M31-M33 system have showed that a close encounter at a pericentre distance of about 40 kpc would excite tidal tails in M33 without severely distorting or disrupting the disc. + These simulations also set the epoch of the encounter to be between 2 and 3 Gyr ago., These simulations also set the epoch of the encounter to be between 2 and 3 Gyr ago. +" However, within this scenario it would be difficult to reconcile the metallicity difference between the structure ((M/H]---1.3) and the disc ((M/H]=--0.7,-0.4) stellar populations, a difference that we also detect within our data set."," However, within this scenario it would be difficult to reconcile the metallicity difference between the structure -1.3) and the disc -0.7,-0.4) stellar populations, a difference that we also detect within our data set." +" On the other hand, if the structure originated from the disruption of a dwarf galaxy such a difference in the metal abundance would not be an issue, and this scenario is also considered as a plausible alternative."," On the other hand, if the structure originated from the disruption of a dwarf galaxy such a difference in the metal abundance would not be an issue, and this scenario is also considered as a plausible alternative." + The lack of a visible progenitor would imply that the dwarf galaxy has been entirely destroyed prior to the current epoch., The lack of a visible progenitor would imply that the dwarf galaxy has been entirely destroyed prior to the current epoch. + From the SFH that we derived in Sect., From the SFH that we derived in Sect. +" 6, the total stellar mass in field NW7 would amount to ~2x10° Mo,, and ?) estimate that the total luminosity of the whole structure is My=—12.7, 6 7)). (?).."," 6, the total stellar mass in field NW7 would amount to $\sim 2 \times 10^6$ , and \citet{2010ApJ...723.1038M} estimate that the total luminosity of the whole structure is $_V = -12.7$ \ref{rad_cmd_south} \ref{rad_cmd_north})\ref{young} \citep{1998ARA&A..36..189K}. \citep{2005ApJ...619L..79T,2007ApJS..173..538T}." + (??).. ?) , \citet{2010AJ....140.1194B} +based on the Chebyshev functions where the sunm is over all primes p and integers 5.,based on the Chebyshev functions where the sum is over all primes $p$ and integers $k$. +" In. Theorem 1.1. normalization of in Theorem ⋅1.1 is bv""n rt according. toDA (3)) and Zis. absolutely convergent for allPCr) ο” z0. whereas in. . (12)) normalization. is. by Yu and the sum X——Sue58. is not absolutely convergent."," In Theorem 1.1, normalization of $\Phi(x)$ in Theorem 1.1 is by $x^\frac{1}{4}$ according to \ref{EQN_D}) ) and$Z$ is absolutely convergent for all $x>0$ , whereas in \ref{EQN_vm}) ) normalization is by $\sqrt{u}$ and the sum $\Sigma \frac{u^{z_k-\frac{1}{2}}}{z_k}$ is not absolutely convergent." + sinilar to Corollary 1.2. it will be appreciated that the left hand side of (12)) will be bounded in the limit of large « if the Riemann hypothesis is (rue.," Similar to Corollary 1.2, it will be appreciated that the left hand side of \ref{EQN_vm}) ) will be bounded in the limit of large $u$ if the Riemann hypothesis is true." + In 822. we give some background on C(2).," In 2, we give some background on $\zeta(z)$." + In 833 we introduce an integral representation of €(2) and derive one oL its integral properties associated with (he singularitv of Q(z) al 2=1., In 3 we introduce an integral representation of $\xi(z)$ and derive one of its integral properties associated with the singularity of $\zeta(z)$ at $z=1$. +" In 844. we apply Cauchy's integral formula to Q(z) to derive a sum of residues associated bv the z,."," In 4, we apply Cauchy's integral formula to $\zeta(z)$ to derive a sum of residues associated by the $z_k$." + The proof Theorem 1.1 is given in 855 by a Fourier transform and. asymptotic analvsis of the expanded Eulers identitv., The proof Theorem 1.1 is given in 5 by a Fourier transform and asymptotic analysis of the expanded Euler's identity. + In. 866. we report on a direct evaluation of (ur) using (he primes up to one trillion. to show the harmonic behavior as as encoded in Z by the first [ew zeros τε.," In 6, we report on a direct evaluation of $\Phi(x)$ using the primes up to one trillion, to show the harmonic behavior as as encoded in $Z$ by the first few zeros $z_k$ ." + We summarize our findings in 877., We summarize our findings in 7. + Our analvsis uses some well known properties of Q(z) ancl ils zeros z;αι+iyi. ο... in Titchmarsh(1986):Lehmer(1988):Dusart(1999):IXeiper(1992):Forel (2002))).," Our analysis uses some well known properties of $\zeta(z)$ and its zeros $z_k=a_k+iy_k$, e.g., in \cite{tit86,leh88,dus99,kei92,for02}) )." + Riemann provided an analytic extension of €(2) to the entire complex plane by expressing each term in terms of T (4). wheresatisfies the asvinptotie property (46r)~Se as cr approaches zero bv the identitv Art)=yr0Cr)n ForB the Jacobi. functionB. 6Ce).!n Evaluation. ofB the integral. (14))FEN on," Riemann provided an analytic extension of $\xi(z)$ to the entire complex plane by expressing each term $n^{-z}$ in terms of $\Gamma\left(\frac{z}{2}\right)$ , wheresatisfies the asymptotic property $\theta_1(x)\sim \frac{1}{2\sqrt{x}}$ as $x$ approaches zero by the identity $\theta(x^{-1})=\sqrt{x}\theta(x)$ for the Jacobi function $\theta(x)$ Evaluation of the integral \ref{EQN_I1}) ) on" +This means that observations could indicate what the most suitable choice of the flux function should be.,This means that observations could indicate what the most suitable choice of the flux function should be. + The results of the double-layered prominences have revealed that a double-layered structure in pressure and density can be created in actual filament configurations., The results of the double-layered prominences have revealed that a double-layered structure in pressure and density can be created in actual filament configurations. +" 'The relative strength of the gravitational potential must be sufficient: if the potential is weak, a ring structure appears, where a cavity surrounds the prominence."," The relative strength of the gravitational potential must be sufficient: if the potential is weak, a ring structure appears, where a cavity surrounds the prominence." +" As for cool prominences, the location of the maximum pressure and density is shifted increasingly downwards if the gravity importance is increased."," As for cool prominences, the location of the maximum pressure and density is shifted increasingly downwards if the gravity importance is increased." +" In our accompanying paper (?), the stability properties of these equilibria will be analyzed, with special attention to the continuous MHD spectrum."," In our accompanying paper \citep{Blokland_2011B}, the stability properties of these equilibria will be analyzed, with special attention to the continuous MHD spectrum." +" Owing the presence of gravity, gaps or even instabilities may appear in this continuous spectrum."," Owing the presence of gravity, gaps or even instabilities may appear in this continuous spectrum." +" Furthermore, inside these gaps new global modes may occur, which provide us with important information about the internal structure of the prominence."," Furthermore, inside these gaps new global modes may occur, which provide us with important information about the internal structure of the prominence." +" Before investigating the possible appearance of global modes, a detailed analysis of the continuous spectrum will be required."," Before investigating the possible appearance of global modes, a detailed analysis of the continuous spectrum will be required." +become possible to. study more significant samples of GC LAINB systems by looking at cxtragalactic sources.,become possible to study more significant samples of GC LMXB systems by looking at extragalactic sources. + These observations of nearby galaxies confirm that their GCs also contain a large fraction of the galaxies LAINBs., These observations of nearby galaxies confirm that their GCs also contain a large fraction of the galaxies' LMXBs. + Unfortunately. investigating dynamical formation in extragalactic clusters is dillicult cue to the small angular sizes of typical cluster cores.," Unfortunately, investigating dynamical formation in extragalactic clusters is difficult due to the small angular sizes of typical cluster cores." + However. relationships between the collision rate ancl presence. of. LAINBs have been suggested in M31. (2)... Cen A (7) ancl possibly in MIST (?7).," However, relationships between the collision rate and presence of LMXBs have been suggested in M31 \citep{Peacock09}, Cen A \citep{Jordan07} and possibly in M87 \citep{Jordan04,Waters07}." +. Lt is also found. both in the Milkv. Way and nearby galaxies. that LAINBs favour brighter (and hence more massive) GC's (e.g.7777).," It is also found, both in the Milky Way and nearby galaxies, that LMXBs favour brighter (and hence more massive) GCs \citep[e.g.][]{Kundu02,Sarazin03,Kim06,Kundu07}." +" ""Phe likely reason [or this is that higher mass clusters will generally. have more stellar interactions and therefore form more LAINBs through dynamical interactions.", The likely reason for this is that higher mass clusters will generally have more stellar interactions and therefore form more LMXBs through dynamical interactions. + However. it is also possible that LMXDs will favour high mass clusters because they may retain more of the neutron stars they produce.," However, it is also possible that LMXBs will favour high mass clusters because they may retain more of the neutron stars they produce." + Neutron gaars that are formed by core collapse may be formed. with -aree kick velocities (c.g.?).., Neutron stars that are formed by core collapse may be formed with large kick velocities \citep[e.g.][]{Hobbs05}. + In this case. the higher escape Pelocities of high mass clusters. may result in more neutron gaars being retained by these clusters.," In this case, the higher escape velocities of high mass clusters, may result in more neutron stars being retained by these clusters." + However. it is also possible that neutron stars with lower kick velocities can be formed via electron capture (e.g.22).," However, it is also possible that neutron stars with lower kick velocities can be formed via electron capture \citep[e.g.][]{Pfahl02,ivanova08}." + 7. demonstrated that 16 GC systems of six elliptical galaxies are consistent with 1e retention of neutron stars from a low kick velocity mocle., \citet{Smits06} demonstrated that the GC systems of six elliptical galaxies are consistent with the retention of neutron stars from a low kick velocity mode. + Previous work on extragalactic LAINBs has also identified that metal rich. clusters are more likely to host LAINBs than metal poor clusters (c.g.2??)...," Previous work on extragalactic LMXBs has also identified that metal rich clusters are more likely to host LMXBs than metal poor clusters \citep[e.g.][]{Bellazzini95,Kundu02,Kundu03}." + Several explanations for this have heen proposed., Several explanations for this have been proposed. + Metal rich stars are likely to be physically larger. which may result in more LAINBs forming through tidal interactions ancl clirect collisions (7)..," Metal rich stars are likely to be physically larger, which may result in more LMXBs forming through tidal interactions and direct collisions \citep{Bellazzini95}." + It was shown by (2). that this effect alone is unlikely to explain the observed. factor 3 enhancement of LAINBs in metal rich. clusters., It was shown by \citep{Maccarone04} that this effect alone is unlikely to explain the observed factor 3 enhancement of LMXBs in metal rich clusters. + They. propose that the irradiation induced. winds in these binaries may explain the observed. dilferences., They propose that the irradiation induced winds in these binaries may explain the observed differences. + These winds are likely to be stronger in metal poor systems due to decreased. line. cooling., These winds are likely to be stronger in metal poor systems due to decreased line cooling. + ? suggested. that the metallicity relationship is a natural consequence of the properties of solar mass donor stars., \citet{Ivanova06} suggested that the metallicity relationship is a natural consequence of the properties of solar mass donor stars. + In this mass range. they show that low metallicity stars lack an outer convective zone.," In this mass range, they show that low metallicity stars lack an outer convective zone." + This is likely to reduce the rate of tidal captures ancl also make it harder for a binary to tighten (and hence form an LMXD system)., This is likely to reduce the rate of tidal captures and also make it harder for a binary to tighten (and hence form an LMXB system). + llere. we investigate LAINBs in M31s GC svstem.," Here, we investigate LMXBs in M31's GC system." + In section 2.. we consider the current optical ancl X-ray catalogues of M3Is clusters.," In section \ref{sec:xray:m31gc}, , we consider the current optical and X-ray catalogues of M31's clusters." + Section 3. presents the rav properties of M3Is clusters. based. on observations of the galaxy. and compares these data with previous X-rav catalogues to investigate transient. sources and potential. contamination in these previous studies.," Section \ref{sec:xray:m31gc_xray} presents the X-ray properties of M31's clusters, based on observations of the galaxy, and compares these data with previous X-ray catalogues to investigate transient sources and potential contamination in these previous studies." + Finally. in section 4.. we investigate the properties of clusters which are found to host LAINBs.," Finally, in section \ref{sec:xray:lmxb_gc_properties}, we investigate the properties of clusters which are found to host LMXBs." + The M31: GC system has been the focus of many studies., The M31 GC system has been the focus of many studies. + Despite this work. it is likely that some contamination and incompleteness currently exists in the M31. cluster catalogues.," Despite this work, it is likely that some contamination and incompleteness currently exists in the M31 cluster catalogues." + To identify. clusters in M31. we use the recent catalogue of 7.hereafter. P10.., To identify clusters in M31 we use the recent catalogue of \citet[][hereafter P10]{Peacock10}. . + Phis catalogue includes. all clusters and. candidates. identified in most major studies of the M31. GC system. (includingthoseof:TTTTTY.," This catalogue includes all clusters and candidates identified in most major studies of the M31 GC system \citep[including those of: ][]{Battistini87,Barmby00,Galleti04,Kim07,Caldwell09}." + b provides updated locations and classifications for all of these clusters., It provides updated locations and classifications for all of these clusters. + Phe locations of these clusters are found to be in eood agreement with those of 7.. but are more accurate iun those used. previously to mateh with X-ray catalogues (e.g.?7).," The locations of these clusters are found to be in good agreement with those of \citet{Caldwell09}, , but are more accurate than those used previously to match with X-ray catalogues \citep[e.g.][]{Barmby00,Galleti04}." + Phe work of PLO and ? has also identified significant contamination in the previous catalogues from. stellar sources. background galaxies anc voung clusters.," The work of P10 and \citet{Caldwell09} has also identified significant contamination in the previous catalogues from stellar sources, background galaxies and young clusters." + AI31 has been extensively surveyed. by most recent observatories including: (ee.2): (og.77): (e.g.2?) and (og.22)..," M31 has been extensively surveyed by most recent X-ray observatories including: \citep[e.g.][]{Trinchieri91}; \citep[e.g.][]{Supper97,Supper01}; \citep[e.g.][]{Shirey01,Trudolyubov04} and \citep[e.g.][]{Kaaret02,Williams04}." + Many of the resulting N-ray source catalogues have attempted to identify which sources are associated with GC's., Many of the resulting X-ray source catalogues have attempted to identify which sources are associated with GCs. +" 2 associated 33 sources in their. survey with known GC's from the combined. GC catalogues of ον, 2. and. 7."," \citet{Supper01} associated 33 sources in their survey with known GCs from the combined GC catalogues of \citet{Battistini87}, \citet{Battistini93} and \citet{Magnier93}." + observations were used by 2.. 2.. 2? and ? to identify. 28. 25. 25 and 26 GC X-ray sources. respectively.," observations were used by \citet{DiStefano02}, \citet{Kong02}, \citet{Kaaret02} and \citet{Williams04} to identify 28, 25, 25 and 26 GC X-ray sources, respectively." + Currently the most complete M31 GC X-ray catalogue was produced by ?.., Currently the most complete M31 GC X-ray catalogue was produced by \citet{Trudolyubov04}. + They combined observations along the disk of M31 with archived observations. to investigate 43 X-ray sources which they associated with GC's (fromtheGCcataloguesof: 2227)..," They combined observations along the disk of M31 with archived observations, to investigate 43 X-ray sources which they associated with GCs \citep[from the GC catalogues of:][]{Battistini87,Magnier93,Barmby01,Galleti04}." + Most recently. ? collated the results of these previous studies to identify 54 unique GC's associated with X-rav sources.," Most recently, \citet{Fan05} collated the results of these previous studies to identify 54 unique GCs associated with X-ray sources." + In this studs. we consider the X-ray. properties of AL31's GC's using all publicly available observations of the galaxy.," In this study, we consider the X-ray properties of M31's GCs using all publicly available observations of the galaxy." + Since the study of 2.. the coverage of M31 has increased. significantly ancl now covers the entire De; ellipse of the galaxy.," Since the study of \citet{Trudolyubov04}, the coverage of M31 has increased significantly and now covers the entire $_{25}$ ellipse of the galaxy." + These data provide more accurate source locations than the study of ? and cover many more clusters than the previous X-ray stuclics of M31Is GCs (??)..," These data provide more accurate source locations than the study of \citet{Supper01} and cover many more clusters than the previous X-ray studies of M31's GCs \citep{DiStefano02,Trudolyubov04}." + In this study we restrict. our analysis to only those clusters classed as confirmed. clusters in the recent catalogue of N31 GCs of PLO., In this study we restrict our analysis to only those clusters classed as confirmed clusters in the recent catalogue of M31 GCs of P10. + Phe previous GC X-ray associations have generally considered all cluster canclicdates in the galaxy., The previous GC X-ray associations have generally considered all cluster candidates in the galaxy. + While the presence of an X-ray source in a cluster does increase the probability of it being a genuine cluster. the inclusion of such sources is also likely to increase contamination.," While the presence of an X-ray source in a cluster does increase the probability of it being a genuine cluster, the inclusion of such sources is also likely to increase contamination." + Over the past decade. M31. has been the target of several observations.," Over the past decade, M31 has been the target of several observations." + The first. LO observations. of ALB} were obtained as part of the science verification. of the telescope., The first 10 observations of M31 were obtained as part of the science verification of the telescope. + Phese observations included five observations along the disk of the galaxy. four observations of the core of the galaxy and a shorter observation of the halo GC Gi.," These observations included five observations along the disk of the galaxy, four observations of the core of the galaxy and a shorter observation of the halo GC G1." + These data are described by 2.. who use it for their study of the galaxys GC's.," These data are described by \citet{Trudolyubov04}, who use it for their study of the galaxy's GCs." + Since these initial observations. several other fields of the galaxy have been observed.," Since these initial observations, several other fields of the galaxy have been observed." + These include: repeated. observations of the bright X-ray sources RNJ20042.6|4115 (a bright Z-source in M31) and D375 (the brightest GC X-ray source in thegalaxy): an observation of the dwarf galaxy NGC 205: an observation on theminor axis of.M31: and four observations to cover the recently discovered. extended halo GCs in the galaxy., These include: repeated observations of the bright X-ray sources RXJ20042.6+4115 (a bright Z-source in M31) and B375 (the brightest GC X-ray source in thegalaxy); an observation of the dwarf galaxy NGC 205; an observation on theminor axis ofM31; and four observations to cover the recently discovered extended halo GCs in the galaxy. + In addition to these observations a survey was recently completed to cover, In addition to these observations a survey was recently completed to cover +Ultraluminous Infrared Galaxies (ULIBGs) have quasar-like bolometric Iuminosities 10?L.. ) dominated by the far-infrared 10007) part of the spectrum (Sanders Mirabel. 1996).,"Ultraluminous Infrared Galaxies (ULIRGs) have quasar-like bolometric luminosities $>10^{12} L_{\odot}$ ) dominated by the far-infrared $\mu$ m) part of the spectrum (Sanders Mirabel, 1996)." + Almost all ULIRGs are interacting or merging galaxies (Clements et al., Almost all ULIRGs are interacting or merging galaxies (Clements et al. + 1996). possibly linking (hem to the transformation of disk galaxies into ellipticals (eg.," 1996), possibly linking them to the transformation of disk galaxies into ellipticals (eg." + Wrieht et al. 1990: Baker Clements. 1997).," Wright et al, 1990; Baker Clements, 1997)." + The prodigious luminosity of ULIRGs is thought to be powered by a massive starburst. a dust.buried AGN or some combination of the two.," The prodigious luminosity of ULIRGs is thought to be powered by a massive starburst, a dust–buried AGN or some combination of the two." + Despite a decade of work we still have not been able to decide between (hese paracdigms., Despite a decade of work we still have not been able to decide between these paradigms. + Various scenarios have also been suggested linking (he evolution of quasars will ULIBGSs (ee., Various scenarios have also been suggested linking the evolution of quasars with ULIRGs (eg. + Sanders et al..," Sanders et al.," + 1983)., 1988). + These suggest (hat part of the liminosity we see Irom some ULIBGs originates in a AGN which later destrovs or expels the enshrouding material., These suggest that part of the luminosity we see from some ULIRGs originates in a dust--obscured AGN which later destroys or expels the enshrouding material. + Meanwhile. studies of the X-rav background (Mushotzky et al. 2000) suggest that dust.enshrouded AGN make a substantial contribution (to its hard component.," Meanwhile, studies of the X-ray background (Mushotzky et al, 2000) suggest that dust–enshrouded AGN make a substantial contribution to its hard component." + Such objects may also be linked (Trentham Blain. 2001: Almaini et al..," Such objects may also be linked (Trentham Blain, 2001; Almaini et al.," + 1999) to the recently discovered Cosmic Infrared Background (Puget et al., 1999) to the recently discovered Cosmic Infrared Background (Puget et al. + 1996: Fixsen οἱ al..," 1996; Fixsen et al.," + 19983) and the objects that contribute to it (Puget οἱ al., 1998) and the objects that contribute to it (Puget et al. + 1999: Sanders 2000 and references therein)., 1999; Sanders 2000 and references therein). + As the most obseurecl objects in the local universe. and as strong candidates for making the CIB. ULIRGs are ideal local laboratories for studying many of these issues.," As the most obscured objects in the local universe, and as strong candidates for making the CIB, ULIRGs are ideal local laboratories for studying many of these issues." +" Arp 220 is the nearest ULIRG. having an 8-10007/ lIumninosity of ~1.2x10PL, and a redshift οἱ:=0.018."," Arp 220 is the nearest ULIRG, having an $\mu$ m luminosity of $\sim 1.2 \times 10^{12}L_{\odot}$ and a redshift of $z=0.018$." + As such it is an ideal target for ULIRG studies., As such it is an ideal target for ULIRG studies. + The consensus since, The consensus since +recent analytic work on (ranslationally invariant magnelohvdrostatic equilibria with uniform ervavily in Carlesian geometry. bv allowing a free boundary between (he prominence flux rope and (he ambient coronal magnetic field ancl allowing one to choose the polvtropic index freely.,"recent analytic work on translationally invariant magnetohydrostatic equilibria with uniform gravity in Cartesian geometry, by allowing a free boundary between the prominence flux rope and the ambient coronal magnetic field and allowing one to choose the polytropic index freely." + The various classes of magnetolvelrostatic solutions discussed in what [ollows each lead to a second order PDE. which FINESSE solves in weak form using a Picard iteration.," The various classes of magnetohydrostatic solutions discussed in what follows each lead to a second order PDE, which FINESSE solves in weak form using a Picard iteration." + We mplemented the various forms obtained for this PDE under different choices of freely chosen flux functions. along with their sealings. as discussed in the Appendix.," We implemented the various forms obtained for this PDE under different choices of freely chosen flux functions, along with their scalings, as discussed in the Appendix." + We restrict our numerical calculations to static solutions which are translationally svimmetric. all of which fall into an elliptic regime where a split between the ecquilibrium and (he perturbations in a forthcoming stability analvsis can meaninglullv be performed.," We restrict our numerical calculations to static solutions which are translationally symmetric, all of which fall into an elliptic regime where a split between the equilibrium and the perturbations in a forthcoming stability analysis can meaningfully be performed." + Consider the static-equilibrium model based on (he one-fuid ideal hvdromagnetic description. denoting the magnetic field. plasma pressure and density by B. p ancl p. respectively.," Consider the static-equilibrium model based on the one-fluid ideal hydromagnetic description, denoting the magnetic field, plasma pressure and density by ${\bf B}$ , $p$ and $\rho$, respectively." + The balance of forces is described bv assumine a uniform local eravily of acceleration g in the —: Cartesian direction., The balance of forces is described by assuming a uniform local gravity of acceleration $g$ in the $-z$ Cartesian direction. + Then the ideal gas law relates the gas pressure p (o the gas density p where Ay is Doltzmann's constant ancl je is the mean particle mass for a fully ionized (monatomic) hydrogen plasma., Then the ideal gas law relates the gas pressure $p$ to the gas density $\rho$ where $k_B$ is Boltzmann's constant and $\mu$ is the mean particle mass for a fully ionized (monatomic) hydrogen plasma. + The solenoidal condition closes the set of equations to determine p. p. and D.," The solenoidal condition closes the set of equations to determine $p$, $\rho$, and ${\bf B}$." + To keep the physical problem simple. we avoid the complication of a full energv equation by applving in tun (wo assumptions: (1) that the plasma temperature is a flux Iunction 7=P(e) Gneluding the isothermal case T—Ty a constant). and (2) the polviropic case where the entropy s=p/p?s(o) is a flux function. (," To keep the physical problem simple, we avoid the complication of a full energy equation by applying in turn two assumptions: (1) that the plasma temperature is a flux function $T=T(\psi )$ (including the isothermal case $T=T_0$ a constant), and (2) the polytropic case where the entropy $s=p/\rho^{\gamma}=s(\psi )$ is a flux function. (" +Thepolvtropic case wilh 5 equal to the ratio of specilic heats describes an adiabatic,Thepolytropic case with $\gamma$ equal to the ratio of specific heats describes an adiabatic +The scattering of radiation in resonance lines plays an miportaut role iu many parts of astroplivsies. iucludiug stellar atmospheres. diffuse nebula. and active galactic nuclei.,"The scattering of radiation in resonance lines plays an important role in many parts of astrophysics, including stellar atmospheres, diffuse nebula, and active galactic nuclei." + In the early universe. resonance scatteriug iu the hydrogen line has been shown to be an crucial process for understanding the st:e of the primordial gas during the recombination era (Peebles1968:Zeldovieh.hurt.&Suuvaev1969).," In the early universe, resonance scattering in the hydrogen line has been shown to be an crucial process for understanding the state of the primordial gas during the recombination era \citep{Peebles68,Zeldovich69}." +. Tt can also can play a critical role in determining the populations of the fiue structure levels iu the LS level of hydrogen (Woutluvseu1952:Field1958.1959).. aud thus affect the formation of the 24cm line. observations of which promise to be au importaut source of information about the carly universe (loganTozzi.Madan.Meiksiun.&Rees 2000).," It can also can play a critical role in determining the populations of the fine structure levels in the $S$ level of hydrogen \citep{Wouthuysen52, Field58, Field59}, and thus affect the formation of the 21cm line, observations of which promise to be an important source of information about the early universe \citep{Hogan79, MMR97, +Tozzi00}." +.. It may also ple a role in direct heating of the eas (Madau.Moeikson.&Rees1997:ChenMiralda-Escudé2001).," It may also play a role in direct heating of the gas \citep{MMR97, Chen04}." + The theoretical description of resonance line scattering is based ou a R. which eives tle probability that an initial photon state will be scattered iuto some final photon state.," The theoretical description of resonance line scattering is based on a $R$, which gives the probability that an initial photon state will be scattered into some final photon state." + The level of description of these photon states depends on the problem treated., The level of description of these photon states depends on the problem treated. + For this paper we coufine our attention to problems where the radiation field is sutiicicutly isotropic that only the anele-averaged form of the redistribution function needs to be used. aud also that the radiation can be considered uuipolarized.," For this paper we confine our attention to problems where the radiation field is sufficiently isotropic that only the angle-averaged form of the redistribution function needs to be used, and also that the radiation can be considered unpolarized." + The redistrbition function then depeuds oulv ou the intitial 7’ and final v frequencies of the scattered pioton. that is. Rl’).," The redistribution function then depends only on the intitial $\nu'$ and final $\nu$ frequencies of the scattered photon, that is, $R(\nu,\nu')$." + For aand other resonance line scattering in low «eusitv iiedia. coliereunt scattering iu the atoms rest frame from a natural (Loreutz) profο ds appropriate.," For and other resonance line scattering in low density media, coherent scattering in the atom's rest frame from a natural (Lorentz) profile is appropriate." + When one :counts for the Doppler effect due to atoms with a Alaxwellian velocity distribution. a scattered photon will have its frequency decreased or iucreased depending ou the components of the atomic velocity along he initial aud. final photon «irections.," When one accounts for the Doppler effect due to atoms with a Maxwellian velocity distribution, a scattered photon will have its frequency decreased or increased depending on the components of the atomic velocity along the initial and final photon directions." + Theappropriate redistribution function under these conditions was first derived bv Tenvey(1911). and. folowing IHhununuer(1962). is usuallv denoted (Gr).," Theappropriate redistribution function under these conditions was first derived by \citet{Henyey41} and, following \citet{Hummer62}, is usually denoted $\rii(\nu,\nu')$." + For mauv cases iu astroplivsics. 2jp captures the dominant plivsics for resonance line transfer.," For many cases in astrophysics, $\rii$ captures the dominant physics for resonance line transfer." + The solution of line. trausfer problems using a full redistribution function Ay is not trivial. since all frequencies are coupled together.," The solution of line transfer problems using a full redistribution function $\rii$ is not trivial, since all frequencies are coupled together." + Dowever. there is au inport:uit class of problems where an approximate formulation can effectively used. namely. when t1e radiation field is sufficieutly smooth ou the scale of the Doppler width of the liue.," However, there is an important class of problems where an approximate formulation can effectively used, namely, when the radiation field is sufficiently smooth on the scale of the Doppler width of the line." + Then it is possible to derive aFokker-Planck (F-P) type of trauster equation. where the redistriibution is taken iuto account by a second-order differcutial operator over frequency space.," Then it is possible to derive a (F-P) type of transfer equation, where the redistribution is taken into account by a second-order differential operator over frequency space." + An equation of this type was first given by Cuno(1952).. and improvements were nade subsequently by Darrington(1973).. Basko (1981).. and by Bybicki&DellAntonio(199L.hereafterRD)..," An equation of this type was first given by \citet{Unno52}, and improvements were made subsequently by \citet{Harrington73}, \citet{Basko81}, and by \citet[][hereafter RD]{RD94}." + Another effect on redistribution is the loss of photon cnerev during scattering due to the recoil of the atom., Another effect on redistribution is the loss of photon energy during scattering due to the recoil of the atom. + This is completely analogous to the ordinary Compton effect. but is smaller by the ratio of electron to atomic mass.," This is completely analogous to the ordinary Compton effect, but is smaller by the ratio of electron to atomic mass." + The recoil effect was first discussed bv Field(1959) for the case of resonance scattering with zero natural line width (Ryinthenotationof, The recoil effect was first discussed by \citet{Field59} for the case of resonance scattering with zero natural line width \citep[$R_{\rm I}$ in the notation of. +1962). Adams(1971). qualitatively considered recoil for Ry iu the context of sscatterineg in the neutral hydrogen of the galactic disk., \citet{Adams71} qualitatively considered recoil for $\rii$ in the context of scattering in the neutral hydrogen of the galactic disk. + Basko(1981) derived the appropriate generalization of the Ry iucluding recoil redistribution function aud showed that it led to a simple additional term in the F-P formulation., \citet{Basko81} derived the appropriate generalization of the $\rii$ including recoil redistribution function and showed that it led to a simple additional term in the F-P formulation. + showed how the Basko tex could be included in them F-P equation aud how it affected its solutions.," \citet{RD94} + showed how the Basko term could be included in their F-P equation and how it affected its solutions." + Iu all the cases treated by Adams. Basko. aud RD the recoil term did not seem to be important. at least for its effect ou the radiation field itself.," In all the cases treated by Adams, Basko, and RD the recoil term did not seem to be important, at least for its effect on the radiation field itself." + IToxcever. Madan.Meiksou.&Rees(1997). argued that the atomic recoil in sscatteriug could be au inportaut heating mechanisin for the intergalactic meditu before reionization. basing their analysis onu a simple formula that iucluded recoil but no other effect.," However, \citet{MMR97} argued that the atomic recoil in scattering could be an important heating mechanism for the intergalactic medium before reionization, basing their analysis on a simple formula that included recoil but no other effect." + This was also investigated by Chen&Miralda-Escudé (2001). who found a ach lower heating rate using the RD F-P equatious with Basko term.," This was also investigated by \citet{Chen04}, , who found a much lower heating rate using the RD F-P equations with Basko term." +the Oosterholl properties of. globular-cluster variables are strongly. connected to their horizontal-branch evolutionary state (Clement&Shelton1999).,the Oosterhoff properties of globular-cluster variables are strongly connected to their horizontal-branch evolutionary state \citep{cs99}. +. Nevertheless. it should be noted that Smith&Sandage(1951) called attention to the fact that no cluster exhibits a large plurality of decreasing period.," Nevertheless, it should be noted that \cite{ss81} called attention to the fact that no cluster exhibits a large plurality of decreasing period." + On the whole. the HB evolution is a plausible explanation for increasing periods.," On the whole, the HB evolution is a plausible explanation for increasing periods." + Stars within/— the instability strip evolve rapidly from blue to red. toward the end of core helium burning. producing a large positive rate of period change.," Stars within the instability strip evolve rapidly from blue to red, toward the end of core helium burning, producing a large positive rate of period change." + In this respect. it is worth mentioning the dillerence between the period-change behaviour of the RRab stars of the clusters M3 and ALS.," In this respect, it is worth mentioning the difference between the period-change behaviour of the RRab stars of the clusters M3 and M5." + Although both clusters belong to Oosterhol-type Land resemble cach other in many aspects. M5 has fewer strongly increasing periods than M3.," Although both clusters belong to Oosterhoff-type I and resemble each other in many aspects, M5 has fewer strongly increasing periods than M3." + In M5. only five out of the 44 RRab (11. per cent) have very large period-increase rate (6320.20 dMyr ty while in ALIS. 29 per cent of the RRab stars have.," In M5, only five out of the 44 RRab (11 per cent) have very large period-increase rate $\beta>0.20$ $^{-1}$ ), while in M3, 29 per cent of the RRab stars have." + In other Ool-tvpe clusters. M14 (Wehlau&Froelich 1994).. M28 (Weblauοἱal.1986). and NCC 7006 (Wehlauetal.1999). the frecqucney of RRab stars with strongly increasing periods are 16. S and 10 per cent. respectively.," In other OoI-type clusters, M14 \citep{wf94}, , M28 \citep{w86} and NGC 7006 \citep{w99} the frequency of RRab stars with strongly increasing periods are 16, 8 and 10 per cent, respectively." + This simple statistic shows that the M5 RRab stars behave like other Ool-tvpe clusters. and only M3 behaves somewhat cdilferentIv.," This simple statistic shows that the M5 RRab stars behave like other OoI-type clusters, and only M3 behaves somewhat differently." + One of the most intriguing issues connected. with the period changes of It Lyrac stars is the large negative values of 2. observed in different clusters.," One of the most intriguing issues connected with the period changes of RR Lyrae stars is the large negative values of $\beta$, observed in different clusters." + Among the 44 Rab stars of M5 that have parabolic or straight-line O—C' diagrams. nine (20 per cent) show decreasing periods with as high rate as d«4Ol HF. that certainly. cannot. be explained by canonical LIB evolution.," Among the 44 RRab stars of M5 that have parabolic or straight-line $O-C$ diagrams, nine (20 per cent) show decreasing periods with as high rate as $\beta<-0.1$ $^{-1}$, that certainly cannot be explained by canonical HB evolution." + It is worth mentioning that the mean period of the sample of 44 λα stars is 0.5622 d. whereas the mean period of the nine ab stars with fast decreasing period is significantly less. 0.5127 d. A comparison with other well-studied globular clusters proves that the occurrence of RRab stars with very [ast period decreases is a general feature. characteristic of both Oosterholl-tvpes.," It is worth mentioning that the mean period of the sample of 44 RRab stars is 0.5622 d, whereas the mean period of the nine ab stars with fast decreasing period is significantly less, 0.5127 d. A comparison with other well-studied globular clusters proves that the occurrence of RRab stars with very fast period decreases is a general feature, characteristic of both Oosterhoff-types." +. For example. ll out of the 35. Rab stars (31 per cent) in M3 (Corwin&Carney2001). and 9 out of the 42 ab variables (21 per cent) in NGC 6934 (Stage&Wehlau1980) exhibit Large period decreases (ή«0.10 D.," For example, 11 out of the 35 RRab stars (31 per cent) in M3 \citep{cc01} and 9 out of the 42 ab variables (21 per cent) in NGC 6934 \citep{sw} exhibit large period decreases $\beta<-0.10$ $^{-1}$ )." + The Ooll-tvpe clusters also have (perhaps relatively less in numbers) RRab stars with strong »eriod decreases., The OoII-type clusters also have (perhaps relatively less in numbers) RRab stars with strong period decreases. + In aw Cen. 29 Bltab stars of the chemically 10mogeneous group have linear period changes. and among hem. four (14 per cent) have strong period decreases (tableTinJuresiketal.2001).," In $\omega$ Cen, 29 RRab stars of the chemically homogeneous group have linear period changes, and among them, four (14 per cent) have strong period decreases \citep[table 7 in][]{ocen}. ." +. In. AILS. there are two out of 13 tab stars (15 per cent) that show strong period decreases (Silbermann&Smith1995)...," In M15, there are two out of 13 RRab stars (15 per cent) that show strong period decreases \citep{ss95}." + The trend that the mean period of the ab stars with fast period. decreases is shorter han the mean period of the whole sample also holds for the clusters mentioned., The trend that the mean period of the ab stars with fast period decreases is shorter than the mean period of the whole sample also holds for the clusters mentioned. +" To resolve the contraction between canonical LB evolutionary model predictions and the observed frecqucney of strong period decreases. it is generally supposed that most of the period changes are due to some kind of ""noise rather than to evolutionary cllects."," To resolve the contradition between canonical HB evolutionary model predictions and the observed frequency of strong period decreases, it is generally supposed that most of the period changes are due to some kind of `noise' rather than to evolutionary effects." + Sweigart&Renzini(1979) have found that the mixing events at the convective core edge. the transfer of helium into the convective core an the subsequent chemical readjustment of the semi-convective zone around the core. is an intrinsically noisy process tha can lead to large period-decrease rates.," \cite{sr79} have found that the mixing events at the convective core edge, the transfer of helium into the convective core and the subsequent chemical readjustment of the semi-convective zone around the core, is an intrinsically noisy process that can lead to large period-decrease rates." + Reeenthy. SilvaAguirreetal.(2008) have given an alternative explanation for the frequent. occurrence. of strong period decreases among the cluster variables.," Recently, \cite{si08} have given an alternative explanation for the frequent occurrence of strong period decreases among the cluster variables." + They constructed pre-ZALLB evolutionary tracks for a chemica composition appropriate to the globular cluster ALB. ane investigated the period-change behaviour of variables in the final approach to the ZALIB location.," They constructed pre-ZAHB evolutionary tracks for a chemical composition appropriate to the globular cluster M3, and investigated the period-change behaviour of variables in the final approach to the ZAHB location." + Γον have found that. before settling on the ZALIB. the variables are subject to à μαrong period decrease with the most likely 3 values around ⋅ ⊥ ∪⋅⇀∫≻∠∟∖↓∙∖⇁↓⋅⋡⋡⋯⊔↓∪↓⋅⋖⋅∢⊾⇀∖⇂↓⋅∢⊾⊔↓∢⊾∖⇁⋜↧↓⋯⋅⊳∖↿∖∪⋅↖∖∠∟∖↓∙∖⇁↓⋅∃⊔↓⋜↧∙∖⇁ ⊥ also take place.," They have found that, before settling on the ZAHB, the variables are subject to a strong period decrease with the most likely $\beta$ values around $-0.3$ $^{-1}$, but more extreme values $-0.8$ $^{-1}$ ) may also take place." + The model simulations have also shown mt some percent of the RR Lyrac population are in the pre-ZALLD. evolutionary state. and the pre-ZALB pulsators are expected. to have longer periods than the bona Lice —D pulsators.," The model simulations have also shown that some percent of the RR Lyrae population are in the pre-ZAHB evolutionary state, and the pre-ZAHB pulsators are expected to have longer periods than the bona fide HB pulsators." + As M5 resembles M3. in dilferent aspects. 1erefore the model caleulations of SilvaAguirreetal.(2008) can be compared with our results.," As M5 resembles M3 in different aspects, therefore the model calculations of \cite{si08} can be compared with our results." + The high percentage of variables with decreasing periods and the relatively shorter mean periods of these stars in ALS show that. likely. the pre-ZALB evolution cannot fully explain the observations.," The high percentage of variables with decreasing periods and the relatively shorter mean periods of these stars in M5 show that, likely, the pre-ZAHB evolution cannot fully explain the observations." + Nevertheless. further model calculations of the pre-ZALB evolutionary phase may leacl to more satisfactory results.," Nevertheless, further model calculations of the pre-ZAHB evolutionary phase may lead to more satisfactory results." + lt is perplexing. however. why the observed: period-increase rates are in very @ood agreement with evolutionary predictions. if the period-decrease rates are not.," It is perplexing, however, why the observed period-increase rates are in very good agreement with evolutionary predictions, if the period-decrease rates are not." + 1 this is indeed the case. some significant difference between Rit Lyrac stars with increasing ancl decreasing period rates should be found. but observationally. there is no evidence of any dillerence between these stars.," If this is indeed the case, some significant difference between RR Lyrae stars with increasing and decreasing period rates should be found, but observationally, there is no evidence of any difference between these stars." + lt is an interesting question whether the evolutionary cllects are apparent in the cdilferent diagrams of cluster variables. e.g. period-amplitude. period-brightness. etc.," It is an interesting question whether the evolutionary effects are apparent in the different diagrams of cluster variables, e.g. period-amplitude, period-brightness, etc." + diagrams., diagrams. + Fig., Fig. + 5 and Fig., \ref{vp} and Fig. + 6 /—show the relationships between the intensitv-averaged— mean Y brightness (35 and period. as well as between the Yamplitude (24).and the period.," \ref{vap} show the relationships between the intensity-averaged mean $V$ brightness $\langle V \rangle$ and period, as well as between the $V$amplitude $A_V$ )and the period." + Phe period-change rate and its direction. are, The period-change rate and its direction are +constructed. from empirical stellar spectra (?)..,constructed from empirical stellar spectra \citep{sanchez06}. + Phe stellar population ages used in the models ranged from 7100 Alves to ~13 GGyers., The stellar population ages used in the models ranged from $\sim$ 100 Myrs to $\sim$ Gyrs. + The spectral resolution of the science data is degraded to match that of the templates., The spectral resolution of the science data is degraded to match that of the templates. + The fitting is then performed. using the penalized. pixel fitting algorithm of ? which fits the spectrum using a combination of input template spectra and simultaneously fitting for the recession velocity and. velocity. dispersion., The fitting is then performed using the penalized pixel fitting algorithm of \citet{cappellari04} which fits the spectrum using a combination of input template spectra and simultaneously fitting for the recession velocity and velocity dispersion. + We measure line equivalent widths from each spectrum using the flux summing technique., We measure line equivalent widths from each spectrum using the flux summing technique. + Ες uses three wavelength bands to define the equivalent width: one centred on the line itself and two Llankine bands on either side of the line to define the expected continuum level by linear extrapolation., This uses three wavelength bands to define the equivalent width; one centred on the line itself and two flanking bands on either side of the line to define the expected continuum level by linear extrapolation. + For lines at the blue end. of the spectrum. including Ld. llis and LL. we measure line strength equivalent: widths on the Lick/Intermediate Dispersion Spectrograph svsten (?7)..," For lines at the blue end of the spectrum, including $\delta$, $\gamma$ and $\beta$, we measure line strength equivalent widths on the Lick/Intermediate Dispersion Spectrograph system \citep{worthey97,trager98}." + Prior to measuring the indices the science. spectra are convolved with a wavelength:dependent Gaussian to the Lick resolution (9 AA))., Prior to measuring the indices the science spectra are convolved with a wavelength–dependent Gaussian to the Lick resolution $\sim$ ). + For lines red-ward of the Lick indices. in. particular Ho and NHJAG5S3 that do not have standard. definitions. we again use the Luxsumming technique with appropriate line and continuum bands.," For lines red-ward of the Lick indices, in particular $\alpha$ and $\lambda 6583$ that do not have standard definitions, we again use the flux–summing technique with appropriate line and continuum bands." + In the third. column of Fig., In the third column of Fig. + 3. we show the equivalent width maps for the Le. Hz. and Lh? lines combined as a straight average.," \ref{fig:images} we show the equivalent width maps for the $\delta$, $\gamma$ and $\beta$ lines combined as a straight average." + Ehe trends in these maps are also present in each of the individual line maps but combining the lines results in greater signal-to-noise., The trends in these maps are also present in each of the individual line maps but combining the lines results in greater signal-to-noise. + The equivalent width maps can be compared. with the distribution of overall. galaxy fight shown in column 2 bv collapsing the light through the original unbinned HEU. elements along the wavelength direction and column 1I which shows an SDSS colour image with the LEU field-of-view superimposed., The equivalent width maps can be compared with the distribution of overall galaxy light shown in column 2 by collapsing the light through the original unbinned IFU elements along the wavelength direction and column 1 which shows an SDSS colour image with the IFU field-of-view superimposed. +αρ. le}A 1 has a uniform very. strong Ηὸ signature spread. across the entire extent of the galaxy., E+A 1 has a uniform very strong $\delta$ signature spread across the entire extent of the galaxy. + lt also dillers to the rest of the sample in other respects: it is the only irregular svstem ancl easily the bluest galaxy in the sample., It also differs to the rest of the sample in other respects: it is the only irregular system and easily the bluest galaxy in the sample. + As mentioned in Table σιA 2 (NGC 3156) is à member of the Spectroscopic Areal Unit For Research on Optical Nebulae (SAUION) sunple (7). enabling us to compare our Balmer absorption line map with the LL? map of? and we note that the maps are in good agreement., As mentioned in Table \ref{tab:targets} E+A 2 (NGC 3156) is a member of the Spectroscopic Areal Unit For Research on Optical Nebulae (SAURON) sample \citep{dezeeuw02} enabling us to compare our Balmer absorption line map with the $\beta$ map of \citet{kuntschner10} and we note that the maps are in good agreement. + In the last column of Fig., In the last column of Fig. + 3. we have azimuthally binned the data before measuring line indices to construct radial Balmer line eracients., \ref{fig:images} we have azimuthally binned the data before measuring line indices to construct radial Balmer line gradients. + The Balmer line enhancement seen in the two dimensional maps are seen as negative Balmer line racial eracients., The Balmer line enhancement seen in the two dimensional maps are seen as negative Balmer line radial gradients. + These radial profiles of the Balmer line equivalent width are similar to those predicted. from merger mocels ο., These radial profiles of the Balmer line equivalent width are similar to those predicted from merger models c.f. + Fig., Fig. + 9 of ον., 9 of \citet{pracy05}. + The observed. gradients are confined to à smaller racius than the models (which show enhancements with a negative gradient over 2 kkpce) but this is expected eiven the models are for significantly brighter galaxies which should have a larger central starburst region., The observed gradients are confined to a smaller radius than the models (which show enhancements with a negative gradient over $\sim$ kpc) but this is expected given the models are for significantly brighter galaxies which should have a larger central starburst region. + 1n Figure 4. we show an age-metallicity diagnostic diagram for our galaxies using the LI and 54668 lines., In Figure \ref{fig:lindia} we show an age-metallicity diagnostic diagram for our galaxies using the $\delta$ and $_{2}4668$ lines. + The line ratios are shown for the radial data with the smallest diamond representing the innermost radial point ancl increasing radii represented by increasing larger symbol sizes., The line ratios are shown for the radial data with the smallest representing the innermost radial point and increasing radii represented by increasing larger symbol sizes. + The age-metallicity erids are from the single stellar population models o£ ?? and assume solar abundance ratios.," The age-metallicity grids are from the single stellar population models of \citet{thomas03,thomas04} and assume solar abundance ratios." + The Balmer line racial gracients can be seen as luminosity weighted age gradients in this plot., The Balmer line radial gradients can be seen as luminosity weighted age gradients in this plot. + In general. the smaller inner radial cata points have vounger ages than those at largerὃν radii.," In general, the smaller inner radial data points have younger ages than those at larger radii." + Phe inner racial regionso have agesὃν l1GCGOvr consistent with what is expected. for I2]A galaxies. ancl similar to the elobal ages of the ? I2|A sample which are overlaid assquares., The inner radial regions have ages $\lesssim 1$ Gyr consistent with what is expected for E+A galaxies and similar to the global ages of the \citet{pracy09} E+A sample which are overlaid as. + We estimated. the mass in. recently formed: stars. [rom the best fitting stellar population templates as described in Section 34., We estimated the mass in recently formed stars from the best fitting stellar population templates as described in Section 3.4. + In this case we constructed. a spatially integrated spectrum. for each of our sample by summing over all spaxels within a circular aperture of radius 11 areseconds., In this case we constructed a spatially integrated spectrum for each of our sample by summing over all spaxels within a circular aperture of radius 11 arcseconds. + We fitted the spectra with a combination of a single old. stellar population of age 13€GGwvr and a set of voung stellar population models with ages ranging rom 100Myr to ~1 αν (all model stellar populations assumed solarM metallicity) and calculated the mass fraction of the voung stellar population., We fitted the spectra with a combination of a single old stellar population of age $\sim 13$ Gyr and a set of young stellar population models with ages ranging from Myr to $\sim 1$ Gyr (all model stellar populations assumed solar metallicity) and calculated the mass fraction of the young stellar population. + This results in burst. mass raction estimates of between 6 ancl 12pper cent for all ealaxies in our sample except. I21X 1 which is best. fitted with pper cent voung mass fraction Le. we are unable o quantify the old stellar population in this galaxy., This results in burst mass fraction estimates of between $\sim 6$ and per cent for all galaxies in our sample except E+A 1 which is best fitted with per cent young mass fraction i.e. we are unable to quantify the old stellar population in this galaxy. + These mass fractions correspond to the νους stellar. population contributing between pper cent anc pper cent of the ight between and5500., These mass fractions correspond to the young stellar population contributing between per cent and per cent of the light between and. +".. ""Phe caleulatecl burst. mass. fractions. are not sensitive to the precise age chosen for the old. stellar population since the spectra of old stellar populations do not change rapidly with age.", The calculated burst mass fractions are not sensitive to the precise age chosen for the old stellar population since the spectra of old stellar populations do not change rapidly with age. + For the voung population there are degeneracies between age and burst fraction in the sense hat decreasing the age of the stellar population has a similar ellect as increasing the burst fraction., For the young population there are degeneracies between age and burst fraction in the sense that decreasing the age of the stellar population has a similar effect as increasing the burst fraction. + To illustrate this we itted again allowing the combination of only two models., To illustrate this we fitted again allowing the combination of only two models. + First we fitted an old ~13 GGyr model anc a voung stellar x»pulation of age MMyrs which resulted. in the mass paction estimates increasing to between Lipper cent and I7pper cent 151A again returns a ppoer cent voung mass fraction and is poorly fitted by this combination), First we fitted an old $\sim 13$ Gyr model and a young stellar population of age Myrs which resulted in the mass fraction estimates increasing to between per cent and per cent (E+A 1 again returns a per cent young mass fraction and is poorly fitted by this combination). + We also fitted the combination of a ~ 13Gvr model and a vounger 500Myr. template which resulted. in the range of mass fractions decreasing to 73 pper cent (le| Al has a voung mass fraction of ~25 pper cent. under. these assumptions)., We also fitted the combination of a $\sim 13$ Gyr model and a younger Myr template which resulted in the range of mass fractions decreasing to $\sim$ per cent (E+A 1 has a young mass fraction of $\sim$ per cent under these assumptions). + These lower burst fractions by mass. still contribute significantly to the overall light (between 40 and 5Opper cent) since the vounger stellar populations have a smaller mass-to-light ratio., These lower burst fractions by mass still contribute significantly to the overall light (between 40 and per cent) since the younger stellar populations have a smaller mass-to-light ratio. + Reducing the age of the voung fraction reduces the burst mass fractions further but results in progressively poorer fits (again the exception is Le|A 1 which is better fitted by a vounger population)., Reducing the age of the young fraction reduces the burst mass fractions further but results in progressively poorer fits (again the exception is E+A 1 which is better fitted by a younger population). + Overall. the recently formed stars account for of order. ppercent," Overall, the recently formed stars account for of order percent" +The analysis of nebular spectra constitutes the best. and ≜ ↓⊔≱∖∪⊔↓⋖⋅≼∙⋜↧≱∖∢⋅≱∖↥⇂↥∢⋅∩⊔↓∙∖⇁∪⊔⋖⋅⊳⊔↓∢⊾↿↓↥⋯⇂⇂∪↓⋅⇂↓↕⋖⊾∠⇂∢⊾∩⋅↓⋅⊔∐⊔⋜∐↓∪⊔ ⋅ ≜≜ of. chemical. abundances in. spiral. ancl irregular. galaxies.. as well as in BEsites of. recent star formation.,"The analysis of nebular spectra constitutes the best, and in some cases the only one, method for the determination of chemical abundances in spiral and irregular galaxies, as well as in sites of recent star formation." +". alThe abundances of several Lolelements like le.He. οO. κ mEanc is‘ can"" in. !principleincinle |be determinedUs bssince strong emission. ilines of these.i elements.l some of them in their dominant ionization states. are present in the optical region of the spectrum."," The abundances of several elements like He, O, N and S can in principle be determined since strong emission lines of these elements, some of them in their dominant ionization states, are present in the optical region of the spectrum." + This requires: knowledge of the electron temperature which: can ‘OU. es NI. . . Dur. ».7 LIπο. ο SameMnaiae ," This requires knowledge of the electron temperature which can be obtained by measuring appropriate line ratios like, $\frac{ \lambda 7327}{\lambda 3727 + \lambda 3729}$ , or $\frac{\lambda 6312}{\lambda 9069 + \lambda 9532}$." +Unfortunately. these. line ratios usually involve. one intrisicallv weak line which can be detected anc measured with confidence only [or the brighter and hotter objects and in many cases — distant galaxies. low surface brightness objects. relatively low excitation regions — they become too faint to be observed.," Unfortunately, these line ratios usually involve one intrisically weak line which can be detected and measured with confidence only for the brighter and hotter objects and in many cases – distant galaxies, low surface brightness objects, relatively low excitation regions – they become too faint to be observed." + In these cases. an empirical method based on. the intensities of the casily observable optical lines is widely used.," In these cases, an empirical method based on the intensities of the easily observable optical lines is widely used." + The method. originally proposed by Pagel (1979) ancl Alloin ((1979). relies on the variation of these lines with oxveen abundance.," The method, originally proposed by Pagel (1979) and Alloin (1979), relies on the variation of these lines with oxygen abundance." +" Pagel (1979).- defined.⋅ απ abundance parameter Ro,23—VENT0HHNIS.Nour which increases with increasing abundance for abundances lower than about solar. and then reverses its. behavior. decreasing with increasing abundance. since above this value a higher oxvgen abundance leads to a more elfective cooling. the electron temperature gets lower and the optical emission lines get weaker."," Pagel (1979) defined an abundance parameter $R_{23} = \frac{[OII] \lambda 3727 +[OIII] \lambda 4959 + \lambda 5007}{H\beta}$ which increases with increasing abundance for abundances lower than about solar, and then reverses its behavior, decreasing with increasing abundance, since above this value a higher oxygen abundance leads to a more effective cooling, the electron temperature gets lower and the optical emission lines get weaker." + ↓⊔↓≻↓⋅↓⊔≼⇍↓↓≻↓⋖⊾⊳↿∐⋖⋅≼∼⋜↧↓↓∣⋡↓⋅⋜∐↓∪⊔∪⇂⇂↓↕∢⊾∫⊐⊐⊽⋝∠⋅↙∣⊳∣∖∣∣∣∖∪⇀∖∙∖⇁⋏∙≟⋖⊾⊔ . ⋅ ≽ abundance relation. can be done empiricallvD. in. the low metallicity↔ regime. where electron. temperatures can. be derived.. directly.. but requires. the use of⋅ theoretical. models for⋅ the so called high. abundance branch.," In principle, the calibration of the $R_{23}$ oxygen abundance relation can be done empirically in the low metallicity regime where electron temperatures can be derived directly, but requires the use of theoretical models for the so called high abundance branch." + Several. cülferente calibrations. have been made (Edmunds: Pagel 1984: AleCall. 1985: Evans: Dopita. 1986:2 SkillmanQu 1989: AMeCGaugh 1991) as more observational data ancl more improved. models have become available., Several different calibrations have been made (Edmunds Pagel 1984; McCall 1985; Evans Dopita 1986; Skillman 1989; McGaugh 1991) as more observational data and more improved models have become available. +. However. two problems that are difficult to solve still remain.," However, two problems that are difficult to solve still remain." + The first one is related to the two-valued nature of the calibration. which can lead to important. errors in the derived: abundances.," The first one is related to the two-valued nature of the calibration, which can lead to important errors in the derived abundances." + The second one concerns the dependence. of fo; on the degree of ionization of the nebula (see Skillman 1989)., The second one concerns the dependence of $R_{23}$ on the degree of ionization of the nebula (see Skillman 1989). + fo: also depends. on density. but. this can be considered: as a second order ellect. for low density regions (ng c 100 7) which constitute the majority of the extragalactic population.," $R_{23}$ also depends on density, but this can be considered as a second order effect for low density regions $n_H$ $\simeq$ 100 $^{-3}$ ) which constitute the majority of the extragalactic population." + These two facts. taken together. produce a large dispersion. of the data. for. values of ού205 and 12|'og(O/H)28.0. with objects with the same value of logH»s having actual abundances which οου by almost an order of magnitude.," These two facts, taken together, produce a large dispersion of the data for values of $logR_{23} \geq 0.8$ and $12+log(O/H) \geq 8.0$, with objects with the same value of $log R_{23}$ having actual abundances which differ by almost an order of magnitude." + Unfortunately. a significant number of objects (about of the observed LIM galaxies: baz ⊔↸1999) haveave fogHis;Mom0.8OS lorfor whichwhie the> calibrationcalibrati is; most uncertain. and this percentage is even higher for LII regions in normal spiral galaxies.," Unfortunately, a significant number of objects (about of the observed HII galaxies; az 1999) have $logR_{23} \geq +0.8$ for which the calibration is most uncertain, and this percentage is even higher for HII regions in normal spiral galaxies." + Llere we present an alternative abundance calibration based on the intensities of the sulphur lines: SII] 66716.," Here we present an alternative abundance calibration based on the intensities of the sulphur lines: [SII] 6716," +(unueling process inthe Minkowski space.,with the conformal block in the Liouville theory. + There are a fewargumentis supporting such interpretation., Hence we could inspect the derivatives with respect to the equivariant parameters at the Liouville side. + Firstnote thatthedyonic instanton can, Of course we would like to gain some new insights from this formal procedure. + be generalized tothe multiple circular tubular D2 branes [8].. The solutio, The main goal is to identify the group of rotation of $R^4$ in Euclidean space or Lorentz group in the Minkowski version in the Liouville theory. +nhas zero net R-R D2 brane charge however there, The naive guess could be that the algebra generated by screening operators should play the key role. + is non-vanishing dipole four-Iorm field streng, We shall not provide the complete answer but a few findings are quite inspiring. +"ths a, = dC, —dBs C(L26) and 3-form dipole moment isproportional to the angularmomentum. Hence there could In the Euclidean analvlic continuation ound for radii radiusinhas[5].. Similaralsonegative theory forlargethe radiuslargeofthe dvonie beenin", The parameters $\epsilon_i$ enter conformal weights of the operators involved into conformal block _i= Q/2 + and the central charge c= 1 Q = b + b^2 The derivative amounts to the substitution of the one of the vertex operators by the operator which is typical logarithmic operator in the CFT. +stantonfound fixedin bvthe itsGoedelangular metrics momentum[23].. Llencethere atis eastiegaltiveatmode the solut, Hence formally the insertion of the U(1) angular momentum in $R^4$ corresponds to the insertion of the Liouville field $\phi$ at the marked points. +ion uponthe analvtic continuation canbe questioned. Themost subtle point concernsthe fateofthe topologicalcharge. Indeed sincethe solution isjust blown up instanton itcarries analvtic continuation fromR!to R*!? Naivelywe getthedressed monopole- antimonopolepair hence (he initial instanton charge has tobe somehow, Similar expression can be derived in the semiclassical approximation where the Liouville correlator $\Phi(z_i)$ can be expressed in terms of the classical Liouville action calculated at the solutions to the equation of motion with the prescribed behavior at the insertion points $z_i$ (z_i) Hence the variation with respect to the equivariant parameters gets reduced to the variation of the classical action with respect to the moduli of the solutions. + divided between them. Sincefrom. Minkowski viewpoint(he instanton corresponds tothe tunneling betweentwo states furt, It is convenient to use the symplectic form on the moduli space of the solutions to the classical equation of motion in the Liouville theory \cite{seminara}. +her investigation. 5 Angular momentum in the Liouville theory 5.1 The logarithmic operators, It involves besides the terms term corresponding to the insertion positions $z_i$ the relevant terms at each point +"inside the solar disk and its shape well approximates a semi-circle, it is probably inclined on the surface.","inside the solar disk and its shape well approximates a semi-circle, it is probably inclined on the surface." + Iu the TRACE 171 filter passband. the selected oop is Inostly visible already since the beeinuine. but it vecolmes Completely visible half au hour later. at about τος UT. aud bright at maxim at 7:30 UT.," In the TRACE 171 filter passband, the selected loop is mostly visible already since the beginning, but it becomes completely visible half an hour later, at about 7:00 UT, and bright at maximum at 7:30 UT." + It beeius to ade significantly about oue hour later aud is no longer visible at about 9:15 UT., It begins to fade significantly about one hour later and is no longer visible at about 9:15 UT. + Iu the 171 images. the right lee of the loop is initially the brighter.," In the 171 images, the right leg of the loop is initially the brighter." + Later ou. he brightness becomes more uuiforii alone the loop aud eventually the left leg becomes the brighter. before the whole structure fades away.," Later on, the brightness becomes more uniform along the loop and eventually the left leg becomes the brighter, before the whole structure fades away." + Iu the TRACE 195 filter passband. the evolution is VAightly different. in that the loop appears to be nonotonically aud uiforulv adiug ou toward the eud of he observation.," In the TRACE 195 filter passband, the evolution is slightly different, in that the loop appears to be monotonically and uniformly fading out toward the end of the observation." + The loop appears to be truucated. quite abruptlv ou he left side for about L/L of its leugth. aud o bright again close to the left footpoiut.," The loop appears to be truncated quite abruptly on the left side for about 1/4 of its length, and to be bright again close to the left footpoint." + We have checkec hat in the dark region the backegrotid ds particularly intense due o a bright intersecting structure still presen in the last nuage., We have checked that in the dark region the background is particularly intense due to a bright intersecting structure still present in the last image. + The presence of this bright structure nay affect the backgroui subtraction there., The presence of this bright structure may affect the background subtraction there. + The right side is initially quite uniformly bright. witha “halo” on the outer shell.," The right side is initially quite uniformly bright, with a “halo"" on the outer shell." + We have checked that the 171 loop overlaps he brightest arch of the 195 backeround-subtracted nuages (see also Sec., We have checked that the 171 loop overlaps the brightest arch of the 195 background-subtracted images (see also Sec. + 2.3. aud 3. 1))., \ref{sec:loop} and \ref{sec:filt}) ). + Tn the TRACE 281 filter passband. the loop structure is quite faint and overlaps oulv the immer part of the loop of the other two passbauds.," In the TRACE 284 filter passband, the loop structure is quite faint and overlaps only the inner part of the loop of the other two passbands." + It fades out rapidly., It fades out rapidly. + The right leg is quite wuiformly bright. the left leg has a eap close to the footpoints.," The right leg is quite uniformly bright, the left leg has a gap close to the footpoints." + Tu the Yohkoh/SXT Al/Me/Mu filter passhaud. a loop structure appears in the initial backerouud-subtracted nuages at a similar location aud with a similar shape as he loop visible in the TRACE passbauds. in spite of the ifercut passband.," In the Yohkoh/SXT Al/Mg/Mn filter passband, a loop structure appears in the initial background-subtracted images at a similar location and with a similar shape as the loop visible in the TRACE passbands, in spite of the different passband." + The right leg of the Yolkoh/SNT loop verlaps well with the right leg of the TRACE loop., The right leg of the Yohkoh/SXT loop overlaps well with the right leg of the TRACE loop. + As ine progresses. the loop becomes fainter aud füuter. aud it is barely visible a THEE UT and no longer at 8:50 UT.," As time progresses, the loop becomes fainter and fainter, and it is barely visible at 7:44 UT and no longer at 8:30 UT." + The bright region southward of the loop also appears to )o variable and fading to the cud of the observation., The bright region southward of the loop also appears to be variable and fading to the end of the observation. + From an inspection of the TRACE images of the loop region before the beeimmine of the campaign. we have checked that the loop is preseut aud bright since about 2 UT (see also Sec. 3.3.2)).," From an inspection of the TRACE images of the loop region before the beginning of the campaign, we have checked that the loop is present and bright since about 2 UT (see also Sec. \ref{sec:lc}) )." + Our next step is to analyze the emission inside the loop and the related diagnostics., Our next step is to analyze the emission inside the loop and the related diagnostics. + We define a strip cuclosing he loop iu the TRACE 171 filter passband. down to he visible footpoiuts aud even beyond them. aud divide it iuto sectors. as shown in Fie. ἐν," We define a strip enclosing the loop in the TRACE 171 filter passband, down to the visible footpoints and even beyond them, and divide it into sectors, as shown in Fig. \ref{fig:loop_sec}." + We have analyzed strips of different widths: here we show results for a width of 10 xxels. which cucloses the bulls of the loop and represents a good compromise: a thinner strip eucloses too few pixels or good euouech statistics aud may be severely affected woslight alignment errors: a wider strip may not warraut chouegh coherence across the loop. ie. it may duclude oop strands in too different conditious to define average xoperties.," We have analyzed strips of different widths; here we show results for a width of 10 pixels, which encloses the bulk of the loop and represents a good compromise: a thinner strip encloses too few pixels for good enough statistics and may be severely affected by slight alignment errors; a wider strip may not warrant enough coherence across the loop, i.e. it may include loop strands in too different conditions to define average properties." + With the choice of a leugth of 10 pixels. we eud up with a nuuber of 27. alinost square. sectors.," With the choice of a length of 10 pixels, we end up with a number of 27, almost square, sectors." + Starting roni the left extreme the first three sectors are hevoud the visible loop. aud the fourth one artially iucludes the loop extreme.," Starting from the left extreme the first three sectors are beyond the visible loop, and the fourth one partially includes the loop extreme." + The fifth sector can be reasonably cousidered as he first visible piece of the loop., The fifth sector can be reasonably considered as the first visible piece of the loop. + Ou the other side. we nav duchide all but the last sector.," On the other side, we may include all but the last sector." + The DN counts are extracted from cach sector. at correspouding locations in the cifferent passbauds of TRACE aud Yohkoh/SNT. after cross-aliguing the iuiages. independently of the degree of overlap of the loop structure in the different passhands (.0.. the bins have the gue solar coordinates m the differcut passbauds to within the coaligument uucertaimties).," The DN counts are extracted from each sector, at corresponding locations in the different passbands of TRACE and Yohkoh/SXT, after cross-aligning the images, independently of the degree of overlap of the loop structure in the different passbands (i.e., the bins have the same solar coordinates in the different passbands to within the coalignment uncertainties)." + The SNT. images have been rebinned to the same pixel size of TRACE. so to use the same TRACE strip aud sectors for tle ciuission extraction.," The SXT images have been rebinned to the same pixel size of TRACE, so to use the same TRACE strip and sectors for the emission extraction." +and so the ecneralized GS equation (17)) has a form Tutroducing the effective pressure Pap=PagQV) as which is equivalent to the ordinary thermodvuamic relation dP=pdapds. one can obtain instead of (19)) For {= Oit has the form found by Nóttzel. Schindler Birn (1985) for planar geometry.,"and so the generalized GS equation \ref{GS}) ) has a form Introducing the effective pressure $P_{\rm eff} = P_{\rm eff}(\Psi)$ as which is equivalent to the ordinary thermodynamic relation ${\rm d}P = \rho {\rm d}w - \rho T{\rm d}s$, one can obtain instead of \ref{GS0}) ) For $I = 0$ it has the form found by Nöttzel, Schindler Birn (1985) for planar geometry." + Equation (17)) is a partial equation of the mixed type., Equation \ref{GS}) ) is a partial equation of the mixed type. + Using the iuplicit relatious resulting iu (15)) (16)). one can find for the secoud-order operator m (17)) where and The form (26)) of equation (17)) coimcides with the oue found for au isotropic pressure (see e.g. Sakurai 1990: Deskiu 1997).," Using the implicit relations resulting in \ref{mm}) \ref{bb}) ), one can find for the second-order operator in \ref{GS}) ) where and The form \ref{op}) ) of equation \ref{GS}) ) coincides with the one found for an isotropic pressure (see e.g. Sakurai 1990; Beskin 1997)." + IIeuce. one can conclude that the traus-field equation is elliptical for D>0 aud Dc—1. and lyperbolic for 1 0$ and $D < -1$, and hyperbolic for $-1 < D < 0$." + It means that the traus-field equation changes from elliptical to hyperbolic ou the surfaces D=0 (fast and slow maguetosouic singularitics) and D=1 (cusp singularity)., It means that the trans-field equation changes from elliptical to hyperbolic on the surfaces $D = 0$ (fast and slow magnetosonic singularities) and $D = -1$ (cusp singularity). + It is necessary to stress that. as in the isotropic case. D can be preseuted as D=dA|dyD?D?. so that DxA for B.= 0.," It is necessary to stress that, as in the isotropic case, $D$ can be presented as $D = d_1A + d_2B_{\varphi}^2/B^2$, so that $D \propto A$ for $B_{\varphi}=0$ ." + This property reflects the fact that for k|B fast or slow maguectosonic velocity coincides with the Alfvénnic oue., This property reflects the fact that for ${\bf k} \parallel {\bf B}$ fast or slow magnetosonic velocity coincides with the Alfvénnic one. + In particular. for a nonrotatiug flow (Op=0. EL=0). when. according to (11)). B.=0. we have Usine now the definitions (13)) aud (27)). one cau obtain for sonic. Alfvéónnic. aud cusp velocities in anisotropic media As we scc. the velocities (31)) (333) coincide exactly with the characteristic velocities propagating imn anisotropic media (Clemunow Dougherty 1969).," In particular, for a nonrotating flow $\Omega_{\rm F} = 0$, $L = 0$ ), when, according to \ref{I}) ), $B_{\varphi} =0$, we have Using now the definitions \ref{A}) ) and \ref{D}) ), one can obtain for sonic, Alfvénnic, and cusp velocities in anisotropic media As we see, the velocities \ref{as}) \ref{vc}) ) coincide exactly with the characteristic velocities propagating in anisotropic media (Clemmow Dougherty 1969)." + Recall that the condition (30 corresponds to the firchose iustabilitv. aud the condition «2<0 — to the mirror lustability.," Recall that the condition $v_{\rm A}^2 < 0$ corresponds to the firehose instability, and the condition $v_{\rm c}^2 < 0$ – to the mirror instability." + As a first example. let us cousider a free (i.e. without eravity effects) outflow aloug a stroug monopole magnetic field from the surface of a nonrotating sphere (with radius ry. Magnetic field By. pressure Py2 is the rms intrinsic shear in each component, which is equal here to 0.22."," Further still, $\bar{n_{i}}$ is the average galaxy number per steradian in bin $i$ and $< \! \gamma_{\mathrm{int}}^{2} \! >^{\frac{1}{2}}$ is the rms intrinsic shear in each component, which is equal here to $0.22$ ." +" Op; denotes the derivative with respect to a parameter p that is varied and Cov is the covariance matrix given by, For our analysis we assume the redshift distribution given in Equation where zo=2m/1.412, a=2 and B—1.5."," $\partial p_{i}$ denotes the derivative with respect to a parameter $p$ that is varied and Cov is the covariance matrix given by, For our analysis we assume the redshift distribution given in Equation where $z_{0} = z_{m}/1.412$, $\alpha = 2$ and $\beta=1.5$." + We allow for five redshift bins with divisions such as to give approximately equal galaxy number in each bin., We allow for five redshift bins with divisions such as to give approximately equal galaxy number in each bin. +" The photometric error is also accounted for by using the parameterisation oz=op(1+z), with σρ taken to be 0.03."," The photometric error is also accounted for by using the parameterisation $\sigma_{z}= \sigma_{p}(1+z)$, with $\sigma_{p}$ taken to be $0.03$ ." +" For the base cosmology we vary, about their fiducial values, the parameters Qm= 0.3, h=0.7, og=0.8, Qn= and ns=1.0, which are common to both analyses, with also wo=—1.0, wa=0.0, y=0.55 and Σο=0 (see Section 3)) for the general parameterisation, and a=0 for the mDGP model."," For the base cosmology we vary, about their fiducial values, the parameters $\Omega_{\mathrm{m}}=0.3$ , $h=0.7$, $\sigma_{8}=0.8$, $\Omega_{\mathrm{b}}=0.05$ and $n_{s}=1.0$, which are common to both analyses, with also $w_{0}=-1.0$, $w_{a}=0.0$, $\gamma = 0.55$ and $\Sigma_{0} = 0$ (see Section \ref{sec:growth}) ) for the general parameterisation, and $\alpha = 0$ for the mDGP model." +" We therefore vary a full 9 parameters for the general modifed gravity parameterisation and 6 parameters for the specific braneworld model-remembering that o specifies its own wo, Wa, y and Xo0."," We therefore vary a full 9 parameters for the general modifed gravity parameterisation and 6 parameters for the specific braneworld model–remembering that $\alpha$ specifies its own $w_{0}$, $w_{a}$ , $\gamma$ and $\Sigma_{0} = 0$." + The resulting forecasts for this future project can be seen clearly in Figure 9.., The resulting forecasts for this future project can be seen clearly in Figure \ref{fig:Euclidforecast}. + The left panel shows that Euclid will be able to put considerable strain on any braneworld-like gravity scenario that resembles the mDGP model., The left panel shows that Euclid will be able to put considerable strain on any braneworld-like gravity scenario that resembles the mDGP model. +" The solid (1c) and dashed (2c) contours are significantly within the a=1, or DGP, bound."," The solid $1\sigma$ ) and dashed $2\sigma$ ) contours are significantly within the $\alpha=1$, or DGP, bound." +" In fact, this demonstrates that Euclid will potentially constrain o to within an error of 0.104 at the 68% confidence level."," In fact, this demonstrates that Euclid will potentially constrain $\alpha$ to within an error of 0.104 at the $68\%$ confidence level." + This is in constrast to Figure 6 where no constraint was possible with a lensing-only study., This is in constrast to Figure \ref{fig:lensingconstraint} where no constraint was possible with a lensing-only study. +" Indeed, note that for this analysis only contributions from |=10 to Imax=500 were considered such that the deeply non-linear regime could be neglected."," Indeed, note that for this analysis only contributions from $l=10$ to $l_{\mathrm{max}} = 500$ were considered such that the deeply non-linear regime could be neglected." + The right panel in Figure 9 again illustrates the expected constraining power of Euclid but nowwith regards to general modified gravity., The right panel in Figure \ref{fig:Euclidforecast} again illustrates the expected constraining power of Euclid but nowwith regards to general modified gravity. + For this general parameterisationwe performed two runs with one corresponding to | contributions from |=10 to Imax= (red contours) and the other withcontributions from |=10to Imax=10000 (black contours)., For this general parameterisationwe performed two runs with one corresponding to l contributions from $l=10$ to $l_{\mathrm{max}} = 500$ (red contours) and the other withcontributions from $l=10$to $l_{\mathrm{max}} = 10000$ (black contours). + Here we see, Here we see +With this in nuiud. we report here new calculations of the expected temperature distribution iu preprotostellar cores.,"With this in mind, we report here new calculations of the expected temperature distribution in pre–protostellar cores." + We note that a rather similar study has receutly been camied ou by Evans et al. (, We note that a rather similar study has recently been carried out by Evans et al. ( +2001. hereafter ERSM).,"2001, hereafter ERSM)." + These authors inve confined themselves to nodels with spherical «πο and lave compared heir model predictions to the observations of Shirley ο al. (, These authors have confined themselves to models with spherical symmetry and have compared their model predictions to the observations of Shirley et al. ( +2000).,2000). + We. in coutrast. have employed a techuique which allows us to simulate non spherically svuumetric situations such as the magnetic field dominated models mentioned earlier.," We, in contrast, have employed a technique which allows us to simulate non spherically symmetric situations such as the magnetic field dominated models mentioned earlier." + We however coucur with ERSM in their conclusion that the decrease of temperature towards the centers of cores strouely affects the observed sub.millimeter cussion., We however concur with ERSM in their conclusion that the decrease of temperature towards the centers of cores strongly affects the observed sub–millimeter emission. + We also use our models to predict the emission clistribution expected on the basis of the CB models aud conclude that areasonable fit to the observations cau be obtained., We also use our models to predict the emission distribution expected on the basis of the CB models and conclude that a reasonable fit to the observations can be obtained. + The structure of this paper is as follows., The structure of this paper is as follows. + In section 2. we describe the model which we have used aud the asstuuptious which we have made.," In section 2, we describe the model which we have used and the assumptions which we have made." + In section 3. we present an analytic treatineut aimed at determining the dust temperature at the center of a spherically svuuuctric cloud.," In section 3, we present an analytic treatment aimed at determining the dust temperature at the center of a spherically symmetric cloud." + In section L. we give nunierical results for both spherically svnunetric models aud models based. on the density distributions of the CB models.," In section 4, we give numerical results for both spherically symmetric models and models based on the density distributions of the CB models." + Then. iu section 5. we consider the iuteusitv distributions which would be expected for nuusubnun maps of our model cores aud compare with observed data.," Then, in section 5, we consider the intensity distributions which would be expected for mm–submm maps of our model cores and compare with observed data." + In section 6. we sunminarize our conclusious.," In section 6, we summarize our conclusions." + Our imnodel caleulatious are aimed a calculating eraiu temperatures uuder physical conditions simular to those +tought to pertain in LISLL aud similar preprotostellar cores., Our model calculations are aimed at calculating grain temperatures under physical conditions similar to those thought to pertain in L1544 and similar pre–protostellar cores. + We have made a iunuboer of simplifving assuniptions in doing this which we justify in the following discussion., We have made a number of simplifying assumptions in doing this which we justify in the following discussion. + ~June of these is that we neelect scatteriug as we are oeiterested in studying cores of more than 10 magnitudes of visual extinction which are mainly penetrated by the external infrared. iuterstellar radiation field for which 1ο Rayleigh hit holds aud thus scattering becomes icelieible., One of these is that we neglect scattering as we are interested in studying cores of more than 10 magnitudes of visual extinction which are mainly penetrated by the external infrared interstellar radiation field for which the Rayleigh limit holds and thus scattering becomes negligible. + Another important assumption which we male is that eraius are only heated by the incident radiation field aud hat other sources of erain heating are uceligible., Another important assumption which we make is that grains are only heated by the incident radiation field and that other sources of grain heating are negligible. + ERSM oxovide a detailed discussion of the rauge of applicability of this and conclude that for represcutative conditions with dust erain temperatures above 5 Is. heating due to he ambient radiatiou field dominates.," ERSM provide a detailed discussion of the range of applicability of this and conclude that for representative conditions with dust grain temperatures above 5 K, heating due to the ambient radiation field dominates." + We follow them iu lis but differ from them in considering leating due othe (attenuated) external rachation field., We follow them in this but differ from them in considering heating due to the (attenuated) external radiation field. + That is to sav. we assume that our model cores are optically thin to their own radiation and that we can ucelect reabsorption of radiation enuütted from within our model itself.," That is to say, we assume that our model cores are optically thin to their own radiation and that we can neglect re–absorption of radiation emitted from within our model itself." + This is au essential siuplification which permits us to consider uou spherically svuuuetric geometries., This is an essential simplification which permits us to consider non spherically symmetric geometries. + However. it restricts us to considering structures with hvadrosen column densities less than a few hundred visual magnitudes of extinction.," However, it restricts us to considering structures with hydrogen column densities less than a few hundred visual magnitudes of extinction." + The rationale behind this cau be understood if one notes that for typical temperatures of order 10 Ik. one expects the bulk of the cussion from a preprotostellar core such as LISLE at wavelengths of order 200300µια.," The rationale behind this can be understood if one notes that for typical temperatures of order 10 K, one expects the bulk of the emission from a pre–protostellar core such as L1544 at wavelengths of order 200–300." + The available observations (see Audré ct al., The available observations (see André et al. + 2000 for the case of LIDLL) fully confirma this., 2000 for the case of L1544) fully confirm this. + Then to maimtain the optical depthbelow. sav. 0.1 at 200 rrequires a coli density of IL ess) than 5s.1093 ccorrespondine:. to roughly 500 1aguitudes of visual extinction.," Then to maintain the optical depth below, say, 0.1 at 200 requires a column density of ${\rm H_2}$ less than $5\times10^{23}$ corresponding to roughly 500 magnitudes of visual extinction." + Available observational data sugeestoo that this coucition is satisfied in all cases., Available observational data suggest that this condition is satisfied in all cases. + We note however that for mocels with a sineulazity at the origina such as the singular isothermal sphere of Shu (1977). this condition is strictly speaking not fulfilled.," We note however that for models with a singularity at the origin such as the singular isothermal sphere of Shu (1977), this condition is strictly speaking not fulfilled." +" We determune the erain temperature at a eiven position simply by applying the ""classical, equilibrium between erain cooling aud heating for a spherical eraiu at position r in the dust cloud. (see c.g. Spitzer LOTS or Boulanger et al.", We determine the grain temperature at a given position simply by applying the “classical” equilibrium between grain cooling and heating for a spherical grain at position $r$ in the dust cloud (see e.g. Spitzer 1978 or Boulanger et al. + 1998 for a discussion).έν xvQy Fur)dv.," 1998 for a discussion), = (r)." +" Tere. the right haud side describes the erain heating due to an incident radiation field of average intensity 4,(r) upon erains of absorption efiiciency Q, at frequency i."," Here, the right hand side describes the grain heating due to an incident radiation field of average intensity $J_{\nu}(r)$ upon grains of absorption efficiency $Q_\nu$ at frequency $\nu$." +" The lett haud side gives the cooling rate for a erain of temperature Tate) and DB, is the Plauck function.", The left hand side gives the cooling rate for a grain of temperature $T_{\rm d}(r)$ and $B_\nu$ is the Planck function. + The only real computational difficulty here is posed by the incident radiation field J.(r) which we suppose to be given by the attenuated interstellar radiation field Jb., The only real computational difficulty here is posed by the incident radiation field $J_{\nu}(r)$ which we suppose to be given by the attenuated interstellar radiation field $J_\nu^{\rm is}$. + Thus. we have: Tere. the integral over solid augle describes the average attenuation due to an optical depth z;(Gr.0.0) im any elven direction.," Thus, we have: (r) = Here, the integral over solid angle describes the average attenuation due to an optical depth $\tau_\nu(r,\theta,\phi)$ in any given direction." + Iu order to compute erain temperature for a model cloud of relatively arbitrary geometry. oue thus must fiud an efBcieut method of performing the auele iutegration of equation 2.," In order to compute grain temperature for a model cloud of relatively arbitrary geometry, one thus must find an efficient method of performing the angle integration of equation 2." + Once the erain temperature is determined or all positions. a simple iutegral allows oue to derive the iuteusitv distribution expected at a given waveleugth.," Once the grain temperature is determined for all positions, a simple integral allows one to derive the intensity distribution expected at a given wavelength." +" One ΠΟΤΟ needs to choose the imceideut interstellar radiation ficld J and the erain absorption efficiency. Q,.", One merely needs to choose the incident interstellar radiation field $J_\nu^{\rm is}$ and the grain absorption efficiency $Q_\nu$. + There iro ao nunnber of choices which one can uake concerning the eraiu opacities., There are a number of choices which one can make concerning the grain opacities. + Mathis (1990) has abulated values expected for “standard” interstellar erains and we have used these for comparison purposes., Mathis (1990) has tabulated values expected for “standard” interstellar grains and we have used these for comparison purposes. + However. within deuse dust clouds. oue expects eraius to acquire ice 1222atles aud this will substantially change their optical properties.," However, within dense dust clouds, one expects grains to acquire ice mantles and this will substantially change their optical properties." + In addition. oue expects at the densities," In addition, one expects at the densities" +"We smooth only over scales larger than A», by starting integration of equation 2.3 at Aj=07(A44) -- the variance on the scale of the mean free path is matched to the one obtained using a top-hat filter in real space — with initial condition ",We smooth only over scales larger than $\mfp$ by starting integration of equation \ref{diffusion} at $\Lambda_i\equiv \sigma^2(\mfp)$ – the variance on the scale of the mean free path is matched to the one obtained using a top-hat filter in real space – with initial condition ]. +The total tonized fraction is obtained by integrating over the distribution at A=o5.," The total ionized fraction is obtained by integrating over the distribution at $\Lambda=\sigma_{\rm min}^2$,." + If the initial condition for II is specified at A=0. (i.e. starting at a scale > x). then this corresponds to smoothing over all scales. and ως)(," If the initial condition for $\Pi$ is specified at $\Lambda=0$ , (i.e. starting at a scale $\rightarrow \infty$ ), then this corresponds to smoothing over all scales, and (z)." +6) To model an evolving value of A44. we assume that the absorption systems are minihalos(e.g..Abel&Mo 1998). ," To model an evolving value of $\lambda_{\rm abs}$ , we assume that the absorption systems are \citep[e.g.,][]{abel/mo:1998}. ." +Given that the halo cross section increases as M. while dnídlnMxM. small objects should dominate the mean free path. subject to photoevaporation effects (e.g..Haimanetal.2001:Shapiro 2004). ," Given that the halo cross section increases as $M^{2/3}$, while $dn/d\ln M\propto M^{-1}$, small objects should dominate the mean free path, subject to photoevaporation effects \citep[e.g.,][]{haiman/etal:2001,shapiro/etal:2004}. ." +Consider a uniform distribution of dark matter halos with anumber density n5(z)=dn/dlInMj., Consider a uniform distribution of dark matter halos with anumber density $n_h(z)\equiv dn/d\ln M_h$. + We will assume that in neutral regions. halos at mass Mj have gas fractions of unity and would serve as Lyman-limit absorptions systems. while in ionized regions. such halos survive for a time f. before being evaporated by the tonizing background.," We will assume that in neutral regions, halos at mass $M_h$ have gas fractions of unity and would serve as Lyman-limit absorptions systems, while in ionized regions, such halos survive for a time $t_{\rm ev}$ before being evaporated by the ionizing background." +" The number of absorption systems evolves according to unmaWEE, Ian where £4=CaQOLty!~260(0/100Myry!."," The number of absorption systems evolves according to ) (z), where $\xi_{\rm ev}\equiv (H_0\Omega_{\rm m}^{1/2}t_{\rm + ev})^{-1}\simeq 260\ (t_{\rm ev}/100\ {\rm Myr})^{-1}$." + We choose M;25.7«10M..[CE+2/10]7. corresponding to the cosmological Jeans mass. and consider three models. in which te=10. 50. and 100 Myr.," We choose $M_h=5.7\times 10^3 M_\odot[(1+z)/10]^{3/2}$, corresponding to the cosmological Jeans mass, and consider three models, in which $t_{\rm ev}=10$, 50, and 100 Myr." + These timescales are relatively long compared with the rather short photoevaporation times for low-mass halos found by Shapiroetal.(2004)., These timescales are relatively long compared with the rather short photoevaporation times for low-mass halos found by \citet{shapiro/etal:2004}. +. However. if reionization. is “photon-starved™. às observations are suggesting (e.g..Bolton&Haehnelt2007b).. then the flux could be low at the end of retonization. leading to longer evaporation times.," However, if reionization is “photon-starved”, as observations are suggesting \citep[e.g.,][]{bolton/haehnelt:2007a}, then the flux could be low at the end of reionization, leading to longer evaporation times." + The mean free path is (SabCO. where μι corresponds to the halo virial radius.," The mean free path is (z), where $R_{\rm vir}$ corresponds to the halo virial radius." + However. the boundaries of the absorption systems are not well-defined due to hydrodynamic effects and departures from spherical symmetry.," However, the boundaries of the absorption systems are not well-defined due to hydrodynamic effects and departures from spherical symmetry." + For our purposes. the minthalo model we describe here is sufficient to incorporate the effect of an evolving absorption system mean free path in our calculations.," For our purposes, the minihalo model we describe here is sufficient to incorporate the effect of an evolving absorption system mean free path in our calculations." + More accurate modeling of absorption systems during reionization will need to incorporate the radiative transfer of ionizing radiation in cosmological hydrodynamics simulations which resolve the Jeans mass., More accurate modeling of absorption systems during reionization will need to incorporate the radiative transfer of ionizing radiation in cosmological hydrodynamics simulations which resolve the Jeans mass. + We start with an initial. guess for Aj(2). only allowing points to cross the barrier at some scale and redshift if that scale is below the current value of μι.," We start with an initial guess for $\lambda_{\rm abs}(z)$, only allowing points to cross the barrier at some scale and redshift if that scale is below the current value of $\lambda_{\rm abs}$." + The values obtained for Αρα) from the simulated ionization field are then fed back into equations ].. 2.4.. and 2.4.. and the process 1s reapeated until convergence is reached.," The values obtained for $\lambda_b(x)$ from the simulated ionization field are then fed back into equations \ref{dxdt}, \ref{nabs}, and \ref{lambdaabs}, and the process is reapeated until convergence is reached." + Fig., Fig. + | shows the bubble mean free path as a function of the neutral fraction for several parameter choices., \ref{bubblemfp} shows the bubble mean free path as a function of the neutral fraction for several parameter choices. +" At the half-ionized epoch. all models exhibit a characteristic bubble scale of A,--10 Mpe. with models with rarer sources (i.e. increasing efficiency of ionizing radiation) leading to somewhat larger bubbles."," At the half-ionized epoch, all models exhibit a characteristic bubble scale of $\lambda_{\rm b}\simeq 10$ Mpc, with models with rarer sources (i.e. increasing efficiency of ionizing radiation) leading to somewhat larger bubbles." +" During percolation. most of the variation m ApCvgi) comes from variation of Άμως. Which is most pronounced at vy,<0.2."," During percolation, most of the variation in $\lambda_{\rm b}({x_{\rm HI}})$ comes from variation of $\mfp$, which is most pronounced at $x_{\rm + HI}\leq 0.2$." + The large values of Aj indicate that simulation volumes in excess of several hundred Mpe on aside are necessary in order to properly model the last ten per cent of the reionization process., The large values of $\lambda_b$ indicate that simulation volumes in excess of several hundred Mpc on a side are necessary in order to properly model the last ten per cent of the reionization process. + At vy)«O.1. Apc in agreement with the model of Miralda-Escudéetal.(2000).. in which a constant number of neutral clouds decrease in size at the same fractional rate at the end of retonization.," At $x_{\rm HI}<0.1$, $\lambda_b\sim x_{\rm + HI}^{-2/3}$, in agreement with the model of \citet{miralda-escude/etal:2000}, in which a constant number of neutral clouds decrease in size at the same fractional rate at the end of reionization." + The reionization history for all of the fixed Άμος models is shown in Fig. 2.., The reionization history for all of the fixed $\lambda_{\rm abs}$ models is shown in Fig. \ref{history}. + The early evolution is not sensitive to Aan. because the photon mean free path is determined by the size of the tonizedbubbles themselves.," The early evolution is not sensitive to $\mfp$, because the photon mean free path is determined by the size of the ionizedbubbles themselves." +" At later times. when the bubble sizes become comparable to Ap. the reionization history is sensitive to Άμις. as can be seen by comparing the evolution for the bracketing values of 8 Mpe/h and 256 Mpe/h. For the Ay,=8 Mpe/h case. the redshift at which the overlap occurs is delayed by Az—1.5. relative to Ayn,=256 Mpe/h. for 7,=0.09 (see also the ""z entries in Table 1)."," At later times, when the bubble sizes become comparable to $\mfp$, the reionization history is sensitive to $\mfp$, as can be seen by comparing the evolution for the bracketing values of 8 Mpc/h and 256 Mpc/h. For the $\mfp=8$ Mpc/h case, the redshift at which the overlap occurs is delayed by $\Delta z\sim 1.5$, relative to $\mfp=256$ Mpc/h, for $\tau_{\rm es}=0.09$ (see also the $z_{\rm ov}$ ” entries in Table 1)." + Also shown in Fig., Also shown in Fig. +" 2 1s the number of ionizing photons per ionized atom. AS δις Σια>Cheon and 22/7,51."," \ref{history} is the number of ionizing photons per ionized atom, As $\mfp\rightarrow \infty$ , ${x} \rightarrow \zeta f_{\rm + coll}$ and $n_\gamma/n_{\rm HII}\rightarrow 1$." + We only count photons up to the moment of overlap (x= 1). as we are concerned here with the consumption of tonizing photons during the retonization process.," We only count photons up to the moment of overlap ${x}=1$ ), as we are concerned here with the consumption of ionizing photons during the reionization process." + This integral converges. since at the end of reionization we expect Ap(v)x σας the remaining diffuse neutral hydrogen patches dissappear.," This integral converges, since at the end of reionization we expect $\lambda_{\rm + b}(x)\propto (1-x)^{-2/3}$ as the remaining diffuse neutral hydrogen patches dissappear." + For Aabs=8 Mpc/h. about 3 photons per atom are consumed in the absorption systems by τον.," For $\mfp=8$ Mpc/h, about 3 photons per atom are consumed in the absorption systems by $z_{\rm ov}$." + In the longest mean free path case. Aabs=256 Mpc/h. the corresponding fraction is about a half.," In the longest mean free path case, $\mfp=256$ Mpc/h, the corresponding fraction is about a half." + Shown in Fig., Shown in Fig. + 3 is the evolution in neutral fraction and absorption system mean free path for the three minihalo absorption system models that we simulated., \ref{absmfp} is the evolution in neutral fraction and absorption system mean free path for the three minihalo absorption system models that we simulated. + Models with longer evaporation times lead to a higher abundance of absorption systems. and hence shorter mean free paths and a relative delay in the time of overlap.," Models with longer evaporation times lead to a higher abundance of absorption systems, and hence shorter mean free paths and a relative delay in the time of overlap." +" The mean free path in the 44,2100 Myr model evolves from about40 Mpewhen NuO.1. to about 80 Mpe at overlap."," The mean free path in the $t_{\rm ev}=100$ Myr model evolves from about40 Mpcwhen $x_{\rm HI}\sim 0.1$, to about 80 Mpc at overlap." + This model is also plotted as the solid black line in Fig. 1.. ," This model is also plotted as the solid black line in Fig. \ref{bubblemfp}, ," +"which shows that the instantaneous Ay, values for the evolvingA,p, model roughly interpolate between those for the fixed Ας models.", which shows that the instantaneous $\lambda_{\rm b}$ values for the evolving$\lambda_{\rm abs}$ model roughly interpolate between those for the fixed $\lambda_{\rm abs}$ models. + This can also be seen by notingthat Ag=Ap(vy)0.1) for the evolving, This can also be seen by notingthat $\lambda_0\equiv \lambda_{\rm b}(x_{\rm HI}=0.1)$ for the evolving +In agreement with the results of Zezasetal.(2005). for the earlier. shorter. eexposure. we find that in the 2008 data the spectrum requires three components. and our best fit gives a X7 of 114 for 107 degrees of freedom.,"In agreement with the results of \citet{zezas} for the earlier, shorter, exposure, we find that in the 2008 data the spectrum requires three components, and our best fit gives a $\chi^2$ of 114 for 107 degrees of freedom." + The first component is a contribution from galaxy gas., The first component is a contribution from galaxy gas. + The overall fit is insensitive to the abundances. and we set them to solar. with results giving AZ=0.61+0.03 keV. The second component is power-law emission of large column density (component PLI).," The overall fit is insensitive to the abundances, and we set them to solar, with results giving $kT = 0.61\pm 0.03$ keV. The second component is power-law emission of large column density (component PL1)." + This was found also by others in the earlier oor XMM-Newton observations (Sambrunaetal.2003:Gliozzieal.2003:ChiabergeetDonato 2004).. and its origin is controversially associated either with the accretion flow or the base of the jet (seeZezasetal.2005)..," This was found also by others in the earlier or XMM-Newton observations \citep{sambruna, gliozzi, +chiaberge, donato}, and its origin is controversially associated either with the accretion flow or the base of the jet \citep[see][]{zezas}." +" For this heavily absorbec component we finda,=0.5Uo. Na,=6615107 and an unabsorbed | keV flux density of Sy)...=NO.ἂν nly."," For this heavily absorbed component we find $\alpha_1 = 0.5^{+0.5}_{-0.3}$, $N_{\rm H_1} = 6.6^{+2.8}_{-1.9} +\times 10^{22}$ $^{-2}$ , and an unabsorbed 1 keV flux density of $S_{1_{1~{\rm keV}}} = 89^{+110}_{-39}$ nJy." + The third is a power law of lower absorption (componen ΡΙ2)., The third is a power law of lower absorption (component PL2). + Zezasetal.(2005). pointed out that the UV and optica continuum from the nucleus seen in ddata is more likely to be related to this less-absorbed power-law component than to the yen absorbed component as suggested by Chiaberge, \citet{zezas} pointed out that the UV and optical continuum from the nucleus seen in data is more likely to be related to this less-absorbed power-law component than to the highly absorbed component as suggested by \citet{chiaberge}. +"etal.(2003)... We find a.=1.1poe Nu,=1111"".107 . antan unabsorbed | keV flux density of Sayy=12 nly."," We find $\alpha_2 = 1.1^{+1.9}_{-1.0}$, $N_{\rm +H_2} = 1.1^{+2.6}_{-1.1} \times 10^{21}$ $^{-2}$, and an unabsorbed 1 keV flux density of $S_{2_{1~{\rm keV}}} = 12^{+16}_{-5}$ nJy." + While the spectral parameters for this sof component are poorly constrained. a fit with only one absorbed power law and a thermal component is unacceptable (47.=En for 109 degrees of freedom).," While the spectral parameters for this soft component are poorly constrained, a fit with only one absorbed power law and a thermal component is unacceptable $\chi^2 = 158$ for 109 degrees of freedom)." + As noted by Zezasetal.(2005). a partial covering model where emission from the nucleus is seen through patchy absorption is an alternative for the combination of PLI and PL2.," As noted by \citet{zezas}, a partial covering model where emission from the nucleus is seen through patchy absorption is an alternative for the combination of PL1 and PL2." + However. a partial covering model implies that the emission region is extended on the scale size of the absorbing gas. and it is reasonable to associate the most obseured region with a region of scale-size comparable to the accretion dise and separate it from less absorbed power-law emission.," However, a partial covering model implies that the emission region is extended on the scale size of the absorbing gas, and it is reasonable to associate the most obscured region with a region of scale-size comparable to the accretion disc and separate it from less absorbed power-law emission." + The parameters for this 3-component model (two absorbed power laws and thermal gas. see Fig. 7))," The parameters for this 3-component model (two absorbed power laws and thermal gas, see Fig. \ref{fig:corespec}) )" + agree within uncertainties with values from the shorter 2000 observation published by Zezasetal.(2005)., agree within uncertainties with values from the shorter 2000 observation published by \citet{zezas}. +.. Weak evidence for a narrow Fe line has been presented by Sambrunaetal.(2003).. based onXMM-Newton.. and Zezausetal.(20051.. fromET the 200üc oobservation.," Weak evidence for a narrow Fe line has been presented by \citet{sambruna}, based on, and \citet{zezas}, from the 2000 observation." + The OS observation does not strengthen this case., The 2008 observation does not strengthen this case. + There is only weak evidence for a line around 6.4 keV in the residuals between the data and the 3-component model (Fig. 7»)., There is only weak evidence for a line around 6.4 keV in the residuals between the data and the 3-component model (Fig. \ref{fig:corespec}) ). + Formally 47 reduces by just 3 if a narrow line of energy keV (equivalent width ~131 eV) is ee, Formally $\chi^2$ reduces by just 3 if a narrow line of energy $6.2\pm 0.2$ keV (equivalent width $\sim 131$ eV) is included. + A combined fit to the 2008 valuesand 200ο ddata gives similar parameter to those above. with a fitting statistic of X7.=ISO for 159 degrees of freedom.," A combined fit to the 2008 and 2000 data gives similar parameter values to those above, with a fitting statistic of $\chi^2 = 180$ for 159 degrees of freedom." + Freeing up the relative normalizations of the power-law components between epochs yields no significant improvement in fit ΟΧΙ<1 for each). and so there is no evidence for variability in either power- component.," Freeing up the relative normalizations of the power-law components between epochs yields no significant improvement in fit $|\Delta \chi^2| < 1$ for each), and so there is no evidence for variability in either power-law component." +" In the remaining discussion. when referring to core components we will adopt the parameter values from the combined. fit:. A7p0.Gl.[EMImos keV. αι=0.56.od-Il. Ng,H=TS2.2So40722 2 Se'=96.US DUnJy ae=0.5alLU. Ng,=2−ie102om 2 oand S,the=(LO8.5 Oday."," In the remaining discussion, when referring to core components we will adopt the parameter values from the combined fit: $kT = 0.61^{+0.02}_{-0.03}$ keV, $\alpha_1 = 0.56^{+0.44}_{-0.34}$, $N_{\rm H_1} = 7.8^{+2.2}_{-1.9} \times 10^{22}$ $^{-2}$, $S_{1_{1~{\rm keV}}} = 96^{+103}_{-40}$ nJy, $\alpha_2 = +0.5^{+1.0}_{-0.4}$, $N_{\rm H_2} = 2^{+14}_{-2} \times +10^{20}$ $^{-2}$, and $S_{2_{1~{\rm keV}}} = 8.5^{+6.1}_{-1.3}$ nJy." + The 0.3-) keV intrinsic luminosities for hiud and soft (PL2) power-law components are 1.4.107. and 1.4.107 ergs respectively.," The 0.3-10 keV intrinsic luminosities for the hard (PL1) and soft (PL2) power-law components are $1.4 \times 10^{41}$ and $1.4 \times +10^{40}$ ergs $^{-1}$, respectively." + Note that PL? contains more than three times the total X-ray luminosity of the resolved jet andcounterjet even if they are assumed to extend to pe-scale distances from the nucleus with constant surface brightness., Note that PL2 contains more than three times the total X-ray luminosity of the resolved jet andcounterjet even if they are assumed to extend to pc-scale distances from the nucleus with constant surface brightness. + The core spectrum has been extracted from a circle of radius 190 pe. and it is possible that some of PL? is contributed by," The core spectrum has been extracted from a circle of radius 190 pc, and it is possible that some of PL2 is contributed by" +We have presented numerical simulations of the cooling of the neutron star crust in both aand ffollowing the end of long aecretion outbursts.,We have presented numerical simulations of the cooling of the neutron star crust in both and following the end of long accretion outbursts. + Our main results are as follows., Our main results are as follows. +encrey-dependent point-spreacl function. (PSE).,energy-dependent point-spread function (PSF). + We use he DP6.VV3 instrument response function. which is the default at the time of writing.," We use the V3 instrument response function, which is the default at the time of writing." +" Integrated data from the ""ull instrument lifetime is used for the σαν sources. and rom fy 5to du|135 s for CRB 090816C€: Ty being the rigecr time of the burst in the CDM instrument."," Integrated data from the full instrument lifetime is used for the AGN sources, and from $T_0 -5$ to $T_0+135$ s for GRB 090816C; $T_0$ being the trigger time of the burst in the GBM instrument." + Note hat 135 s is nearly 3 times the interval of GeV emission rom the GRB presented in Abdoetal.(2009).., Note that 135 s is nearly 3 times the interval of GeV emission from the GRB presented in \citet{abdo09a}. + The photons within the 95 per cent containment region of the PSE around the AGN source in each energy jin are then assumed. to be associated with the source., The photons within the 95 per cent containment region of the PSF around the AGN source in each energy bin are then assumed to be associated with the source. + For GRB 080916C. the 99 per cent containment. region is used.," For GRB 080916C, the 99 per cent containment region is used." + To determine the normalization parameter (21) in Equation 14. above. we use counts between energies of 500 MeV. and 5 GeV for GRB 080916C. and 1: and 10 GeV for the four AGN.," To determine the normalization parameter $A$ ) in Equation \ref{eq:nex} above, we use counts between energies of 500 MeV and 5 GeV for GRB 080916C, and 1 and 10 GeV for the four AGN." + An alternative method. is to consider. the combined probabilities of having 1 photons at or above the highest observed. photon energy for cach source. to put a stronger constraint on background fields.," An alternative method is to consider the combined probabilities of having $>1$ photons at or above the highest observed photon energy for each source, to put a stronger constraint on background fields." + Phat is. we consider the combined. probability of detecting photons from all sources considered. and exclude background scenarios that lead toa {μι less than a given value.," That is, we consider the combined probability of detecting photons from all sources considered, and exclude background scenarios that lead to a $P_{tot}$ less than a given value." +" However. a potential pitfall of this method is that £7, can be considerably less than 1 even in the absence of a pop-HIE contribution: due to the impact of the p-EDL. which is quite uncertain at high redshifts."," However, a potential pitfall of this method is that $P_{tot}$ can be considerably less than 1 even in the absence of a pop-III contribution; due to the impact of the p-EBL, which is quite uncertain at high redshifts." + As discussed in GOO and ΟΡΟΙ this uncertainty in the UV background is a factor of several at z22.," As discussed in G09 and GSPD11, this uncertainty in the UV background is a factor of several at $z \gtrsim 2$." + For high determinations of the UV. background. like the fiducial model in GSPDII. the optical depth. for the highest enerev photons can be as high as 1. as shown in Table 1..," For high determinations of the UV background, like the fiducial model in GSPD11, the optical depth for the highest energy photons can be as high as 1, as shown in Table \ref{tab:latsources}." + The p-EBL ellect is therefore not something that can be ignored here., The p-EBL effect is therefore not something that can be ignored here. + Result derived using Eq., Result derived using Eq. + 10. above will be necessarily be à strong function of the assumed star-formation model., \ref{eq:ptotunnorm} above will be necessarily be a strong function of the assumed star-formation model. + In Table 1.. we also show the expected number of photons expected above fyign for each source. and the associated probability of detecting at least one photon at or above the highest photon energy.," In Table \ref{tab:latsources}, we also show the expected number of photons expected above $E_{high}$ for each source, and the associated probability of detecting at least one photon at or above the highest photon energy." + As we are interested. in isolating the impact of the r-IZBL. we first compensate for the impact of the p-EBL on our results by renormalizing the combined probability Dua to 1. after convolving the observed spectrum with a given p-EBL opacity.," As we are interested in isolating the impact of the r-EBL, we first compensate for the impact of the p-EBL on our results by renormalizing the combined probability $P_{tot}$ to 1, after convolving the observed spectrum with a given p-EBL opacity." + Fhus we define where Pipees( 1) is the probability. of 1 or more photons from a source. after considering only an assumed: p-IEEBL. model. while 2(21) considers both background components.," Thus we define where $P_{i,pEBL} (\geq 1$ ) is the probability of 1 or more photons from a source, after considering only an assumed p-EBL model, while $P_i(\geq 1)$ considers both background components." + This change effectively isolates the impact of the r-IZBE on photon detection probability., This change effectively isolates the impact of the r-EBL on photon detection probability. + The resulting limits on the reionization-era background are then only a weak function of the p-EDL: we find a variance of only about LO per cent in our results for the pop-LL star formation rate limits if the p-EDL Dux is increased. or decreased by a factor of 2., The resulting limits on the reionization-era background are then only a weak function of the p-EBL; we find a variance of only about 10 per cent in our results for the pop-III star formation rate limits if the p-EBL flux is increased or decreased by a factor of 2. + The following results assume the p-IEBL predicted by the fiducial mocel of GSPDII., The following results assume the p-EBL predicted by the fiducial model of GSPD11. + In Figs., In Figs. + 3. and ει. we show the overall [limits on SERD obtained using both the combined. model. and a singular analysis using only ChB 080916C'. Singular analyses with the other sources always lead to comparatively weak upper bounds. Z1 ve+ at the 20 level.," \ref{fig:sfrd_lar} and \ref{fig:sfrd_sal}, we show the overall limits on SFRD obtained using both the combined model, and a singular analysis using only GRB 080916C. Singular analyses with the other sources always lead to comparatively weak upper bounds, $\gtrsim 1$ $^{-1}$ $^{-3}$ at the $2\sigma$ level." + A collection ofobservational data. as well as the model results for SGPDIL are shown as well: however most of these measurements rellect. the luminosity of the brightest sources seen at these epochs. and are generally assumed to be due to population L/Lb stars in environments too metal-rich to support pop-IHE star formation.," A collection of observational data, as well as the model results for SGPD11 are shown as well; however most of these measurements reflect the luminosity of the brightest sources seen at these epochs, and are generally assumed to be due to population I/II stars in environments too metal-rich to support pop-III star formation." + Ehe measurement based on observed GARB rates are [ree from this bias. however they sullerfrom their own systematic uncertainties (Ixistlerctal.2009:Beckman&Ciammanco 2010).," The measurement based on observed GRB rates are free from this bias, however they sufferfrom their own systematic uncertainties \citep{kistler09,beckman10}." +. The pop-HLE SETUD in our model is assumed to be constant in time from. redshift 15 to the indicated cutolf redshift ον., The pop-III SFRD in our model is assumed to be constant in time from redshift 15 to the indicated cutoff redshift $z_r$. + Phe choice of a functional form for the SERD history is necessary and arbitrary here. and we have chosen a constant history for simplicity.," The choice of a functional form for the SFRD history is necessary and arbitrary here, and we have chosen a constant history for simplicity." +" In practice. the strongest ellect on gamma-rav opacity will come from photons emitted near ον. as evidenced. by the rapid. increase in SERD upper limits with increasing 2, in these figures."," In practice, the strongest effect on gamma-ray opacity will come from photons emitted near $z_r$, as evidenced by the rapid increase in SFRD upper limits with increasing $z_r$ in these figures." +" Results in these figures can therefore be considered as approximate SERD limits al z,.", Results in these figures can therefore be considered as approximate SFRD limits at $z_r$. + These limits are necessarily conservative. due to the renormalization that we have made in Eq.," These limits are necessarily conservative, due to the renormalization that we have made in Eq." + 17. that limits he influence of the poorly-constrained p-EBL on our results., \ref{eq:combprop} that limits the influence of the poorly-constrained p-EBL on our results. + If the p-EDL contribution to the UV is high. then he actual limits on pop-Lll stars alter considering the otal background. photon population would. be stronger han what is cepicted in the figures.," If the p-EBL contribution to the UV is high, then the actual limits on pop-III stars after considering the total background photon population would be stronger than what is depicted in the figures." + We have also shown in Fie., We have also shown in Fig. + 3 the limits on ΟΡ growth that exist. due to constraints on global metallicity and barvons available in collapsed structures., \ref{fig:sfrd_lar} the limits on pop-III growth that exist due to constraints on global metallicity and baryons available in collapsed structures. +" ""air-instability supernovae (SNqt4)). are. responsible or a large release of metals| into the IGM and ISAL which can potentially lead to. contliet with/ the measured. enrichment in. high-redshift. Lyman-a--forest observations (e.g. Schaveetal. 20032)."," Pair-instability supernovae ) are responsible for a large release of metals into the IGM and ISM, which can potentially lead to conflict with the measured enrichment in high-redshift -forest observations (e.g. \citealp{schaye03}) )." + As a very simple enrichment model. we assume that all massive stars with 140 < M « 260 undergo upon death. and release half their mass into the IGM as metals (Portinari. 1998)..," As a very simple enrichment model, we assume that all massive stars with 140 $<$ M $<$ 260 undergo upon death, and release half their mass into the IGM as metals \citep{portinari98}. ." + Enrichment from lower mass stars is ignored., Enrichment from lower mass stars is ignored. + For our Larson IME. about 9 per cent of all stellar mass falls in the range. leading to," For our Larson IMF, about 9 per cent of all stellar mass falls in the range, leading to" +A inodel in which the bulk of the CO(21) emission arises from a tilted. expaudiue disk prodiced by constant nass loss fits the data well.,"A model in which the bulk of the CO(2–1) emission arises from a tilted, expanding disk produced by constant mass loss fits the data well." + This model is sketched in Fig., This model is sketched in Fig. + 5axd the model aud observed line profiles are compared in Fie. 6.., \ref{fig5} and the model and observed line profiles are compared in Fig. \ref{fig6}. +" The northern part of the disk is ited away from the observer at an anele of 55"" to the liie of sight.", The northern part of the disk is tilted away from the observer at an angle of $\rm 55^o$ to the line of sight. + The telerature profile is approximated as a power law: T(r) = 3 OTS Crοen)V7. as found im deailed models of AGD star winds (Colreich Scoville (1 976): Iwan Linse (19823).," The temperature profile is approximated as a power law: T(r) = 300 K $(r/10^{15} ~ cm)^{-0.7}$, as found in detailed models of AGB star winds (Goldreich Scoville \cite{goldreich}) ); Kwan Linke \cite +{kwan}) )." +" The best fit model vas a disk radius of 5«1HÓ ona thic]zness of 1015 οι. and is produced by a constant lass loss rate of |2.106NL,sv1."," The best fit model has a disk radius of $\rm 5 \times 10^{16}$ cm, a thickness of $\rm 10^{16}$ cm, and is produced by a constant mass loss rate of $\rm 1.2 \times 10^{-6} ~ M_{\odot} ~ yr^{-1}$." + The 1dial expansion velocity in the plane o το disk is 15 kuns.. ldncreasingd slightly to 18 kins| at the poles. andà the turbuleut velocity is 1 kans|.," The radial expansion velocity in the plane of the disk is 15 $\rm km~s^{-1}$, increasing slightly to 18 $\rm km~s^{-1}$ at the poles, and the turbulent velocity is 1 $\rm km~s^{-1}$." + Tt was also foind that better aecomment width the «ata is obtained if the telescope poliiting ds offse from the ceuter of the ¢mvelope by 5it in ¢leclination (note that declination axl zenith angle off«ts are approximately equivalent for οservatious froui Tawar ofobjecs which lie at very southern declinations)., It was also found that better agreement with the data is obtained if the telescope pointing is offset from the center of the envelope by $\rm +5''$ in declination (note that declination and zenith angle offsets are approximately equivalent for observations from Hawai`i of objects which lie at very southern declinations). + The outflow velocity in the disk agrees well ith the value of 1332kins1 observed for eas in the deise Haner regdolnis as observed in tre SiO(G5) line (Table 1|.," The outflow velocity in the disk agrees well with the value of $\rm 13 \pm 2 ~ +km~s^{-1}$ observed for gas in the dense inner regions as observed in the SiO(6–5) line (Table 1)." + The model shown iu Figures 5 and 6. of an expanding disk tilted iu the north-south direction. reproduces the observations well. aix| also agrees with the higher spatial resolution observations of 892. which show that tje enission from the euclope is elliptical with the major axis Iving cas-west.," The model shown in Figures 5 and 6, of an expanding disk tilted in the north-south direction, reproduces the observations well, and also agrees with the higher spatial resolution observations of S92, which show that the emission from the envelope is elliptical with the major axis lying east-west." + The difference between the discitsslou bv S92 and that here is oue of interpretation: 892 suggests that the spatialv separated horn features arise fron a bipolu fiow perpendicular to the disk. while our mocl ideutifics them with the northern aud southerji halves of the tited disx (cf.," The difference between the discussion by S92 and that here is one of interpretation; S92 suggests that the spatially separated horn features arise from a bipolar flow perpendicular to the disk, while our model identifies them with the northern and southern halves of the tilted disk (cf." + Fieure 55) whose projected major axis lies east-west., Figure 5) whose projected major axis lies east-west. + While the fast wind from 7a! Cau is uot explicitly 1oeled. the observatious sugecst hat it is likely to )6 a continution οthe velocity increase towards the poles.," While the fast wind from $\rm \pi^1$ Gru is not explicitly modeled, the observations suggest that it is likely to be a continuation of the velocity increase towards the poles." +" The model diss which rexoduces most of the emission from the immer envelope is wich siunaller than the envelope ONeut of ~6«1017 C1i observed via GO pau emission from dus (Young. PhilIps and I&uapp 1993). aud the mass loss bate reqπο] to produce the observed eimdssiou. from the disk is much higher (1.2«1EONDSsv P) than the mean value ([4105M,vro even by the CO line intensity and 60 jin flux densitv."," The model disk which reproduces most of the emission from the inner envelope is much smaller than the envelope extent of $\rm \sim 6 \times 10^{17}$ cm observed via 60 $\rm \mu m$ emission from dust (Young, Phillips and Knapp 1993), and the mass loss rate required to produce the observed emission from the disk is much higher $\rm 1.2 \times 10^{-6} ~ +M_{\odot}~yr^{-1}$ ) than the mean value $\rm \sim 4 \times 10^{-7} +~ M_{\odot} ~ yr^{-1}$ ) given by the CO line intensity and 60 $\rm +\mu m$ flux density." +" The euvelope may thus be roughly spherical. with a strorie density increase towards the plane oftie disk: alnatively, the mass loss rate of zb Gru ταν have unuCreoje a large increase in the last 1JOO vears."," The envelope may thus be roughly spherical, with a strong density increase towards the plane of the disk; alternatively, the mass loss rate of $\rm \pi^1$ Gru may have undergone a large increase in the last 1000 years." + The nodel proposed here for the envelope of a+ Cau Is siuilar to flat sugerested for the euvelope of the carbou star V Iva bx Kuap) et al. (1997))., The model proposed here for the envelope of $\rm \pi^1$ Gru is similar to that suggested for the envelope of the carbon star V Hya by Knapp et al. \cite{knapp}) ). + The molecular line enission from both ewelopes is sila: the lines emitted roni the πιο eunvelo»e have simple parabolic shapes. the CO lines have compCX. ouble horned shapes. aud the velocity separation of the horns is sieuificantlvOo smaller han the velocity raise of the “high density” cussion.," The molecular line emission from both envelopes is similar: the lines emitted from the inner envelope have simple parabolic shapes, the CO lines have complex, double horned shapes, and the velocity separation of the horns is significantly smaller than the velocity range of the “high density” emission." +" Also. both stars have fast (V,>50lans 13 molecular winds."," Also, both stars have fast $\rm V_o > 50 ~ km~s^{-1}$ ) molecular winds." + Fie., Fig. + 7 reproduces the IRAS color-color diagram or evolved stars witi fast molecular winds frou Αα) et al. (," \ref{fig7} + reproduces the IRAS color-color diagram for evolved stars with fast molecular winds from Knapp et al. (" +1997) with thie| data for a Cru added Jorisseu Ίνταyp (1998)}): the eolors are plotted for the two epochs at which the star was observed.,1997) with the data for $\rm \pi^1$ Gru added Jorissen Knapp \cite{jk}) ); the colors are plotted for the two epochs at which the star was observed. +" Like V. να, and uulike all tio other stars with fas molectlar winds. 7 Cru still has he 1ubared colors of an ACB star."," Like V Hya, and unlike all the other stars with fast molecular winds, $\rm \pi^1$ Gru still has the infrared colors of an AGB star." + The structure of the x Gan euvelope is remiscent of structure seen. in some planetary uebulae., The structure of the $\rm \pi^1$ Gru envelope is remiscent of structure seen in some planetary nebulae. + For cxaimple. Mauchacο et al. (198 063) ," For example, Manchado et al. \cite{manchado}) )" +have pointed ou the existeice of a class of quadrupolar dlanetary nebulae. which they attribute to the presence of two bipolar outHows ejectec 11 different directions.," have pointed out the existence of a class of quadrupolar planetary nebulae, which they attribute to the presence of two bipolar outflows ejected in different directions." + Their xoposed model for these fkDs (see also Livio Pringle 1996: Guerrero aud Manchado 1L998)) 1s that the bipolar flow is iutermutteit and that the flow axis precesses diwe to the precession of a collimating disk., Their proposed model for these flows (see also Livio Pringle \cite{livio}; Guerrero and Manchado \cite{guerrero}) ) is that the bipolar flow is intermittent and that the flow axis precesses due to the precession of a collimating disk. + The similarity of this structure to hat sugecsed from these observations of the π-1 Cau envelope shows that this complex structure is already: preseut in the, The similarity of this structure to that suggested from these observations of the $\rm \pi^1$ Gru envelope shows that this complex structure is already present in the +One can simply extend the point-source equation for scattering (Eqn.(11)) to a convolution-type operation on a continuous intensity. field by relating flux-density with intensity times area.,One can simply extend the point-source equation for scattering \ref{eqn:scattering_psf}) )) to a convolution-type operation on a continuous intensity field by relating flux-density with intensity times area. + In that case one readily sees that We note that this is a two-dimensional convolution with a three dimensional kernel., In that case one readily sees that We note that this is a two-dimensional convolution with a three dimensional kernel. + This makes it more difficult to deconvolve using simple two-dimensional Fourier techniques., This makes it more difficult to deconvolve using simple two-dimensional Fourier techniques. +" For a small field of view. one can simply set 5,—so,=O and perform a two dimensional convolution through fast Fourier transform methods."," For a small field of view, one can simply set $s_{w}-s_{0,w}=0$ and perform a two dimensional convolution through fast Fourier transform methods." + For wider fields of view this can not be done., For wider fields of view this can not be done. +" However. one can rewrite the equation as a three dimensional convolution as follows where 0s,=Soy.—(155275ο)- and ὃν Is a Kronecker delta function."," However, one can rewrite the equation as a three dimensional convolution as follows where $\delta s_{w} = s_{0,w}-(1-s_{0,u}^{2}-s_{0,v}^{2})^{1/2}$ and $\delta_{\rm k}$ is a Kronecker delta function." + Note that in this equation so should no longer be treated as a unit vector but still that (1—304E~304.3)>0.," Note that in this equation $\vc{s}_{0}$ should no longer be treated as a unit vector but still that $(1-s_{0,u}^{2}-s_{0,v}^{2})\ge 0$." +" The intensity 7?""p is à cylinder of radius unity that has the same value as D(So)(Sou.So.) for each value of s."," The intensity $I^{(i)}_{\rm 3D} (\vc{s}_{0})$ is a cylinder of radius unity that has the same value as $I^{(i)}(s_{0,u},s_{0,v})$ for each value of $s_{w}$." + Writing the equation like this. makes it a three dimensional convolution which can be performed using Fourier transform techniques. but at the cost of more memory and computational effort.," Writing the equation like this, makes it a three dimensional convolution which can be performed using Fourier transform techniques, but at the cost of more memory and computational effort." + Here we derive an expression for the full ionospheric power spectrum m terms of the scattered intensity field and the incident field., Here we derive an expression for the full ionospheric power spectrum in terms of the scattered intensity field and the incident field. + To do this. first we define the rescaled version of the scattered intensity as and ὃν(tn)=[[o7Ussv)eUSEMyds as its Fourier transform.," To do this, first we define the rescaled version of the scattered intensity as and $\delta \tilde{J}^{(s)}(u,v) = \iint \delta J^{(s)}(s_{u},s_{v}) e^{+ 2\pi i (s_{u} u+ s_{v} v)} ds_{u} ds_{v}$ as its Fourier transform." + note that the scattered intensity is zero if s;+We>|., We note that the scattered intensity is zero if $s_{u}^{2}+s_{v}^{2}>1$. + If we now defineitationEnd we obtain We note that this equation can be integrated over infinity. as long as the intensities are zero (as they are) when [so]>1.," If we now define we obtain We note that this equation can be integrated over infinity, as long as the intensities are zero (as they are) when $|\vc{s}_{0}|>1$." + Using the relation between convolution and Fourier transforms. we can now write this às with autocorrelationARpa={If(fJApn?)Gode—PDüisa-senso andTF(OG) being the function of the tonospheric scattering function.," Using the relation between convolution and Fourier transforms, we can now write this as with $\tilde{J}^{(i)}_{\rm 3D}(\vc{u}) = \iiint {J}^{(i)}_{\rm 3D}(\vc{s}_{0}) e^{- 2 \pi i \vc{s}_{0} \cdot \vc{u}} d\vc{s}_{0}$ and ${\cal F}(|\tilde{\Phi}(\vc{s}) |^{2})$ being the autocorrelation function of the ionospheric scattering function." + This remarkable equation shows that the two dimensional field 6?(4.v) contains information about the full three dimensional structure of the ionosphere if reference field J7'τρία) is available: this is closely related to the technique of “holography”.," This remarkable equation shows that the two dimensional field $\delta \tilde{J}^{(s)}(u,v)$ contains information about the full three dimensional structure of the ionosphere if a reference field $\tilde{J}^{(i)}_{\rm 3D}(\vc{u})$ is available; this is closely related to the technique of “holography”." + We can now go one step further and show after a little algebra that being a two-dimensional convolution. with was control parameter.," We can now go one step further and show after a little algebra that being a two-dimensional convolution, with $w$ as control parameter." + The function with -Vic+37 ds a Hankel transform. of einiγιοςDM., The function with $u_{\rm 2D} = \sqrt{u^{2}+v^{2}}$ is a Hankel transform of $e^{-2 \pi i w \sqrt{1-s_{u}^{2}-s_{v}^{2}}}$. +" Putting this all together. we find the final result Hence. the three dimensional power spectrum of the ionosphere or its autocorrelation function. can. be reconstructed from the ratio between the Fourier transform of the rescaled scattered intensity field and the Fourier transform of the incident radiation. field convolved with a Hankel function,"," Putting this all together, we find the final result Hence, the three dimensional power spectrum of the ionosphere or its autocorrelation function can be reconstructed from the ratio between the Fourier transform of the rescaled scattered intensity field and the Fourier transform of the incident radiation field convolved with a Hankel function." +mean? Looking carefully at the equation. we see that 71(u.viw) is the Fourier transform of a unit phasor with a phase that is determined by the distance (in wavelength) from a half-sphere of radius w to the «v plane along a line perpendicular to the latter.," Looking carefully at the equation, we see that ${\cal H}(u,v;w)$ is the Fourier transform of a unit phasor with a phase that is determined by the distance (in wavelength) from a half-sphere of radius $w$ to the $uv$ plane along a line perpendicular to the latter." + In other words.optical /H(u.vive) aet as the Fourier transform of a complex transfer function in the pupil plane1985). which in this case is the full sky and not (as usual) the interferometer plane itself.," In other words, ${\cal H}(u,v;w)$ act as the Fourier transform of a complex optical transfer function in the pupil plane, which in this case is the full sky and not (as usual) the interferometer plane itself." + Equivalently. Hivw) acts as à complex point spread function in uv space cconvolving 7'(:. v).," Equivalently, ${\cal H}(u,v;w)$ acts as a complex point spread function in $uv$ space convolving $\tilde{I}^{(i)}(u,v)$ )." + Turning this around. a convolution in wy space is a multiplication of the sky intensity with the reciprocal of the convolution kernel.," Turning this around, a convolution in $uv$ space is a multiplication of the sky intensity with the reciprocal of the convolution kernel." + Hence. Hir.viw) causes a complex beam of unit amplitude on the sky equal to the phasor in. Eqn(22)).," Hence, ${\cal H}(u,v;w)$ causes a complex beam of unit amplitude on the sky equal to the phasor in \ref{eqn:Hankel}) )." + This exactly extracts the information from 6/(i.v). on a particular w-slice cut through the three dimensional autocorrelation function of the ionosphere.," This exactly extracts the information from $\delta \tilde{J}^{(s)}(u,v)$ on a particular $w$ -slice cut through the three dimensional autocorrelation function of the ionosphere." +" Hence by simply multiplying the sky model 77(5,.5.) with the complex phasor in Eqn.(22)) one obtains a complex sky-intensity cube."," Hence by simply multiplying the sky model ${I}^{(i)}(s_{u},s_{v})$ with the complex phasor in \ref{eqn:Hankel}) ) one obtains a complex sky-intensity cube." + Fourier transforming this back slice by slice provides the denominator in Eqn.(23))., Fourier transforming this back slice by slice provides the denominator in \ref{eqn:powerspectrum}) ). +" To illustrate this further. imagine that the sky contains only one point source of unit flux-density at (so...50,)."," To illustrate this further, imagine that the sky contains only one point source of unit flux-density at $(s_{0,u}, s_{0,v})$." + In that case. Substituting Eqn.(16)) back into this equation shows that the left and right-hand sight of the equation are identical as required.," In that case, Substituting \ref{eqn:cont_field2}) ) back into this equation shows that the left and right-hand sight of the equation are identical as required." + By bringing the denominator to the left side of the equation. we find for a point source This is the inversion of Eqn.(11)) for a single point source.," By bringing the denominator to the left side of the equation, we find for a point source This is the inversion of \ref{eqn:scattering_psf}) ) for a single point source." + Hence every point source in the sky probes the ionospheric power spectrum on an Ewald sphere of reflection., Hence every point source in the sky probes the ionospheric power spectrum on an Ewald sphere of reflection. + The full sky probes the power spectrum of the ionosphere. as encoded in Eqn.(23)). on the surface of many offset Ewald spheres of," The full sky probes the power spectrum of the ionosphere, as encoded in \ref{eqn:powerspectrum}) ), on the surface of many offset Ewald spheres of" +An cnigmatic radio bursting source. CCRT J1715-3009. was discovered receutlv i the direction of the Calactic Ceuter UIvinan et al.,"An enigmatic radio bursting source, GCRT J1745-3009, was discovered recently in the direction of the Galactic Center (Hyman et al." + 2005)., 2005). + This source exhibited 5 peculiar consecutive outbursts at 0.33 GITz with a period of 77.13 mnünutes and a duration of ~10 minutes for each outburst., This source exhibited 5 peculiar consecutive outbursts at 0.33 GHz with a period of $77.13$ minutes and a duration of $\sim 10$ minutes for each outburst. + The radiation is very likely coherent as long as the distance is Lhuger than 7O pc., The radiation is very likely coherent as long as the distance is larger than 70 pc. + Although mauyv efforts have been made to interpret it (Iviman ct al., Although many efforts have been made to interpret it (Hyman et al. + 2005: I&ullguui Phinney 2005: Zhu Xu 2005: 'Turolla et al., 2005; Kulkarni Phinney 2005; Zhu Xu 2005; Turolla et al. + 2005). this behavior is hard to understaud in a straightforward wav within the framework of known astroplivsical objects.," 2005), this behavior is hard to understand in a straightforward way within the framework of known astrophysical objects." + This source has been claimed to be the prototype of a hitherto uuknown class of trausicut radio sources (IIviman et al., This source has been claimed to be the prototype of a hitherto unknown class of transient radio sources (Hyman et al. + 2005)., 2005). +" Tere we show that the phenomenon is naturally understood if CCRT J1715-3009 is a stronely magnetized white dwarf. whose dipolar magnetic field defines a ""light house” beam from the polar cap region. just like what happens in a radio pulsar."," Here we show that the phenomenon is naturally understood if GCRT J1745-3009 is a strongly magnetized white dwarf, whose dipolar magnetic field defines a “light house” beam from the polar cap region, just like what happens in a radio pulsar." + The Til3aniuute cvcle is the rotation period of the white dwarf. aud the ~ 10-3niuute faring duration correspouds to the epoch when the radio beam sweeps our liue of sight.," The $77.13$ -minute cycle is the rotation period of the white dwarf, and the $\sim 10$ -minute flaring duration corresponds to the epoch when the radio beam sweeps our line of sight." + The bursting epoch corresponds to the episodes when the pair production coudition is satisfied. so that the white dwarf can behave like a radio pulsar.," The bursting epoch corresponds to the episodes when the pair production condition is satisfied, so that the white dwarf can behave like a radio pulsar." + When the pair production is turned off. the fare ceases and the white dwarf enters its dormant state.," When the pair production is turned off, the flare ceases and the white dwarf enters its dormant state." + White dwarts are intermediate compact objects that ridge normal main sequence stars aud more compaect jeutron stars., White dwarfs are intermediate compact objects that bridge normal main sequence stars and more compact neutron stars. + When our Sun collapses to a white dw. he radius shrinks bv a factor ~100.," When our Sun collapses to a white dwarf, the radius shrinks by a factor $\sim +100$." + Conserving angular nomentiun gives a white dwarf period of a few minutes., Conserving angular momentum gives a white dwarf period of a few minutes. + Iu reality. the observed white dwarf rotation period is louger. vpically hours to davs (sawaler 2001: Wickramasinghe Ferrario 2000).," In reality, the observed white dwarf rotation period is longer, typically hours to days (Kawaler 2004; Wickramasinghe Ferrario 2000)." + Our suggested period ~77 min falls iuto he lower eud of the distribution. which is cousisteut with he fact that this is the first one that was detected. since it takes a longer tine to ideutifv the periodicity of the ones with longer periods. aud since a shorter period favors pair production which is the couditiou for colerent radio Cluission.," Our suggested period $\sim 77$ min falls into the lower end of the distribution, which is consistent with the fact that this is the first one that was detected, since it takes a longer time to identify the periodicity of the ones with longer periods, and since a shorter period favors pair production which is the condition for coherent radio emission." + Conserving magnetic iux iu the Sun during the collapse gives a dipolar imaguctic field of only ~10!6 at the white dwarf surface., Conserving magnetic flux in the Sun during the collapse gives a dipolar magnetic field of only $\sim 10^4$ G at the white dwarf surface. + Towever. in reality there is a group of magnetized white dwarfs thatlave a surface laguctic field in the range of 10° C (Wiclamnasiughie Ferrario 2000).," However, in reality there is a group of magnetized white dwarfs thathave a surface magnetic field in the range of $10^6 - 10^9$ G (Wickramasinghe Ferrario 2000)." + Some of them spin rapidly with periods around an hour. which could be explained im terms of binary evolution (Ferrario ct al.," Some of them spin rapidly with periods around an hour, which could be explained in terms of binary evolution (Ferrario et al." + 1997)., 1997). + These fast-rotating magnetized white dwarfs are the objects we propose here to interpret the pulsating behavior of CCRT J1715-3009., These fast-rotating magnetized white dwarfs are the objects we propose here to interpret the pulsating behavior of GCRT J1745-3009. + Alaeuetic white dwarfs con uumic pulsars in various aspects., Magnetic white dwarfs can mimic pulsars in various aspects. + In particular. it is well known that for a rotating. stronely-maegnetized object. the clectromaguctic force dominates gravitv and thermal forces. aud the natural outcome ix a corotating charge-separated maguetosphere (Goldreich Julian 1969).," In particular, it is well known that for a rotating, strongly-magnetized object, the electromagnetic force dominates gravity and thermal forces, and the natural outcome is a corotating charge-separated magnetosphere (Goldreich Julian 1969)." + Because of the unipolar effect. a large potential drop develops across the polar cap region defined by the last open field lines (Ruderman Sutherland 1975).," Because of the unipolar effect, a large potential drop develops across the polar cap region defined by the last open field lines (Ruderman Sutherland 1975)." + The magnetized white dwarf idea has been adopted to interpret the anomalous X-ray pulsars (Pacz*uuski 1990: Usov 1993. cf.," The magnetized white dwarf idea has been adopted to interpret the anomalous X-ray pulsars (Paczýnnski 1990; Usov 1993, cf." + IIulleuiu et al., Hulleman et al. + 2000)., 2000). + Below we show that the magnetized white dwarf model eives a straightforward interpretation to the observational data of GCBRE J1715-3009., Below we show that the magnetized white dwarf model gives a straightforward interpretation to the observational data of GCRT J1745-3009. + A period of P—7T? miu defines a light exliuder radius Ry—cePj2x2222«107?ci(P/7Tminu).," A period of $P \sim 77$ min defines a light cylinder radius $R_{lc} = cP/2 \pi = 2.2 \times 10^{13} ~{\rm +cm} ~ (P/77~{\rm min})$." +" Given a tvpical white dwarf radius vj=5s105 cu. the polar cap radius 15 llereafter the convention GQ,=(Q/10"") is adopted in ces units"," Given a typical white dwarf radius $R_{\rm +WD} = 5\times 10^8$ cm, the polar cap radius is Hereafter the convention $Q_x =(Q / 10^x)$ is adopted in cgs units." + Lacking a measurement of the period derivative P. one can not reliably estimate the spin down rate aud the dipolar surface maguetic field at the inaguetic pole. D.," Lacking a measurement of the period derivative $\dot P$, one can not reliably estimate the spin down rate and the dipolar surface magnetic field at the magnetic pole, $B_p$ ." +" Iu the following8 we assume 2,/=10? G. The maxinmm", In the following we assume $B_p = 10^9$ G. The maximum +The effect of this correction is to increase the column density by a factor that is twpically between one and wo.,The effect of this correction is to increase the column density by a factor that is typically between one and two. +" Values of (he ratio f,=Y are given on table 1. column 10."," Values of the ratio $f_c \ \equiv \ \frac{N_c}{N_t}$ are given on table 1, column 10." + These correction factors show typical values of 1.4 to 1.6. which is in agreement with similar correction factors found by Dickey ancl Benson (1982).," These correction factors show typical values of 1.4 to 1.6, which is in agreement with similar correction factors found by Dickey and Benson (1982)." +" Note that the .N; values on Table 1. column 8 are (vpically lareer (han IN. on column 9 because the range of integration is broader for the former than for the latter. the full inner Galaxy range for the former. and only to the recombination line velocity for the latter,"," Note that the $N_t$ values on Table 1, column 8 are typically larger than $N_c$ on column 9 because the range of integration is broader for the former than for the latter, the full inner Galaxy range for the former, and only to the recombination line velocity for the latter." + Finally we can combine the velocity integrals of the emission ancl absorption to get a velocily averaged spin temperature. which is (he nominal value of the spin temperature needed to give the emission and absorption integrals if the eas were al a single temperature.," Finally we can combine the velocity integrals of the emission and absorption to get a velocity averaged spin temperature, which is the nominal value of the spin temperature needed to give the emission and absorption integrals if the gas were at a single temperature." + This is given on table 1. column 11 for the velocity range corresponding to columns 7 and 9.," This is given on table 1, column 11 for the velocity range corresponding to columns 7 and 9." + Comparison of the emission and absorption spectra channel-by-channel shows that (his value is far [rom realistic. even under (he assumption.," Comparison of the emission and absorption spectra channel-by-channel shows that this value is far from realistic, even under the ``one-phase'' assumption." + Methods for combining the emission aud absorption spectra to find the distribution of spin temperatures in the interstellar can get complicated., Methods for combining the emission and absorption spectra to find the distribution of spin temperatures in the interstellar can get complicated. + The complications arise from blending of gas at clillerent temperatures in (he same spectral channel., The complications arise from blending of gas at different temperatures in the same spectral channel. + Anv line of sight ad low Galactic latitudes will contain a mixture of several cool clouds which appear as Gaussian line components in the absorption spectrum. plus warm gas which is hardly visible in the absorption spectrum. but which contributes the bulk of the emission.," Any line of sight at low Galactic latitudes will contain a mixture of several cool clouds which appear as Gaussian line components in the absorption spectrum, plus warm gas which is hardly visible in the absorption spectrum, but which contributes the bulk of the emission." + The challenge is to combine the absorption and emission spectra in a wav which separates these two thermal phases. eiving an estimate of the temperature of the cool gas without the bias introduced bv the warn gas emission.," The challenge is to combine the absorption and emission spectra in a way which separates these two thermal phases, giving an estimate of the temperature of the cool gas without the bias introduced by the warm gas emission." + In this section we discuss and compare several mathematical techniques Lor (his., In this section we discuss and compare several mathematical techniques for this. +5truei BStrueiu Cnr Cnr Cnr Cnr σα1) clussilü ον CLUSSS ciusshbxlO 1102 ciutir clurd cutis clures 12pt,"5truein 8truein cmr8 cmr8 cmr8 cmr8 cmr10 cmssi10 cmss10 cmss8 cmssbx10 2 cmti7 cmr6 cmti8 cmr8 \def\ref{\par\noindent\hangindent 15pt} + = 12pt" +"indicators were obtained simultaneously, X-ray observations were performed at a different time.","indicators were obtained simultaneously, X-ray observations were performed at a different time." + This result illustrates the importance of using simultaneous observations to build flux-flux relationships and avoid the time variability of activity levels., This result illustrates the importance of using simultaneous observations to build flux–flux relationships and avoid the time variability of activity levels. +" Contrarily to what was observed for the chromospheric flux— relationships, our result with X-ray emission is quite different than that obtained by ?.."," Contrarily to what was observed for the chromospheric flux--flux relationships, our result with X-ray emission is quite different than that obtained by \citet{1996ASPC..109..657M}." +" In the latter study, the authors used only binary systems for their study, many of them with both stars emitting in X-rays and/or in optical chromospheric lines."," In the latter study, the authors used only binary systems for their study, many of them with both stars emitting in X-rays and/or in optical chromospheric lines." +" In some occasions, they could separate both components in their optical spectra, but never in X-rays (the authors used data from the not corrected for binarity)."," In some occasions, they could separate both components in their optical spectra, but never in X-rays (the authors used data from the not corrected for binarity)." + This introduces systematical uncertainties and much more spread in the relationships., This introduces systematical uncertainties and much more spread in the relationships. +" Therefore, the difference between our determined value for the slope of the coronal-chromospheric flux relationships and that found by ? does not apply due to the systematic uncertainties introduced from determining X-ray emission from binary stars in the latter study."," Therefore, the difference between our determined value for the slope of the coronal–chromospheric flux relationships and that found by \citet{1996ASPC..109..657M} does not apply due to the systematic uncertainties introduced from determining X-ray emission from binary stars in the latter study." +a monochromatic source of photons ving on (he equatorial plane al a radial distance +.,"a monochromatic source of photons lying on the equatorial plane at a radial distance $\, r$." + For reasons of simplicity. let us assume Chat photons directed. toward (he axis undergo a single scattering αἱ some height z before leaving the region. as illustrated schematically in Figure 4..," For reasons of simplicity, let us assume that photons directed toward the axis undergo a single scattering at some height $z$ before leaving the region, as illustrated schematically in Figure \ref{Fig1}. ." +" [os=hr, and τι=hi4 are the initial and final photon energy respectively. ancl ἕ—z/r. we have where 0 is the angle between (he axis and the photon direction before the scattering. and 04 is (he fixed angle of observation."," If $\eps= h\nu\, $ and $\eps_1=h\nu_1\,$ are the initial and final photon energy respectively, and $\xi=z/r$, we have where $\,\theta$ is the angle between the axis and the photon direction before the scattering, and $\,\theta_1$ is the fixed angle of observation." + From equation (1)) we see that the ratio 24/2 may be either larger or smaller (han unity. depending on the value of £.," From equation \ref{compt}) ) we see that the ratio $\eps_1/\eps$ may be either larger or smaller than unity, depending on the value of $\,\xi$." + Then photons may eain or lose energv depending on the height at which they. are scattered., Then photons may gain or lose energy depending on the height at which they are scattered. + Of course. in a less schematic view. we need to consider the emission from the whole disk.," Of course, in a less schematic view, we need to consider the emission from the whole disk." + Moreover scattering does involve an extended portion of the jet and obevs to a probabilistic law that depends on the eas density., Moreover scattering does involve an extended portion of the jet and obeys to a probabilistic law that depends on the gas density. + As it will be shown in Section ??.. adopting a more realistic configuration and assuming a cold relativistic jet (i.e. the electron thermal velocity much lower than the bulk velocity) Comptonization by bulk motion leads to (he formation of a diluted blackbody energv distribution.," As it will be shown in Section \ref{sec-monte}, adopting a more realistic configuration and assuming a cold relativistic jet (i.e. the electron thermal velocity much lower than the bulk velocity) Comptonization by bulk motion leads to the formation of a diluted black–body energy distribution." + This distribution is roughv similar to the familiar multicolor spectrum of (he unperturbed disk. but differs [rom it because its maximum is shifted (o higher frequencies and it has a more extended hard tail.," This distribution is roughly similar to the familiar multicolor spectrum of the unperturbed disk, but differs from it because its maximum is shifted to higher frequencies and it has a more extended hard tail." + One cammol exclude. however. the possibility that the inner portion of the jet is heated by. e.g. turbulence. radiative Iriction or magnetic dissipation.," One cannot exclude, however, the possibility that the inner portion of the jet is heated by, e.g, turbulence, radiative friction or magnetic dissipation." + If these mechanisms are capable of maintainiig electrons in nearly virial equilibrium with the bulk motion. the combination of thermal and dynamical Comptonization leads to the ormation of a powerlaw (ail that is practically indistinguishable [rom that produced by a ιοί corona.," If these mechanisms are capable of maintaining electrons in nearly virial equilibrium with the bulk motion, the combination of thermal and dynamical Comptonization leads to the formation of a power–law tail that is practically indistinguishable from that produced by a hot corona." + This model has also implications on the timing properties of (he observed radiation., This model has also implications on the timing properties of the observed radiation. + In act. photons scattered at different: z-coordinates describe different path lengths. arriving al infinity with different energies and delavs.," In fact, photons scattered at different $\,z$ -coordinates describe different path lengths, arriving at infinity with different energies and delays." + A straightforward caleulation vields the following unctonal relation between the phase delay (in radians) and the geometrical parameters (we ignore an inessential constant related to the travel time of the radiation from the source to ihe Earth): where © is (he angular coordinate of the point source. / and /44; the Gime of emission and observation. respectively.," A straightforward calculation yields the following functional relation between the phase delay (in radians) and the geometrical parameters (we ignore an inessential constant related to the travel time of the radiation from the source to the Earth): where $\phi$ is the angular coordinate of the point source, $t\, $ and $\, t_{obs}\, $ the time of emission and observation, respectively." +" In equation ( 2)). in=AL/AL. and ris inunits of r,ο (here and in the lollowing all distances will be expressed in gravitational units)."," In equation ( \ref{time}) ), $m=M/M_\odot$ and $r$ is inunits of $r_g=GM/c^2$ (here and in the following all distances will be expressed in gravitational units)." +iin Fig.,in Fig. +" 1 (as well as those discussed in Paper I), a major fraction of the pixels (>80%) in our maps are due to the diffuse ionised gas component, which is much less contaminated by the local dynamical effects such as effects of supernovae and winds from individual rregions."," \ref{fig:allmaps} (as well as those discussed in Paper I), a major fraction of the pixels $> 80\%$ ) in our maps are due to the diffuse ionised gas component, which is much less contaminated by the local dynamical effects such as effects of supernovae and winds from individual regions." +" Deep oobservations of 77793 (?),, and imaging of the SINGS sample (?) further confirm the contribution of the diffuse component."," Deep observations of 7793 \citep{Dicaireetal2008}, and imaging of the SINGS sample \citep{Oeyetal2007} further confirm the contribution of the diffuse component." +" Combined with the typical star formation rates, «1 ffor half of our sample, estimated by (?),, ?,, and ?,, we expect that only a minor fraction of the velocities in the observed fields are affected by local effects such as winds from star forming complexes."," Combined with the typical star formation rates, $<1$ for half of our sample, estimated by \citep{Kennicuttetal2003}, \citet{MartinFriedli1997}, and \citet{GonzalezDelgado1997}, we expect that only a minor fraction of the velocities in the observed fields are affected by local effects such as winds from star forming complexes." +" Secondly, the gaseous motions which do not share the velocity field of the global pattern may, in large part, cancel due to global symmetries (arms, bar) or local symmetry (the expansion of individual rregions)."," Secondly, the gaseous motions which do not share the velocity field of the global pattern may, in large part, cancel due to global symmetries (arms, bar) or local symmetry (the expansion of individual regions)." + The bi-symmetric streaming motions along the bar and the arms must cancel quite well in order to restrict the mean gas inflow rates towards the centre of a galaxy., The bi-symmetric streaming motions along the bar and the arms must cancel quite well in order to restrict the mean gas inflow rates towards the centre of a galaxy. +" Local interruptions to continuous flow, while real, are on average circularly symmetric in the plane of the galaxy and any departure from regularity which might cross out continuity will cancel because there is sufficient symmetry in these departures."," Local interruptions to continuous flow, while real, are on average circularly symmetric in the plane of the galaxy and any departure from regularity which might cross out continuity will cancel because there is sufficient symmetry in these departures." + Example for such departures include star formation at the ends of a bar or two regular arms littered with rregions., Example for such departures include star formation at the ends of a bar or two regular arms littered with regions. +" Thus, the resulting values for the pattern speed are not necessarily less accurate than those obtained using the stellar component, especially as the latter are subject to relatively poor signal-to-noise conditions, and would need exposures more than one order of magnitude longer to give similar signal-to-noise ratios to those we find here."," Thus, the resulting values for the pattern speed are not necessarily less accurate than those obtained using the stellar component, especially as the latter are subject to relatively poor signal-to-noise conditions, and would need exposures more than one order of magnitude longer to give similar signal-to-noise ratios to those we find here." +" Regarding any possible effects of the spiral density wave in triggering star formation, there are two points to note. ("," Regarding any possible effects of the spiral density wave in triggering star formation, there are two points to note. (" +"I) Using the stellar continuum as our weighting function Table 4,, and further discussion on this point in section(see 6)) systematic effects from ddue to the presence of newly formed stars are ruled out.","I) Using the stellar continuum as our weighting function (see Table \ref{tab:patternspeeds}, , and further discussion on this point in section \ref{sec:results}) ) systematic effects from due to the presence of newly formed stars are ruled out." +" Furthermore, when we use the eemission intensity for weighting the velocities, columns 3 and 4 inTable 4 show that the resulting"," Furthermore, when we use the emission intensity for weighting the velocities, columns 3 and 4 inTable \ref{tab:patternspeeds} show that the resulting" +fraanework of the MIID.,framework of the MHD. + Iu our simulation. however. the velocity distribution at the N-point is far from the Maswell-Boltzmann distribution as secu in Figures 6.. Ts and &. which iuplics the treatment of the plasma as a Inagnetized fuid is not appropriate.," In our simulation, however, the velocity distribution at the X-point is far from the Maxwell-Boltzmann distribution as seen in Figures \ref{figure6}, , \ref{figure7}, , and \ref{figure8}, which implies the treatment of the plasma as a magnetized fluid is not appropriate." + Furthermore. although they assuned that the filament is isolated aud other flaments assert a negligible effect. two peaks in the velocity distribution at the X-poiut resultant from our siuulatiou show that the outskirts of filameuts coexist around the X-poiut.," Furthermore, although they assumed that the filament is isolated and other filaments assert a negligible effect, two peaks in the velocity distribution at the X-point resultant from our simulation show that the outskirts of filaments coexist around the X-point." + The model proposed by. Medvedevetal.(2005). is based on a toy model., The model proposed by \cite{m05} is based on a toy model. + Although this model ignores the effect of the dissipation of the magnetic field euergv via reconnection of the maenetic fields. it is expected in the framework of the resistive MIID.," Although this model ignores the effect of the dissipation of the magnetic field energy via reconnection of the magnetic fields, it is expected in the framework of the resistive MHD." + Our simulation docs not show auv sigu of the reconnection., Our simulation does not show any sign of the reconnection. + As stated earlier. we attribute the lack of the maguctic reconnection to the absence of the reconnection laver )otween the filaments.," As stated earlier, we attribute the lack of the magnetic reconnection to the absence of the reconnection layer between the filaments." + But. this can also be due to the coarseness of the simulation.," But, this can also be due to the coarseness of the simulation." + While judging whether the ack of the maguetic reconnection is real or not needs careful investigation. the results of our simulation justify he treatment of the coalescence in Aledvedeyetal. (2005).," While judging whether the lack of the magnetic reconnection is real or not needs careful investigation, the results of our simulation justify the treatment of the coalescence in \cite {m05}." +. Chaneetal.(2008) modeled the decay of the naenetic turbulence generated by the Weibel iustability., \cite{csa08} modeled the decay of the magnetic turbulence generated by the Weibel instability. + This treatinent is appropriate only iu the region where he magnetic trapping is not so nuportant., This treatment is appropriate only in the region where the magnetic trapping is not so important. + Actually. Chaneetal.(2008) confirm that their model caunot xediet the time evolution of magnetic field streneth iu the presence of a maguctic field with loug waveleneth.," Actually, \cite{csa08} confirm that their model cannot predict the time evolution of magnetic field strength in the presence of a magnetic field with long wavelength." + While. the detailed dynamical behavior of the filamentary structure is revealed in this study. some problems. for example. the loue-term evolution of the filaments and whether the critical scale-leneth above which the equilibrimm is stable exists or not. remain unclear.," While the detailed dynamical behavior of the filamentary structure is revealed in this study, some problems, for example, the long-term evolution of the filaments and whether the critical scale-length above which the equilibrium is stable exists or not, remain unclear." + In addition. because the distribution fiction is assuned to be uniforii along the direction of the initial omlk flow of plasmas. we cannot deal with some 3D verturbation on the equilibrium. for example. bending and twisting of the filaments.," In addition, because the distribution function is assumed to be uniform along the direction of the initial bulk flow of plasmas, we cannot deal with some 3D perturbation on the equilibrium, for example, bending and twisting of the filaments." + The stability of the οπήπι described by Equatious (25))-(28)). which is xesunablv a kev ineredicut for a strong magnetic field Oo survive in loug term and serve as an accelerator of outiceles iu the trausitiou laver of a collisiouless shock ront. should be iuvestigated rigorously including 3D effects.," The stability of the equilibrium described by Equations \ref{electron}) \ref{Beq}) ), which is presumably a key ingredient for a strong magnetic field to survive in long term and serve as an accelerator of particles in the transition layer of a collisionless shock front, should be investigated rigorously including 3D effects." +" Although this study treats nou-relativistic plasias. relativistic effects become vital iu some astroplysica phenomena. ce. GRDB afterglows. jets from ACN,"," Although this study treats non-relativistic plasmas, relativistic effects become vital in some astrophysical phenomena, e.g., GRB afterglows, jets from AGN." + Suzuki(2008) provides the relativistic extension of Suzuki&Shigevama(2008). i6. stationary solutions of the relativistic Vlasov-Maxwoell system.," \cite{s08} provides the relativistic extension of \cite{ss08}, i.e, stationary solutions of the relativistic Vlasov-Maxwell system." + It is not nrolevanut that one expects the equilibrium coustructe by Suzuki(2008) to provide an appropriate mode for the flamentary structure resultingfromthe Weibe instability iu relativistic plasimas as the non-relativistic counterpart does., It is not irrelevant that one expects the equilibrium constructed by \cite{s08} to provide an appropriate model for the filamentary structure resultingfromthe Weibel instability in relativistic plasmas as the non-relativistic counterpart does. +Alillisecond oscillations im the Xrav helt curves of svstenis known to contaüun neutron stars or possibly black holes have been observed for several vears with the Rossi XRav Timing Explorer (see vanderEKlis(2000). for a review).,Millisecond oscillations in the X–ray light curves of systems known to contain neutron stars or possibly black holes have been observed for several years with the Rossi X–Ray Timing Explorer (see \cite{vdk00} for a review). + Recently. it has been poiuted out that the centroid frequencies of the corresponding Ποιατς quasi periodic oscillations (kIIz QPOs) are in rational ratios of small integers. as 3:2 (Abramowicz&&Remillard2003:Abranmowiczetal. 2008a.15)..," Recently, it has been pointed out that the centroid frequencies of the corresponding kilohertz quasi periodic oscillations (kHz QPOs) are in rational ratios of small integers, as 3:2 \citep{ak01,rmmo02,Mc03,abbk03,akklr03}." + This supports sugecstious that a resonance of some kind is responsible for the observed properties (Wlugniak&Abyamowicz2001.2003:Titarchux 20023.," This supports suggestions that a resonance of some kind is responsible for the observed properties \citep{ka01,ka03,t02}." +". Iu addition. for at least one svsteni in which coherent pulsations have been detected. indicating the spin frequency (07,=0 II in SAN Jiso0s.3658). the separation in frequency between the kIIz peaks has been receutly reported to be consistent with 1/2 (Wijnandsetal.2003).. nuplving that the pulsar is exciting notions iu the accretion disk iu a nonlinear fashion (Ixluzuiaketal. 2003)."," In addition, for at least one system in which coherent pulsations have been detected, indicating the spin frequency $\nu_{s}=401$ Hz in SAX J1808.4-3658), the separation in frequency between the kHz peaks has been recently reported to be consistent with $\nu_{s}/2$ \citep{wetal03}, implying that the pulsar is exciting motions in the accretion disk in a nonlinear fashion \citep{kakls03}." +. Iu this Letter we show that the ΚΙΤΣ oscillatious detected in SAN JIs08.1-3658 cau be attributed to forcing of epicyclic motions iu the accretion disk by the 2.5 ms pulsar. which iuduces resonance at selected frequencies.," In this Letter we show that the kHz oscillations detected in SAX J1808.4-3658 can be attributed to forcing of epicyclic motions in the accretion disk by the 2.5 ms pulsar, which induces resonance at selected frequencies." + The coupling between the pulsar and the disk could be due to the maguetic field. or to some structure on the surface of the star.," The coupling between the pulsar and the disk could be due to the magnetic field, or to some structure on the surface of the star." + In other. similar svstenis. a frequency separation equal to the stellay spin frequency ds," In other, similar systems, a frequency separation equal to the stellar spin frequency is" +The location of cach radio source relative to the centre of the cluster is given in Table 4.. together with details of any optical galaxies with £<26. that Lie within 2.5 aresee of the radio source.,"The location of each radio source relative to the centre of the cluster is given in Table \ref{radopttab}, together with details of any optical galaxies with $I<26$, that lie within 2.5 arcsec of the radio source." + If multiple optical candidates are Found. only those within 3 magnitudes of the brightest. galaxy. are listed. to minimise potential galaxy deblending problems.," If multiple optical candidates are found, only those within 3 magnitudes of the brightest galaxy are listed, to minimise potential galaxy deblending problems." + The 2.5 aresec radius considered is larecr than the 0.2 arcsec uncertainty in the astrometric frame discussed above. primarily due to uncertainties in both the radio and optical positions.," The 2.5 arcsec radius considered is larger than the 0.2 arcsec uncertainty in the astrometric frame discussed above, primarily due to uncertainties in both the radio and optical positions." +been discussed most is the a effect. the first term on the RIDS of Eq. (3)).,"been discussed most is the $\alpha$ effect, the first term on the RHS of Eq. \ref{Electromotive}) )." + This has been shown to generate magnetic field at large scale for a helical turbulence., This has been shown to generate magnetic field at large scale for a helical turbulence. + Thus. it is à perlect candidate to explain magnetic fields in svstems influenced by Coriolis force (which produces a net helicitv) such as in stellar convection zones.," Thus, it is a perfect candidate to explain magnetic fields in systems influenced by Coriolis force (which produces a net helicity) such as in stellar convection zones." + This (wpe of dvnamo is thus classified as α if the O effect. (measured by the strength of the shear Q in our notations) is stronger than the a effect. or a? tvpe if the a effect dominates over the Q effect.," This type of dynamo is thus classified as $\alpha\Omega$ if the $\Omega$ effect (measured by the strength of the shear $\Omega$ in our notations) is stronger than the $\alpha$ effect, or $\alpha^2$ type if the $\alpha$ effect dominates over the $\Omega$ effect." + The second term in the RIIS is Eq. (3)), The second term in the RHS is Eq. \ref{Electromotive}) ) + is the turbulent. diffusivity which adds up to the molecular diffusivity i., is the turbulent diffusivity which adds up to the molecular diffusivity $\eta$. + Consequently. if 4 is positive. it inhibits the growth of magnetic field.," Consequently, if $\beta$ is positive, it inhibits the growth of magnetic field." + Recently. numerical simulations have shown dvnamo action at large scale in non-helical turbulence in the presence of shear (?)..," Recently, numerical simulations have shown dynamo action at large scale in non-helical turbulence in the presence of shear \citep{Yousef08}." + This is an interesting result as the a effect is olten thought to vanish in a turbulence without helicity., This is an interesting result as the $\alpha$ effect is often thought to vanish in a turbulence without helicity. + Various mechanisms have been invoked to explain this large-scale dynanmo: stochastic a effect (2).. shear aniplilication of small-scale dvuamo (?).. magnetic effect driven by current helicity flux (?) or negative diffusivity (?)..," Various mechanisms have been invoked to explain this large-scale dynamo: stochastic $\alpha$ effect \citep{Proctor07}, shear amplification of small-scale dynamo \citep{Blackman98}, magnetic effect driven by current helicity flux \citep{Vishniac01} or negative diffusivity \citep{Urpin02}." + Another possibility is the shear current effect. (2?) which appears in a turbulent flow with a mean shear flow., Another possibility is the shear current effect \citep{Rogachevskii03} which appears in a turbulent flow with a mean shear flow. +" In that case. the expression of the coellicient can be rewritten J;;4,=—3Teju+Fi(VUp) where 34 is the turbulent magnetic diffusion while the second term proportional to shear VU, acts as a source of magnetic field (2).."," In that case, the expression of the $\beta$ coefficient can be rewritten $\beta_{ijk} = - \beta^T \epsilon_{ijk} + F_{ijk}({\bf \nabla} \UU_0)$ where $\beta^T$ is the turbulent magnetic diffusion while the second term proportional to shear ${\bf \nabla} \UU_0$ acts as a source of magnetic field \citep{Rogachevskii03}." + It is thus of prime importance to investigate how the electromotive force (ancl consequently the a and 9 coefficients) depends on a large-scale shear flow (????)..," It is thus of prime importance to investigate how the electromotive force (and consequently the $\alpha$ and $\beta$ coefficients) depends on a large-scale shear flow \citep{Rogachevskii03,Rogachevskii04,Radler06,Brandenburg08}." + In all (hese previous studies. strong shear is conductive (ο dynamo as il creates magnetic οποιον via the © effect. acts as a source of magnetic field (e.g. via the shear-current effect). causes instability (7).. etc.," In all these previous studies, strong shear is conductive to dynamo as it creates magnetic energy via the $\Omega$ effect, acts as a source of magnetic field (e.g. via the shear-current effect), causes instability \citep{Tobias04}, etc." + One interesting problem. which has not been investigated by most previous authors. is the elect of a stable shear flow on turbulent transport through the modification of the properties of turbulence alone. without direct influence on (B) (i.e. no O-effect. shear-current elect).," One interesting problem, which has not been investigated by most previous authors, is the effect of a stable shear flow on turbulent transport through the modification of the properties of turbulence alone, without direct influence on $\langle {\bf B} \rangle$ (i.e. no $\Omega$ -effect, shear-current effect)." + A strong shear flow. without altering (B) directly. can reduce turbulent transport as," A strong shear flow, without altering $\langle {\bf B} \rangle$ directly, can reduce turbulent transport as" +but their barvonic masses differ by a factor of 5.,but their baryonic masses differ by a factor of $5$. + We have shown that the rotation curve of IToIT is not compatible with MOND uuless the inclination is fine-tuned to a very uulikelv value., We have shown that the rotation curve of HoII is not compatible with MOND unless the inclination is fine-tuned to a very unlikely value. + This inclination is the one required for Πο to satisfv the barvonic Tully-Fisher relation., This inclination is the one required for HoII to satisfy the baryonic Tully-Fisher relation. + We would like to thank Elias Brinks for his encouragement to make these results public., We would like to thank Elias Brinks for his encouragement to make these results public. + This work was supported by CONACYT project GO526F and PAPIIT project INL21609., This work was supported by CONACyT project 60526F and PAPIIT project IN121609. +corresponding to net heating (left of the thermal equilibrium asymptote) and net cooling (right of the equilibrium asymptote).,corresponding to net heating (left of the thermal equilibrium asymptote) and net cooling (right of the equilibrium asymptote). +" These two contours nearly near the (density-dependent) thermal equilibrium temperature, slightly above 10!K, where the net cooling time goes to infinity."," These two contours nearly near the (density-dependent) thermal equilibrium temperature, slightly above $10^4\,\K$, where the net cooling time goes to infinity." +" Below this temperature, the heating time is dictated by the photo-heating rate."," Below this temperature, the heating time is dictated by the photo-heating rate." + For T>10°K photo-ionization has no effect on a metal-free gas because the plasma is already fully ionized by collisional processes.," For $T\gg 10^5\,\K$ photo-ionization has no effect on a metal-free gas because the plasma is already fully ionized by collisional processes." + In this regime the plasma cools predominantly via the emission of Bremsstrahlung and/or inverse Compton scattering of CMB photons., In this regime the plasma cools predominantly via the emission of Bremsstrahlung and/or inverse Compton scattering of CMB photons. + The latter process is the dominant cooling mechanism for most of the baryons at high redshift (z> 7)., The latter process is the dominant cooling mechanism for most of the baryons at high redshift $z > 7$ ). +" In the plot inverse Compton cooling off the CMB dominates the radiative cooling rate at low densities and high temperatures, but the corresponding cooling time exceeds the Hubble time."," In the plot inverse Compton cooling off the CMB dominates the radiative cooling rate at low densities and high temperatures, but the corresponding cooling time exceeds the Hubble time." +" For diffuse, intergalactic gas (i.e., for density contrasts 5< 103, corresponding to ng<10?cm? at z=3, much lower than expected in virialized objects, citealtColes2002)) of primordial composition, radiation increases the cooling time at 10°K by at least an order of magnitude and by much more at lower temperatures."," For diffuse, intergalactic gas (i.e., for density contrasts $\delta +\ll 10^2$ , corresponding to $n_{\rm H} \ll 10^{-3}\,\cm^{-3}$ at $z=3$, much lower than expected in virialized objects, \\citealt{Coles2002}) ) of primordial composition, radiation increases the cooling time at $10^5\,\K$ by at least an order of magnitude and by much more at lower temperatures." +" Since the cooling times in this regime are comparable to the Hubble time, radiation will have a large effect on the fraction of the baryons that are hot."," Since the cooling times in this regime are comparable to the Hubble time, radiation will have a large effect on the fraction of the baryons that are hot." +" At densities corresponding to collapsed objects (5>10? or ngZ10?cm? at z= 3), the increase in the cooling time is generally smaller, although it can still easily be an order of magnitude at temperatures as high as 10*5K."," At densities corresponding to collapsed objects $\delta \ga 10^2$ or $n_{\rm H} \ga 10^{-3}\,\cm^{-3}$ at $z=3$ ), the increase in the cooling time is generally smaller, although it can still easily be an order of magnitude at temperatures as high as $10^{4.5}\,\K$." +" 'The top-right panel shows that heavy elements strongly increase the cooling rate of a collisionally ionized plasma for 10'K«TX10'K (e.g,?).."," The top-right panel shows that heavy elements strongly increase the cooling rate of a collisionally ionized plasma for $10^4\,\K \ll T \la +10^7\,\K$ \cite[e.g.,][]{Boehringer1989}." +" Comparing the model with primordial abundances (dashed contours) to the one assuming solar metallicity (solid contours), we see that the cooling times typically differ by about an order of magnitude."," Comparing the model with primordial abundances (dashed contours) to the one assuming solar metallicity (solid contours), we see that the cooling times typically differ by about an order of magnitude." + The presence of metals allows radiative cooling through collisional excitation of a large number ofions at a variety of temperatures., The presence of metals allows radiative cooling through collisional excitation of a large number ofions at a variety of temperatures. + For T>107K the difference," For $T> 10^7\,\K$ the difference" +The referee of this paper has pointed. out that tidal downsizing hypothesis does not currently have explanations for at least the following observations of the Solar System: the Late Heavy Bombardment event. the exact chemical composition of the rocky inner planets. anc the orbital evolution of the outer giant planets.,"The referee of this paper has pointed out that tidal downsizing hypothesis does not currently have explanations for at least the following observations of the Solar System: the Late Heavy Bombardment event, the exact chemical composition of the rocky inner planets, and the orbital evolution of the outer giant planets." + These issues are outside of the scope of this paper. but we hope to clarify them in our future work.," These issues are outside of the scope of this paper, but we hope to clarify them in our future work." + In this short article we estimated. the rotation rate of xanets. both terrestrial and giant. in the context of the tidal downsizing hypothesis for planet formation.," In this short article we estimated the rotation rate of planets, both terrestrial and giant, in the context of the tidal downsizing hypothesis for planet formation." + We showed that such planets could potentially be rotating near their break up limit at formation. although there are mechanisms for owering the initial spins.," We showed that such planets could potentially be rotating near their break up limit at formation, although there are mechanisms for lowering the initial spins." + Phe default direction of the spins coincides with that of the parent disc., The default direction of the spins coincides with that of the parent disc. + This may explain he fast ancl coherent rotation pattern of most of the Solar System planets., This may explain the fast and coherent rotation pattern of most of the Solar System planets. + Exceptions to the coherent rotation may »( due to embryvo-embryo interactions that appear to occur requentIy in the simulations., Exceptions to the coherent rotation may be due to embryo-embryo interactions that appear to occur frequently in the simulations. + We also argued that the Moon could. have formed. inside the same parent embryo as the Earth. explaining compositional similarities between the two »odies.," We also argued that the Moon could have formed inside the same parent embryo as the Earth, explaining compositional similarities between the two bodies." + Theoretical astrophysics rescarch at the University of Leicester is supported by aS TEC Rolling grant., Theoretical astrophysics research at the University of Leicester is supported by a STFC Rolling grant. + The authors thanks Seung-Lloon Cha for his permission to use the simulation cata of Cha&Navakshin(2010). to illustrate the analytical theory presented here., The authors thanks Seung-Hoon Cha for his permission to use the simulation data of \cite{ChaNayakshin10} to illustrate the analytical theory presented here. + Ehe. author thanks the anonvmous referee for a useful report that mace the shortcomings of the tical downsizing hypothesis clearer., The author thanks the anonymous referee for a useful report that made the shortcomings of the tidal downsizing hypothesis clearer. +through the calculation of a relativistic transfer function (Cunningham L975).,through the calculation of a relativistic transfer function (Cunningham 1975). + The following assumptions are mace to compute the transfer function: 7) the accretion disc. is thin (disc height much smaller than disc radius). 77) the gas follows prograde circular orbits outside the marginally stable radius ris. ££) the disc is Dat and lies in the equatorial plane of the black hole and ie) the gas emits isotropically in its rest frame.," The following assumptions are made to compute the transfer function: $i$ ) the accretion disc is thin (disc height much smaller than disc radius), $ii$ ) the gas follows prograde circular orbits outside the marginally stable radius $r_{ms}$, $iii$ ) the disc is flat and lies in the equatorial plane of the black hole and $iv$ ) the gas emits isotropically in its rest frame." +" Note that this model does not emit inside r,,..", Note that this model does not emit inside $r_{ms}$. + ‘The dise model is discussed in more detail in Agol Ixrolik (1999)., The disc model is discussed in more detail in Agol Krolik (1999). + Several attempts have been made το understand. the accretion disc in Q2237|0305 by comparing model light curves with observed microlensing events (eg., Several attempts have been made to understand the accretion disc in Q2237+0305 by comparing model light curves with observed microlensing events (eg. + Rauch Blanclord 1901: Jaroszvnski et al., Rauch Blandford 1991; Jaroszynski et al. + 1992: Jaroszvnski AMlarek 19904: C'zorny et al., 1992; Jaroszynski Marck 1994; Czerny et al. + 1994)., 1994). + Phe approach of these papers is to discuss the luminosity of the quasar considering the predicted: magnification of the macro-images as well as the limits on source size imposed by microlensing observations., The approach of these papers is to discuss the luminosity of the quasar considering the predicted magnification of the macro-images as well as the limits on source size imposed by microlensing observations. + In this paper we compute light-curves for the accretion disc in 1l frequeney bands (see table 1)): The quoted frequency is the band centre in the quasar rest frame. he first 4 filters are HIST filters.," In this paper we compute light-curves for the accretion disc in 11 frequency bands (see table \ref{freqs}) ): The quoted frequency is the band centre in the quasar rest frame, the first 4 filters are HST filters." + Fig., Fig. + 10. shows the cross-sections of the intensity profiles in the U (light line). R (thick dark lino) and Ix. (thin dark line).," \ref{sourcees} shows the cross-sections of the intensity profiles in the U (light line), R (thick dark line) and K (thin dark line)." + The source size (5) must be interpreted in terms of its intensity. profile., The source size $S$ ) must be interpreted in terms of its intensity profile. + We define the source size such that the event length produced w the source is equivalent to that. produced. by à. iu profile of ciameter S., We define the source size such that the event length produced by the source is equivalent to that produced by a top-hat profile of diameter $S$ . + We have used the example of a Mack hole mass of 10AZ. which at 1077df: (B-band) corresponds to a source radius of 51077em.," We have used the example of a black hole mass of $10^{8}M_{\odot}$ which at $\times 10^{15}\,Hz$ (R-band) corresponds to a source radius of $5\times 10^{14}\,cm$." + This model sullers the difficulties that were pointed out in the case of a thermal accretion disc by Rauch Blandford (1991). namely that it severely underestimates the observed. (lux.," This model suffers the difficulties that were pointed out in the case of a thermal accretion disc by Rauch Blandford (1991), namely that it severely underestimates the observed flux." + However our focus here is to combine a detailed accretion disc model with high resolution microlensing models to simulate. microlensing induced. spectral change. during a caustic crossing., However our focus here is to combine a detailed accretion disc model with high resolution microlensing models to simulate microlensing induced spectral change during a caustic crossing. + The source profile is computed. over a. nested. grid. of cells (with side length 50074) down to a resolution of 0.5 ry in each of the 11 bands., The source profile is computed over a nested grid of cells (with side length $r_g$ ) down to a resolution of 0.5 $r_g$ in each of the 11 bands. + Phe grid contains 4864 cells which lic on 192 parallel source tracks., The grid contains 4864 cells which lie on 192 parallel source tracks. +" Phe light-curves were computed using the method described by Wyithe Webster (1999). and computed at a resolution of 10.η, along the source line."," The light-curves were computed using the method described by Wyithe Webster (1999), and computed at a resolution of $\times 10^{-4}\eta_o$ along the source line." + At an ellective galactic transverse velocity of &msee. Lopethis corresponds to a temporal resolution. of ~0.5 days.," At an effective galactic transverse velocity of $\,km\,sec^{-1}$, this corresponds to a temporal resolution of $\sim 0.5$ days." + We calculate the microlensed light-curves of an accretion disc source having a central black-hole mass of 10941. (Spo104em in H-band).," We calculate the microlensed light-curves of an accretion disc source having a central black-hole mass of $10^{8}M_{\odot}$ $S_R\sim 10^{15}\,cm$ in R-band)." + Phe mean microlens mass in the simulation was (mi=O.LAL. ancl the microlensing parameters corresponded to image A (5.4= 0.4)., The mean microlens mass in the simulation was $\langle m\rangle =0.1M_{\odot}$ and the microlensing parameters corresponded to image A $\gamma_{A}=0.4$ ). + The results [or S and £m of WATALOO suggest that these parameters are respectively near the upper ancl lower limits expected [or (Q2237|0305., The results for $S$ and $\langle m\rangle$ of WWTM00 suggest that these parameters are respectively near the upper and lower limits expected for Q2237+0305. + Phe colour changes found are therefore conservative for this class of cise model., The colour changes found are therefore conservative for this class of disc model. + Example light-curves with the aforementioned. parameters are. presented in Fie. 11.., Example light-curves with the aforementioned parameters are presented in Fig. \ref{lcurves}. + Phree curves are shown corresponding to the source profiles in Fig. 10.., Three curves are shown corresponding to the source profiles in Fig. \ref{sourcees}. + The light-curves show magnitude change plus an offset equal to the dillerence in unlensed Dux., The light-curves show magnitude change plus an offset equal to the difference in unlensed flux. + Ensembles of mock experiments are produced. for. two wpothetical triggers: Y=5 and Y=15 magnitudes per vear., Ensembles of mock experiments are produced for two hypothetical triggers: $T=5$ and $T=15$ magnitudes per year. + Below we simulate a TOO comprising 3 spectroscopic observations taken at intervals designated at the time ofthe rigger., Below we simulate a TOO comprising 3 spectroscopic observations taken at intervals designated at the time of the trigger. +" Phe first two observations are scheduled. according o when the triggering function Of,(2.2)/OLP predicts an IHIME: 2)4 weeks following the small trigger and 1.2 weeks ollowing the large trigger."," The first two observations are scheduled according to when the triggering function $\partial F_{T}(T,P)/\partial P$ predicts an HME: $2-4$ weeks following the small trigger and $1-2$ weeks following the large trigger." + A third observation ismade 10 weeks following the trigger to provide à comparison with re spectrum of a (hopefully) non-cillerentially magnified SOULCC., A third observation ismade 10 weeks following the trigger to provide a comparison with the spectrum of a (hopefully) non-differentially magnified source. + We assume a likely ellective galactic transverse velocity, We assume a likely effective galactic transverse velocity +The 15pum cdillerential counts put à severe constraint on the magnitude of the luminosity evolution at lower redshift in the presence of density evolution.,The $\umu$ m differential counts put a severe constraint on the magnitude of the luminosity evolution at lower redshift in the presence of density evolution. + At S50Lun. the ellect of the addition. of. luminosity evolution is quite spectacular.," At $\umu$ m, the effect of the addition of luminosity evolution is quite spectacular." + Phe shift to the right in the HgCNo)/Tg(9) plane can ellectively fit the SCUBA counts at lluxes both fainter and brighter than 2m., The shift to the right in the $lg(N) / lg(S)$ plane can effectively fit the SCUBA counts at fluxes both fainter and brighter than 2mJy. +" There is little dillerence. between the high. or low redshift evolutionary scenarios implying that many. of the SCUBA sources are at redshifts higher than unity allowing the z,=2 scenario to compete with the combined effect of the Luminosity and density evolution in the z,,1 scenario.", There is little difference between the high or low redshift evolutionary scenarios implying that many of the SCUBA sources are at redshifts higher than unity allowing the $z_{p}=2$ scenario to compete with the combined effect of the luminosity and density evolution in the $z_{p}=1$ scenario. + However. it should be noted that there is à significant. dillerence between the two Gaussian scenarios and the plateau scenario.," However, it should be noted that there is a significant difference between the two Gaussian scenarios and the plateau scenario." + It would seem that constant. luminosity evolution over the entire redshift range z=1-2 is ruled out by the count constraints., It would seem that constant luminosity evolution over the entire redshift range z=1-2 is ruled out by the count constraints. + As with the density evolution. analvsis. the SCUBA Nb5ÜLun counts are constrained by the evolution at. higher redshift while the 15pum counts are severely constrained at lower redshift.," As with the density evolution analysis, the SCUBA $\umu$ m counts are constrained by the evolution at higher redshift while the $\umu$ m counts are severely constrained at lower redshift." +" Phis bipolar constraint is highlighted in the way that the plateau curve /rnugs the 2,=1 Gaussian luminosity evolution curve at. 15]. while at S5Opum there is à more clearer superposition of the 2 Gaussian scenarios."," This bipolar constraint is highlighted in the way that the plateau curve the $z_{p}=1$ Gaussian luminosity evolution curve at $\umu$ m, while at $\umu$ m there is a more clearer superposition of the 2 Gaussian scenarios." + From the analvsis of the effects. and constraints. from density and. luminosity evolution of the Ht high luminosity. population (assumed to be ULICSs) in the previous section. the following points / constraints can be mace. From these considerations a model can be envisioned that includes. both density evolution at. lower. recshilt (peaking at z~1) and luminosity evolution. peaking at higher redshift.," From the analysis of the effects and constraints from density and luminosity evolution of the IR high luminosity population (assumed to be ULIGs) in the previous section, the following points / constraints can be made, From these considerations a model can be envisioned that includes both density evolution at lower redshift (peaking at $z \sim 1$ ) and luminosity evolution peaking at higher redshift." + Phe exact. details of the evolution. are constrained by fits to the source counts which will depend on both the magnitude of the evolution and the degree of in the redshift space between the tails of the density and luminosity evolution., The exact details of the evolution are constrained by fits to the source counts which will depend on both the magnitude of the evolution and the degree of in the redshift space between the tails of the density and luminosity evolution. + Phe magnitude of the evolution at high redshift will ultimately be constrained by the cosmic infrared. background., The magnitude of the evolution at high redshift will ultimately be constrained by the cosmic infrared background. + Using these 3 constraints (15pum differential counts. S5Opun integral counts and the CLRB) and the results from the previous analysis. the following evolutionary scenario is presented.," Using these 3 constraints $\umu$ m differential counts, $\umu$ m integral counts and the CIRB) and the results from the previous analysis, the following evolutionary scenario is presented." + Lhe basic framework of the eppltlt model is retained with the galaxy population consisting of 4 main components., The basic framework of the cppRR model is retained with the galaxy population consisting of 4 main components. + Normal (cirrus) galaxies are represented: by hecool GOpun LRAS luminosity function and are essentially non-evolving although a gradual. decline towards higher redshift’ is ineluded to represent. gradual formation and/or ransition through a starburst) phase., Normal (cirrus) galaxies are represented by the $\umu$ m IRAS luminosity function and are essentially non-evolving although a gradual decline towards higher redshift is included to represent gradual formation and/or transition through a starburst phase. + Phe HUS ealaxies (starbursts) and Sevfert galaxies are represented by he GOpum ancl μαι LAS luminosity functions respectively and evolve in luminosity at arate x(1ο) to z22.5 and hen gradually decline at higher redshifts thus eliminating he artificial eut olf employed previously in the eppRR model ancl pointed. out by. Rowan-Robinson (2000) as being a general shortcoming with many models emploving the approach to galaxy. evolution., The IRAS galaxies (starbursts) and Seyfert galaxies are represented by the $\umu$ m and $\umu$ m IRAS luminosity functions respectively and evolve in luminosity at a rate $\propto (1+z)^{3.2}$ to z=2.5 and then gradually decline at higher redshifts thus eliminating the artificial cut off employed previously in the cppRR model and pointed out by Rowan-Robinson \shortcite{RR00} as being a general shortcoming with many models employing the approach to galaxy evolution. + Choosing a »ealkk in the Luminosity evolution at high. redshift. (z=2.5) is consistent. with the higher redshift galaxies contributing more to the counts/hackgrounc at. longer. wavelengths (Gispertet.al.2000), Choosing a peak in the luminosity evolution at high redshift (z=2.5) is consistent with the higher redshift galaxies contributing more to the counts/background at longer wavelengths \cite{gispert00} . + The high. luminosity enc of. the IR. 601. luminosity function. the LIG/ULICG component. labsoja~LOL.. evolves in both number density. and uminositv.," The high luminosity end of the IR $\umu$ m luminosity function, the LIG/ULIG component, $lgL*_{60\mu m} \sim 11.6 L_{\sun}$, evolves in both number density and luminosity." + Phe censity evolution is strong and exponential. ollowing eqn.," The density evolution is strong and exponential, following eqn." + 7 peaking at a redshift of 1 with the magnitude of the evolution. g=220 and Gaussian. width. m=0.25.," \ref{Dz} peaking at a redshift of 1 with the magnitude of the evolution, $g=220$ and Gaussian width, $\sigma =0.25$." + The luminosity evolution rises exponentially as eqn., The luminosity evolution rises exponentially as eqn. +" S. with a magnitudo &=40. ¢=0.58 to a maximum redshift. z,,=2.5 and then slowly declines exponentially to higher redshift."," \ref{Lz} with a magnitude $k=40$, $\sigma =0.58$ to a maximum redshift, $z_{p}=2.5$ and then slowly declines exponentially to higher redshift." + Phe magnitude of the luminosity evolution at the peak redshift in the starburst. Sevfert and ULIC: components is similar although the latter sulfers a steeper decline towards lower redshift reflecting the more violent star formation within these galaxies.," The magnitude of the luminosity evolution at the peak redshift in the starburst, Seyfert and ULIG components is similar although the latter suffers a steeper decline towards lower redshift reflecting the more violent star formation within these galaxies." + Fig., Fig. + S— shows the [its of the new evolutionary model to the source countsas observed. by ISO) (15. 90. 1r0tun). LIGAS (GOpun) SCUBA (S50tun).," \ref{newcount} shows the fits of the new evolutionary model to the source countsas observed by ISO (15, 90, $\umu$ m), IRAS $\umu$ m) SCUBA $\umu$ m)." + The new mocel incorporating the strongly evolving LIG/ULICG component, The new model incorporating the strongly evolving LIG/ULIG component +around 0.45 - 0.50 km s,around $0.45$ - $0.50$ km $^{-1}$. + Llowever. the clumps in the SPILL simulations tend to cluster at lower temperature (7100 IX) and there is less gas at higher temperatures than in the grid. simulations (Fig. 8)).," However, the clumps in the SPH simulations tend to cluster at lower temperature $T<100$ K) and there is less gas at higher temperatures than in the grid simulations (Fig. \ref{f:temphist}) )." + This is probably a result. of SPL intrinsic over-cooling., This is probably a result of SPH intrinsic over-cooling. + Lagrangian hwdrodynamical methods such as Smootheel Particle Uycdrodyvnamics (SPIL) ave an attractive tool to simulate astrophysical problems with a wide range of spatial scales. such as sell-eravitating objects or thermally unstable Hows.," Lagrangian hydrodynamical methods such as Smoothed Particle Hydrodynamics (SPH) are an attractive tool to simulate astrophysical problems with a wide range of spatial scales, such as self-gravitating objects or thermally unstable flows." + However. due to the numerical implementations. the reliability o£ SPL for such applications has been questioned.," However, due to the numerical implementations, the reliability of SPH for such applications has been questioned." + We compare a SPL implementation and à erid-based method in an application to Iow-driven molecular cloud formation., We compare a SPH implementation and a grid-based method in an application to flow-driven molecular cloud formation. + This is a challenging astrophysical problem for any numerical method. because of the turbulence. the high density and temperature contrasts. and the rapidly shrinking scales of the cold clouds.," This is a challenging astrophysical problem for any numerical method, because of the turbulence, the high density and temperature contrasts, and the rapidly shrinking scales of the cold clouds." + The morphologies between particle and. grid. based methods agree well globally. vet the cold gas structures are more fragmented in the SPL mocels (Fig. 1)).," The morphologies between particle and grid based methods agree well globally, yet the cold gas structures are more fragmented in the SPH models (Fig. \ref{temp_dens_snap}) )." + Temperature and density gradients in SPIEL tend to be “rounder” than in the grid. method. as à consequence of deriving. physical quantities by averaging over a set of nearest neighbors., Temperature and density gradients in SPH tend to be “rounder” than in the grid method as a consequence of deriving physical quantities by averaging over a set of nearest neighbors. + Llowever. this drawback is countered by the higher spatial resolution. vielding more [filigree structure in the SPLI models.," However, this drawback is countered by the higher spatial resolution, yielding more filigree structure in the SPH models." + The mass fractions of gas in cilfercnt temperature regimes cdiller slishtly (Eig. 3))., The mass fractions of gas in different temperature regimes differ slightly (Fig. \ref{time_vs_massfrac}) ). + SPLE models start collecting mass in the cold stable regime later than the grid mocels. leading to a constant offset. in the mass with time.," SPH models start collecting mass in the cold stable regime later than the grid models, leading to a constant offset in the mass with time." + This is à consequence of the strong overheating in the initial How collision due to SPLIUs artificial viscosity., This is a consequence of the strong overheating in the initial flow collision due to SPH's artificial viscosity. + Phe slopes of the CIMES (Fig. 4)), The slopes of the ClMFs (Fig. \ref{f:cmf}) ) + are consistent with results [rom earlier numerical models with similar physics., are consistent with results from earlier numerical models with similar physics. + They. are also consistent with observational results, They are also consistent with observational results +"have already stressed that there are different contributing factors to FIR πλοςλος, and in particulary carly spiral ealaxies often exhibit low temperature. relatively Ligh FIR huninositics attributable to dust heating roni the eeucral stellar radiation feld. aud not directly related to SER (I&eunicutt 1998)).","have already stressed that there are different contributing factors to FIR luminosities, and in particular early spiral galaxies often exhibit low temperature, relatively high FIR luminosities attributable to dust heating from the general stellar radiation field, and not directly related to SFR (Kennicutt \cite{kenni}) )." + Tt has been claimed that a more reliable discriniinaut of the SFR is he infrared excess Ley Ly (og., It has been claimed that a more reliable discriminant of the SFR is the infrared excess $_{\rm FIR}$ $_{\rm B}$ (eg. +o Γωνία et al. 1996))., Tomita et al. \cite{tomita}) ). + This is because by normalizing to the due huninosity we partially remove the effect of the general radiation field., This is because by normalizing to the blue luminosity we partially remove the effect of the general radiation field. + In Table 7 we report the SN rates iun SNu for galaxies with differcut infrared excess. aloug with that of galaxies uot detected by IRAS.," In Table \ref{lfirlb} we report the SN rates in SNu for galaxies with different infrared excess, along with that of galaxies not detected by IRAS." +" Though in general we cannot translate ""not detected” into a precise upper limit. itis reasonable to assume that. for our RC3 galaxy sample. the average FIR luminosity of the undetected siuuple is sanaller than that of the detected sample."," Though in general we cannot translate “not detected” into a precise upper limit, it is reasonable to assume that, for our RC3 galaxy sample, the average FIR luminosity of the undetected sample is smaller than that of the detected sample." + Support for this belief comes frou the fact that the distance distributions of the detected aud not detected RC3 galaxy samples are snnilar., Support for this belief comes from the fact that the distance distributions of the detected and not detected RC3 galaxy samples are similar. + The rate of core collapse SNe is higher iu the IR detected galaxies compared with the not detected sample. whereas this is not the case for SN Ia (Table 7)) whilst there are no significant differcuces between galaxies with sanall and large infrared excess.," The rate of core collapse SNe is higher in the IR detected galaxies compared with the not detected sample, whereas this is not the case for SN Ia (Table \ref{lfirlb}) ) whilst there are no significant differences between galaxies with small and large infrared excess." + This again supports the idea that. whereas a fraction of the FIR Iuuüunositv originates from SF regions. the other contributing factors to the IR cussion of galaxies clininate. at least iu normal ealaxies. the relation between Ley; aud SFR.," This again supports the idea that, whereas a fraction of the FIR luminosity originates from SF regions, the other contributing factors to the IR emission of galaxies eliminate, at least in normal galaxies, the relation between $_{\rm FIR}$ and SFR." + It is generally believed that unclear activity stimulates --1ο SF (Rodviguez-Espinoza et al. 1987)), It is generally believed that nuclear activity stimulates the SF (Rodriguez-Espinoza et al. \cite{rodri}) ) +" aud therefore —IH the rate of core-collapse SNe in AGN ust be higher atIH Lin normal ealaxies,", and therefore that the rate of core-collapse SNe in AGN must be higher than in normal galaxies. + An open issue is whether the SF is stimmlated throughout the whole ACN host ealaxy or only in the circiunnuclear region., An open issue is whether the SF is stimulated throughout the whole AGN host galaxy or only in the circumnuclear region. +" From the observational point of view. in the first case we would expect an eulauced etection rate. whereas due to the high extinction in the unclear starburst regions this may not occur in the latter Case,"," From the observational point of view, in the first case we would expect an enhanced detection rate, whereas due to the high extinction in the nuclear starburst regions this may not occur in the latter case." + To address this question we crossed our RC3 galaxy list with the Catalog of Quasars and Active Galactic Nuclei of Véerron-Cetty Verron (1998)) (istributed by the CDS)., To address this question we crossed our RC3 galaxy list with the Catalog of Quasars and Active Galactic Nuclei of Vérron-Cetty Vérron \cite{veron}) ) (distributed by the CDS). + This catalog contaius a list of almost. 15000 quasars auk AGN inost of which are too distant for normal SN searches (ouly ~1100 have recession velocities smaller thau 15000 kin 1 |.," This catalog contains a list of almost 15000 quasars and AGN most of which are too distant for normal SN searches (only $\sim +1100$ have recession velocities smaller than 15000 km $^{-1}$ )." + We found that 283 galaxies out of our combined RC3 sample. (~ 3%)) are also listed in the Verrou-Cetty Vorrou catalog (this simply reflects the relative occurence of AGN in the local Universo).," We found that 283 galaxies out of our combined RC3 sample, $\sim$ ) are also listed in the Vèrron-Cetty Vèrron catalog (this simply reflects the relative occurrence of AGN in the local Universe)." +" Most of them, (~ are Sevfort and the rest IIT galaxies.", Most of them $\sim$ ) are Seyfert and the rest HII galaxies. + Iu these galaxies our searches have discovered 17 SNe. that is total SN sauuple.," In these galaxies our searches have discovered 17 SNe, that is of the total SN sample." + This could be taken as evidence that the SN rate in ACN is enhanced compared with the eeneral sample., This could be taken as evidence that the SN rate in AGN is enhanced compared with the general sample. + However. when the control tine method is applied. the average SN rate in the AGN sample is 0.60.1 SNu (0.140.1. SNu for core-collapse SNe). ideutical to that of the general sample (0.73:0.1 SNu for all SNe aud 0.50.1 SNu for core-collapses).," However, when the control time method is applied, the average SN rate in the AGN sample is $0.6\pm0.1$ SNu $0.4\pm0.1$ SNu for core-collapse SNe), identical to that of the general sample $0.7\pm0.1$ SNu for all SNe and $0.5\pm0.1$ SNu for core-collapses)." + We note that the ACN sample shows roughlv the same distribution of morphological types as the general sample., We note that the AGN sample shows roughly the same distribution of morphological types as the general sample. + There are two reasous why the high detection rate iu our ACN galaxy ssiuple does not reflect iu higher SN rates in SNu., There are two reasons why the high detection rate in our AGN galaxy sample does not reflect in higher SN rates in SNu. + First of all. the average control time for a galaxy of the ACN ealaxy sample (5.08 vr) is almost twice that of the general galaxy sample (2.67 vr).," First of all, the average control time for a galaxy of the AGN galaxy sample (5.08 yr) is almost twice that of the general galaxy sample (2.67 yr)." + Secondly. the galaxies of the ACN sample are over 2 times more Dnuninous Lp>=3.1 UT) than the average “normal” galaxies (=lL.LP Loy ," Secondly, the galaxies of the AGN sample are over 2 times more luminous $ = 3.1^{10} L_\odot$ ) than the average “normal” galaxies $ = 1.4^{10} L_\odot$ )." +This stresses the risks of interpreting statistics derived from general SN samples aud uot from actual search logs., This stresses the risks of interpreting statistics derived from general SN samples and not from actual search logs. + A similar conclusion was reached by Richmoud ct al. (1998)), A similar conclusion was reached by Richmond et al. \cite{richm}) ) + as the result of a dedicated SN search in 112 jearby starburst galaxies., as the result of a dedicated SN search in 142 nearby starburst galaxies. + They obtained 1.1 SNu (scaled oll)= 75) for the total rate and 0.7 for core-collapse only. somewhat larger than our corresponding estimates.," They obtained 1.1 SNu (scaled to $H_0=75$ ) for the total rate and 0.7 for core-collapse only, somewhat larger than our corresponding estimates." + However. their statistical error is also quite huge (they mad a suuple of only 5 SNe) and allowing also for the different computational protocols. the difference should rot be regarded as siguificaut.," However, their statistical error is also quite large (they had a sample of only 5 SNe) and allowing also for the different computational protocols, the difference should not be regarded as significant." + The conclusion is that the SN rate in active galaxies is the same as in normal ones (cf Petrosian Turatto 1995))., The conclusion is that the SN rate in active galaxies is the same as in normal ones (cf Petrosian Turatto \cite{petro}) ). + More precisely. this finding only applies to the AGN host galaxies aud not to the AGNs themselves. which because of the high extiuclon rate cannot be probed by optical SN searches.," More precisely, this finding only applies to the AGN host galaxies and not to the AGNs themselves, which because of the high extinction rate cannot be probed by optical SN searches." + TheYefore our clin is that the unclear enenme docs not sigUficautly stimulate the SFR outside the nuclear region of the host galaxy., Therefore our claim is that the nuclear engine does not significantly stimulate the SFR outside the nuclear region of the host galaxy. + We have preseuted new estimates of the SN rates in ealaxies. obtained bv includiusg the updated log of the Evans visual SN search in our database.," We have presented new estimates of the SN rates in galaxies, obtained by including the updated log of the Evans' visual SN search in our database." + Iu this way, In this way +outer radius cut.,outer radius cut. + The outer cut is to exclude a known ~5 warp (2)., The outer cut is to exclude a known $\sim8\arcdeg$ warp \citep{Gar02}. + The fitting function assumes a single position angle at all radii and does not describe warps well., The fitting function assumes a single position angle at all radii and does not describe warps well. +" We have investigated the disk's outer behavior by also deriving fits from the -220"" data alone.", We have investigated the disk's outer behavior by also deriving fits from the $>$ data alone. + A radial scale length. compatible with. but noisier than. the Table AI. value was found with a significant change in position angle. a reflection of the warp.," A radial scale length compatible with, but noisier than, the Table \ref{tab_MC} value was found with a significant change in position angle, a reflection of the warp." + While we cannot definitively prove that these galaxies maintain their extrapolated hydrogen profiles over the galactocentric distances we will discuss in. §$2.2.. such an assumption is reasonable with the current 21 cm data.," While we cannot definitively prove that these galaxies maintain their extrapolated hydrogen profiles over the galactocentric distances we will discuss in \ref{sec_mod_fit}, such an assumption is reasonable with the current 21 cm data." + There is no evidence for flaring in these galaxies. and the superthin shape implies an undisturbed history.," There is no evidence for flaring in these galaxies, and the superthin shape implies an undisturbed history." + In UGC 7321. ? have searched for low-mass compansions and found none to the limit of Mjj;=2.2«10° M... within 12/035 kpe).," In UGC 7321, \citet{Uso03} have searched for low-mass compansions and found none to the limit of $_{HI}=2.2\times10^{6}$ $_{\odot}$ within (35 kpc)." + The nearest optical companions are two dwarf galaxies at minimum distances of 340 kpe. implying minimum times to last encounter of 1.6«10? years.," The nearest optical companions are two dwarf galaxies at minimum distances of 340 kpc, implying minimum times to last encounter of $1.6\times10^{9}$ years." + So. it is unlikely that gas has been stripped from the regions over which we have extrapolated a density profile.," So, it is unlikely that gas has been stripped from the regions over which we have extrapolated a density profile." + However. we have calculated an alternative limit using data bounded by the HI data in a manner similar to the analysis in 222? as an alternative. which is equivalent to assuming that the gas is completely truncated. where the 21 em signal falls below the noise.," However, we have calculated an alternative limit using data bounded by the HI data in a manner similar to the analysis in \citet{Sto91,Vog95,Don95,Wey01} as an alternative, which is equivalent to assuming that the gas is completely truncated where the 21 cm signal falls below the noise." + In those works. a single. simple equation based on global photoionization equilibrium is used and here repeated in Equation 10..," In those works, a single, simple equation based on global photoionization equilibrium is used and here repeated in Equation \ref{eq_projarea}." +" The variable © is the one-sided incident ionizing UVB flux in units of ? !. {μι is the Ha surface brightness in units of iR. f,, is the fraction of incident photons that become absorbed when passing through the face-on cloud. fj; is the fraction of excited recombinations that produce an Ha photon. «νο is the projected area covered by spectroscopy and 21em data. and <\;,, is the total surface area for the regions in projection that can absorb Lyman limit photons."," The variable $\Phi$ is the one-sided incident ionizing UVB flux in units of $^{-2}$ $^{-1}$, $I_{H\alpha}$ is the $\alpha$ surface brightness in units of $\mu$ R, $f_{a}$ is the fraction of incident photons that become absorbed when passing through the face-on cloud, $f_{H\alpha}$ is the fraction of excited recombinations that produce an $\alpha$ photon, $A_{proj}$ is the projected area covered by spectroscopy and 21cm data, and $A_{tot}$ is the total surface area for the regions in projection that can absorb Lyman limit photons." + The area aspect ratio is usually determined from 21em data., The area aspect ratio is usually determined from 21cm data. + This calculation takes no account of the spatial stratification between 21em and Ho that can realistically occur for very thin gas distributions. as we will see later in $2.2. where the predicted Ha surface brightness is derived. and requires Ha searches and interpretations to be restricted to area covered by deep 21em data.," This calculation takes no account of the spatial stratification between 21cm and $\alpha$ that can realistically occur for very thin gas distributions, as we will see later in \ref{sec_mod_fit} where the predicted $\alpha$ surface brightness is derived, and requires $\alpha$ searches and interpretations to be restricted to area covered by deep 21cm data." + However. for mild aspect ratios (~< 10) or large 21em beams. this method delivers similar predictions as those in $2.1.," However, for mild aspect ratios $\sim <10$ ) or large 21cm beams, this method delivers similar predictions as those in \ref{sec_mod_HI}." + We now discuss the evaluation of the few terms in this model., We now discuss the evaluation of the few terms in this model. + The assumption in the HI bounded limit 15 that the hydrogen resides within some well-defined area represented by the noise floor of the 21em data., The assumption in the HI bounded limit is that the hydrogen resides within some well-defined area represented by the noise floor of the 21cm data. + It is not obvious how the area should be defined in a continuous gas distribution. but we adopt the photoionization front we have previously defined in Equations 5. and 6 as a realistic edge.," It is not obvious how the area should be defined in a continuous gas distribution, but we adopt the photoionization front we have previously defined in Equations \ref{eq_rc} and \ref{eq_zc} as a realistic edge." + In 82.2 we determine gas geometries for our target galaxies., In \ref{sec_mod_fit} we determine gas geometries for our target galaxies. +" In particular for the area in UGC 7321 covered by fibers. with ↽⋅ 5 parameters in Table⊀∖∐∫↓∩↓⊽≱∁⋯−⋅∐⋯↿⋔⊜ Al.. we E Polla ⊓⋯↿↴∙οcC)=""SENI2ps!.ys."," In particular for the area in UGC 7321 covered by fibers, with $N_{HI}>10^{19}$ $^{-2}$ , and the parameters in Table \ref{tab_MC}, we find $\langle\frac{A_{tot}}{A_{proj}}\rangle=24.8^{+3.4}_{-1.5}$." +" This. value is in good agreement with the 21cm axis ratio of 29 determined at the 10?"" em? contour in ?.Table3..", This value is in good agreement with the 21cm axis ratio of 29 determined at the $10^{20}$ $^{-2}$ contour in \citet[][Table 3]{Uso03}. +" By adopting this distribution in face-on column density and a UVB spectral index of ./=1.5. we can evaluate f,,."," By adopting this distribution in face-on column density and a UVB spectral index of $\beta=1.8$, we can evaluate $f_{a}$." + We find (d=22.8!blin UGC 7321., We find $\langle\frac{A_{tot}f_{a}}{A_{proj}}\rangle=22.8^{+4.4}_{-1.8}$ in UGC 7321. +" With the same calculations appliedm"" to UGC 1281. we find To)=19.0!TA and {5ap=13.6!ae"," With the same calculations applied to UGC 1281, we find $\langle\frac{A_{tot}}{A_{proj}}\rangle=19.0^{+5.6}_{-1.8}$ and $\langle\frac{A_{tot}f_{a}}{A_{proj}}\rangle=13.6^{+6.2}_{-2.0}$." +" Identically to ?.. we adopt fy,=0.15 as appropriate for case B and a L0'K electron temperature."," Identically to \citet{Wey01}, we adopt $f_{H\alpha}=0.45$ as appropriate for case B and a $10^{4}$ K electron temperature." + We also carry out this analysis in Tables AI. and A?) for continuity with previous work. but we emphasize that our preferred limit comes from the comparisons to the model in 82.1. as it incorporates the spatial segregation between the brightest Ho regions and the HI data that is natural in very thin. edge-on geometries.," We also carry out this analysis in Tables \ref{tab_MC} and \ref{tab_lims} for continuity with previous work, but we emphasize that our preferred limit comes from the comparisons to the model in \ref{sec_mod_HI} as it incorporates the spatial segregation between the brightest $\alpha$ regions and the HI data that is natural in very thin, edge-on geometries." + We have obtained new integral field spectroscopy positioned along the major axes of UGC 7321 and UGC 1281 targeting Hea with the Visible Integral-field Replicable Unit Spectrograph Prototype (VIRUS-P.?) on the McDonald 2.7m telescope.," We have obtained new integral field spectroscopy positioned along the major axes of UGC 7321 and UGC 1281 targeting $\alpha$ with the Visible Integral-field Replicable Unit Spectrograph Prototype \cite[VIRUS-P,][]{Hil08a} on the McDonald 2.7m telescope." + We observed UGC 1281 on 2009 October 22-24 with R = 1288 from ffor 21 photometric hours and UGC 7321 on 2010 April 9 and 11 with a resolution of R = 3860 from ffor 15 hours under non-photometric conditions., We observed UGC 1281 on 2009 October 22-24 with R = 1288 from for 21 photometric hours and UGC 7321 on 2010 April 9 and 11 with a resolution of R = 3860 from for 15 hours under non-photometric conditions. + Between the R = 1288 and R = 3860 observations. made possible by à new grating. we not only gam in sensitivity. scaled by the square root of the resolution but resolve the bright skylines. OH A6568.779 and geocoronal Ha. from our target wavelengths.," Between the R = 1288 and R = 3860 observations, made possible by a new grating, we not only gain in sensitivity scaled by the square root of the resolution but resolve the bright skylines, OH $\lambda$ 6568.779 and geocoronal $\alpha$, from our target wavelengths." + We have set the controller to bin pixels by two in the wavelength direction which samples the spectra just at the Nyquist criterion and minimizes read noise., We have set the controller to bin pixels by two in the wavelength direction which samples the spectra just at the Nyquist criterion and minimizes read noise. + The VIRUS-P field covers a 1/66«1766 field with 246 fibers of 27005 radius with a one-third fill-factor., The VIRUS-P field covers a $\times$ 6 field with 246 fibers of 05 radius with a one-third fill-factor. + We split our observations into three dithers to cover the entire field., We split our observations into three dithers to cover the entire field. +" In UGC 1281 we split our time further between two overlapping fields to cover the outer plane better in the presence of a possible <8"" wwarp (2?) yielding a total of six dithers.", In UGC 1281 we split our time further between two overlapping fields to cover the outer plane better in the presence of a possible $<$ warp \citep{Gar02} yielding a total of six dithers. + Spectrophotometric flux standard stars from ? were measured once or twice nightly., Spectrophotometric flux standard stars from \citet{Mas88} were measured once or twice nightly. + We tracked the transparency through the offset guiding camera., We tracked the transparency through the offset guiding camera. + Galactic extinction. corrections were made with Ay=0.09 and Ay=0.15 for UGC 7321 and UGC 1281] respectively.," Galactic extinction corrections \citep{Sch98,Odo94} were made with $_{\mbox{V}}$ =0.09 and $_{\mbox{V}}$ =0.15 for UGC 7321 and UGC 1281 respectively." + A spectral airmass/extinction curve specifically modelled for the McDonald Observatory site was applied., A spectral airmass/extinction curve specifically modelled for the McDonald Observatory site was applied. + We estimate its systematic uncertainty by comparing it to the Kitt Peak curve supplied with the IRAF packageonedspec., We estimate its systematic uncertainty by comparing it to the Kitt Peak curve supplied with the IRAF package. + We find a rms difference between the wavelengths of 6000-7000A., We find a rms difference between the wavelengths of . +. The two curves deviate systematically at \>5900A., The two curves deviate systematically at $\lambda > 5900$. +. We believe the site specific McDonald curve to be more accurate to our data., We believe the site specific McDonald curve to be more accurate to our data. + However. we propagate the difference as a potential. systematic uncertainty.," However, we propagate the difference as a potential, systematic uncertainty." + The flux calibration uncertainty due to the airmass/extinction curve at the data’s median airmass of 1.09 is 0.023 magnitudes., The flux calibration uncertainty due to the airmass/extinction curve at the data's median airmass of 1.09 is $\pm$ 0.023 magnitudes. + The ooffset guiding camera is an Apogee Alta with a 20.251! field-of-view under a B+V (Amean= 5000À)) filter., The offset guiding camera is an Apogee Alta with a $\sq\arcmin$ field-of-view under a B+V $\lambda_{\mbox{mean}}=5000$ ) filter. + Guider images were read out and saved every few seconds., Guider images were read out and saved every few seconds. + Stacks of guider images that overlapped in time with each individual VIRUS-P exposure (20 minutes each on UGC 1281]. 30 minutes each on UGC 7321.and | minute each on the flux standards) were combined.," Stacks of guider images that overlapped in time with each individual VIRUS-P exposure (20 minutes each on UGC 1281, 30 minutes each on UGC 7321,and 1 minute each on the flux standards) were combined." + We make a relative photometry correction to each science framebased on the stack of, We make a relative photometry correction to each science framebased on the stack of +term introducing a handedness into the flow (e.g. 1999).,term introducing a handedness into the flow \citep[e.g.][]{wardle99disk}. + 1C we follow the dynamics further we find that the Wil instability. in the presence of high Lall resistivity does not saturate to à quasi-steady state as it does in. for example. he full-Low-hr case.," If we follow the dynamics further we find that the KH instability, in the presence of high Hall resistivity does not saturate to a quasi-steady state as it does in, for example, the full-low-hr case." + As the z components of the current and magnetic field continue to grow. the Llall effect now acts on the non-parallel currents ancl magnetic fields that rave arisen between the z-directions and the wy-plane.," As the $z$ components of the current and magnetic field continue to grow, the Hall effect now acts on the non-parallel currents and magnetic fields that have arisen between the $z$ -directions and the $xy$ -plane." + This mas the result of re-orienting some of the magnetic field. and electron [uid How. back onto the àcg-plane.," This has the result of re-orienting some of the magnetic field, and electron fluid flow, back onto the $xy$ -plane." + During this orocess the electron [uid obtains a velocity away from the KEE vortex. which results in à. broader volume of plasma xing disturbed.," During this process the electron fluid obtains a velocity away from the KH vortex, which results in a broader volume of plasma being disturbed." + This feeds the continuous growth of the magnetic energy in the wy-plane. ancl thus causes continuous erowth of the electron transverse kinetic energy. as can be seen in figure 20..," This feeds the continuous growth of the magnetic energy in the $xy$ -plane, and thus causes continuous growth of the electron transverse kinetic energy, as can be seen in figure \ref{fig:ek-electron}." + In this particular simulation. the size of the simulation grid. is set so that it provides a sullicientlv large region of ordered [low that can be transformed. into clisorelerecdl How during the time of the simulation.," In this particular simulation, the size of the simulation grid is set so that it provides a sufficiently large region of ordered flow that can be transformed into disordered flow during the time of the simulation." + The instability will naturally saturate when it has exhausted the area of ordered [ow available to it., The instability will naturally saturate when it has exhausted the area of ordered flow available to it. + To summarise. through their strong decoupling [rom the magnetic field. the clvnamics of the bulk Iuid. ancl ion [uid demonstrate behaviour very similar to that of hd-zero-hr in which the WIE vortex remains intact.," To summarise, through their strong decoupling from the magnetic field, the dynamics of the bulk fluid and ion fluid demonstrate behaviour very similar to that of hd-zero-hr in which the KH vortex remains intact." + Phe high Πα, The high Hall +((1994) who sought to model DACs in emission lines.,(1994) who sought to model DACs in emission lines. +" Our objective is to obtain a reference model for the global wind morphology that we can use for interpreting the H,, polarization.", Our objective is to obtain a reference model for the global wind morphology that we can use for interpreting the $_\alpha$ polarization. + We consider a corotating stucture as a simple spiral that is top-bottom symmetric about the plane of the star's rotational equator., We consider a corotating stucture as a simple spiral that is top-bottom symmetric about the plane of the star's rotational equator. + Hence. the spiral structure has a guiding center that is always 1n the equatorial plane.," Hence, the spiral structure has a guiding center that is always in the equatorial plane." +" This center obeys an equation of motion for the radial wind velocity law and conservation of angular momentum in the rotating frame. so it follows a ""streak line” (e.g.. see Ignace. Bjorkman. Cassinelli 1998)."," This center obeys an equation of motion for the radial wind velocity law and conservation of angular momentum in the rotating frame, so it follows a “streak line” (e.g., see Ignace, Bjorkman, Cassinelli 1998)." +" We adopt a standard 7.;-Iaw"" for the radial flow: where «=&./r and b.<1 determines the radial speed of the wind at its base. with ry=co. (Lb)."," We adopt a standard $\beta$ -law” for the radial flow: where $u=R_\ast/r$ and $b<1$ determines the radial speed of the wind at its base, with $v_0 = v_\infty (1-b)^\beta$ ." + Velocity laws with 9=1 and}=2 were considered. and the case of ./=1 produced a better match to the data.," Velocity laws with $\beta=1$ and $\beta=2$ were considered, and the case of $\beta=1$ produced a better match to the data." + In this case the location of the guiding center is given analytically with azimuth + by where wy=ey/ex and O=27/P., In this case the location of the guiding center is given analytically with azimuth $\varphi$ by where $w_0=v_0/v_\infty$ and $\Omega = 2\pi/P$. + The density for the spiral-shaped perturbed region is treated as an of density above the otherwise spherically symmetric wind., The density for the spiral-shaped perturbed region is treated as an of density above the otherwise spherically symmetric wind. +" This density excess in the spiral pattern is taken to seale with the spherical wind density in our ""toy"" model. thus we conveniently parametrize the excess by a constant factor jj=Hoxecss/Hi FOr iy) the spherical wind density."," This density excess in the spiral pattern is taken to scale with the spherical wind density in our “toy” model, thus we conveniently parametrize the excess by a constant factor $\eta = n_{\rm excess}/ +n_{\rm sph}$ , for $n_{\rm sph}$ the spherical wind density." + In addition to the solution for the guiding center. we also need the cross-section of the spiral.," In addition to the solution for the guiding center, we also need the cross-section of the spiral." + The cross-section (i.e.. the intersection of the spiral pattern with a spherical shell) ts treated as circular.," The cross-section (i.e., the intersection of the spiral pattern with a spherical shell) is treated as circular." + This spherical “cap” is axisymmetric. and so assuming the electron scattering Is optically thin. the polarization from any given slice of the spiral is given by Brown McLean (1978). along with the finite star depolarization correction factor of Cassinellt. Nordsieck. Murison (1987).," This spherical “cap” is axisymmetric, and so assuming the electron scattering is optically thin, the polarization from any given slice of the spiral is given by Brown McLean (1978), along with the finite star depolarization correction factor of Cassinelli, Nordsieck, Murison (1987)." + Summing up contributions from all the caps yields the polarization from the structure as a function of rotational phase and viewing inclination for the rotation axis of the star., Summing up contributions from all the caps yields the polarization from the structure as a function of rotational phase and viewing inclination for the rotation axis of the star. + Note that our model accounts for occultation of scattered. light by the intervening star. but only i an approximate way.," Note that our model accounts for occultation of scattered light by the intervening star, but only in an approximate way." + We consider a slice as entirely occulted if its guiding center lies behind the star. anc unocculted otherwise.," We consider a slice as entirely occulted if its guiding center lies behind the star, and unocculted otherwise." + The principal model parameters are the density excess +. the half-opening angle of the spiral à. a orientation angle between the observer QU axes anc those of the star system c. and finally the inclinatio of the rotation axis of the star /j.," The principal model parameters are the density excess $\eta$, the half-opening angle of the spiral $\delta$, an orientation angle between the observer $Q-U$ axes and those of the star system $\psi_0$, and finally the inclination of the rotation axis of the star $i_0$." + Using a reduced chi-square evaluation for a grid of model polarizatio light curves. Table 2 lists the model parameters that provide the best fit to the observed data.," Using a reduced chi-square evaluation for a grid of model polarization light curves, Table \ref{tab2} lists the model parameters that provide the best fit to the observed data." + The star and wind properties of HD 92207 are take from Przybilla ((2006). except that the mass-loss rate is taken from Kudritzki ((1999) and does not account for clumping.," The star and wind properties of HD 92207 are taken from Przybilla (2006), except that the mass-loss rate is taken from Kudritzki (1999) and does not account for clumping." +" The most reasonable match to the observed continuum polarizations 1n the neighborhood of H,, is shown in Figure 3..", The most reasonable match to the observed continuum polarizations in the neighborhood of $_\alpha$ is shown in Figure \ref{fig3}. + The upper panel is for 2) and the lower one for P. displayed as percentage polarizations.," The upper panel is for $P_Q$ and the lower one for $P_U$, displayed as percentage polarizations." + The rotational phases dependon the star's rotation period., The rotational phases dependon the star's rotation period. +" Given the radius and minimum rotation speed from Table 2.. the maximum period is Pua,c 376dd. The true period is P,=Dsin/y. where /y 1s constrained from our model fitting."," Given the radius and minimum rotation speed from Table \ref{tab2}, the maximum period is $P_{\rm max} +\approx 376$ d. The true period is $P_{\rm rot} = P_{\rm max}/\sin i_0$, where $i_0$ is constrained from our model fitting." +" As the ephemeris is not known. we assigned the rotational phase ""O7 to the date of our first observation. andthe phases appearing in Figure 3. represent values for our best fit model at 4j= 70""."," As the ephemeris is not known, we assigned the rotational phase “0” to the date of our first observation, andthe phases appearing in Figure \ref{fig3} + represent values for our best fit model at $i_0 = 70^\circ$ ." + For the model fitting. there are seven free parameters:," For the model fitting, there are seven free parameters:" +is plotted in Fig.,is plotted in Fig. + 16 (poiuts)., 16 (points). + Radio relies. are proposed to be either reninants of radio galaxies or sites of accretion/ merger shocks where urtieles are accelerated. to. relativistic energies., Radio relics are proposed to be either remnants of radio galaxies or sites of accretion/ merger shocks where particles are accelerated to relativistic energies. + The roinants of radio galaxies can be ageing lobes or lobes compressed by shocks in the intracluster medimu (ICM)., The remnants of radio galaxies can be ageing lobes or lobes compressed by shocks in the intracluster medium (ICM). + Iu the case of A1038. SLOT attemptec a fit considerimg he relie as a remnant of a radio galaxy.," In the case of A4038, SL01 attempted a fit considering the relic as a remnant of a radio galaxy." + The SLOL fits were based ou estinates of volue and magnetic ποια. using the extent of fre relic (LES-—56 kpc) as detected by SLOT at 1.4 GIIz., The SL01 fits were based on estimates of volume and magnetic field using the extent of the relic $=$ 56 kpc) as detected by SL01 at 1.4 GHz. + This extent of the relic is an underestimate due to he discoveries of exteuded eatures of the relie at loweY frequencies., This extent of the relic is an underestimate due to the discoveries of extended features of the relic at lower frequencies. + Further the uodels considered by SLOL reelected energy losses due o expansion of the lobes., Further the models considered by SL01 neglected energy losses due to expansion of the lobes. + We describe our attempt to fit he integrated spectrum of tje relie with a model which overcomes the above mentiored cdaawhacls., We describe our attempt to fit the integrated spectrum of the relic with a model which overcomes the above mentioned drawbacks. + Revival of fossil radio lobes x adiabatie Compression X passage of shocks is one of the models favored for racio relies (Ensshu&Gopal-Izxislhua2001) (ECOL hereafter)., Revival of fossil radio lobes by adiabatic compression by passage of shocks is one of the models favored for radio relics \citep[]{ens01} (EG01 hereafter). + The framework of ECOL cousiders revival of fossil radio cocoon bv adiabatic compression due to the passage of shocks in the ICAL, The framework of EG01 considers revival of fossil radio cocoon by adiabatic compression due to the passage of shocks in the ICM. + The evolution of the spectrum of a radio galaxw before aud after the jets cease to be active and after adiabatic compression of he lobes can © obtained., The evolution of the spectrum of a radio galaxy before and after the jets cease to be active and after adiabatic compression of the lobes can be obtained. + Energy losses due to svuchrotrou. inverse Compton (IC) aud expansion are accounted or.," Energy losses due to synchrotron, inverse Compton (IC) and expansion are accounted for." + There are five phases of evolution. viz.," There are five phases of evolution, viz." + iujectio-. OXpausion. urkimue. flashing and fading.," injection, expansion, lurking, flashing and fading." + The salieut features of the uodel aud the application in the context of radio relics cau be found in Wale&Dwarakanath(2009)., The salient features of the model and the application in the context of radio relics can be found in \citet[]{kal09}. +. The largest linear extent of he relic in ALO3s is 210 spe., The largest linear extent of the relic in A4038 is 210 kpc. + It is is located close to the cD galaxy. aac resides almost at the cluster ceuter (in projection)., It is is located close to the cD galaxy and resides almost at the cluster center (in projection). + The volume of the complete relie was approximated to be he suni of the volumes of the main relic (110&75ς kpe?} and that of the NW-Est (25° kpe?)., The volume of the complete relic was approximated to be the sum of the volumes of the main relic $110\times75\times75$ $^3$ ) and that of the NW-Ext $^3$ $^3$ ). + A magnetic field of was estimated using the minim euergy coudition SjnuderC standard assumptions., A magnetic field of $3\mu$ G was estimated using the minimum energy condition under standard assumptions. + Best fits to the integrated spectrum of A1038 relic iu ‘Hashing’ and “facing” phases were obtained., Best fits to the integrated spectrum of A4038 relic in `flashing' and `fading' phases were obtained. +" The reduced Chi-square∢⋅↴⋠⋅∖ (A7,2 ) was estimated to be 5.96 and 5.19 in the two fits respectively,", The reduced Chi-square $\chi^2_{red}$ ) was estimated to be 5.96 and 5.49 in the two fits respectively. + The parameters used in the model for the best fit are listed in Table Lt., The parameters used in the model for the best fit are listed in Table 4. + The model fits alone with the observed spectrum are plotted in Fig, The model fits along with the observed spectrum are plotted in Fig. + 13 aud L1 (loft)., 13 and 14 (left). + The best fits are denoted by black lines., The best fits are denoted by black lines. + The model spectra iu other phases are also plotted iu the sale figures for comparison., The model spectra in other phases are also plotted in the same figures for comparison. + The righ: liaud side panels: in Figs., The right hand side panels in Figs. + 13 aud 1L show he best fits alone with model spectra obtained when the valucs of the duration of the shases were changed by E30%., 13 and 14 show the best fits along with model spectra obtained when the values of the duration of the phases were changed by $\pm30\%$. + Note the deviation from he observed spectra., Note the deviation from the observed spectrum. + The relie in AT661 is at a distance of 1.15 AIpc from he center of the cluster., The relic in A1664 is at a distance of $\sim1.13$ Mpc from the center of the cluster. + Best fit to the spectruni was ound when the relic was assumed to )o in the Iurkius phase (Fie., Best fit to the spectrum was found when the relic was assumed to be in the `lurking' phase (Fig. + 15)., 15). + The best fit parameters are listed in Table tL., The best fit parameters are listed in Table 4. + The duration of the ‘hiking’ phase was found o be 1«10* vx., The duration of the `lurking' phase was found to be $4\times10^7$ yr. + The ECOL model was used to fit the iutegrated spectrmu of the relie near ATS6., The EG01 model was used to fit the integrated spectrum of the relic near A786. + A best fit was obtained when the relie was asstuned to be in the ‘lurking’ phase., A best fit was obtained when the relic was assumed to be in the `lurking' phase. + The best fit paraiucters are reported in Table Land the fit ix shown in Fig., The best fit parameters are reported in Table 4 and the fit is shown in Fig. + 16 (left)., 16 (left). + The plots showing deviation frou. the best fit when the timescale was changed by 430% are shown in Fie., The plots showing deviation from the best fit when the timescale was changed by $\pm 30\%$ are shown in Fig. + 16 (rieht)., 16 (right). +" The duration of the lurking phase phase was found to be 6<10* ντ,", The duration of the lurking phase phase was found to be $6\times10^7$ yr. + The imaging of the three racio relics in galaxy clusters AΙ00δ. Al661 aud A786 at low frequencies (<1 GIIz) as revealed several new properties of the relics.," The imaging of the three radio relics in galaxy clusters A4038, A1664 and A786 at low frequencies $< 1$ GHz) has revealed several new properties of the relics." + huages of comparable seusitivitv aud resolution were produced w the use of the GMBT. the WSRT aud the VLA over he frequency range of 150-1100. MIIz.," Images of comparable sensitivity and resolution were produced by the use of the GMRT, the WSRT and the VLA over the frequency range of 150-1400 MHz." + The inteerated spectra sampled at more than three frequencies were xoduced., The integrated spectra sampled at more than three frequencies were produced. + The spectra are curved and steep (a<1) and unlike a flat power-law expected of vouug reshlv accelerated plasma (a~—0.7)., The spectra are curved and steep $\alpha<-1$ ) and unlike a flat power-law expected of young freshly accelerated plasma $\alpha\sim-0.7$ ). + The adiabatic colupression model was used to fit the inteerated spectra., The adiabatic compression model was used to fit the integrated spectra. + The models of radio galaxy cocoons of ages 210* vr fit the spectra., The models of radio galaxy cocoons of ages $\gtrsim10^7$ yr fit the spectra. + The spectral iudex maps show complex distributions., The spectral index maps show complex distributions. + The gradieuts in the spectral iudex maps do not show edges of flat spectral indices that are characteristic of plasma accelerated at shock frouts., The gradients in the spectral index maps do not show edges of flat spectral indices that are characteristic of plasma accelerated at shock fronts. + The spectral indices are steep and vary across the extent of the τος by as much as 1. (Aa~1)., The spectral indices are steep and vary across the extent of the relic by as much as $1$ $\Delta\alpha\sim1$ ). + These properties nuply that these relies contain aged relativistic plasiua and can be termed as relies of radio galaxies’., These properties imply that these relics contain aged relativistic plasma and can be termed as `relics of radio galaxies'. + The model of shock accelerated plasma is disfavored by the observations., The model of shock accelerated plasma is disfavored by the observations. + The properties of the relics are discussed below., The properties of the relics are discussed below. + Our seusitfive low frequency observations with the GAIRT have led to the ciscovery of steep spectrum enission in addition to the relic known from earlier biel frequency studies., Our sensitive low frequency observations with the GMRT have led to the discovery of steep spectrum emission in addition to the relic known from earlier high frequency studies. + The largest linear extent of the relic iu Α[038 as seen at 210 MITz is ~210 kpe as opposed to 56 kpc detected at 1.1 GIIz., The largest linear extent of the relic in A4038 as seen at 240 MHz is $\sim210$ kpc as opposed to 56 kpc detected at 1.4 GHz. + The relic is elongated along the N-S direction., The relic is elongated along the N-S direction. + A low surface brightness extension to the relic toward the NW has been discovered at 210. MIIz., A low surface brightness extension to the relic toward the NW has been discovered at 240 MHz. + Due to limitations of the sensitivities of observations at 150 aud 606 NIIz. the NW-Ext was not detected at these frequencies.," Due to limitations of the sensitivities of observations at 150 and 606 MHz, the NW-Ext was not detected at these frequencies." + Deeper observatious at these frequeucies are required to detect and determine the spectral iudex of the NW-Ext., Deeper observations at these frequencies are required to detect and determine the spectral index of the NW-Ext. + We used the adiabatic compression model (ECOL) to fit the integrated spectrum of the relic., We used the adiabatic compression model (EG01) to fit the integrated spectrum of the relic. + The ECOL model accounts for the energy losses due to expansion aud also the resulting chauge in the iuagnuetic field due to chauge iu volune., The EG01 model accounts for the energy losses due to expansion and also the resulting change in the magnetic field due to change in volume. + Further. it also considers the case in which a shock in the ICAL compresses Iurking radio cocoons and leads to cnlauced emissiou frou them.," Further, it also considers the case in which a shock in the ICM compresses lurking radio cocoons and leads to enhanced emission from them." +" The best fits were obtained in the ""Hashiug and the fading! phases.", The best fits were obtained in the `flashing' and the `fading' phases. + The duratious of the phases of injection. expausion aud hirking are the same in both the cases.," The durations of the phases of injection, expansion and lurking are the same in both the cases." + However the extent of the compression in the ‘flashine” phases differs., However the extent of the compression in the `flashing' phases differs. + Tn the case of “flashing” phase beiug the best ft. the volume changes by a factor of ~9.3. whereas in the case of fading beime the best fit. the change is by a factor of 23.5.," In the case of `flashing' phase being the best fit, the volume changes by a factor of $\sim9.3$, whereas in the case of `fading' being the best fit, the change is by a factor of $\sim3.5$." + The relation between the compression factor (C) aud the pressure ratio (P)/P2) is given by. C—(P/P;yV," The relation between the compression factor $C$ ) and the pressure ratio $P_1/P_2$ ) is given by, $C=(P_1/P_2)^{3/4}$." + This implies that the pressure. jumps at the shock that caused the compression are factors of ~20 and ~Ὁ5 in the ‘flashing and the “facing” best, This implies that the pressure jumps at the shock that caused the compression are factors of $\sim20$ and $\sim 5$ in the `flashing' and the `fading' best +Floc'h et al.,Floc'h et al. + 2003)., 2003). + Thus. indirect (1.e. late-epoch photometric) observations of the presence of a SN are still important in the study of the GRB-SN connection.," Thus, indirect (i.e. late-epoch photometric) observations of the presence of a SN are still important in the study of the GRB-SN connection." + GRBO000911 was detected by the Inter-Planetary Network (IPN) satellites on 2000 September 11.30237 UT as a very long (7500 s) burst (Hurley et al., GRB000911 was detected by the Inter-Planetary Network (IPN) satellites on 2000 September 11.30237 UT as a very long $\sim$ 500 s) burst (Hurley et al. + 2000: Price et al., 2000; Price et al. + 2002)., 2002). + Shortly thereafter. Berger et al. (," Shortly thereafter, Berger et al. (" +2000) found a variable radio source inside the GRB error box and. at the radio position. Price et al. (,"2000) found a variable radio source inside the GRB error box and, at the radio position, Price et al. (" +"2000. 2002) detected an optical transient (OT) at coordinates RA = 02 |8"" 3436. Dec = +07° 44' 27765 (12000) which faded according to a power-law decay F(t) x£"" with index a = 1.46.","2000, 2002) detected an optical transient (OT) at coordinates RA = $^{\rm h}$ $^{\rm m}$ $\fs$ 36, Dec = $^{\circ}$ $'$ $\farcs$ 65 (J2000) which faded according to a power-law decay $F$ $t$ ) $\propto t^{-\alpha}$ with index $\alpha$ = 1.46." + This behaviour. together with the positional coincidence with the mentioned transient radio source. strongly suggested that this OT was indeed the optical afterglow of GRBOOO9I1.," This behaviour, together with the positional coincidence with the mentioned transient radio source, strongly suggested that this OT was indeed the optical afterglow of GRB000911." + Smith et al. (, Smith et al. ( +2001) reported no detection of transient emission at sub-mm (850 jm) wavelengths.,2001) reported no detection of transient emission at sub-mm (850 $\mu$ m) wavelengths. + In this same band. Berger et al. (," In this same band, Berger et al. (" +2003) reported the detection of emission from the host galaxy of GRBOOO9]1: this detection was however questioned by Tanvir et al. (,2003) reported the detection of emission from the host galaxy of GRB000911; this detection was however questioned by Tanvir et al. ( +2004) on the basis of the former sub-mm upper limit of Smith et al. (,2004) on the basis of the former sub-mm upper limit of Smith et al. ( +2001) for the combined host plus afterglow emission.,2001) for the combined host plus afterglow emission. + Extensive optical and NIR observations of the afterglow have been reported by Lazzati et al. (, Extensive optical and NIR observations of the afterglow have been reported by Lazzati et al. ( +2001). who inferred the presence of a SN reaching maximum light at about 18 days after the GRB (in the rest frame at z = 1.0585: Djorgovski et al.,"2001), who inferred the presence of a SN reaching maximum light at about 18 days after the GRB (in the rest frame at $z$ = 1.0585: Djorgovski et al." + 2001: Price et al., 2001; Price et al. + 2002)., 2002). + The underlying host galaxy appears to be a starburst with moderate dust absorption. te. with 0.11 «E(B-V) 0.21 (Lazzati et al.," The underlying host galaxy appears to be a starburst with moderate dust absorption, i.e. with 0.11 $< E(B-V) <$ 0.21 (Lazzati et al." + 2001)., 2001). + No follow-up observations of this GRB were performed in X-rays., No follow-up observations of this GRB were performed in X–rays. + As part of our ESO program. in the framework of the collaboration. we observed the field of GRBO00911 with both optical and NIR cameras.," As part of our ESO program, in the framework of the collaboration, we observed the field of GRB000911 with both optical and NIR cameras." + Our observations started as soon as the precise position of the radio counterpart was made public: we then followed up the optical/NIR afterglow for more than one year with various telescopes located at ESO and at the Canary Islands Observatories., Our observations started as soon as the precise position of the radio counterpart was made public; we then followed up the optical/NIR afterglow for more than one year with various telescopes located at ESO and at the Canary Islands Observatories. + In this paper we present our data and compare the results with those published in Lazzati et al. (, In this paper we present our data and compare the results with those published in Lazzati et al. ( +2001).,2001). + In particular. since our dataset is more complete in terms of time coverage and contains twice as many measurements as reported by those authors. we have a chance to test with higher confidence the presence of a SN.," In particular, since our dataset is more complete in terms of time coverage and contains twice as many measurements as reported by those authors, we have a chance to test with higher confidence the presence of a SN." + Moreover. our late-time observations allowed us to study in detail the broadband optical/NIR emission from the host galaxy of GRBO009I.," Moreover, our late-time observations allowed us to study in detail the broadband optical/NIR emission from the host galaxy of GRB000911." +" Throughout this paper we will assume a cosmology with Ho=65 km s! Mpe!. Q4=0.7. Q,,=0.3."," Throughout this paper we will assume a cosmology with $H_0 = +65$ km $^{-1}$ $^{-1}$, $\Omega_{\Lambda} = 0.7$, $\Omega_{\rm m} = +0.3$." + Throughout the text. unless otherwise stated. errors and upper limits are at lo and 3c confidence level. respectively.," Throughout the text, unless otherwise stated, errors and upper limits are at $\sigma$ and $\sigma$ confidence level, respectively." + We started our observational campaign on the OT of GRBO000911 at ESO on September 16. 2000.," We started our observational campaign on the OT of GRB000911 at ESO on September 16, 2000." + The complete log of our imaging observations ts reported in Table |., The complete log of our imaging observations is reported in Table 1. + Optical BVRI data were collected at Cerro Paranal (Chile) with plus FORS| and with plus FORS2 over a baseline of more than 13 months., Optical $BVRI$ data were collected at Cerro Paranal (Chile) with plus FORS1 and with plus FORS2 over a baseline of more than 13 months. + FORSI and FORS2 were equipped with a Tektronix and a SITE CCD. respectively. in both cases with a 2048x2048 pixel array: both instruments covered a 6:8x6:8 field in the standard resolution imaging mode. giving a scale of 02 pix!.," FORS1 and FORS2 were equipped with a Tektronix and a SiTE CCD, respectively, in both cases with a $\times$ 2048 pixel array; both instruments covered a $\farcm$ $\times$ $\farcm$ 8 field in the standard resolution imaging mode, giving a scale of $\farcs$ 2 $^{-1}$." + A single B-band pointing was obtained on September 23. 2000. with TNG+DOLoRes at La Palma. Canary Islands (Spain): the imaging spectrograph DOLoRes carried a 2048x2048 pixel Loral backside-illuminated CCD which images a field of 9/5x9/5 with a scale of 07275 pix!.," A single $B$ -band pointing was obtained on September 23, 2000, with TNG+DOLoRes at La Palma, Canary Islands (Spain); the imaging spectrograph DOLoRes carried a $\times$ 2048 pixel Loral backside-illuminated CCD which images a field of $\farcm$ $\times$ $\farcm$ 5 with a scale of $\farcs$ 275 $^{-1}$." + Early I-band and late-time R- and /-band observations were acquired at NOT (La Palma. Canary Islands). with the ALFOSC instrument.," Early $I$ -band and late-time $R$ - and $I$ -band observations were acquired at NOT (La Palma, Canary Islands), with the ALFOSC instrument." + This also was equipped with a 2048x2048 pixel Loral CCD. giving a field of view of 6/4«6!4 and an image scale of 0188 pix.," This also was equipped with a $\times$ 2048 pixel Loral CCD, giving a field of view of $\farcm$ $\times$ $\farcm$ 4 and an image scale of $\farcs$ 188 $^{-1}$." + Optical images were bias-subtracted and flat-fielded with the standard reduction procedure., Optical images were bias-subtracted and flat-fielded with the standard reduction procedure. + In general. frames taken on the same night in the same band were summed together in order to increase the signal-to-noise ratio.," In general, frames taken on the same night in the same band were summed together in order to increase the signal-to-noise ratio." +" We performed photometry with standard Point Spread Funetion (PSF) fitting using the image data analysis package PSF-fitting algorithm (Stetson 1987) withinMIDAS"".", We performed photometry with standard Point Spread Function (PSF) fitting using the image data analysis package PSF-fitting algorithm (Stetson 1987) within. +. The PSF-fitting photometry is accomplished by modeling a two-dimensional Gaussian profile with two free parameters (the half width at half maxima along x and v coordinates of each frame) on at least 5 unsaturated bright stars in each image., The PSF-fitting photometry is accomplished by modeling a two-dimensional Gaussian profile with two free parameters (the half width at half maxima along $x$ and $y$ coordinates of each frame) on at least 5 unsaturated bright stars in each image. + The errors associated with the measurements reported in Table | represen= statistical uncertainties obtained with the standard PSF-fittingσι procedure., The errors associated with the measurements reported in Table 1 represent statistical uncertainties obtained with the standard PSF-fitting procedure. + For the late-epoch observations (1e. those taken startingσι December 2000). when the OT was faint and a substantial contribution from an underlying host galaxy became apparent (see Sect.," For the late-epoch observations (i.e. those taken starting December 2000), when the OT was faint and a substantial contribution from an underlying host galaxy became apparent (see Sect." + 3.1). we checked the results of the PSF-fittingσι algorithm by determining the optical magnitudes of the object with the aperture photometry method.," 3.1), we checked the results of the PSF-fitting algorithm by determining the optical magnitudes of the object with the aperture photometry method." + In this case we used an aperture diameter equal to the Full Width at Half Maximum (FWHM) of each summed image., In this case we used an aperture diameter equal to the Full Width at Half Maximum (FWHM) of each summed image. + Comparison between the results obtained with the two methods indicates no appreciable difference within the uncertainties., Comparison between the results obtained with the two methods indicates no appreciable difference within the uncertainties. + As we shall see below. this has implications for the compactness and the morphology of the host of GRB00091I.," As we shall see below, this has implications for the compactness and the morphology of the host of GRB000911." + To be consistent with optical magnitude measurements appearing on the GCN circularsarchive*.. the photometric calibration was done using the BVAI magnitudes. as measured by Henden (2000). of several field stars checked for their magnitude constancy.," To be consistent with optical magnitude measurements appearing on the GCN circulars, the photometric calibration was done using the $BVRI$ magnitudes, as measured by Henden (2000), of several field stars checked for their magnitude constancy." + We find this magnitude calibration to be accurate to within3%., We find this magnitude calibration to be accurate to within. +. However. this calibration ts offset with," However, this calibration is offset with" +This work was partially supported by RIEBR grants. 05-02-00491 and 08-02-90106. the RAN Program Formation and evolution of stars and galaxies’ and Russian Federation President. Grant for Support of Leading Scientific Schools NSh-3458.2010.2.,"This work was partially supported by RFBR grants 08-02-00491 and 08-02-90106, the RAN Program 'Formation and evolution of stars and galaxies' and Russian Federation President Grant for Support of Leading Scientific Schools NSh-3458.2010.2." + The work of OYuT was also. partially supported by the Dynasty Foundation anc Russian Feeleration President Grant for Support of Young Scientists ALK-S696.2010.2., The work of OYuT was also partially supported by the Dynasty Foundation and Russian Federation President Grant for Support of Young Scientists MK-8696.2010.2. +and (he locations of the II» knots with respect to the field centers are listed in Table 1..,and the locations of the $_2$ knots with respect to the field centers are listed in Table \ref{loctab}. . + Table lists the surface brightness measurements for II and the optical line (racers at the knot position., Table \ref{surbrtab} lists the surface brightness measurements for $_2$ and the optical line tracers at the knot position. + The average surface brightness of the H» knot emission (DN/pixel) was determined for a circular aperture enclosing the brightest part of the II emission (~3 pixel radius centered on (the +)., The average surface brightness of the $_2$ knot emission (DN/pixel) was determined for a circular aperture enclosing the brightest part of the $_2$ emission $\sim$ 3 pixel radius centered on the +). + We then converted (his average into physical units by mulüplving by 2.44929x10 eres 7A ! (DN = counts per second). which is the photometry conversion kevword derived for the NICMOS. NICS camera. filler F212N lor the 77.1 Ix detector. appropriate for observations taken alter January 2002.," We then converted this average into physical units by multiplying by $2.44929\times10^{-18}$ erg $^{-1}$ $^{-2}$ $^{-1}$ $^{-1}$ (DN = counts per second), which is the photometry conversion keyword derived for the NICMOS, NIC3 camera, filter F212N for the 77.1 K detector, appropriate for observations taken after January 2002." + Finally. (o arrive al the units in Table 2.. we mulitplied by 212.1 wwhich is the filter bandwidth of the F212N filter. and divided by 2.2350443x1019 sr which is the solid angle of the 0710 pseudo-pixel.," Finally, to arrive at the units in Table \ref{surbrtab}, we mulitplied by 212.1 which is the filter bandwidth of the F212N filter, and divided by $2.2350443\times10^{-13}$ sr which is the solid angle of the $0\farcs10$ pseudo-pixel." + For each of the measured Il» knots in the NICMOS fields. we measured the surface brightness of the ionized gas emission lines. Ha |NII]. POUL. Iho and [SI]. in the same way and list Che results in Table 2..," For each of the measured $_2$ knots in the NICMOS fields, we measured the surface brightness of the ionized gas emission lines, $\alpha$ [NII], [OIII], $\beta$ and [SII], in the same way and list the results in Table \ref{surbrtab}." +" A conversion factor of 1.66x10!"" was used to convert ADUs/pixel to photons | 7 ! for all the CTIO images and then each image was multipliel bv its photon energy. he to determine tlie surface brightness in units of erg tem 7 !. the same as the NICMOS IL, line measurements."," A conversion factor of $1.66\times10^{10}$ was used to convert ADUs/pixel to photons $^{-1}$ $^{-2}$ $^{-1}$ for all the CTIO images and then each image was multiplied by its photon energy, $h c \over \lambda$ to determine the surface brightness in units of erg $^{-1}$ $^{-2}$ $^{-1}$, the same as the NICMOS $_2$ line measurements." + For the cross-culs shown in Figure 15.. we applied the same conversion factors.," For the cross-cuts shown in Figure \ref{nicprof}, we applied the same conversion factors." + Figures 2.. 11.. 12.. 12. and 14. compare the NICAIOS [ly 2.12 lline emission images to the ionized gas (racers of [OH]. Ilo. Hao /[NH] and [SII] from [or the respective field positions 1. 2. 3. 4. and 5.," Figures \ref{nicpos1}, \ref{nicpos2}, \ref{nicpos3}, \ref{nicpos4} and \ref{nicpos5} compare the NICMOS $_2$ 2.12 line emission images to the ionized gas tracers of [OIII], $\beta$, $\alpha$ /[NII] and [SII] from \cite{odell04} for the respective field positions 1, 2, 3, 4, and 5." + Our NICS images have better sensitivity and angular resolution than (he image in the Specketal.(2002) and we observe IIs line emission ad much larger distances (han seen in their large scale. groundbased mosaic.," Our NIC3 images have better sensitivity and angular resolution than the image in the \cite{speck02} and we observe $_2$ line emission at much larger distances than seen in their large scale, groundbased mosaic." + The NICMOS fielcl positions 1 and 2 lie closer to the central star al approximately (he same projected distance., The NICMOS field positions 1 and 2 lie closer to the central star at approximately the same projected distance. + The fielcl position 3 follows next in radial distance with positions 5 and 4 overlapping at the farthest radial distances (Fig. 15))., The field position 3 follows next in radial distance with positions 5 and 4 overlapping at the farthest radial distances (Fig. \ref{nicprof}) ). + In all of the NICAIOS field positions (he Hà» emission is highly structured revealing ares aud pillars of emission that point towards the central star (Figures 2- 14))., In all of the NICMOS field positions the $_2$ emission is highly structured revealing arcs and pillars of emission that point towards the central star (Figures \ref{nicpos1}- \ref{nicpos5}) ). + This highly structured appearance contrasts wilh the more smooth. ancl less structured appearance of the ionized lines.," This highly structured appearance contrasts with the more smooth, and less structured appearance of the ionized lines." + This difference indicates (hat the II» line emission is confined to the high density neutral gas of the cometary knots 1996)., This difference indicates that the $_2$ line emission is confined to the high density neutral gas of the cometary knots \citep{odell96}. +. On the other hand. the ionized gas emission arises from both the more diffuse nebula (50 *) and the cometary knots.," On the other hand, the ionized gas emission arises from both the more diffuse nebula (50 $^{-3}$ ) and the cometary knots." + Closer inspection of all 5 positions reveals that the IL3 emission structures correlates very well with the structures observed in I>., Closer inspection of all 5 positions reveals that the $\beta$ emission structures correlates very well with the structures observed in $_2$. + The SL] emission appears to correlate with the II» emission in positions 1 and 2. but does not show the structure as well as the IL5.," The [SII] emission appears to correlate with the $_2$ emission in positions 1 and 2, but does not show the structure as well as the $\beta$ ." + This suggests that the[SH] emission is more extended.," This suggests that the[SII] emission is more extended," +shown in Figure 7 at time f=12.,shown in Figure \ref{figrj2a} at time $t=12$. + Initial conditions for this test are listed in Table 1. as RJ2a., Initial conditions for this test are listed in Table \ref{tabshocktubes} as RJ2a. + This test is otherwise set up in the same manner and ou the same domain as the Drio-Wu test., This test is otherwise set up in the same manner and on the same domain as the Brio-Wu test. + A lieh resolution solution was computed with Athenafor comparison., A high resolution solution was computed with Athenafor comparison. +" As Stoneetal.(2008) point out. this test is particularly interesting because it requires modeling a fast magnetosouic shock and a rotational discontinuity dn each clirection of propagation. as well as a contact discontinuity in the center,"," As \citet{2008ApJS..178..137S} point out, this test is particularly interesting because it requires modeling a fast magnetosonic shock and a rotational discontinuity in each direction of propagation, as well as a contact discontinuity in the center." + No visible ringing is seen at the shocks., No visible ringing is seen at the shocks. + The largest cohereut. VB. errors. are also seen near the fast shocks. but the largest scatter in particle VB values is located at he cofact discontinuity.," The largest coherent $\divb$ errors are also seen near the fast shocks, but the largest scatter in particle $\divb$ values is located at the contact discontinuity." + Tjo fes shown in Figure ld of Ryu&Jones is shown in Figure & at tine f11.5., The test shown in Figure 4d of \cite{1995ApJ...442..228R} is shown in Figure \ref{figrj4d} at time $t=11.5$. + This test Was rtn witli the same computational domain aud resolution 1ws the xevious test but with the left aud right states listcc Lin Tiile Pas test RJEd., This test was run with the same computational domain and resolution as the previous test but with the left and right states listed in Table \ref{tabshocktubes} as test RJ4d. + A small overshoot cal be see lontie leftmost rarefaction wave., A small overshoot can be seen on the leftmost rarefaction wave. + This is a result of the bulk viscosity of the scheme., This is a result of the bulk viscosity of the scheme. + The test shown by Falle(2002) in his Figure 6 is shown in Figure 9 at time f 2.9., The test shown by \cite{2002ApJ...577L.123F} in his Figure 6 is shown in Figure \ref{figfalle2002} at time $t=2.9$ . + This test was, This test was +Tere. y; represcuts the time from L700 (with unit of voar).,"Here, $y_{i}$ represents the time from 1700 (with unit of year)." + Then let the following stun to become maid: Iu above equations. Πρ aud. B; preseut tle values of the fitted empirical fiction and the observations of ASN. respectively.," Then let the following sum to become minimum: In above equations, $R_{oi}$ and $R_{i}$ present the values of the fitted empirical function and the observations of ASN, respectively." + As Equation (1) is a nouliucar function. we couldu't obtain the true values of paramctcrs A. D. C. D. and E from the standard square-least-iicthod.," As Equation (1) is a nonlinear function, we couldn't obtain the true values of parameters A, B, C, D, and E from the standard square-least-method." +" Tlowever. we may try to list a series of [À. D. C. D. E| and calculate the values of QCGA.B.C.D.E). respectively,"," However, we may try to list a series of [A, B, C, D, E] and calculate the values of $Q(A,B,C,D,E)$, respectively." + Then fiud out the πα value of QUA.B.C.D.E) aud the correspouding parameters of ΙΑ. D. C. D. E].," Then find out the minimum value of $Q(A,B,C,D,E)$ and the corresponding parameters of [A, B, C, D, E]." + The hick dot-dashed curve iu the upper panel of Fig.l is the fitted empirical fuuction. which can be expressed as: From the empirical function we may find that the period of long-term variation of ASN is 103 vears. which is very close to the secular cvele.," The thick dot-dashed curve in the upper panel of Fig.1 is the fitted empirical function, which can be expressed as: From the empirical function we may find that the period of long-term variation of ASN is 103 years, which is very close to the secular cycle." + We may imnibered the seculi eveles as G1 (Gucludes the Sclavabe evele EA. and 14). G2 Gueludes the Sclavabe evele 6 11). G3 (includes the Sclavabe evele 15 21). aud GL (after the Sclavabe cycle 21) since 1700. respectively marked iu Fie.," We may numbered the secular cycles as $G1$ (includes the Schwabe cycle E – A, and 1 – 5), $G2$ (includes the Schwabe cycle 6 – 14), $G3$ (includes the Schwabe cycle 15 – 24), and $G4$ (after the Schwabe cycle 24) since 1700, respectively marked in Fig." + 1., 1. + At present the Sum is ina vale between G3 aud GL., At present the Sun is in a vale between $G3$ and $G4$. + The last term in the zieht haud of Equ.(3) implies that secular evcles have a gradually cnhlaucemenut. aud the Suu Ίαν have a tendency to become more and more active at the timescale of several hundred vears.," The last term in the right hand of Equ.(3) implies that secular cycles have a gradually enhancement, and the Sun may have a tendency to become more and more active at the timescale of several hundred years." + Many previous studies also presented the evidences of the secular evcles (Nagovitsvu. 1997: Frick et al. 1997: Le Wane. 2003: Donev. Penev. Sello. 2001: Ticrmath. 2006. ete).," Many previous studies also presented the evidences of the secular cycles (Nagovitsyn, 1997; Frick et al, 1997; Le Wang, 2003; Bonev, Penev, Sello, 2004; Hiermath, 2006, etc.)." + The Grand Mininia (6... Spórer Aliniumna. Maunuder Mininiunu. Daltou Minimi. etc) implies that the Suu nieht have experienced the dearth of activity in its evolutionary listory.," The Grand Minima (e.g., $\ddot{o}$ rer Minimum, Maunder Minimum, Dalton Minimum, etc) implies that the Sun might have experienced the dearth of activity in its evolutionary history." + Auc there is no complete conseusus amone the solu comunity whether such eraud minima are chaotic or regular., And there is no complete consensus among the solar community whether such grand minima are chaotic or regular. + This work may confirm the periodicity of the solar secular eveles., This work may confirm the periodicity of the solar secular cycles. + From the upper panel of Fig.l we can not ect the obvious evidence of the cevele with period of 51.5 vx., From the upper panel of Fig.1 we can not get the obvious evidence of the cycle with period of 51.5 yr. + However. the evidence is verv strong in the Fourier power spectra in lower paucl of Fig.l.," However, the evidence is very strong in the Fourier power spectra in lower panel of Fig.1." + In fact. from the upper panel of Fie.," In fact, from the upper panel of Fig." + 1 we aay find something of that. around each peak of the secular cvcle. the Schwabe eveles ave im mildly weals amplitudes in ASN.," 1 we may find something of that, around each peak of the secular cycle, the Schwabe cycles are in mildly weak amplitudes in ASN." + Secular cycles seeui to segment iuto two sub-peaks., Secular cycles seem to segment into two sub-peaks. +" For example. the solar Sclsvabe evcle A and 1 around the peak of G1. the solar Schwahe evele LO around the peak 6G2, aud the solar Sclavahe evcle 20 arouncl the peal of G3."," For example, the solar Schwabe cycle A and 1 around the peak of $G1$, the solar Schwabe cycle 10 around the peak of $G2$, and the solar Schwabe cycle 20 around the peak of $G3$." + Possibly. these facts are the indicator of the existence of P» component.," Possibly, these facts are the indicator of the existence of $P_{2}$ component." + Le Wang (2003) investigated the wavelet transformation of ASN series from L700 2002. and found the evidence of solar cycles with period of Ll-vr. 53r-vr. and 101-2.," Le Wang (2003) investigated the wavelet transformation of ASN series from 1700 – 2002, and found the evidence of solar cycles with period of 11-yr, 53-yr, and 101-yr." + Iu this work. the ASN series is spanned from 1700 2009. and we rectify the periods as 1-1. 51.5-vear. aud 103-vx.," In this work, the ASN series is spanned from 1700 – 2009, and we rectify the periods as 11-yr, 51.5-year, and 103-yr." + Our results are very close to that of Le Wane (2003)., Our results are very close to that of Le Wang (2003). +" Additionally. we find that there is an interesting phenomenon P/P,=9.36 is obviously departed from any integers: however. £7Py=2.00 is fitly equal to au integer of 2."," Additionally, we find that there is an interesting phenomenon: $P_{1}/P_{0}=9.36$ is obviously departed from any integers; however, $P_{1}/P_{2}=2.00$ is fitly equal to an integer of 2." + This evidence shows that P4 aud P» are originally connected with cach other. aud. £2 seems to be a second harmomics of Z4.," This evidence shows that $P_{1}$ and $P_{2}$ are originally connected with each other, and $P_{2}$ seems to be a second harmonics of $P_{1}$." +" Towever. there is uo such relationships between P, aud P. P»."," However, there is no such relationships between $P_{0}$ and $P_{1}$, $P_{2}$." + Table 1l preseuts another interesting feature: most of the asviunetric parameters are less than 1.00 (there are 22 Sclwwabhe evcles with Asy<1.00 among the total 28 cvcles; and the proportion is )). the averaged value of asvuuuectric parameters is about 0.722. aud this tuples that most Sclavabe cvcles are left asvuuuctric.," Table 1 presents another interesting feature: most of the asymmetric parameters are less than 1.00 (there are 22 Schwabe cycles with $Asy<1.00$ among the total 28 cycles, and the proportion is ), the averaged value of asymmetric parameters is about 0.722, and this implies that most Schwabe cycles are left asymmetric." + They have rapidly rising phases aud slowly decay phases., They have rapidly rising phases and slowly decay phases. + Aud the evele evolution cannot be modelled by sole simple amplitude-modulated sinusoids., And the cycle evolution cannot be modelled by some simple amplitude-modulated sinusoids. + Sucht phenomenon ds called as Waldimieier effect (1961)., Such phenomenon is called as Waldmeier effect (1961). + Among the total 28 evceles. there are only 3 Selisvabe evcles with syiuuuetrie profiles. aud 3 Sclavabe cycles with right asvuumetric profiles.," Among the total 28 cycles, there are only 3 Schwabe cycles with symmetric profiles, and 3 Schwabe cycles with right asymmetric profiles." + The sviumetric cycles (No., The symmetric cycles (No. +D. No.5. and No.16) are very close to the vale of the secular cveles.,"D, No.5, and No.16) are very close to the vale of the secular cycles." + The No.? cvele is a bizarrerie for the super loug rise-time (7 vears) aud super short decay-time (3 vears) with a super large asvuuuetric parameter (elsy= 2.33)., The No.7 cycle is a bizarrerie for the super long rise-time (7 years) and super short decay-time (3 years) with a super large asymmetric parameter $Asy=2.33$ ). + Additionally. there is an auti-correlated relationship between asviuinuetrie parameter and imnaxinnun ASN amone 28 solar Sclavahe cycles.," Additionally, there is an anti-correlated relationship between asymmetric parameter and maximum ASN among 28 solar Schwabe cycles." + The correlate coctiicicut is -0.55., The correlate coefficient is -0.55. + 1c. the stronger the solar Schwabe evcle. the more left asvuumetric the evcle profile.," i.e. the stronger the solar Schwabe cycle, the more left asymmetric the cycle profile." + It is very important to forecast the forthcoming solar evcles;, It is very important to forecast the forthcoming solar cycles. + May people make ereat efforts ou this problems (Pesnell. 2008: Tircmath. 2008: Wane et al. 2009: Strong Saba. 2009: Tathaway. 2009: ete).," Many people make great efforts on this problem (Pesnell, 2008; Hiremath, 2008; Wang et al, 2009; Strong Saba, 2009; Hathaway, 2009; etc)." + According, According +2011).,. +. The results of these investigations suggest a correlation between absorber equivalent width and host star-formation rate. though many galaxy hosts of large equivalent width: absorbers remain undetected in even the deepest imagine.," The results of these investigations suggest a correlation between absorber equivalent width and host star-formation rate, though many galaxy hosts of large equivalent width absorbers remain undetected in even the deepest imaging." + Recent elforts to determine the typical physical xoperties of galaxies hostingLl absorbers rave attempted: statistical analyses using large absorber catalogues., Recent efforts to determine the typical physical properties of galaxies hosting absorbers have attempted statistical analyses using large absorber catalogues. + Phe typical luminosities and colors of hosts 1àve been inferred from the stacking of residual light around housands of quasars exhibitingLL absorption (Zibettiet.2007:Caloretal. 2010).," The typical luminosities and colors of hosts have been inferred from the stacking of residual light around thousands of quasars exhibiting absorption \citep{Zibetti07, Caler10}." +. Host. star-formation rates and dust. properties have been inferred from. spectral stacks of iuncdreds of identified: absorbers (Yorkctal.2006:WileletAlénardetal.2010:Noterdacme 2010)... and average absorber dark matter halo masses have been indirectly obtained from clustering measurements (Bouchéetal.2006:Luncerenet2009:Gauthierct 2009).," Host star-formation rates and dust properties have been inferred from spectral stacks of hundreds of identified absorbers \citep{York06,Wild07, Menard09, MC09, Menard10, ND10}, and average absorber dark matter halo masses have been indirectly obtained from clustering measurements \citep{B06, L09, Gauthier09}." +. The imaging and spectral stacking analyses collectively indicate a general correlation. between equivalent width and the star formation rate of the host galaxy. whilst the clustering analvses suggest a weak global. anti-correlation of the absorber equivalent width with galaxy halo mass.," The imaging and spectral stacking analyses collectively indicate a general correlation between equivalent width and the star formation rate of the host galaxy, whilst the clustering analyses suggest a weak global anti-correlation of the absorber equivalent width with galaxy halo mass." + ‘Taken together. these findings disfavor the classical picture in which strong absorption is primarily produced. by virialised gas in the extended haloes of massive galaxics.," Taken together, these findings disfavor the classical picture in which strong absorption is primarily produced by virialised gas in the extended haloes of massive galaxies." + Now a new paradigm seems to be emerging in which the majority of strong absorbers originate in galactic disks on scales «10 | kpe and in star formation-criven outIows on larger scales. out to 7150 kpc.," Now a new paradigm seems to be emerging in which the majority of strong absorbers originate in galactic disks on scales $<$ 10 $^{-1}$ kpc and in star formation-driven outflows on larger scales, out to $\sim$ 150 kpc." + Deep imaging and spectroscopic follow-up of galaxy-absorber pairs at zZ2:0.7 have confirmed the existence of a strong correlation between WemZ2A absorbers and starburst galaxies (Bouchéοἱ2007:Nestoretal. 2010).," Deep imaging and spectroscopic follow-up of galaxy-absorber pairs at $>$ 0.7 have confirmed the existence of a strong correlation between $^{\lambda2796}_{r}\ga$ absorbers and starburst galaxies \citep{B07,Nestor10}." +. Further strengthening the case for supernovae-driven outllows is the recent determination that the redshift number density evolution of strong absorbers traces the global star formation rate (Ménardοἱal.2009:Chelouche&Bowen 2010).," Further strengthening the case for supernovae-driven outflows is the recent determination that the redshift number density evolution of strong absorbers traces the global star formation rate \citep{Menard09,CB10}." +. Llowever. studies of absorbers in. the local Universe have shown that the origins are less clear in the case of the much larger population of absorbers with WAP«2A," However, studies of absorbers in the local Universe have shown that the origins are less clear in the case of the much larger population of absorbers with $^{\lambda2796}_{r}\la$." + [n an examination of such lower equivalent widthll absorbers at z~0.2. Chenetal.(2010). found no compelling evidence of a correlation between absorption »operties and the recent star formation histories of galaxies.," In an examination of such lower equivalent width absorbers at $\sim$ 0.2, \citet{Chen10} found no compelling evidence of a correlation between absorption properties and the recent star formation histories of galaxies." + Furthermore. recent studies of the galactic counterparts of WAZx2A absorbers at 20.1 [ind no evidence or oulllows from star formation (Ixacprzakctal.2011).. suggesting that absorption primarily probes infalling eas from disk/halo processes in normal galaxies. at least or absorbers with similar equivalent widths in the local Universe.," Furthermore, recent studies of the galactic counterparts of $^{\lambda2796}_{r}\la$ absorbers at $\sim$ 0.1 find no evidence for outflows from star formation \citep{K11}, suggesting that absorption primarily probes infalling gas from disk/halo processes in normal galaxies, at least for absorbers with similar equivalent widths in the local Universe." + To what extent galaxy evolution or galaxy sample selection biases may be able to reconcile the contradictory inclines of origins in star lormation-clriven outllows at 220.5 and cold mode accretion at οι still remains to be determined., To what extent galaxy evolution or galaxy sample selection biases may be able to reconcile the contradictory findings of origins in star formation-driven outflows at $\ga$ 0.5 and cold mode accretion at $\la$ 0.3 still remains to be determined. + For large data sets. clustering measurements can be used: to. determine the typical environments of any well-defined. sample of extragalactic objects.," For large data sets, clustering measurements can be used to determine the typical environments of any well-defined sample of extragalactic objects." + The space density of strong absorbers is. low on average. only 0.3 absorbers with WnLOGAN are observed. per unit redshift’ along quasar sightlines at) z=0.5 (Nestorctal.2005) soLL clustering estimates in the aforementioned works utilisecl two-point cross-correlations with much more numerous Luminous galaxies in order to extract an absorber clustering signal of measurable strength.," The space density of strong absorbers is low – on average, only 0.3 absorbers with $^{\lambda2796}_{r}\ga$ are observed per unit redshift along quasar sightlines at z=0.5 \citep{Nestor05} – so clustering estimates in the aforementioned works utilised two-point cross-correlations with much more numerous luminous galaxies in order to extract an absorber clustering signal of measurable strength." + Luminous reel ealaxies (LRGs) have thus far been a favored galaxy saniple or this purpose. since their observable redshift range in the SDSS has a large overlap withLE absorbers.," Luminous red galaxies (LRGs) have thus far been a favored galaxy sample for this purpose, since their observable redshift range in the SDSS has a large overlap with absorbers." +" In addition o their convenient redshift range. LRGs are excellent tracers of structure in the Universe (e.g.Eisensteinetal.2005:Ze- and thev exhibit minimal stellar mass evolution over their observable redshift, range in the SDSS (2908) (Wakeetal.2006.20082:Brown2007.2008:Cool2008)."," In addition to their convenient redshift range, LRGs are excellent tracers of structure in the Universe \citep[e.g.,][]{Eisenstein05a, Zehavi05, Ross07, Blake08, Wake08a}, and they exhibit minimal stellar mass evolution over their observable redshift range in the SDSS $\la$ 0.8) \citep{Wake06, Wake08a, Brown07, Brown08, Cool08}." +. Phe dark matter halo bias of Εις is thus precisely measured (Blakeetal.2008:Wake2008a:Pad- 2009).. making these galaxies a [avorable population for amplifving the clustering signals of quasars ancl absorbers.," The dark matter halo bias of LRGs is thus precisely measured \citep{Blake08, Wake08a, NP09}, , making these galaxies a favorable population for amplifying the clustering signals of quasars and absorbers." + Measurements of the Mgll-LItG. two-point cross-Correlation have converged on a typical dark matter halo mass of ~ 1095 AL: at z~0.6 (Bouchéetal.2004.2006:Lundgrenetal.2009:Gauthicrct 2009).," Measurements of the -LRG two-point cross-correlation have converged on a typical dark matter halo mass of $\sim$ $^{12}$ $_{\sun}$ at $\sim$ 0.6 \citep{B04, B06, L09, Gauthier09}." +. Few deep spectroscopic surveys exist with sullicient numbers of galaxies to attempt measurements of larec-scale absorber clustering (and thus. the dark matter bias) at higher redshifts (210.60).," Few deep spectroscopic surveys exist with sufficient numbers of galaxies to attempt measurements of large-scale absorber clustering (and thus, the dark matter bias) at higher redshifts $>$ 0.6)." + Lyman break galaxies (LBCGs) have been used to examine the bias of strong quasar absorption lines at zz2: Xdelbergerctal.(2005) measured the clustering of triplv-ionised. Carbon IV). absorption lines (AA 1548.1551) around. UV-selected galaxies(C at 2<2<3 finding that absorbers cluster similarly to typical star-forming galaxies.," Lyman break galaxies (LBGs) have been used to examine the bias of strong quasar absorption lines at $>$ 2; \citet{Adelberger05} measured the clustering of triply-ionised Carbon ) absorption lines $\lambda\lambda$ 1548,1551) around UV-selected galaxies at $<$ $<$ 3 finding that absorbers cluster similarly to typical star-forming galaxies." + Still. a similar analvsis has not vet been performed for a sample of absorbers. which trace gas with a lower ionization temperature ancl are thus not always coincident with absorption.," Still, a similar analysis has not yet been performed for a sample of absorbers, which trace gas with a lower ionization temperature and are thus not always coincident with absorption." + Vhe DEEP? Galaxy Redshift Survey (Davisetal.2003) provides a sample of ~32.000 galaxies with spectroscopically confirmed redshifts in the range 0.7 «z« 1.45. ideal for use in correlations with detected in the SDSS.," The DEEP2 Galaxy Redshift Survey \citep{Davis03} provides a sample of $\sim$ 32,000 galaxies with spectroscopically confirmed redshifts in the range $<$ $<$ 1.45, ideal for use in correlations with detected in the SDSS." + This galaxy sample is particularly interesting for. investigations. as its star-forming population has been recently found. to exhibit. ubiquitous outflows (observed: as. bbueshifted intrinsic absorption in the stacked rest-frame galaxy spectra) across a wide range of galaxy properties (Weineretal. 2009).," This galaxy sample is particularly interesting for investigations, as its star-forming population has been recently found to exhibit ubiquitous outflows (observed as blueshifted intrinsic absorption in the stacked rest-frame galaxy spectra) across a wide range of galaxy properties \citep{Weiner09}." +. Phe outflows reported for the DEEP2 galaxies have . D. ↿∙∖⇁≻⊔∼⋜↧↓≼∼∪↓⊔⊔↓⊔∠⇂⋖⋅⊔⊳∖⊔⊓⋅⊳∖∪⇂⇀∖⊓∿↓∪≼⇍⊔↓⋜⋯∠⇂∖⇁⋖⊾↥⋯∙⊔⊓⋅≱∖∪⇂⋅⇁⊐⊓ 2 ↔ ~400 knis L. LE, The outflows reported for the DEEP2 galaxies have typical column densities of $N_{H}\sim10^{20}$ $^{-2}$ and velocities of $\sim$ 400 km $^{-1}$. +SThese values are consistent. with. observations. from quasar absorption line data. and Weineretal.(2009) Esveculate that the ejected gas could. eventually reach projected. separations of 50 tkpe.," These values are consistent with observations from quasar absorption line data, and \citet{Weiner09} speculate that the ejected gas could eventually reach projected separations of 50 $^{-1}$ kpc." + However. no direct connection between feedback from normal star-formineg ealaxies and quasar absorption lines has vet been observed.," However, no direct connection between feedback from normal star-forming galaxies and quasar absorption lines has yet been observed." + In this work. we calculate the two-point redshift-space Cross-correlation of the full sample of DEEP2 galaxies with 21 absorbers identifiedin SDSS DRT quasar spectra," In this work, we calculate the two-point redshift-space cross-correlation of the full sample of DEEP2 galaxies with 21 absorbers identifiedin SDSS DR7 quasar spectra" +be significant uncertainties.,be significant uncertainties. + The time-dependent thickness of the ice buildup varied with position on the solid state detector. producing an extra absorption component (equivalent Lo absorption of between 107 and 107! 7)) that is significantly larger (han many of the columus being measured.," The time-dependent thickness of the ice buildup varied with position on the solid state detector, producing an extra absorption component (equivalent to absorption of between $10^{20}$ and $10^{21}$ ) that is significantly larger than many of the columns being measured." + The standard model lor the behavior of the ice buildup attempts to correct for (he extra absorption. and is valid to a low energy cut-off near the oxvgen edge al 0.5 keV (Alaclejskietal.1991)..," The standard model for the behavior of the ice buildup attempts to correct for the extra absorption, and is valid to a low energy cut-off near the oxygen edge at 0.5 keV \citep{mmwau}." + Unfortunately. low and intermediate Galactie columns (Nex510? 7)) are most readily measured in the 0.14-0.5 keV band (AB). limiting confidence in these measurements.," Unfortunately, low and intermediate Galactic columns $\NHgx \leq 5\tenup{20}$ ) are most readily measured in the 0.14-0.5 keV band (AB), limiting confidence in these measurements." + Although the data no longerrequire extra Ny. il mar be possible to accomodate extra absorbing material in certain models Johnstone1998:Wise&Sarazin 1999).," Although the data no longer extra $\NHxo$, it may be possible to accomodate extra absorbing material in certain models \citep{ssj,ws}." +. We would like to acknowledge financial support [rom NASA grant. NAG5-3247., We would like to acknowledge financial support from NASA grant NAG5-3247. + We would also like to thank Urwin ancl SSulkanen for many useful discussions., We would also like to thank Irwin and Sulkanen for many useful discussions. +What is important for model fitting is the feature of a template map. not the absolute amplitude.,"What is important for model fitting is the feature of a template map, not the absolute amplitude." +" For example. the WMADP foreground removal will be the same even if the three foreeround templates /;. /,,H and /, are all doubled."," For example, the WMAP foreground removal will be the same even if the three foreground templates $t_d$ , $t_{_H}$ and $t_s$ are all doubled." + In this work. the result of removing pseudo-dipole signal is not dependent to what auplitude is assumed for the direction error: larger amplitude leads to lower fitted coefficient in model fitting and the final correction {ο the CMD map is Che same.," In this work, the result of removing pseudo-dipole signal is not dependent to what amplitude is assumed for the direction error: larger amplitude leads to lower fitted coefficient in model fitting and the final correction to the CMB map is the same." + Here it is worth to mention that the characteristic feature of template map of the pseudo-dipole signal induced by a pointing or timing error obtained from our previous work (Liu.Niong&Li2010) or shown in Fig., Here it is worth to mention that the characteristic feature of template map of the pseudo-dipole signal induced by a pointing or timing error obtained from our previous work \citep{liu10} or shown in Fig. + l of this work has already been confirmed by other independent works (Moss.Scott&Sigurdson2010:Roukema2010).," 1 of this work has already been confirmed by other independent works \citep{mos10,rou10}." +. Our result demonstrates Chat a pseudo-dipole field can produce deviations in the sky temperature map wilh a structure very similar to the CMD cequadrupole pattern published by ihe WMADP team., Our result demonstrates that a pseudo-dipole field can produce deviations in the sky temperature map with a structure very similar to the CMB quadrupole pattern published by the WMAP team. + The template map of pseudo-dipole induced temperature deviation shown in Fie., The template map of pseudo-dipole induced temperature deviation shown in Fig. + l are generated from a differential dipole field which is completely determined by the spacecrall velocity ancl overall-equivalent error of differential direction. without. using any CAIB signal., 1 are generated from a differential dipole field which is completely determined by the spacecraft velocity and overall-equivalent error of differential direction without using any CMB signal. + The pseudo-dipole signal in the differential datiun lor a WALAP observation distorts the temperatures for corresponding sky pixels varving observation by observation., The pseudo-dipole signal in the differential datum for a WMAP observation distorts the temperatures for corresponding sky pixels varying observation by observation. + Therefore. (he pseudo-dipole induced temperature map is generated by (he pseudo-dipole signal combined with the WAIAP sean pattern. which is highlv relative to the ecliptic plane (Llinshawetal.2007:Li2009).," Therefore, the pseudo-dipole induced temperature map is generated by the pseudo-dipole signal combined with the WMAP scan pattern, which is highly relative to the ecliptic plane \citep{hin07, li09}." +. The WMADP CAB quadrupole component being hiehly aligned. aud close to the ecliptic plane is a long lime puzzle in cosmology. which now can be naturally explained by the pseudo-dipole signal effect.," The WMAP CMB quadrupole component being highly aligned and close to the ecliptic plane is a long time puzzle in cosmology, which now can be naturally explained by the pseudo-dipole signal effect." + IXeeping insist that the published WALAP quadrupole is really cosmological origin now becomes more cilficult: it is needed the primordial density [Iuctuations not only occasionally being laid down in the plane of the solar svstem. but also occasionally having almost the same phase as (hie scan strategv of the WMADP mission!," Keeping insist that the published WMAP quadrupole is really cosmological origin now becomes more difficult: it is needed the primordial density fluctuations not only occasionally being laid down in the plane of the solar system, but also occasionally having almost the same phase as the scan strategy of the WMAP mission!" + This work is supported by the National Natural Science Foundation (Grant No., This work is supported by the National Natural Science Foundation (Grant No. + 10821061). National Basic Research Program of China (Grant No.," 10821061), National Basic Research Program of China (Grant No." + 2009CB-824800). the CAS project IXJCX2-YW-TO03 and China Postdoctoral Science Foundation funded project 911217344. The data analvsis made use of the WMAP data archive and theHIZALPix software package 2005)..," 2009CB-824800), the CAS project KJCX2-YW-T03 and China Postdoctoral Science Foundation funded project H91I21734A. The data analysis made use of the WMAP data archive and theHEALPix software package \citep{gor05}. ." +llameury 1998: Menon et al.,Hameury 1998; Menou et al. + 1999) and hence NS X-ray novae and BIL X-ray novae with similar orbital periods are likely (o have similar mass accretion rates., 1999) and hence NS X-ray novae and BH X-ray novae with similar orbital periods are likely to have similar mass accretion rates. + The fact that (heir luminosities are so different is (hen both surprising ancl significant. ancl must reflect some fundamental difference between the two kinds of object.," The fact that their luminosities are so different is then both surprising and significant, and must reflect some fundamental difference between the two kinds of object." + While a lew counter-explanations have been proposed (see Naravan. Garcia MeClintoek 2002: Hametury et al.," While a few counter-explanations have been proposed (see Narayan, Garcia McClintock 2002; Hameury et al." + 2003: MeClintock et al., 2003; McClintock et al. + 2004 for references and rebuttals). (he most natural explanation of the observations is (hat accretion in quiescent ARBs occurs via an ADAF: the DII candidates are dimmer because they have event horizons through whieh they swallow all the advected οποιον.," 2004 for references and rebuttals), the most natural explanation of the observations is that accretion in quiescent XRBs occurs via an ADAF; the BH candidates are dimmer because they have event horizons through which they swallow all the advected energy." + In other words.black relative to other compact objects with surfaces!," In other words, relative to other compact objects with surfaces!" + A related argument is based on the X-rav spectra of quiescent X-ray. novae., A related argument is based on the X-ray spectra of quiescent X-ray novae. + Most quiescent NSs have X-ray spectra consisting of (vo distinct components: a power-law component and a thermal blackbods-like component., Most quiescent NSs have X-ray spectra consisting of two distinct components: a power-law component and a thermal blackbody-like component. + The former is identified with a hot (likely accretion flow. and the latter with emission from the surface of the NS.," The former is identified with a hot (likely advection-dominated) accretion flow, and the latter with emission from the surface of the NS." + MeClintock et al. (, McClintock et al. ( +"2004) analvzed the spectrum of the DII X-ray nova NTE J11182-480 in quiescence and established a very Geht limit on a thermal component: Ly,«9.4x10Ueros loa the confidence level. (","2004) analyzed the spectrum of the BH X-ray nova XTE J1118+480 in quiescence and established a very tight limit on a thermal component: $L_{\rm th} < +9.4\times10^{30} ~{\rm erg\,s^{-1}}$ at the confidence level. (" +There is a very clear power-law component in the spectrum. as one would expect for a hot ADAF.),"There is a very clear power-law component in the spectrum, as one would expect for a hot ADAF.)" + In comparison. the thermal component in NS svstems is ivpically much brighter. ~fewxLO to fewx10eres1.," In comparison, the thermal component in NS systems is typically much brighter, $\sim {\rm few} \times 10^{32}$ to ${\rm few}\times10^{33} ~{\rm erg\,s^{-1}}$." + Since the thermal component in NSs is identified wilh surface emission. the lack of a similar component in NTE J11182-430 argues lor the lack of a surface in this source. i.e.. the object must have an event horizon.," Since the thermal component in NSs is identified with surface emission, the lack of a similar component in XTE J1118+480 argues for the lack of a surface in this source, i.e., the object must have an event horizon." + This independent argument. based on (he spectrum bolsters the previous discussion. which was based purely on Iuminositx.," This independent argument based on the spectrum bolsters the previous discussion, which was based purely on luminosity." + When an accretion disk. especially one with relatively cool gas in the “high soft state.” is present around a compact star. a narrow viscous boundary laver will form at the radius where the rapidly orbiting gas meets the surface of the star.," When an accretion disk, especially one with relatively cool gas in the “high soft state,” is present around a compact star, a narrow viscous boundary layer will form at the radius where the rapidly orbiting gas meets the surface of the star." + A considerable amount of heat enerev is expected to be liberated in this boundary laver., A considerable amount of heat energy is expected to be liberated in this boundary layer. + No boundary laver is expected if the central object is a black hole., No boundary layer is expected if the central object is a black hole. + sunvaev Revunivisey (2000) showed that the variability. power spectra of NS XRBs have significant power even al frequencies as high as | KIlz. whereas the power spectra of DII XRBs decline strongly. above about. 50 Iz.," Sunyaev Revnivtsev (2000) showed that the variability power spectra of NS XRBs have significant power even at frequencies as high as 1 kHz, whereas the power spectra of BH XRBs decline strongly above about 50 Hz." + Part of the difference is explained by the mass difference between the (wo objects. since characteristic dynamical frequencies scale as," Part of the difference is explained by the mass difference between the two objects, since characteristic dynamical frequencies scale as" +SAL. + assuming the stream footpoiut covers of the stellar surface aud that the iuflow velocity is |. he density of material in the inner stream can be expected to reach perhaps 7«10 tle4 5m. Or about 5<10%Hem i)>2. consistent with the required density estimated above.,"$_{\odot}$ $^{-1}$ assuming the stream footpoint covers of the stellar surface and that the inflow velocity is $^{-1}$, the density of material in the inner stream can be expected to reach perhaps $7\times10^{-11}$ g $^{-3}$, or about $5 \times 10^{13}$ $^{-3}$, consistent with the required density estimated above." + We note that ταν observations of II-like triplets in the N-vav spectrmu of the nearby accreting T Tami stay TW να also dudicates densities of the order 100 t in the line-forming region. (Iastner ct al..," We note that X-ray observations of He-like triplets in the X-ray spectrum of the nearby accreting T Tauri star TW Hya also indicates densities of the order $10^{13}$ $^{-1}$ in the line-forming region, (Kastner et al.," + 2002)., 2002). + Since for free-free absorption the optical depth. for ⋅⋅ ⋅ ≻⋜↧↴∖↴↕⊔⋜↧↸∖↕⊔↕↴∖↴↴∖↴↕∪∐↕↴∖↴∣−∖⊼∕−∙↴∖↴⋯⊳∐↸∖∐∐↴∖∷∖↴↕∪∐↖↖⇁∪∏∐↴⋈∖s ⋅⋅ expected to be heavily absorbed.," Since for free-free absorption the optical depth for plasma emission is $\tau \propto \nu^2$, such emission would be expected to be heavily absorbed." + A density scale leneth of less than 100 kin would be necessary for this process ) account for the emission. assuming second larmonic (Deuz. 2002. eq.," A density scale length of less than 100 km would be necessary for this process to account for the emission, assuming second harmonic (Benz, 2002, eq." + 11.2.5)., 11.2.5). + The ποος size would have o be the salue scale or even καλο and a brightuess emperature iu excess of LOMTS is required., The source size would have to be the same scale or even smaller and a brightness temperature in excess of $10^{18}$ K is required. + This exceeds solar radio bursts by three orders of magnitude., This exceeds solar radio bursts by three orders of magnitude. + Lower lmits to the brightness temperature at various ines were cstimated for the upper Πιτ source size and are shown in Table L.., Lower limits to the brightness temperature at various times were estimated for the upper limit source size and are shown in Table \ref{temps}. + A second estimate was also uade asstuine the upper luit source size is a constant hi8 as. the maxiuuni size for the quiescent source vetween the beeiuuiug of the observation ac UT=6 jours.," A second estimate was also made assuming the upper limit source size is a constant 0.48 mas, the maximum size for the quiescent source between the beginning of the observation and UT=6 hours." + This coustraiu was preferred because it is the most reliable. iuchiding the ong Effelsbere-VLA baselines. and it is considered unlikely that the source would imerease in size.," This constraint was preferred because it is the most reliable, including the long Effelsberg-VLA baselines, and it is considered unlikely that the source would increase in size." + The larger upper limits for the subsequent data seements are clearly driven bw the lack of the long VLA-Effelshere baseliues, The larger upper limits for the subsequent data segments are clearly driven by the lack of the long VLA-Effelsberg baselines. + The brightuess temperatures are at the high cud of the rauge typically seen in solar evrosvuchrotron flares (10! 10K)., The brightness temperatures are at the high end of the range typically seen in solar gyrosynchrotron flares $10^7$ – $10^8$ K). + The VLBI coustraints show that the evrosvuchrotron conipact source is contained within a volunie approximately 15 Rk. ln radius., The VLBI constraints show that the gyrosynchrotron compact source is contained within a volume approximately 15 $_{\odot}$ in radius. + The streneth of the maenetic field implicated iu the maser strongly suggests an origin for this Cluission close to the stellar surface. in the region with strouges magnetic field streneth.," The strength of the magnetic field implicated in the maser strongly suggests an origin for this emission close to the stellar surface, in the region with strongest magnetic field strength." +" The value of 1.5-8kC is consistent with values οταν, in sunspots.", The value of 1.5-3kG is consistent with values found in sunspots. + It is also broadly cousisteut with values found using other techuiques for T Tami stars., It is also broadly consistent with values found using other techniques for T Tauri stars. + For example. CGueuther et al. (," For example, Guenther et al. (" +1999) used a techuique based on Zeca broadcuing of infrared. Fe lines aud. determined magnetic feld strengths of 2.35 kG iu the case of T Tami N. aud 1.1 κ for LkCa 15. a weak-lined T Tawi star.,"1999) used a technique based on Zeeman broadening of infrared Fe lines and determined magnetic field strengths of 2.35 kG in the case of T Tauri N, and 1.1 kG for LkCa 15, a weak-lined T Tauri star." + Mavreinal detectious of kiloganuss streneth fields were uade for two other stars. one classical (accreting) aud oue wealk-lined (non-accretiug).," Marginal detections of kilogauss strength fields were made for two other stars, one classical (accreting) and one weak-lined (non-accreting)." + It should be noted that hese fields represent the average fek over the cutire stellar surface. so that local field streugths could be much üieher.," It should be noted that these fields represent the average field over the entire stellar surface, so that local field strengths could be much higher." + Dasri et al. (, Basri et al. ( +1992) also used a similar teclinique to uae one detection aud establish one upper limit ou two wealline: T Tawi stars.,1992) also used a similar technique to make one detection and establish one upper limit on two weak-lined T Tauri stars. + Johus-drull et al (, Johns-Krull et al. ( +1999a) used spectropoluduetry of the accretiug T Tauri star BP Tau o detect a field of 2.UsG associated with the Πο I A5876 ine. Which is believe to form in a ligh temperature accretion shock.,"1999a) used spectropolarimetry of the accreting T Tauri star BP Tau to detect a field of 2.4kG associated with the He I $\lambda5876$ line, which is believed to form in a high temperature accretion shock." +" Am ] result. frou, photospheric lines indicates that this strone field is no elobally preseut aud »oiuts to maenetically fuunelled accretion im this source.", A null result from photospheric lines indicates that this strong field is not globally present and points to magnetically funnelled accretion in this source. + Our observations point to strong imaguetic fields aud reconnection in the mnuuediate environmen ( 25) can be obtained without additional telescope time (with respect to imaging)., A large number of photometric redshifts of very faint sources $m_B > 25$ ) can be obtained without additional telescope time (with respect to imaging). + For the Hubble Deep Field more than one thousand photometric redshifts have been estimated (Lanzetta 11996)., For the Hubble Deep Field more than one thousand photometric redshifts have been estimated (Lanzetta 1996). + Moreover. the technique can be rather accurate (provided that a good set of filters is used).," Moreover, the technique can be rather accurate (provided that a good set of filters is used)." + For example. in a first test on a sample of 27 galaxies in the Hubble Deep Field. by comparison with the spectroscopic redshifts now available. more than 65*4 of the photometric redshifts have errors [A:|< 0.1. and all redshifts have errors [A:|«0.3 (Hoggal.," For example, in a first test on a sample of 27 galaxies in the Hubble Deep Field, by comparison with the spectroscopic redshifts now available, more than $68\%$ of the photometric redshifts have errors $| \Delta z | < 0.1$ , and all redshifts have errors $| \Delta z | < 0.3$ (Hogg." + 1998)., 1998). + This suggests that in a not far future we, This suggests that in a not far future we +bx 1). whereas the accreted mass above which 1 is screened. 4:1/./3. is independent of b.,"$b\gg 1$ ), whereas the accreted mass above which $\mu$ is screened, $4 M_{\rm c}/3$, is independent of $b$." + This theoretical prediction conforms with observations in (wo kev respects., This theoretical prediction conforms with observations in two key respects. +" First. most accreting millisecond pulsars have b>10 (2). and hence ena,&10* from (3)). consistent with the upper limit e<10? inferred [rom spin down (??) and the failure of bar antennas and interferometers to detect gravitational waves so far (2).."," First, most accreting millisecond pulsars have $b \gtrsim 10$ \citep{lit01} + and hence $\epsilon_{\rm max} \lesssim 10^{-7}$ from \ref{eq:gra6d}) ), consistent with the upper limit $\epsilon\lesssim 10^{-5}$ inferred from spin down \citep{dhu96,bra98} + and the failure of bar antennas and interferometers to detect gravitational waves so far \citep{sch99}." +" Contours of ea, are plotted in the Du plane in Figure 6b.", Contours of $\epsilon_{\rm max}$ are plotted in the $\psi_\ast$ $T$ plane in Figure \ref{fig:gra2}$ $b$. +"Second. the floormagnelicmomentofrecycledneulronstars. whichisobservedlobei (for M,~LO LU.) from (7))."," Second, the floor magnetic moment of recycled neutron stars, which is observed to be `universal', is given by $\mu_{\rm min} \sim 10^{26}\,{\rm G\,cm^{-3}}$ (for $M_{\rm a}\sim 10^{-1}M_{\sun}$ ) from \ref{eq:gra6c}) )." +" Theoretically. it is independent of 6 (and hence AM) in the regime {η/,. and weakly dependent on M, in the regime /4Mq: see re[sec:gra2b)).", The dipole and quadrupole moments saturate at $\mu(M_{\rm d})$ and $\epsilon(M_{\rm d})$ respectively when Ohmic diffusion dominates $M_{\rm a} > M_{\rm d}$; see \\ref{sec:gra2b}) ). + From (4)). (5)). and (9)). we obtain Contours of M4 in the M;-7' plane are displaved in Figure 7..," From \ref{eq:gra5}) ), \ref{eq:gra6a}) ), and \ref{eq:gra6e}) ), we obtain Contours of $M_{\rm d}$ in the $\dot{M}_{\rm a}$ $T$ plane are displayed in Figure \ref{fig:gra0}." + The distorted magnetic field in Figure 5iuneybedisrupledbyinterechange. Parker. anddoublydi [[usivei (???).," The distorted magnetic field in Figure \ref{fig:gra1}$ $a$ may be disrupted by interchange, Parker, and doubly diffusive instabilities wherever the local field strength exceeds $B \sim 10^{10}\,{\rm G}$ \citep{cum01,lit01,pay04}." + However. more work is required to settle this issue: existing stability calculations are linear ancl plane-parallel. unlike (he situation in Figure ba.," However, more work is required to settle this issue; existing stability calculations are linear and plane-parallel, unlike the situation in Figure \ref{fig:gra1}$ $a$." +" fheequilibriumfieldmagnolbedi. lyingboundarycondilion. whichconstrainsthemobilil yo f{closelypacked flurtubes? In a separate effect. 2? proved analvlically that the magnetic field develops bubbles for AL,210LV.: the source term on the right-hand side of (2)) creates this surfaces xΕΠώ)AL, that are disconnected from the star (6< 0. c> vy).Further work is required to determine how the bubbles evolve in the large-M, regime M,~LO1M. ). where the theory in breaks down."," The equilibrium field may not be disrupted completely if the instability saturates promptly in the nonlinear regime; for example, the interchange instability is inhibited topologically by the line-tying boundary condition, which constrains the mobility of closely packed flux In a separate effect, \citet{pay04} proved analytically that the magnetic field develops bubbles for $M_{\rm a} \gtrsim 10^{-4} M_{\sun}$; the source term on the right-hand side of \ref{eq:gra2}) ) creates flux surfaces $\propto F'(\psi) \propto M_{\rm a}$ that are disconnected from the star $\psi<0$ , $\psi >\psi_\ast$ ).Further work is required to determine how the bubbles evolve in the $M_{\rm a}$ regime $M_{\rm a} \sim 10^{-1} M_{\sun}$ ), where the theory in \\ref{sec:gra2a} breaks down." + The mass distribution resulting from polar magnetic burial is not rotationally svinnietric, The mass distribution resulting from polar magnetic burial is not rotationally symmetric +"where c—va is the reduced stream function. and the brackets are defined by (A.B)=0,4A0,DOBO,A.","where $\tilde{\psi}=\psi/a^2$ is the reduced stream function, and the brackets are defined by $\{A, +B\}=\partial_{\theta}A\partial_{\phi}B-\partial_{\theta}B +\partial_{\phi}A$." + The left-hand side of ((6)) contains only linear terms. while the right-hand side is the nonlinear advection term.," The left-hand side of \ref{maineqn}) ) contains only linear terms, while the right-hand side is the nonlinear advection term." + Let us neglect this nonlinear part for a moment and look for a solution to the linearized equation in the form where à is a constant., Let us neglect this nonlinear part for a moment and look for a solution to the linearized equation in the form where $\alpha$ is a constant. + lt is then easy to work out the dispersion relation for the linear part of ((6)): ↾∐↕⊀↓⊳∖⊀↓⊳∖↿↓↥⋖⋅∖∖⋎⋖⋅∐−↳⊔∪∖∖⊽⊔∠⇂⊲↓⊳∖↓≻∢⊾↓⋅⊳∖⊀↓∪⊔↓⋅∢⊾⇂⋜⊔⊲↓∪⊔⇂∎∪↓⋅∐∪≱∖≱∖∣, It is then easy to work out the dispersion relation for the linear part of \ref{maineqn}) ): This is the well-known dispersion relation for Rossby waves. +⋡∙∖⇁ ∖∖⊽⋜↧∖⇁∢⊾⊳∖⊳↳∖↓∪↓⋅⋖⊾∪∖⇁⋖⋅↓⋅⊳⊳∖⊲↓⊔⊓⊾≖↾∣⋯↕⊳∖⋜⋯⋖⊾⊲↓⋏∙≟⋖⊾⊔⇂⋅⊔⋯⇍↿⊲↓∪⊔∪⇂⋅↿↓↥⋖⊾ ∟⋜↧↓≻↓⋯⋰↓⋜⋯⊳↿↓↥⋖⋅↓↥∢≱↓↕↓↕↓↕∢⋅⋜↧↓⋅⇂∢⋅↓⋅↓↕↓↕↓↕∣⊲⇀⊲⊏↥⊳∩∖≼∩⊐⋖⊾⊏↥⊔⋜↧↓⊳∖∠∢⊾↓⋅∪∖," Moreover, since $Y_{lm}$ is an eigenfunction of the Laplacian, the nonlinear term in \ref{maineqn}) ) equals zero when $\psi\propto +Y_{lm}$." +∖⋎↓↕⋖⋅⊔ ∣⋎∖≖↾∣⋯⊳↾↓∖↓↕∢⊾↓⋅∢⊾⇂⋅∪↓⋅⋖⋅∣⊲⇀⊲⊏↥⊳∩∖⊤∩↕⊳∖⋜⋯↙∣⊽∣∣≺∣∣≱∖∪↓⋯⋠↓∪⊔∪⇂⋅↿↓∐⋅∐⊔⊲⊔⇂ equations of motion. for arbitrarily large a.," Therefore \ref{rmode}) ) is an solution of the fluid equations of motion, for arbitrarily large $\alpha$." + Consider now the angular momentum and energy of the solution (7))., Consider now the angular momentum and energy of the solution \ref{rmode}) ). + The total angular momentum of the Duid shell is given by where Εμμ ts the angular momentum of the shell when the r-mode amplitude a is zero. and is the physical change in angular momentum of the shell due to the r-mocde.," The total angular momentum of the fluid shell is given by where $L_{\rm background}$ is the angular momentum of the shell when the r-mode amplitude $\alpha$ is zero, and is the physical change in angular momentum of the shell due to the r-mode." + Llere pis the surface density of the uid., Here $\rho$ is the surface density of the fluid. + ]t is then clear from Eqs (1)) and (7)) that [or all mσὲ0., It is then clear from Eqs \ref{velocity}) ) and \ref{rmode}) ) that for all $m\neq0$. + Modes with m=0 have zero frequeney ancl are calledcurrents: we will come back to them later when we discuss nonlinear evolution of the r-miocles., Modes with $m=0$ have zero frequency and are called; we will come back to them later when we discuss nonlinear evolution of the r-modes. + On the other hand. the canonical angular momentum of a ltossby wave with /2m. computed from (8.4) of Owen et (1905). is Clearly different from the physical angular momentum.," On the other hand, the canonical angular momentum of a Rossby wave with $l=m$, computed from (3.4) of Owen et (1998), is clearly different from the physical angular momentum." +" ""Phe total kinetic energy of the shell is given by For r-modes with m not equal to zero. the terms linear in P on the right-hand. side of ((13)) vanish after integration over ©."," The total kinetic energy of the shell is given by For r-modes with $m$ not equal to zero, the terms linear in $v$ on the right-hand side of \ref{energy}) ) vanish after integration over $\phi$." +" Therefore. the total cnere of the star with the r-mocdoe is The physical r-mocde energy ££,45,4 is therefore greater than zero."," Therefore, the total energy of the star with the r-mode is The physical r-mode energy $E_{\rm r-mode}$ is therefore greater than zero." + Both this and. Lyase=0 see ((11))] is contrary to the common belief. which holds that Lyusus and Lyyee are both negative.," Both this and $L_{\rm r-mode}=0$ [see \ref{amomentum}) )] is contrary to the common belief, which holds that $E_{\rm r-mode}$ and $L_{\rm r-mode}$ are both negative." + The source. of misunderstanding is the confusion between canonical anc physical quantities. which are not equal to cach other for r-modes.," The source of misunderstanding is the confusion between canonical and physical quantities, which are not equal to each other for r-modes." + In. their seminal. work. Friedman and Schutz (LO7Sa) have shown that canonical quantities are cqual to the physical ones. so long as the Lagrangian change in vorticity is zero to second order in the perturbation amplitude.," In their seminal work, Friedman and Schutz (1978a) have shown that canonical quantities are equal to the physical ones, so long as the Lagrangian change in vorticity is zero to second order in the perturbation amplitude." + The last condition cannot be true for r-mocdes: this fact is intricately connected to the work by Rezzolla. Lamb and Shapiro (1999).," The last condition cannot be true for r-modes; this fact is intricately connected to the work by Rezzolla, Lamb and Shapiro (1999)." + These authors track the motion of a Iuid. particle for the case when the ILuid stream function is given by coxJoo.," These authors track the motion of a fluid particle for the case when the fluid stream function is given by $\psi\propto +Y_{22}$." + They find that the particle experiences a drift along stellar latitude: the speed of the drift depends on the latitude., They find that the particle experiences a drift along stellar latitude; the speed of the drift depends on the latitude. + Pherefore. the authors argue. the presence of an r-mode implies the presence of a differential drift in thestar.," Therefore, the authors argue, the presence of an r-mode implies the presence of a differential drift in the." +.. This is clearly. incompatible with the zero Lagrangian vorticity perturbations: therefore. the Friedman-Schutz condition is not satislied ancl one cannot equate canonical and physical energy ancl angular.," This is clearly incompatible with the zero Lagrangian vorticity perturbations; therefore, the Friedman-Schutz condition is not satisfied and one cannot equate canonical and physical energy and angular." +. Friedman and Schutz (1978b) had shown that the CES instability occurs whenever there is a mode with negative canonical angular momentum. which is dragged Forward by the stellar rotation relative to an inertial observer. and which is coupled. to some radiation field.," Friedman and Schutz (1978b) had shown that the CFS instability occurs whenever there is a mode with negative canonical angular momentum, which is dragged forward by the stellar rotation relative to an inertial observer, and which is coupled to some radiation field." + This radiation field. can, This radiation field can +thev will also show whether they have the same metallicity as the bulge giants. toward sightlines closer to the plane. (hereby providing an independent test and calibration of the metallicity gradient. detected by Zoecaliοἱal.(2008)..,"they will also show whether they have the same metallicity as the bulge giants toward sightlines closer to the plane, thereby providing an independent test and calibration of the metallicity gradient detected by \citet{2008A&A...486..177Z}." + Unfortunately. the method used in most of (his paper cannot be cirectly applied to double-clumip fields. due to the varvine separation between (he two RCs and their varving relative population densities. as well as the fact these varialions are nol vel well-parametrized.," Unfortunately, the method used in most of this paper cannot be directly applied to double-clump fields, due to the varying separation between the two RCs and their varying relative population densities, as well as the fact these variations are not yet well-parametrized." + In. Figure 4. we plot the sum οἱ residuals to the fits of single RCO + RG distribution to thousands of sightlines toward both single-clump fields and double-clump fields., In Figure \ref{Fig:DoubleBump} we plot the sum of residuals to the fits of single RC + RG distribution to thousands of sightlines toward both single-clump fields and double-clump fields. + The residuals for the double-chump fields betray nol only the presence of a second RC. but also of two RGBBs.," The residuals for the double-clump fields betray not only the presence of a second RC, but also of two RGBBs." + The third line of evidence is that the brightness peak of the RGBB we report here. AIBCSS—0.71. is consistent with that expected from stellar evolution models and globular cluster calibrations.," The third line of evidence is that the brightness peak of the RGBB we report here, ${\Delta}I^{RGBB}_{RC}=0.71$, is consistent with that expected from stellar evolution models and globular cluster calibrations." + In their analvsis of 54 Galactic globular clusters observed with HIST. Rielloetal.(2003) reported a difference in brightness AF555 between the RGDD and the Zero Age Horizontal Branch (ZAILID) evaluated at the RR Lyrae instability strip.," In their analysis of 54 Galactic globular clusters observed with HST, \citet{2003A&A...410..553R} reported a difference in brightness ${\Delta}F555W$ between the RGBB and the Zero Age Horizontal Branch (ZAHB) evaluated at the RR Lyrae instability strip." + Thev found that AF555)=0.45 for NGC5927 and 0.53 for NGC6624. two metal-rich globular clusters (Carrettaetal.2009)..," They found that ${\Delta}F555W=0.45$ for NGC5927 and $0.53$ for NGC6624, two metal-rich globular clusters \citep{2009A&A...508..695C}." + For the metallicity of the Galactic bulge. ΑΕΙ &0.0 (Fulbrightal.2008:Densbyet 2010).. (he best-fit model presented by has AF555]V=0.639 mag for a LO Gyr stellar population. and AF555)=0.741 mag for a 12 Gyr stellar population.," For the metallicity of the Galactic bulge, [M/H] $\approx 0.0$ \citep{2006ApJ...636..821F, 2007ApJ...661.1152F, 2008A&A...486..177Z, 2010A&A...512A..41B}, the best-fit model presented by \citet{2003A&A...410..553R} has ${\Delta}F555W=0.639$ mag for a 10 Gyr stellar population, and ${\Delta}F555W=0.741$ mag for a 12 Gyr stellar population." + Similar results are obtained by DiC'eccoetal.(2010) in an investigation of AVPFP [or 15 Galactic globular clusters;, Similar results are obtained by \citet{2010ApJ...712..527D} in an investigation of ${\Delta}V_{ZAHB}^{RGBB}$ for 15 Galactic globular clusters. + We plot various examples from the literature as well as our own in Figure 3.., We plot various examples from the literature as well as our own in Figure \ref{Fig:BumpEmpiricalHistory}. + We introduce the clump-centric coloramagnitude diagram (CCCMDS) as a diagnostic means to study the fine details of large stellar populations in the presence ol differential reddening and geometry., We introduce the clump-centric color-magnitude diagram (CCCMD) as a diagnostic means to study the fine details of large stellar populations in the presence of differential reddening and geometry. + It is the color and magnitude of every star within a large angular range relative to (he nearest RC centroid., It is the color and magnitude of every star within a large angular range relative to the nearest RC centroid. + CAIDs are among the most powerful observational tools in Astronomy., CMDs are among the most powerful observational tools in Astronomy. + Unlortimately. optimizing (heir construction for stellar populations such as that of the Galactic bulge is a non-trivial task.," Unfortunately, optimizing their construction for stellar populations such as that of the Galactic bulge is a non-trivial task." + Over small angular scales. their diagnostic power will be limited by Poisson noise. restricting (lie analysis of a stellar population to only its most prominent features.," Over small angular scales, their diagnostic power will be limited by Poisson noise, restricting the analysis of a stellar population to only its most prominent features." + For exanple. within the CMDs used in our previous work on the double RC (Nataletal.2010).. we used CAIDs just large enough to contain 1200 ποΕμ stars. so as to minimize any possible gradients.," For example, within the CMDs used in our previous work on the double RC \citep{2010ApJ...721L..28N}, we used CMDs just large enough to contain 1200 RC+RG stars, so as to minimize any possible gradients." + With that ummber we would only expect ~30 RGBB stars per sightline.," With that number we would only expect $\sim$ 30 RGBB stars per sightline," +with the observations: discussion of the Padova isochrones is postponed to the next ,with the observations; discussion of the Padova isochrones is postponed to the next sub-section. +The corrected Salaris LF for a model with 11 Gvrs is represented in Figure 3. as the (hin line.," The corrected Salaris LF for a model with 11 Gyrs is represented in Figure \ref{fig3} + as the thin line." + The consequence of correcting our model predictions for (his effect is illustrated as the arrow in Figure 18. for the 9 diagram., The consequence of correcting our model predictions for this effect is illustrated as the arrow in Figure \ref{fig9} for the $$ $H\beta$ diagram. + Since the giant light contribution is increased. (he inleeratecl spectrum becomes redder. metal lines become stronger. ancl hydrogen lines become weaker.," Since the giant light contribution is increased, the integrated spectrum becomes redder, metal lines become stronger, and hydrogen lines become weaker." + With this correction to the LE. the spectroscopic age based on {19 is reduced [rom 2 14 to 11 Gvr. in excellent agreement with the isochrone age in Figure 1..," With this correction to the LF, the spectroscopic age based on $H\beta$ is reduced from $\simgreat$ 14 to 11 Gyr, in excellent agreement with the isochrone age in Figure \ref{fig1}." + We checked the size of the corrections by recomputing the integrated spectrum directly [rom the CMD as in Paper LI. but excluding AGB/RGB stars so as to force agreement with the theoretical uncorrected luminosity [unction.," We checked the size of the corrections by recomputing the integrated spectrum directly from the CMD as in Paper I, but excluding AGB/RGB stars so as to force agreement with the theoretical uncorrected luminosity function." + Differences between the line indices obtained in Paper I and the ones computed with the exclusion of AGD/RGD stars are essentially the same as (he ones obtained adopting the two LEs shown in Figure 3..D which validates the corrections estimated here.," Differences between the line indices obtained in Paper I and the ones computed with the exclusion of AGB/RGB stars are essentially the same as the ones obtained adopting the two LFs shown in Figure \ref{fig3}, which validates the corrections estimated here." + Figures 19. and 20. compare the LE-corrected model predictions with (he observations for the other indices., Figures \ref{fig10} and \ref{fig11} compare the LF-corrected model predictions with the observations for the other indices. + Virtually all line indices are well fit for ages ranging lrom 9 to 14 Qvrs., Virtually all line indices are well fit for ages ranging from 9 to 14 Gyrs. + The best fitting age for 7755-444 is 11.12 Gvrs. in agreement with the age inferred from Jf and CMD-fitting.," The best fitting age for $H\gamma_{\sigma<130}$ is 11–12 Gyrs, in agreement with the age inferred from $H\beta$ and CMD-fitting." + The notable exception is fo). for which the best-fit(àng age is slightly higher: ~ 14 Gyrs.," The notable exception is $H\delta_F$, for which the best-fitting age is slightly higher: $\sim$ 14 Gyrs." +" The latter result was anticipated in Paper I. because the model spectrum computed directly from the CMD of the cluster also overestimates fd). and when we considered the correction of 178, due to the effect of CN-strong stars. (he mismatch was further increased."," The latter result was anticipated in Paper I, because the model spectrum computed directly from the CMD of the cluster also overestimates $H\delta_F$, and when we considered the correction of $H\delta_F$ due to the effect of CN-strong stars, the mismatch was further increased." +" However. as discussed in Section 5.3 of Paper I. we have reason to believe that our correction for this effect on 770, may be in error."," However, as discussed in Section 5.3 of Paper I, we have reason to believe that our correction for this effect on $H\delta_F$ may be in error." + In any case it was already. clear in Paper L that £795 was aberrant., In any case it was already clear in Paper I that $H\delta_F$ was aberrant. + All the metal-line indices are well fit bv models with ages of 11-12 Gvrs. including Ca4227. which was greatly improved alter correction for the ellect of CN-line contamination. derived in Paper I. Finally. (he integrated of the cluster is also matched [or an age of 11 Givis.," All the metal-line indices are well fit by models with ages of 11-12 Gyrs, including Ca4227, which was greatly improved after correction for the effect of CN-line contamination, derived in Paper I. Finally, the integrated of the cluster is also matched for an age of 11 Gyrs." + The ratio of the contribution to the integrated light of turn-olff stars to giant stars (IID stars excluded) provides a good gauge of the impact of the underestimate of the number of bright stars in the theoretical isochrone., The ratio of the contribution to the integrated light of turn-off stars to giant stars (HB stars excluded) provides a good gauge of the impact of the underestimate of the number of bright stars in the theoretical isochrone. + In Paper I we computed the fractional contribution io the integrated light bv dillerent evolutionary stages at a number of reference wavelengths., In Paper I we computed the fractional contribution to the integrated light by different evolutionary stages at a number of reference wavelengths. + Those nunbers are given in Table 5 of Paper I. They are fairly robust. since they are based on a statistically representative CMD of the cluster.," Those numbers are given in Table 5 of Paper I. They are fairly robust, since they are based on a statistically representative CMD of the cluster." +" From Table 5 of Paper 1. it can be seen that the ratio of turn-off light to giant light is 0.50 and 0.23 in the regions of (fo, and {1 respectively."," From Table 5 of Paper I, it can be seen that the ratio of turn-off light to giant light is 0.50 and 0.28 in the regions of $H\delta_F$ and $H\beta$ respectively." + If the uncorrected theoretical LF is adopted. those figures change to 0.77 and 0.47 respectively.," If the uncorrected theoretical LF is adopted, those figures change to 0.77 and 0.47 respectively." + data reduction was done using the SAS version 7.1.0., data reduction was done using the SAS version 7.1.0. + In order to produce a homogeneously calibrated data set. we processed all the observations using the observation data files with the latest calibration files as of March 2008.," In order to produce a homogeneously calibrated data set, we processed all the observations using the observation data files with the latest calibration files as of March 2008." +" The reduction was done according to the User's guide to the Science Analysis Specifically. we used the event selections “FLAG==0 PATTERN <=4"" and “#XXMMEA_EEM PATTERN<=12"" for the EPIC-pn and EPIC-mos instruments. respectively."," The reduction was done according to the User's guide to the Science Analysis Specifically, we used the event selections $==$ 0 $<=$ 4"" and EM $<=$ 12"" for the EPIC-pn and EPIC-mos instruments, respectively." + observations were reduced using the CIAO 3.0.1 software., observations were reduced using the CIAO 4.0.1 software. + We processed all the observations with calibration files from CALDB 3.4.3 following the science We used cireular source extraction regions of varying radii (between 207 to 407 for and 47 to 127 for Chandra)., We processed all the observations with calibration files from CALDB 3.4.3 following the science We used circular source extraction regions of varying radii (between 20” to 40” for and 4” to 12” for ). + Close-by source free regions were used as a The resulting background subtracted spectral data were binned to require at least 20 counts per bin to ensure adequate statistics for the XSPEC spectral fitting., Close-by source free regions were used as a The resulting background subtracted spectral data were binned to require at least 20 counts per bin to ensure adequate statistics for the XSPEC spectral fitting. + To ensure the best possible spectral quality. the time periods of high background were eliminated from the dati for both and observations.," To ensure the best possible spectral quality, the time periods of high background were eliminated from the data for both and observations." + In the case of the exclusion was done by removing the time periodu where the 12 keV full field count rate was above 0.4 cts -- and 0.35 ets + for EPIC pn and mos. respectively.," In the case of the exclusion was done by removing the time periods where the $-$ 12 keV full field count rate was above 0.4 cts $^{-1}$ and 0.35 cts $^{-1}$ for EPIC pn and mos, respectively." + ForChandra. we used the Script on a source free event file to remove the high background periods.," For, we used the script on a source free event file to remove the high background periods." + We used three models to describe the observed spectra: aPOWERLAW. a MCD model in XSPEC) and a combination of these two models.," We used three models to describe the observed spectra: a, a MCD model in XSPEC) and a combination of these two models." + The effect of the interstellar medium was taken into account with the model in XSPEC., The effect of the interstellar medium was taken into account with the model in XSPEC. + The hydrogen column density was let as a free parameter. but was required to have at least the Galactic value (Dickey&Lock-man 1990).," The hydrogen column density was let as a free parameter, but was required to have at least the Galactic value \citep{DL90}." +. In some cases. none of these simple models gave statistically acceptable fits to the data.," In some cases, none of these simple models gave statistically acceptable fits to the data." + In most of these cases. the fits could have been improved by adding more model components like gaussians at 1 keV (NGC 5204 ULX-1. OBSID 3933. see Robertsetal.(2006): NGC 5408 ULX-1. OBSID 0302900101) or by changing metal abundances of the absorber (HoT ULX-I. see Goadetal. (200611).," In most of these cases, the fits could have been improved by adding more model components like gaussians at $\lesssim 1$ keV (NGC 5204 ULX-1, OBSID 3933, see \citet{RKW06}; NGC 5408 ULX-1, OBSID 0302900101) or by changing metal abundances of the absorber (HoII ULX-1, see \citet{GRR06}) )." + We checked that our best fitting parameters did not change significantly by adding these components. so we decided to ignore these facts. because we wanted to keep our models as simple as possible.," We checked that our best fitting parameters did not change significantly by adding these components, so we decided to ignore these facts, because we wanted to keep our models as simple as possible." + We fit the spectra in the 10 keV band (tor up to energies which are not noise dominated)., We fit the spectra in the $-$ 10 keV band (or up to energies which are not noise dominated). + XMM-Newton provides spectral coverage down to 0.2 keV. but we decided to restrict our fitting range to 0.4 keV because of the known calibration uncertainties below this All the parameter errors in the following figures are given at the 90 per cent confidence level.," XMM-Newton provides spectral coverage down to $\sim 0.2$ keV, but we decided to restrict our fitting range to 0.4 keV because of the known calibration uncertainties below this All the parameter errors in the following figures are given at the $90$ per cent confidence level." + The errors for the fluxes were computed using the convolution model in XSPEC., The errors for the fluxes were computed using the convolution model in XSPEC. + In the case of the model. the luminosities were calculated for the 10 keV band.," In the case of the model, the luminosities were calculated for the $-$ 10 keV band." + The MCD component luminosities are bolometric., The MCD component luminosities are bolometric. + A simple absorbed model provides a good fit for most of the observations in our sample (see Table A13)., A simple absorbed model provides a good fit for most of the observations in our sample (see Table \ref{bestfits}) ). + We find a correlation between the luminosity and the photon index (hereafter LxV correlation) for most of the ULXs. see Fig. l..," We find a correlation between the luminosity and the photon index (hereafter $\Lx-\Gamma$ correlation) for most of the ULXs, see Fig. \ref{pofitresults}. ." + Similar correlations— were also observed for NGC 1313 ULX-I (Feng&Kaaret2006b) and Antennae X-11 (Feng&Kaaret2006a)., Similar correlations were also observed for NGC 1313 ULX-1 \citep{FeKa06} and Antennae X-11 \citep{FeKa06b}. +. The ULXs with the Zx—EL correlation are NGC 253 X-4. IC 342 X- NGC 1313 ULX-I. Holmberg II ULX-1. Holmberg IX ULX-I. GC 5204 ULX-1 and NGC 5408 ULX-I.," The ULXs with the $\Lx-\Gamma$ correlation are NGC 253 X-4, IC 342 X-6, NGC 1313 ULX-1, Holmberg II ULX-1, Holmberg IX ULX-1, NGC 5204 ULX-1 and NGC 5408 ULX-1." + In contrast. two ULXs of the sample. NGC 253 X-? and NGC 1313 ULX-2. show an correlation between the luminosity and L (seeFig.| and Feng&Kaaret2006a.b.for comparison).," In contrast, two ULXs of the sample, NGC 253 X-2 and NGC 1313 ULX-2, show an anti-correlation between the luminosity and $\Gamma$ \citep[see Fig. \ref{pofitresults} and ][for ." + We also tind that the luminosity of NGC 253 X-9 is clearly not correlated with Land that NGC 6946 X-6 is not significantly variable to make firm conclusions., We also find that the luminosity of NGC 253 X-9 is clearly not correlated with $\Gamma$ and that NGC 6946 X-6 is not significantly variable to make firm conclusions. + For NGC 1313 ULX-I. Holmberg IX ULX-1 and NGC 5204 ULX-1. the modelled absorption column ;Vg is also correlated with | (seealsofig.|inFeng&Kaaret2009.forNGC5204ULX-1)..," For NGC 1313 ULX-1, Holmberg IX ULX-1 and NGC 5204 ULX-1, the modelled absorption column $\NH$ is also correlated with $\Gamma$ \citep[see also fig. 1 in][for NGC 5204 ULX-1]{FK09}." +" If this correlation has no physical origin. then the luminosities of the softest spectra would be ""artificially boosted’."," If this correlation has no physical origin, then the luminosities of the softest spectra would be `artificially boosted'." + To evaluate this effect on the derived luminosities. we fixed the absorption columns to their mean values. and fitted the data again.," To evaluate this effect on the derived luminosities, we fixed the absorption columns to their mean values, and fitted the data again." + This leadto somewhat worse fits for the cases where the best fitting absorption columns differ most from the mean. but the Lx{ correlations," This leadto somewhat worse fits for the cases where the best fitting absorption columns differ most from the mean, but the $\Lx-\Gamma$ correlations" +In the 1970s a series of studies showed the existence of filamentary distribution of galaxies in clusters ancl superclusters and large void. regions. among such filaments.,In the 1970s a series of studies showed the existence of filamentary distribution of galaxies in clusters and superclusters and large void regions among such filaments. +. Gregory Thompson (1978) found in galaxy redshift surveys. in the direction of the Coma cluster. a filamentary structure that is. part. of the nowadays. denominated “Great Wall (Geller Lluchra 1989).," Gregory Thompson (1978) found in galaxy redshift surveys, in the direction of the Coma cluster, a filamentary structure that is part of the nowadays denominated `Great Wall' (Geller Huchra 1989)." + Εμίν supercluster is encompassed by a large region of low mass density (or void)., This supercluster is encompassed by a large region of low mass density (or void). +" Additional investigations by Gregory. Thompson Vult (1981) and. Chincarini. Rood “Phompson (1951) showed similar results for the Hercules and. Perseus-Disces superelusters and. later. other redshift surveys showed that the superclusters are. boundaries. of uncercense regions ""m(Ciovanelli. Haynes Chincarini 1986: de Lapparent. Geller &Iuchra 1986: ca Costa ct al."," Additional investigations by Gregory, Thompsom Tifft (1981) and Chincarini, Rood Thompson (1981) showed similar results for the Hercules and Perseus-Pisces superclusters and, later, other redshift surveys showed that the superclusters are boundaries of underdense regions (Giovanelli, Haynes Chincarini 1986; de Lapparent, Geller Huchra 1986; da Costa et al." + LOSS)., 1988). + A redshift’ survey in the Doóttes region (Ixirshner et al., A redshift survey in the Boöttes region (Kirshner et al. + 981) discovered a large void structure whose estimat«xd dianjeter is ~605.tAlpe.," 1981) discovered a large void structure whose estimated diameter is $ +\sim 60h^{-1}{\rm Mpc}$." + Later. observations showed iial (his region in Bobttes is not totally empty of matter - it conains some galaxies (Lhuan. Gott Schneider 1987: Dev. Strauss Huchra 1990).," Later, observations showed that this region in Boöttes is not totally empty of matter - it contains some galaxies (Thuan, Gott Schneider 1987; Dey, Strauss Huchra 1990)." + In spite of this. the void in Boottes has a lower mass density as compared to the mass density oftjo Universe.," In spite of this, the void in Boöttes has a lower mass density as compared to the mass density of the Universe." + In particular. Dew et al. (," In particular, Dey et al. (" +1990) found. 21 galaxies (of whichi: 13 areAS sources) in Boottes. which led the authors to estimate the average density contrast of this region to,"1990) found 21 galaxies (of which 13 are sources) in Boöttes, which led the authors to estimate the average density contrast of this region to" +the most energetic particles can be found.,the most energetic particles can be found. +" Since we probe the region upstream at a diffusion length for Emax, this is where the peak of the upstream spectrum is found."," Since we probe the region upstream at a diffusion length for $E_{\rm max}$, this is where the peak of the upstream spectrum is found." +" At the same distance downstream, the slope of the spectrum is slightly steeper than at the shock."," At the same distance downstream, the slope of the spectrum is slightly steeper than at the shock." +" The spectrum is loss-limited for the electrons, as is evident from the sharper cut-off."," The spectrum is loss-limited for the electrons, as is evident from the sharper cut-off." +" In (semi-)analytical models, the spectrum at the shock in the presence of losses is often described by (e.g. ?):: with a=1 for protons and a=2 for electrons."," In (semi-)analytical models, the spectrum at the shock in the presence of losses is often described by \citep[e.g.][]{2001MalkovDrury}: : with $\alpha=1$ for protons and $\alpha=2$ for electrons." + We find that the simulated spectra quite nicely follow this exponential cut-off prescription for the cumulative particle spectrum., We find that the simulated spectra quite nicely follow this exponential cut-off prescription for the cumulative particle spectrum. +" At the shock, the cut-off for protons is slightly sharper than usually assumed: we find aού1.2—1.3."," At the shock, the cut-off for protons is slightly sharper than usually assumed: we find $\alpha \approx 1.2-1.3$." +" For electrons, the cut-off is less sharp, but still sharper than for protons: it closely follows o£z1.7."," For electrons, the cut-off is less sharp, but still sharper than for protons: it closely follows $\alpha \approx 1.7$." + This will depend on to what extent the electron spectrum isterminated by synchrotron losses., This will depend on to what extent the electron spectrum isterminated by synchrotron losses. +forbidden line. are found to be strong throughout the 2009 oobservation of4051.,"forbidden line, are found to be strong throughout the 2009 observation of." +. The low centroid velocity of the OVILE Lyman-a broad line is consistent with an origin in the limb-brightened shell of post-shock gas. with emission from the near-orthogonal component of the [low seen in continuum. absorption at ~5000 kin," The low centroid velocity of the OVIII $\alpha$ broad line is consistent with an origin in the limb-brightened shell of post-shock gas, with emission from the near-orthogonal component of the flow seen in continuum absorption at $\sim$ 5000 km $^{-1}$." + The same limb-brightened gcometry provides a natural explanation for the sharp onset of absorption to the blue side of zero velocity. found in all individual velocity. profiles. being interpreted as a consequence of the radial Dow through the limb-brightened shell leading all absorbing gas to have a blue shift relative to the source of emission.," The same limb-brightened geometry provides a natural explanation for the sharp onset of absorption to the blue side of zero velocity, found in all individual velocity profiles, being interpreted as a consequence of the radial flow through the limb-brightened shell leading all absorbing gas to have a blue shift relative to the source of emission." + The detection of RRC of. NVLE and CVE which vary in both flux ancl velocity profile. as the continuum level changes. has vielded an important measure. of the recombination timescale for ionised gas in the related high velocity How.," The detection of RRC of NVII and CVI which vary in both flux and velocity profile, as the continuum level changes, has yielded an important measure of the recombination timescale for ionised gas in the related high velocity flow." + Breaking the degeneracy between radius and particle density. that so often limits the assessment. of AGN outllows. has allowed the radius and thickness of the shell of post-shock gas to be estimated. and in turn has confirmed that the high velocity How is able to recombine sulliciently fast to maintain the observed correlation of ionisalion parameter and velocity reported in Paper I. Strone low velocity absorption renders. the OVIIL resonance line essentially unconstrained. and leads to narrow components of OVILE Lyman-a and other resonance lines in ((and perhaps more generally in tvpe E Sevferts) to be poorly determined.," Breaking the degeneracy between radius and particle density, that so often limits the assessment of AGN outflows, has allowed the radius and thickness of the shell of post-shock gas to be estimated, and in turn has confirmed that the high velocity flow is able to recombine sufficiently fast to maintain the observed correlation of ionisation parameter and velocity reported in Paper I. Strong low velocity absorption renders the OVII resonance line essentially unconstrained, and leads to narrow components of OVIII $\alpha$ and other resonance lines in (and perhaps more generally in type I Seyferts) to be poorly determined." + Together with the observational dillicultv of detecting. much broader. (and. hotter). RRC. we conclude hat a significant. thermal contribution to the soft. X-ray emission of4051.. cannot be ruled out.," Together with the observational difficulty of detecting much broader (and hotter) RRC, we conclude that a significant thermal contribution to the soft X-ray emission of, cannot be ruled out." + Nevertheless. with the relatively low particle densities in the post-shock low. two-bocky cooling is likely to remain less important I=an Compton cooling which we have argued (Paper L. Ixing 2003) will be strong so close to the AGN continuum.," Nevertheless, with the relatively low particle densities in the post-shock flow, two-body cooling is likely to remain less important than Compton cooling which we have argued (Paper I, King 2003) will be strong so close to the AGN continuum." + The results. reported. here are. based. on observations obtained with.XAZAZ-Neiwlon.. an ESA science mission with instruments ancl contributions cirectly funded. by ESA Alember States and the USA (NASA).," The results reported here are based on observations obtained with, an ESA science mission with instruments and contributions directly funded by ESA Member States and the USA (NASA)." + The authors wish to thank Andrew Ixing anc Alike Goad for useful discussions. the referee for a careful reading of the manuscript. ancl the SOC and SSC teams for organising the oobservations and initial data reduction.," The authors wish to thank Andrew King and Mike Goad for useful discussions, the referee for a careful reading of the manuscript, and the SOC and SSC teams for organising the observations and initial data reduction." + In this section we describe the method used to produce the line velocity. profiles which are the basis of the analysis in this paper., In this section we describe the method used to produce the line velocity profiles which are the basis of the analysis in this paper. + We choose the velocity. plots as they provide a convenient (and accurate) wav of combining different cata sets. and. present the parameters of interest in the directly relevant velocity. coordinates.," We choose the velocity plots as they provide a convenient (and accurate) way of combining different data sets, and present the parameters of interest in the directly relevant velocity coordinates." + Each ROS observation was first processed. usingRGSPROC to produce a set of first-order source and background spectra. along with appropriate response matrices. from each of RGSI and ROS2. with 3400 wavelength channels.," Each RGS observation was first processed using to produce a set of first-order source and background spectra, along with appropriate response matrices, from each of RGS1 and RGS2, with $3400$ wavelength channels." + The simplest way to produce a velocity. profile. for several lines [rom several observations is to sum the counts in cach spectral channel across the observations. transform he wavelengths of the channels around each line of interest o velocity shifts relative to the (source-[ramoe) wavelength of the line. anc then average (or sum) over the cdilferent ines.," The simplest way to produce a velocity profile for several lines from several observations is to sum the counts in each spectral channel across the observations, transform the wavelengths of the channels around each line of interest to velocity shifts relative to the (source-frame) wavelength of the line, and then average (or sum) over the different lines." + Unfortunately this simple procedure is complicated by hree facts about the RGS data., Unfortunately this simple procedure is complicated by three facts about the RGS data. + Firstly. the ROS ellective area can change sharply due to bad. pixels. columns. or even whole CCDs.," Firstly, the RGS effective area can change sharply due to bad pixels, columns or even whole CCDs." + Secondly. small differences in. pointing tween the observations mean that the wavelength-channel conversion dillers slightly. between observations. (," Secondly, small differences in pointing between the observations mean that the wavelength-channel conversion differs slightly between observations. (" +At least. his is true for the standard products produced bx RGSPROC).,"At least, this is true for the standard products produced by )." + And thirdlv. the wavelength. resolution of the R&S is approximately constant across the spectral range. meaning hat the velocity resolution dillers for lines at cillerent wavelengths.," And thirdly, the wavelength resolution of the RGS is approximately constant across the spectral range, meaning that the velocity resolution differs for lines at different wavelengths." +" Taken together the first two facts mean that co-adding spectra by summing the counts in cach channel will result in a degradation (blurring) of the line response unction. and may produce spurious line-like features (clue ο narrow ""drop outs” in the spectra) if not corrected. using an ellective area curve computed for the merged data."," Taken together the first two facts mean that co-adding spectra by summing the counts in each channel will result in a degradation (blurring) of the line response function, and may produce spurious line-like features (due to narrow “drop outs” in the spectra) if not corrected using an effective area curve computed for the merged data." + The hird point means that the velocity bins for one line will not x: well matched to those of other lines. making it cdillicult o average the counts in velocity bins over dillerent lines.," The third point means that the velocity bins for one line will not be well matched to those of other lines, making it difficult to average the counts in velocity bins over different lines." + The solution we employ is to convert cach spectrum. rom counts per channel. with a corresponding channel to wavelength range conversion. to a list. of wavelengths for each event.," The solution we employ is to convert each spectrum from counts per channel, with a corresponding channel to wavelength range conversion, to a list of wavelengths for each event." + We do this by randomising the wavelength, We do this by randomising the wavelength +Galaxy interactions are considered a Κον process in galaxy formation since these violent events could. be able. to redistribute mass and angular momentum very. efficiently (e.g.Barnes&Hernquist1996:Tissera2000:DiMatteoetal. 2008).,"Galaxy interactions are considered a key process in galaxy formation since these violent events could be able to redistribute mass and angular momentum very efficiently \citep[e.g.][]{BH96,tissera00,dimatteo08}." +. As a consequence. chemical elements can be stirred up alfecting their distribution. ancl metallicity patterns such as gradients.," As a consequence, chemical elements can be stirred up affecting their distribution and metallicity patterns such as gradients." + Phere are numerous observational works dedicated to the study of galaxy pairs2011)., There are numerous observational works dedicated to the study of galaxy pairs. +. ut only in the last few vears. i has en. possible to focus on the elfects of galaxy interactions on chemical abundances.," But only in the last few years, it has been possible to focus on the effects of galaxy interactions on chemical abundances." + Interacting galaxies. galaxy pairs. ultra-Iuminous infrared. galaxies. and merger remnants have ovn found to exhibit low gas-phase metallicity at a given stellar mass compared with the mean mass-metalicity relation (c.g.Ixewlevetal.2006:πάρκο2008:LLal.2009:SolAlonsoet 2010).," Interacting galaxies, galaxy pairs, ultra-luminous infrared galaxies, and merger remnants have been found to exhibit low gas-phase metallicity at a given stellar mass compared with the mean mass-metallicity relation \citep[e.g.][]{KGB06,rupke08,ellison08,LMD08,peeples09,alonso10}." +. Recently. Ixewlev.οἱal.(2010) analysecl the metallicity gradients of galaxy," Recently, \citet{kewley10} analysed the metallicity gradients of galaxy" +fixed to 1.0 because all light curve solutions converged at this value.,fixed to $1.0$ because all light curve solutions converged at this value. + The bolometric albedo of the primary was also fixed to 1.0., The bolometric albedo of the primary was also fixed to $1.0$. + The (temperature of the sdB was taken from the spectral analvsis (Zig(1)=26Ix 000).," The temperature of the sdB was taken from the spectral analysis $T_{\rm eff}(1)=26\,000\,{\rm K}$ )." + The remaining adjustable parameters are (he inclination. the temperature of the second component (Z;5(2)). the Roche potentials (0455). the bolometric albedo of the secondary (ls). the radiation pressure parameter (04) ancl the liminosity of the hot component.," The remaining adjustable parameters are the inclination, the temperature of the second component $T_{\rm eff}(2)$ ), the Roche potentials $\Omega_{1,2}$ ), the bolometric albedo of the secondary $A_{2}$ ), the radiation pressure parameter $\delta_1$ ) and the luminosity of the hot component." + The fractional Roche radii (743) in units of the orbital separation @ were calculated using the Roche potentials and (he mass ratio q.," The fractional Roche radii $r_{1,2}$ ) in units of the orbital separation $a$ were calculated using the Roche potentials and the mass ratio $q$." + We used (he binary mass functüon derived from spectroscopy to ealeulate possible mass ratios for a range of primary masses., We used the binary mass function derived from spectroscopy to calculate possible mass ratios for a range of primary masses. + A grid of light curve solutions with different mass ratios was calculated., A grid of light curve solutions with different mass ratios was calculated. + In order to derive errors we created 500 new datasets wilh a bootstrapping algoritlim bv ταο sampling with replacement from the original dataset., In order to derive errors we created $500$ new datasets with a bootstrapping algorithm by random sampling with replacement from the original dataset. + In each case a light curve solution was caleulated in the wav described above., In each case a light curve solution was calculated in the way described above. + The standard deviations of these results were adopted as the error estimates for the parameters., The standard deviations of these results were adopted as the error estimates for the parameters. + The flat-bottomed eclipses. and the way the secondary. eclipses reach down to the flux level just before and after primary eclipse. indicate Chat the secondary is totally eclipsed by ihe primary.," The flat-bottomed eclipses, and the way the secondary eclipses reach down to the flux level just before and after primary eclipse, indicate that the secondary is totally eclipsed by the primary." + The eclipses ensure that the inclination of the svstem and (he relative radii of the components are very well constrained. but the usual degeneracy still remains in the mass ralio and the ratio of the components. radii and (he size of the orbit.," The eclipses ensure that the inclination of the system and the relative radii of the components are very well constrained, but the usual degeneracy still remains in the mass ratio and the ratio of the components' radii and the size of the orbit." + Table 1. shows light curve solutions for the most likely sdB masses after combining the photometric and spectroscopic analvses., Table \ref{tab:par} shows light curve solutions for the most likely sdB masses after combining the photometric and spectroscopic analyses. + Fig., Fig. + 2. shows an example model fit to the light curve., \ref{light} shows an example model fit to the light curve. + Atmospheric parameters have been determined by fitting a grid of svuthetic spectra. calculated from line-blanketecl. solax-netalicity LEE model atiospheres (Lleberetal.2000).. to the hvdrogen Balmer and helium lines ofthe SDSS and SOAR. spectra in the wav described in Geieretal.(2010a).," Atmospheric parameters have been determined by fitting a grid of synthetic spectra, calculated from line-blanketed, solar-metalicity LTE model atmospheres \citep{heber00}, to the hydrogen Balmer and helium lines of the SDSS and SOAR spectra in the way described in \citet{geier10}." +. The single spectra have been corrected for their orbital motion and coacdcded., The single spectra have been corrected for their orbital motion and coadded. + In order to investigate svstematic effects introduced by the individual instruments. especially the dillerent resolutions and wavelength coverages. (he parameters have been derived separately [roii spectra taken wilh SDSS (S/N=8S3. fug=26000&1000Ix. logg=5.37dE 0.14) and SOAR (S/N=61. Tuy=269004300K. lopg=5.514 0.04). respectively.," In order to investigate systematic effects introduced by the individual instruments, especially the different resolutions and wavelength coverages, the parameters have been derived separately from spectra taken with SDSS $S/N=83$, $T_{\rm eff}=26000\pm1000\,{\rm K}$, $\log{g}=5.37\pm0.14$ ) and SOAR $S/N=61$, $T_{\rm eff}=26900\pm300\,{\rm K}$, $\log{g}=5.51\pm0.04$ ), respectively." + The weighted mean values have been calculated and adopted as final solutions (see Table 1))., The weighted mean values have been calculated and adopted as final solutions (see Table \ref{tab:par}) ). + The contribution of light [rom the irradiated surface of the cool companion in Vir, The contribution of light from the irradiated surface of the cool companion in Vir +region.,region. + Tables of the central beam positions in each survey are included in the supporting online material., Tables of the central beam positions in each survey are included in the supporting online material. +" A large observing bandwidth of 576 MHz, covered by a series of 192 filterbank channels each of width 3 MHz, was used in order to counteract the effects of interstellar dispersion."," A large observing bandwidth of 576 MHz, covered by a series of 192 filterbank channels each of width 3 MHz, was used in order to counteract the effects of interstellar dispersion." +" This dispersion causes a time delay in seconds, across an observing bandwidth of Av which is centred at frequency v (both in MHz)."," This dispersion causes a time delay in seconds, across an observing bandwidth of $\Delta\nu$ which is centred at frequency $\nu$ (both in MHz)." +" During each pointing, the data were one-bit sampled every 125us, written to a local computer disk at the Parkes site and, once the pointing was completed, were written to DLT-S4 tape."," During each pointing, the data were one-bit sampled every $125\,\mu \mathrm{s}$, written to a local computer disk at the Parkes site and, once the pointing was completed, were written to DLT-S4 tape." +" This amounted to ~5 TB of data, which were subsequently processed offline at the Jodrell Bank Observatory, while a second copy of the survey was kept on tape at the the Australia Telescope National Facility for backup and for quick access to data in the event of discoveries."," This amounted to $\sim$ 5 TB of data, which were subsequently processed offline at the Jodrell Bank Observatory, while a second copy of the survey was kept on tape at the the Australia Telescope National Facility for backup and for quick access to data in the event of discoveries." +" The limiting flux density, in mJy, of a pulsar search can be calculated by In this expression (S/N)min is the minimum detectable signal-to-noise ratio, 6 is the degradation factor which takes into account effects such as signal digitisation, Ty; is the system temperature (defined as the sum of the sky, spillover and receiver temperatures), G is the telescope gain, np is the number of polarisations summed (np= 2), toys is the observation time and Av is the bandwidth in MHz."," The limiting flux density, in mJy, of a pulsar search \citep[see][]{dewey1985} can be calculated by In this expression $(S/N)_{\rm min}$ is the minimum detectable signal-to-noise ratio, $\beta$ is the degradation factor which takes into account effects such as signal digitisation, $T_{\rm sys}$ is the system temperature (defined as the sum of the sky, spillover and receiver temperatures), $G$ is the telescope gain, $n_{\rm p}$ is the number of polarisations summed $n_p = 2$ ), $t_{\rm obs}$ is the observation time and $\Delta\nu$ is the bandwidth in MHz." +" P, the pulse period, and Weg, the effective pulse width as defined in equation (5)), are properties of the pulsar to be detected, rather than survey parameters."," P, the pulse period, and $_{\rm eff}$, the effective pulse width as defined in equation \ref{weffeq}) ), are properties of the pulsar to be detected, rather than survey parameters." + Fig., Fig. +" 4 shows the computed sensitivity curves for dispersion measures of 0 and 1000cmpc respectively, using a mean sky temperature of 0.5 K, assuming? 8."," \ref{sens_plot} shows the computed sensitivity curves for dispersion measures of 0 and $1000\,\mathrm{cm}^{-3}\,\mathrm{pc}$ respectively, using a mean sky temperature of 0.5 K, assuming $S/N_{\rm min}=8$ ." +" The intrinsic width of the pulse is assumed to be and we use the scattering model of ?,, shown in equation (6))."," The intrinsic width of the pulse is assumed to be and we use the scattering model of \citet{bcc+04}, shown in equation \ref{bhatscatter}) )." +" The curves indicate that at periods greater than about 10 ms, the sensitivity is approximately 0.15 mJy."," The curves indicate that at periods greater than about 10 ms, the sensitivity is approximately 0.15 mJy." +" It is also evident that the large change in DM between the two curves results in a very small change in limiting sensitivity at periods above ~100 ms, which is an effect of the high observing frequency used in this survey, discussed further in Section ??.."," It is also evident that the large change in DM between the two curves results in a very small change in limiting sensitivity at periods above $\sim$ 100 ms, which is an effect of the high observing frequency used in this survey, discussed further in Section \ref{sec:high_f}." +" For the Galactic-centre region, the sensitivity is affected by the background temperature of the Galactic centre itself."," For the Galactic-centre region, the sensitivity is affected by the background temperature of the Galactic centre itself." +" Using the maps of ?,, we estimate this contribution to be ~4 K in the outer regions of the survey, ~12 K in the inner regions and ~90 K at the GC."," Using the maps of \citet{seiradakis1989}, we estimate this contribution to be $\sim$ 4 K in the outer regions of the survey, $\sim$ 12 K in the inner regions and $\sim$ 90 K at the GC." +" The detection threshold of S/Nmin=9 is then ~28 uJy (outer regions), ~32 Jy (inner regions) and ~81 uJy at the GC."," The detection threshold of $S/N_{\rm min}=9$ is then $\sim$ 28 $\mu$ Jy (outer regions), $\sim$ 32 $\mu$ Jy (inner regions) and $\sim$ 81 $\mu$ Jy at the GC." +" The processing pipeline used the SIGPROC-4.2 software to perform dedispersion of the data up to a DM of 2000οπιpc — chosen to ensure the survey was capable of observing 5pulsars at the Galactic centre — using a DM step size of 7.18cm?pc, derived from equation (3)), ensuring that the residual dispersive time delay between the highest and lowest frequency channels is no greater than one sample."," The processing pipeline used the SIGPROC-4.2 software to perform dedispersion of the data up to a DM of $2000\,\mathrm{cm}^{-3}\,\mathrm{pc}$ — chosen to ensure the survey was capable of observing pulsars at the Galactic centre — using a DM step size of $7.18\,\mathrm{cm}^{-3}\,\mathrm{pc}$, derived from equation \ref{dispersion}) ), ensuring that the residual dispersive time delay between the highest and lowest frequency channels is no greater than one sample." +" These dedispersed time series were fast Fourier-transformed (FFT), and the spectrum was searched for significant peaks, as were spectra with 2, 4, 8 and 16 harmonics summed in order to ensure power was obtained from narrow pulses (?).."," These dedispersed time series were fast Fourier-transformed (FFT), and the spectrum was searched for significant peaks, as were spectra with 2, 4, 8 and 16 harmonics summed in order to ensure power was obtained from narrow pulses \citep{mld+95}." +" The Pulsar Hunter was then used to search in period and DM space around the values output from the FFT search, in order to maximise the S/N ratio of each candidate."," The Pulsar Hunter was then used to search in period and DM space around the values output from the FFT search, in order to maximise the S/N ratio of each candidate." +" The pipeline was run on ‘DCore’, a beowulf cluster with"," The pipeline was run on `DCore', a beowulf cluster with" +An examination of Figure 20. highlights eurious differences between these (wo regions.,An examination of Figure \ref{contour3109} highlights curious differences between these two regions. + 11 contains very weak [Ne II] 12.8 san emission: it clearly harbors an embedded LR source. since it is has no associated UV emission. is fairly weak in the IRAC & san band. but very luminous at 24 jan. This suggests a cool thermal dust component at this location.," 1 contains very weak [Ne II] 12.8 $\mu$ m emission; it clearly harbors an embedded IR source, since it is has no associated UV emission, is fairly weak in the IRAC 8 $\mu$ m band, but very luminous at 24 $\mu$ m. This suggests a cool thermal dust component at this location." + Taken together. these properties suggest that (he radiation field strength is low at the location of 1l and that the PÀIIs present have a significant neutral component.," Taken together, these properties suggest that the radiation field strength is low at the location of 1 and that the PAHs present have a significant neutral component." + 33 and 4 are in close physical proximity ancl present an interesting local environment with significant variations over small physical scales., 3 and 4 are in close physical proximity and present an interesting local environment with significant variations over small physical scales. + ΕΕ is very. bright in the IRAC 8 yan band and is coincident with a high surface brightness optical cluster., 4 is very bright in the IRAC 8 $\mu$ m band and is coincident with a high surface brightness optical cluster. + 33 is much fainter at 8 yan. vet it has the largest [Ne H]/(PALD) ratios of any of the regions in 33109.," 3 is much fainter at 8 $\mu$ m, yet it has the largest [Ne II]/(PAH) ratios of any of the regions in 3109." + Despite these dramatic changes in environmental properties. (he ratios of PAIL features presented in Table 7 are statistically indistinguishable.," Despite these dramatic changes in environmental properties, the ratios of PAH features presented in Table \ref{ratios3109_1} are statistically indistinguishable." + Even a cursory exaanination of the panels in Figure 20. highlights the complexity of the relationship between PAIL emission and local properties in galaxies (e.g.. slope of the local infrared spectral energy distribution (SED). UV intensity. infrared. emission line radiance. ete.).," Even a cursory examination of the panels in Figure \ref{contour3109} highlights the complexity of the relationship between PAH emission and local properties in galaxies (e.g., slope of the local infrared spectral energy distribution (SED), UV intensity, infrared emission line radiance, etc.)." + The data for NGC/323109. while only available for selected regions. provides support lor the hypothesis of constant PALI ratios within dwarl galaxies.," The data for 3109, while only available for selected regions, provides support for the hypothesis of constant PAH ratios within dwarf galaxies." + We examine ten 52.5 pe radius apertures within the observed reeion of 55152., We examine ten 52.5 pc radius apertures within the observed region of 5152. + The extracted PAIL/PAIL radiance ratios are presented in Table 9.., The extracted PAH/PAH radiance ratios are presented in Table \ref{ratios5152_1}. + Of the 50 ratios shown in that table. only 1 (the (7.7 jmm)/(6.2 pan) ratio for 55) shows a deviance from the weighted mean at even the 20 level.," Of the 50 ratios shown in that table, only 1 (the (7.7 $\mu$ m)/(6.2 $\mu$ m) ratio for 5) shows a deviance from the weighted mean at even the $\sigma$ level." + Similarly. as shown in Table 10.. there are few variations of the ratios of [Ne II] to PAIL emission. or of the ratios of 24 jam to PAIL emission. that are statistically significant.," Similarly, as shown in Table \ref{ratios5152_2}, there are few variations of the ratios of [Ne II] to PAH emission, or of the ratios of 24 $\mu$ m to PAH emission, that are statistically significant." + The constancy of these ratios again arises from a wide variety of local conditions within 55152., The constancy of these ratios again arises from a wide variety of local conditions within 5152. + In the most extreme example in our limited sample. the UR. optical. and UV morphologies are decidedly different in 1€:55152.," In the most extreme example in our limited sample, the IR, optical, and UV morphologies are decidedly different in 5152." + Most of the UV clusters have associated Ih emission. but (he converse in not (rue: a significant. LR component exists in (his svstem that has no associated UV. optical or near-infrared emission.," Most of the UV clusters have associated IR emission, but the converse in not true; a significant IR component exists in this system that has no associated UV, optical or near-infrared emission." + Similarly. (he dominant cluster in the UV. optical ancl near-infrared has very little associated PAIL or dust emission.," Similarly, the dominant cluster in the UV, optical and near-infrared has very little associated PAH or dust emission." + This dichotomy has been seen previously in nearby cwarls (e.g..Cannonοἱαἱ.2006) and is suggestive of a substantial embedded star-lorming population in 55152.," This dichotomy has been seen previously in nearby dwarfs \citep[e.g.,][]{Cannon06a} and is suggestive of a substantial embedded star-forming population in 5152." +" The5, — 69 transition of methanol (CH3OH) at GGHz is one of the most prominent Galactie maser lines (Menten 1991).",The $_1$ $\rightarrow$ $_0$ $^{+}$ transition of methanol $_3$ OH) at GHz is one of the most prominent Galactic maser lines (Menten 1991). + In our Galaxy. the line reaches flux densities of up to several thousand Jy. not quite as much as the brightest 22GGHz H;O maser (e.g.. Matveyenko et al.," In our Galaxy, the line reaches flux densities of up to several thousand Jy, not quite as much as the brightest GHz $_2$ O maser (e.g., Matveyenko et al." + 2003) but exceeding the flux densities of any known OH masers., 2003) but exceeding the flux densities of any known OH masers. + The CH;OH masers at GGHz are observed exclusively in star-forming regions. while OH masers near GGHz are observed in the same regions and are often comeident on subaresecond scales (e.g.. Menten et al.," The $_3$ OH masers at GHz are observed exclusively in star-forming regions, while OH masers near GHz are observed in the same regions and are often coincident on subarcsecond scales (e.g., Menten et al." + 1992)., 1992). + Hundreds of Galactic GGHz methanol masers have been discovered since the early 1990s (Pestalozzi et al., Hundreds of Galactic GHz methanol masers have been discovered since the early 1990s (Pestalozzi et al. + 2005)., 2005). + The GGHz CH;OH line is also found to show absorption in certain regions: notably. deep absorption was found toward our Galactic centre (Menten 199]).," The GHz $_3$ OH line is also found to show absorption in certain regions; notably, deep absorption was found toward our Galactic centre (Menten 1991)." + emission from methanol at GGHz was detected as early às two decades ago toward two nearby external galaxies. 2253 and 3342 (Henkel et al.," emission from methanol at GHz was detected as early as two decades ago toward two nearby external galaxies, 253 and 342 (Henkel et al." + 1987)., 1987). +" This detection. the large number of luminous Galactic masers. and the existence of even more luminous Π.Ο and OH ""megamasers"" (e.g.. Lo 2005) have provided strong motivation to search for GGHz maser emission toward extragalactic sources."," This detection, the large number of luminous Galactic masers, and the existence of even more luminous $_2$ O and OH “megamasers” (e.g., Lo 2005) have provided strong motivation to search for GHz maser emission toward extragalactic sources." + Existing surveys targeted known OH megamaser galaxies and objects with high infrared fluxes. but surprisingly. no detections were obtained (Ellingsen et al.," Existing surveys targeted known OH megamaser galaxies and objects with high infrared fluxes, but surprisingly, no detections were obtained (Ellingsen et al." + 1994a; Phillips et al., 1994a; Phillips et al. + 1998: Darling et al., 1998; Darling et al. + 2003: Goldsmith et al., 2003; Goldsmith et al. + 2008)., 2008). + The only three detections reported so far are from the Large Magellanic Cloud (Sinclair et al., The only three detections reported so far are from the Large Magellanic Cloud (Sinclair et al. + 1992: Ellingsen et al., 1992; Ellingsen et al. + 19948: Beasley et al., 1994b; Beasley et al. + 1996)., 1996). + The intrinsic brightness of these masers is similar to those of their stronger Galactic counterparts., The intrinsic brightness of these masers is similar to those of their stronger Galactic counterparts. + Methanol masers form two distinct families., Methanol masers form two distinct families. + Class I masers are often separated from the main source of excitation. whereas Class IL masers directly trace sites of high-mass star formation (Menten 1991).," Class I masers are often separated from the main source of excitation, whereas Class II masers directly trace sites of high-mass star formation (Menten 1991)." + The GGHz transition has become Class II maser line of choice to study. but it requires intense emission from warm dust and relatively cool gas to become inverted (Cragg et al.," The GHz transition has become Class II maser line of choice to study, but it requires intense emission from warm dust and relatively cool gas to become inverted (Cragg et al." + 2005)., 2005). +" In regions characterised by Class I excitation. Le.. in the absence of a strong far infrared (FIR) radiation field. the line is seen in absorption (Menten 1991),"," In regions characterised by Class I excitation, i.e., in the absence of a strong far infrared (FIR) radiation field, the line is seen in absorption (Menten 1991)." + Hence. if one intends to detect the GGHz line. instead of searching for maser emission. an alternative approach involves absorption line studies against a strong background continuum. tracing lines-of-sight toward active galactic nuclei (AGN).," Hence, if one intends to detect the GHz line, instead of searching for maser emission, an alternative approach involves absorption line studies against a strong background continuum, tracing lines-of-sight toward active galactic nuclei (AGN)." + Whilst all previous extragalactic methanol surveys at GGHz have been aiming at maser emission. the studies were also sensitive to absorption.," Whilst all previous extragalactic methanol surveys at GHz have been aiming at maser emission, the studies were also sensitive to absorption." + Nevertheless. none has been reported so far.," Nevertheless, none has been reported so far." + We therefore conducted à survey optimized for absorption and present the first detection of GGHz methanol absorption toward an extragalactic source., We therefore conducted a survey optimized for absorption and present the first detection of GHz methanol absorption toward an extragalactic source. +" The sample of sources observed by us consists of eight Seyfert 2 or LINER galaxies with a known high X-ray absorbing column (Ny>107 eem) and a radio continuum flux density Soa,> 50mmly or a previous detection of a molecular absorption line 11052: Liszt Lucas 2004: 44261: Impellizzeri et al.."," The sample of sources observed by us consists of eight Seyfert 2 or LINER galaxies with a known high X-ray absorbing column $N_{\rm H} > +10^{23}$ $^{-2}$ ) and a radio continuum flux density $S_{\rm 6\,cm} +>$ mJy or a previous detection of a molecular absorption line 1052: Liszt Lucas 2004; 4261: Impellizzeri et al.," + in preparation)., in preparation). + We made spectroscopic observations. interspersed by continuum measurements. with the mm telescope. of the MPIfR near Bonn. Germany. during 2006 February to June and in 2007 March and November.," We made spectroscopic observations, interspersed by continuum measurements, with the m telescope of the MPIfR near Bonn, Germany, during 2006 February to June and in 2007 March and November." + We used a dual-polarization HEMT receiver at the primary focus., We used a dual-polarization HEMT receiver at the primary focus. + System temperatures were KK. corresponding to a system equivalent flux density of about JJy.," System temperatures were K, corresponding to a system equivalent flux density of about Jy." + The full width at half power (FWHP) beam size was120”., The full width at half power (FWHP) beam size was. +.. The observations were carriedout in a position-switchingfe mode. integrating three minutes off- and three minutes on-source.," The observations were carriedout in a position-switching mode, integrating three minutes off- and three minutes on-source." +" We used alternating 4,8 focus shifts to eliminate standing waves in the resulting spectra.", We used alternating $\pm$$\lambda$ /8 focus shifts to eliminate standing waves in the resulting spectra. + The backend was the AK90 autocorrelator with a total of eight bands. each consisting of 512 channels and covering MMHz.," The backend was the AK90 autocorrelator with a total of eight bands, each consisting of 512 channels and covering MHz." + The channel spacing was kkHz. corresponding to ~3.5kkmss7!.," The channel spacing was kHz, corresponding to $\sim$ $^{-1}$." +" The pointing. obtained by cross scans toward continuum sources. was accurate to about 10""—15"".."," The pointing, obtained by cross scans toward continuum sources, was accurate to about ." + Amplitude, Amplitude +Until recently. the number of dwarf spheroidal (dSph) galaxies around the Milky Way was small compared to expectations from ACDM (?)..,"Until recently, the number of dwarf spheroidal (dSph) galaxies around the Milky Way was small compared to expectations from $\Lambda$ CDM \citep{moore1999}." + However. in the past few years several new systems have been found through systematic searches 99)," However, in the past few years several new systems have been found through systematic searches \citep[e.g.][]{belokurov.boo,belokurovcats}." + In general. dSph galaxies are some of the most tenuous stellar systems that we know of.," In general, dSph galaxies are some of the most tenuous stellar systems that we know of." + This 1s especially true for the newly found dSph galaxies which have very low stellar luminosities (seee.g..?)..," This is especially true for the newly found dSph galaxies which have very low stellar luminosities \citep[see +e.g., ][]{martin08}." + The new dSphs are ultra-faint and show low metallicities as. indicated by low-resolution spectroscopy (??)..," The new dSphs are ultra-faint and show low metallicities as indicated by low-resolution spectroscopy \citep{kirbyletter,kochbierman}." + ? found unusual abundance patterns in two red giant stars (RGB) in the ultra-faint Hercules dSph galaxy., \citet{koch2008Her} found unusual abundance patterns in two red giant stars (RGB) in the ultra-faint Hercules dSph galaxy. + Because of the low baryonic mass for these system it has been speculated that the elemental abundances in the stars in these systems might show us the results of individual supernova events (?).., Because of the low baryonic mass for these system it has been speculated that the elemental abundances in the stars in these systems might show us the results of individual supernova events \citep{koch2008Her}. . + The recently found dSph galaxy in Boóttes (BoótesI...2) provides an excellent opportunity to test whether or not unusual elemental abundance ratios are a common feature of ultra-faint dSph galaxies. thanks to its low baryonic mass. ? estimate. based on a colour magnitude diagram. that the II dSph galaxy is a purely old and metal-poor system.," The recently found dSph galaxy in Boöttes \citep[Bo\""otes\,I, +][]{belokurov.boo} provides an excellent opportunity to test whether or not unusual elemental abundance ratios are a common feature of ultra-faint dSph galaxies, thanks to its low baryonic mass, \citet{belokurov.boo} estimate, based on a colour magnitude diagram, that the I dSph galaxy is a purely old and metal-poor system." + Low-resolution spectroscopic data confirm this (??) at find «[Fe/H]» 2-2.5.," Low-resolution spectroscopic data confirm this \citep{martin07,norris2008} at find $<$ $>$ =–2.5." + With My~—5.8 this dSph galaxy is one of the least luminous galaxies known (?).. ?..," With $M_{\rm V} \sim -5.8$ this dSph galaxy is one of the least luminous galaxies known \citep{belokurov.boo}. \citet{fellhauer2008}," + modelled the system and find that if this galaxy ever had a dark matter halo. it must still have it.," modelled the system and find that if this galaxy ever had a dark matter halo, it must still have it." + This implies that. since the dark matter provides a deep potential well. the stars that originally formed in the dSph galaxy are still there and. moreover. the depth of the well should have helped retain the ejecta from core-collapse supernova.," This implies that, since the dark matter provides a deep potential well, the stars that originally formed in the dSph galaxy are still there and, moreover, the depth of the well should have helped retain the ejecta from core-collapse supernova." + For Hercules. ? conclude that about 10 supernova are needed to pollute the interstellar medium to the observed atypical abundance ratios.," For Hercules, \citet{koch2008Her} conclude that about 10 supernova are needed to pollute the interstellar medium to the observed atypical abundance ratios." + Given that BoóttesII has an even lower baryonic mass than Hercules. we might expect to be able to see enrichment from individual supernovae m the elemental abundance trends (which would show up as large scatter in element ratios from star to star).," Given that I has an even lower baryonic mass than Hercules, we might expect to be able to see enrichment from individual supernovae in the elemental abundance trends (which would show up as large scatter in element ratios from star to star)." + We have obtained high-resolution. moderate S/N spectra for seven RGB stars in the BoóttesII dSph galaxy.," We have obtained high-resolution, moderate S/N spectra for seven RGB stars in the I dSph galaxy." + Here we report on the mean metallicity. the metallicity spread. and atypical abundance ratios similar to those found in the Hercules (?) and Draco dSph galaxies (?)..," Here we report on the mean metallicity, the metallicity spread, and atypical abundance ratios similar to those found in the Hercules \citep{koch2008Her} and Draco dSph galaxies \citep{fulbright2004Draco}." + Thus. II becomes the third system to show unexpected abundances ratios.," Thus, I becomes the third system to show unexpected abundances ratios." + Observations using the High Resolution Echelle Spectrometer (HIRES) (?) on KeckII were carried out in June 2006., Observations using the High Resolution Echelle Spectrometer (HIRES) \citep{1994SPIE.2198..362V} on I were carried out in June 2006. + We obtained spectra of reasonable quality for seven RGB stars i1 the II dSph galaxy., We obtained spectra of reasonable quality for seven RGB stars in the I dSph galaxy. + A full description. of the construction of the linelist. determination of stellar parameters. ete.," A full description of the construction of the linelist, determination of stellar parameters, etc." + will be σίνοι elsewhere., will be given elsewhere. + Briefly. we derived Των from infrared 2MASS photometry (?) using the calibrations by ?. and ?..," Briefly, we derived $T_{\rm eff}$ from infrared 2MASS photometry \citep{2006AJ....131.1163S} using the calibrations by \citet{houdashelt2000} and \cite{{alonso1999calib}}." + We found that all stars could be modelled using Των KK. apart from Boo-094. which has a somewhat cooler model.," We found that all stars could be modelled using $T_{\rm eff}$ = K, apart from Boo-094, which has a somewhat cooler model." +" Once Zr was determined. microturbulence (€,) was checked by requiring all lines to yield the same Fe abundance regardless of linestrength."," Once $T_{\rm eff}$ was determined, microturbulence $\xi_{\rm t}$ ) was checked by requiring all lines to yield the same Fe abundance regardless of linestrength." + Given the quality of the spectra. a common & of kkmss! yields a consistent result for all stars.," Given the quality of the spectra, a common $\xi_{\rm t}$ of $^{-1}$ yields a consistent result for all stars." + Surface gravity (logg) was set to ddex for all stars. apart from Boo- for which we adopt ddex.," Surface gravity $\log g$ ) was set to dex for all stars, apart from Boo-094, for which we adopt dex." + Boo-094 is clearly more evolved: e.g.. lines sensitive to logg. such as the line at nnm. show that this star has a low logg.," Boo-094 is clearly more evolved; e.g., lines sensitive to $\log g$, such as the line at nm, show that this star has a low $\log g$." + Our results are not sensitive to the adopted logg (compare Fig.2))., Our results are not sensitive to the adopted $\log g$ (compare \ref{params.fig}) ). + Assuming that local thermodynamical equilibrium. will hold. we performed a standard abundance analysis using MARCS model atmospheres (?) and accompanying programs for abundance analysis.," Assuming that local thermodynamical equilibrium will hold, we performed a standard abundance analysis using MARCS model atmospheres \citep{gustafsson2008} and accompanying programs for abundance analysis." + These codes take the sphericity of the stellaratmospheres into account. which is necessary because our stars are quite evolved.," These codes take the sphericity of the stellaratmospheres into account, which is necessary because our stars are quite evolved." + Using nonspherical models results, Using nonspherical models results +Heh vesolition simulations have been attempted.,high resolution simulations have been attempted. + Lictal.(2001) have performed the snuulation of a ucreiue ealaxy using TreeSPID code GADGET., \citet{li04} have performed the simulation of a merging galaxy using Tree+SPH code GADGET. + Iu Us sinulation. mass and spatial resolutions were 1ype ancl 6.6«105AL. respectively.," In this simulation, mass and spatial resolutions were $10~\rm{pc}$ and $6.6\times 10^3~M_{\odot}$, respectively." +" T10v asstuued al -isotlραermal ISM and used sink partices, that absorb an surrounding eas. to represent chisters."," They assumed an isothermal ISM and used sink particles, that absorb their surrounding gas, to represent clusters." + They have shownu that a nuniber of massive clusers form in the uereine process., They have shown that a number of massive clusters form in the merging process. + In this simulation. fie nuost massive cluster has mass of 7.8«10*A... Bour," In this simulation, the most massive cluster has mass of $7.8 \times 10^7~M_{\odot}$." +iucetal.(2008) have performed the simulations of ucreiue ealaxies using sticky particles. that collide iueasticallv. iusteacd 6: solviug lydrodvuauiuics.," \citet{bou08} have performed the simulations of merging galaxies using sticky particles, that collide inelastically, instead of solving hydrodynamics." + In these simulations. mass ixd spatial resolutions were 32pc aid 7<107AL... respectively.," In these simulations, mass and spatial resolutions were $32~\rm{pc}$ and $7\times 10^3~M_{\odot}$, respectively." + They have also shown formations of massive star ¢Tusters with masses of LO?6AL..., They have also shown formations of massive star clusters with masses of $10^{5-7}~M_{\odot}$. + These simulations are. however. uiealistie idu a seuse that dvuauical evolution of star clusters themselves caunot be proerly followed due to the liuitation of the sticky andsink. particle methods.," These simulations are, however, unrealistic in a sense that dynamical evolution of star clusters themselves cannot be properly followed due to the limitation of the sticky andsink particle methods." + Saitohetal.(2009) nuproved the spatial aud mass resolutious (5-20pe and 107MAL) and the ISM model tha is allowed to cool to 10Ik., \citet{sai09a} improved the spatial and mass resolutions $5$ $20~\rm{pc}$ and $10^{3-4}~M_{\odot}$ ) and the ISM model that is allowed to cool to $10~\rm{K}$. + These simulations showed that the behavior «ft the multiphase ISM in the mereie eaaxies is considerablv alterec and the formation of shoc‘-induced star clusters is natirally reproduced (Saitohetal.2009. 2011)..," These simulations showed that the behavior of the multiphase ISM in the merging galaxies is considerably altered and the formation of shock-induced star clusters is naturally reproduced \citep{sai09a,sai11}. ." + There axe several lüeh resolution simulations of mcreing» galaxies. which resolve the low temperature eas (3h 10-5000 Ik) using adaptive mesh refineueut CAMIR) methods (simetal.2009:Tovsserotal. 2010).," There are several high resolution simulations of merging galaxies, which resolve the low temperature gas $300$ $500~\rm{K}$ ) using adaptive mesh refinement (AMR) methods \citep{kim09,tey10}." +. These simulations also showed the differcuce in the behavior of the multiphase ISM from that of ISM used in tje previous simulations., These simulations also showed the difference in the behavior of the multiphase ISM from that of ISM used in the previous simulations. + Twinetal.(2009) considered. the mereer of low-niass ealaxios (~LS<1080 AL)., \citet{kim09} considered the merger of low-mass galaxies $\sim 1.8\times 10^10~M_{\odot}$ ). + Several spikv peaks of star ornuatfion rate were secu i tlicr simulation although the nost pronunet starburst was foiud at the beginning the sinmualtious and the significant yaction of the ISM was down away by cnerectic wind before the mereiue event., Several spiky peaks of star formation rate were seen in thier simulation although the most prominet starburst was found at the beginning the simualtions and the significant fraction of the ISM was blown away by energetic wind before the merging event. + Thus. dM would be hard to invesigate detailed evolution of the ISM in iiereing galaxies.," Thus, it would be hard to investigate detailed evolution of the ISM in merging galaxies." + In Tevssieretal.(2010).. he volvtropic equation of state was used instead of solviic the energy equation. which is essenutiallv different YOU Saitohetal.(2009) aud present paper.," In \citet{tey10}, the polytropic equation of state was used instead of solving the energy equation, which is essentially different from \citet{sai09a} and present paper." + The validity of thIs approxination is unclear for τιiderstanding the evolition of the ISM in the mereine ooea]axies., The validity of this approximation is unclear for understanding the evolution of the ISM in the merging galaxies. +" Iligehaesolutiou images of the local (U)LIBGis obtained bv tie integral field spectroscopy usiιοTelescope (Ciarcfa-Maríuetal.20Wad) andOS (Alonso-Terreroetal.2009,2070:Monreal-Iberootal.2010:RodríguezZaurinct2010) showed that (UOGLIBRGs generally have very couplex structures. such as Πα bright knots. rings. and idal tails."," High-resolution images of the local (U)LIRGs obtained by the integral field spectroscopy using \citep{gar09b,gar09a} and \citep{alo09,alo10,mon10,Rod10} showed that (U)LIRGs generally have very complex structures, such as $\alpha$ bright knots, rings, and tidal tails." + As iu the ¢‘ase of formation of star clusters. the reason why these structures have not been reprodiced ii muaerical siuulations uieht be just the inadequate treatinent of ISM. aud lanited resolution.," As in the case of formation of star clusters, the reason why these structures have not been reproduced in numerical simulations might be just the inadequate treatment of ISM and limited resolution." + Thus. hieh resolution simulations resolving multiphase ISM are essential to comprehend he complex structures m (UOLIRCGs.," Thus, high resolution simulations resolving multiphase ISM are essential to comprehend the complex structures in (U)LIRGs." + We| have performed high-resolutionji αμαΊος of moreine galaxies with suff&icieutlv high spatial resolution and cooling muction of ISAL that covers a wide range of temperature (LOI&«T.105 Is)., We have performed high-resolution simulations of merging galaxies with sufficiently high spatial resolution and cooling function of ISM that covers a wide range of temperature $10~\rm{K}37.," Only two associations were found from this, with a relatively large offset of $>3\arcsec$." + We therefore. cdo not. believe that there is significant contamination from chance associations in the sample., We therefore do not believe that there is significant contamination from chance associations in the sample. + Table 2. lists all old ancl candidate clusters associated with X-ray sources in the 2XMMi catalogue., Table \ref{tab:m31gc_2xmmi} lists all old and candidate clusters associated with X-ray sources in the 2XMMi catalogue. +" lt can be seen from table 2. that most of the clusters ave well matehecl to their. proposed. X-ray counterparts. with separations of «2""."," It can be seen from table \ref{tab:m31gc_2xmmi} that most of the clusters are well matched to their proposed X-ray counterparts, with separations of $<$ $\arcsec$." + However. three. of the clusters have velatively large ollsets of 37 ," However, three of the clusters have relatively large offsets of $>$ $\arcsec$." +Comparison with published observations (discussed. in. the next section) confirms that two of these sources. BOO ancl D146. are associated with the clusters.," Comparison with published observations (discussed in the next section) confirms that two of these sources, B094 and B146, are associated with the clusters." + Both the ancl locations of the source associated with DOO4 are slightLy olfset from the centre of the cluster., Both the and locations of the source associated with B094 are slightly offset from the centre of the cluster. + Phis may potentially align with a faint optical source on the edge of this cluster., This may potentially align with a faint optical source on the edge of this cluster. + since LAINBs are expected to reside in the cores of the clusters. (where the density is highest). it is possible that this source could. be a chance alignment with the cluster.," Since LMXBs are expected to reside in the cores of the clusters (where the density is highest), it is possible that this source could be a chance alignment with the cluster." + llowever. given its proximity to the cluster. we keep this source in our analysis. but note that its association is relatively uncertain.," However, given its proximity to the cluster, we keep this source in our analysis, but note that its association is relatively uncertain." + It is found that the cluster 035 does not appear to be associated with the matched N-ray source., It is found that the cluster B035 does not appear to be associated with the matched X-ray source. + Another faint counterpart. is identified. in Ix-band. images that is in good agreement with the X-ray source location., Another faint counterpart is identified in K-band images that is in good agreement with the X-ray source location. + We therefore believe that this may be a chance alignment with a non-cluster object and remove it from our analysis., We therefore believe that this may be a chance alignment with a non-cluster object and remove it from our analysis. +" For each GC X-ray source. table 2 includes hardness ratios for the source and its total luminosity (£,.0.2 12keV)."," For each GC X-ray source, table \ref{tab:m31gc_2xmmi} includes hardness ratios for the source and its total luminosity $L_{x}, 0.2-12$ keV)." +" These cata are taken from the 2PNAIAT ""sua catalogue.", These data are taken from the 2XMMi `slim' catalogue. + This is a reduced version of the main catalogue and contains only unique sources., This is a reduced version of the main catalogue and contains only unique sources. + Many. of these. sources are expected to vary. during the observations and some are located in more than one observation., Many of these sources are expected to vary during the observations and some are located in more than one observation. + For these sources. this catalogue quotes the mean locations anc Dluxes.," For these sources, this catalogue quotes the mean locations and fluxes." +" The hardness ratios (IR) of a source are defined as: lere. D; are the narrow energy bands: By =0.2-0.5 keV: Beo=0.5-1.0 keV: D5—1.0-2.0 keV: D4,22.0-4.5 keV: Bs =4.5-12 keV. Table 2. also includes the summary πας (SUMELG) from the 2XMMi catalogue."," The hardness ratios (HR) of a source are defined as: Here, $_{i}$ are the narrow energy bands: $_{1}$ =0.2-0.5 keV; $_{2}$ =0.5-1.0 keV; $_{3}$ =1.0-2.0 keV; $_{4}$ =2.0-4.5 keV; $_{5}$ =4.5-12 keV. Table \ref{tab:m31gc_2xmmi} also includes the summary flag (SUMFLG) from the 2XMMi catalogue." + This gives an indication of the reliability of the detection., This gives an indication of the reliability of the detection. + The relevant Hags 7T) are: 0 = good 1 = source parameters may be alfected 2 = possibly spurious 3 = located in a region where spurious detections may OCCUL lt can be seen that many of the cetections have non- warning llags., The relevant flags \citep[taken from][]{Watson09} are: 0 = good 1 = source parameters may be affected 2 = possibly spurious 3 = located in a region where spurious detections may occur It can be seen that many of the detections have non-zero warning flags. + This is likely due to the crowded nature of AI31. with most of the SUAIPLG=8 sources near the centre of the galaxy.," This is likely due to the crowded nature of M31, with most of the SUMFLG=3 sources near the centre of the galaxy." + ? suggest that sources with Llaes 0-2 should be ecnuine. although sources with Hags | or 2 have some of the automated spurious detection [aes set.," \citet{Watson09} suggest that sources with flags 0-2 should be genuine, although sources with flags 1 or 2 have some of the automated spurious detection flags set." +" Class 3 sources are confirmed by ""manual. Llageine.", Class 3 sources are confirmed by `manual' flagging. + However. they have all of the 2NXMMi automated detection Hags set to spurious. and maw be spurious detections.," However, they have all of the 2XMMi automated detection flags set to spurious, and may be spurious detections." + Of the 43 old clusters associated with X-ray sources. 13 have SUMELCG-23.," Of the 43 old clusters associated with X-ray sources, 13 have SUMFLG=3." + We note. from comparison with previous observations. that 10 of these 13 GC's have already been identified independently (rom. observations.," We note, from comparison with previous observations, that 10 of these 13 GCs have already been identified independently from observations." + These sources are therefore unlikely to be spurious., These sources are therefore unlikely to be spurious. + The thumbnail images for all of the 2XNMAL GC were also. visually examined to identify any artifacts (for example due to chip gaps)., The thumbnail images for all of the 2XMMi GC were also visually examined to identify any artifacts (for example due to chip gaps). + This examination suggested that the source in the cluster ΑΙΟΙ was unlikely to be reliable and we remove it [rom our catalogue., This examination suggested that the source in the cluster AU010 was unlikely to be reliable and we remove it from our catalogue. + In addition to the observations. used. here. other X-ray. observations of M31. have associated. X-ray sources with its GCs.," In addition to the observations used here, other X-ray observations of M31 have associated X-ray sources with its GCs." + This previous work is summarised in section 2.., This previous work is summarised in section \ref{sec:xray:m31gc}. + Given the transient nature expected. [roni some LAINBs. it is likely that they may only be detected at certain epochs.," Given the transient nature expected from some LMXBs, it is likely that they may only be detected at certain epochs." + For this reason. we consider which elusters in table 2 were previously detected and identify any additional clusters with proposed X-ray. emission.," For this reason, we consider which clusters in table \ref{tab:m31gc_2xmmi} were previously detected and identify any additional clusters with proposed X-ray emission." + Alb confirmed clusters were matched. το sources identified from: observations by. 2z observations by 2.. 2.. 7.. 2. and and. observations by 7..," All confirmed clusters were matched to sources identified from: observations by \citet{Supper01}; observations by \citet{DiStefano02}, \citet{Kong02}, \citet{Kaaret02}, \citet{Williams04} and and observations by \citet{Trudolyubov04}." + Phe M31 cluster catalogue used in this study has more accurate locations. and some additional clusters. compared with those used in these previous studies.," The M31 cluster catalogue used in this study has more accurate locations, and some additional clusters, compared with those used in these previous studies." + We therefore. consider all X-ray sources in these previous catalogues., We therefore consider all X-ray sources in these previous catalogues. + Table ο lists all confirmed. clusters which are associated with X-ray sources from the 2XMMi catalogue or these previous studies., Table \ref{tab:m31gc_xray_all_old} lists all confirmed clusters which are associated with X-ray sources from the 2XMMi catalogue or these previous studies. + Lt can be seen that 38 of the clusters identified in the 2XMMi catalogue were identified previously bv one of these studies. while three are newly identified.," It can be seen that 38 of the clusters identified in the 2XMMi catalogue were identified previously by one of these studies, while three are newly identified." +"direction rather than NE-SW, as in the case of H5 0-0 S(1) in Fig. 12)).","direction rather than NE-SW, as in the case of $_2$ 0-0 S(1) in Fig. \ref{fig:rotation-maps}) )." +" A similar difference in velocity structure is observed in the aand H5 0-0 S(2) velocity maps and panels in Fig. 12,,"," A similar difference in velocity structure is observed in the and $_2$ 0-0 S(2) velocity maps and panels in Fig. \ref{fig:rotation-maps}," + respectively)., respectively). +" These different kinematic components may be caused by different origins related to the species emitting, or by different levels of extinction (extinction law at different wavelengths), which allow us to probe deeper regions at one wavelength than another."," These different kinematic components may be caused by different origins related to the species emitting, or by different levels of extinction (extinction law at different wavelengths), which allow us to probe deeper regions at one wavelength than another." + This is further discussed in Sect. ??.., This is further discussed in Sect. \ref{sec:H2-gas}. +" On the other hand, the relatively uniform central region of the vvelocity field may be due to the lack of spectral resolution and the lower (factor 1 to 100) S/N level obtained in this line."," On the other hand, the relatively uniform central region of the velocity field may be due to the lack of spectral resolution and the lower (factor 1 to 100) S/N level obtained in this line." +" This implies that we are unable to spectrally resolve, at a reliable level, the rather small (z50 kms!) velocity shifts in the lline."," This implies that we are unable to spectrally resolve, at a reliable level, the rather small $\lesssim50~\kms$ ) velocity shifts in the line." +" Nevertheless, with a higher spectral resolution we would expect a weaker rotation of iin comparison to the rotation shown by the starburst tracers (from about —120kms! to ~100km s)."," Nevertheless, with a higher spectral resolution we would expect a weaker rotation of in comparison to the rotation shown by the starburst tracers (from about $-120~\kms$ to $\sim100~\kms$ )." +" If the iis exclusively related to the AGN NLR, this would mean that the NLR gas does not feel the gravitational pull of the large gas mass interior to the starburst ring."," If the is exclusively related to the AGN NLR, this would mean that the NLR gas does not feel the gravitational pull of the large gas mass interior to the starburst ring." + But it would feel the pull, But it would feel the pull +zone gains sulficient mass for the disk to become sell-gravitating.,zone gains sufficient mass for the disk to become self-gravitating. + The disk state then enters the GAL branch., The disk state then enters the GM branch. + There exists a range of mass accretion rates for which no steady state solution exists., There exists a range of mass accretion rates for which no steady state solution exists. + This range is indicated by the lower shaded region in Fig. 1.., This range is indicated by the lower shaded region in Fig. \ref{diagram}. + This gap comes about because the GM branch terminates at an M for which T.=They. while the higher MRI branch starts al a larger value of M that is also at T.=Toy.," This gap comes about because the GM branch terminates at an $\dot{M}$ for which $T_{\rm c}=T_{\rm crit}$, while the higher MRI branch starts at a larger value of $\dot{M}$ that is also at $T_{\rm c}=T_{\rm crit}$." + As we will see in Section 4.. a disk that has an accretion rate Iving in this range will quickly transition to either of these steady state branches.," As we will see in Section \ref{num}, a disk that has an accretion rate lying in this range will quickly transition to either of these steady state branches." + As a consequence of such transitions. the disk undergoes outbursts.," As a consequence of such transitions, the disk undergoes outbursts." + We are considering a disk that undergoes accretion [rom an external source al à constant accrete rate., We are considering a disk that undergoes accretion from an external source at a constant accrete rate. + The XM. diagram applies at each disk radius., The $\Sigma$ $\dot{M}$ diagram applies at each disk radius. + The range of unstable accretion rates shown as the lower shaded region in Fig., The range of unstable accretion rates shown as the lower shaded region in Fig. + 1. varies with radius., \ref{diagram} varies with radius. + For a disk to be globally stable against gravo-magneto outbursts. there should be no radius at which the disk accretion rate lies within this range.," For a disk to be globally stable against gravo-magneto outbursts, there should be no radius at which the disk accretion rate lies within this range." + The ease of outbursts involving the thermal-viscous instability occurs at higher disk temperatures and accretion rates (han the eravo-magneto instability., The case of outbursts involving the thermal-viscous instability occurs at higher disk temperatures and accretion rates than the gravo-magneto instability. + This regime is sketclied as the well-known 5-curve in (he upper portion of Fie. 1l.., This regime is sketched as the well-known S-curve in the upper portion of Fig. \ref{diagram}. + The instability occurs along the middle portion of the S-curve (the upper dotted line within (he upper shaded region)., The instability occurs along the middle portion of the S-curve (the upper dotted line within the upper shaded region). + This middle portion consists of unstable steady state solutions that occur between other the two stable branches., This middle portion consists of unstable steady state solutions that occur between other the two stable branches. + The situation with the gravo-magneto outbursts is different because there are no intermediate unstable steady state solutions. ie.. there are no steady state solutions in the lower shaded region.," The situation with the gravo-magneto outbursts is different because there are no intermediate unstable steady state solutions, i.e., there are no steady state solutions in the lower shaded region." + For a given accretion rate. it is possible for the disk to develop the thermal-viscous instability at small radii and the gravo-magneto instability further out.," For a given accretion rate, it is possible for the disk to develop the thermal-viscous instability at small radii and the gravo-magneto instability further out." +A (ACDM) Coleetal.2008:Neistein&Dekel2008 (CL.>L) 2<] 2007). Khochfar&Burkert(2003.2005). L —6.3 ο 2<1 (DeLuciaetal. (Boylan-K,"$\Lambda$ $\Lambda$ \citealt{cole08,neistein08} $L>L^*$ $z < 1$ \citealt{delucia06,delucia07}) \cite{khochfar03, +khochfar05} $L^*$ $\sim 6.3 \times 10^{10}$ $_{\odot}$ $z < 1$ \citep{delucia06, +khochfar08}." +olchinetal.2005.2006) reproduce the internal structure of local ellipticals (Naabetal.2006. 2007).," \citep{boylan05,boylan06} reproduce the internal structure of local ellipticals \citep{naab06,naab07}." +". The first examples of dry mergers. in significant numbers. were observed as close pairs of galaxies on the red sequence in deep images of high redshift clusters (vanDokkumetal.1999, 2001).. where approximately of galaxies were expected to have undergone a dry merger to the present epoch."," The first examples of dry mergers, in significant numbers, were observed as close pairs of galaxies on the red sequence in deep images of high redshift clusters \citep{vandokkum99, +vandokkum01}, where approximately of galaxies were expected to have undergone a dry merger to the present epoch." + In the local universe. vanDokkum(2005). estimated that ~ of ;<0.1 bright ellipticals in the MUSYC and NDFWS surveys showed residual structural features indicative of a dry merger 1n the “recent” past.," In the local universe, \cite{vandokkum05} estimated that $\sim 30\%$ of $z < 0.1$ bright ellipticals in the MUSYC and NDFWS surveys showed residual structural features indicative of a dry merger in the `recent' past." + Belletal.(2006a) used close pairs in the Combo-17 survey having similar photometric redshiftsand showing evidence of interactions to infer an integrated merger rate of ~80% since +<0.8 for red galaxies with Mp<20.5|5loghi. while Linetal.(2008) used dynamically close— pairs in the DEEP? survey to derive an integrated dry merger rate of 2l4 at:<1.2 for galaxies with 21<0.12 for galaxies with AL,<21.2|Slogh."," However, \cite{hsieh08} identify close pairs in the RCS survey and derive an integrated merger rate of only $6\%$ per Gyr since $z=0.8$ for galaxies with $-25 < M_r -5 \log h < -20$ , and \cite{wen09} use the same approach as \cite{bell06a} on LRGs in the SDSS survey to determine a merger rate of $0.8\%$ per Gyr at $z < 0.12$ for galaxies with $M_r < -21.2 + 5 \log h$." + Bundyetal.(2009) find evidence of few to zero pairs of red galaxies at»<1.21n the GOODS data.," \cite{bundy09} find evidence of few to zero pairs of red galaxies at $z < +1.2$in the GOODS data." + The small scale correlation function of LRGs in the SDSS at;«0.36 analyzed by Masjedietal.(2006.2008) τς consistent with an upper limit of <1.7% per Gyr to the dry merger rate for galaxies with 1M;<22.75|Slogh at 0.16«:0.30.," The small scale correlation function of LRGs in the SDSS at $z < 0.36$ analyzed by \cite{masjedi06, +masjedi08} is consistent with an upper limit of $< 1.7\%$ per Gyr to the dry merger rate for galaxies with $M_i < -22.75 + 5 \log h$ at $0.16 < z < 0.30$." + Belletal.(2006b) used this method to derive a merger rate of 14 per Gyrfor Mp<—20.5|Slogh galaxies at 0.1<20.8., \cite{bell06b} used this method to derive a merger rate of $4\%$ per Gyr for $M_B < -20.5 + 5 \log h$ galaxies at $0.4 < z < 0.8$. + Whiteetal.(2007) obtain an integrated merger rate of ~30% for LRGs at 0.5«-0.9 in the NDFWS survey.," \cite{white07} + obtain an integrated merger rate of $\sim 30\%$ for LRGs at $0.5 < z < 0.9$ in the NDFWS survey." +" Finally. Wakeetal.(2008) apply the correlation function method to galaxies the 2SLAQ survey to ""Serive a merger rate of 2.1%per Gyr at 0.10τς (0.55."," Finally, \cite{wake08} apply the correlation function method to galaxies the 2SLAQ survey to derive a merger rate of $2.4\%$per Gyr at $0.19 < z < 0.55$ ." + The galaxy merger rate has been usually measured via the fraction of galaxies in close pairs. often with the added requirement of closeness in velocity space to cull interlopers (e.g.. Pattonetal.2000.2002 — hereafter. POO.PO2). and," The galaxy merger rate has been usually measured via the fraction of galaxies in close pairs, often with the added requirement of closeness in velocity space to cull interlopers (e.g., \citealt{patton00,patton02} – hereafter, P00,P02), and" +spe-scale jets or their lobes. that disappear rapidly ollowiug too wich expansion. the observed. persistence of weak unresolved radio cores is a strong iudicator that nass-loss via a disk wind acconpanies ou-goinug disk accretion.,"kpc-scale jets or their lobes, that disappear rapidly following too much expansion, the observed persistence of weak unresolved radio cores is a strong indicator that mass-loss via a disk wind accompanies on-going disk accretion." + Indeed. it seenis increasingly likely that radio-ouduess iu quasars is a somewhat short-lived phase of chhanced augular momentum loss via jets. analogous o that in nuücroquasars. aud that the more common neans of angular moment loss is via louger-lived phases of mmass-loxs via disk winds.," Indeed, it seems increasingly likely that radio-loudness in quasars is a somewhat short-lived phase of enhanced angular momentum loss via jets, analogous to that in microquasars, and that the more common means of angular momentum loss is via longer-lived phases of mass-loss via disk winds." +" Separately frou the daring iode associated with jet-cjection episodes iu wicroquasars. Nipotietal.(2005) identifv a second. chief mode of energy loss. which they term the ""coupled node” during which microquasars are observed to have closely coupled X-ray. and racio huninosities aud to be nuresolved “cores”."," Separately from the flaring mode associated with jet-ejection episodes in microquasars, \citet{Nipoti05} identify a second, chief mode of energy loss, which they term the “coupled mode"" during which microquasars are observed to have closely coupled X-ray and radio luminosities and to be unresolved “cores""." + Tf the quiescent radio core enmissionu is due to a hot (~10* KIS) disk wind. then the observed racio/X-ray correlation could be attributed to a common disk origin for the radio (disk wind) aud soft N-rav (disk wind | disk blackbody) cutission.," If the quiescent radio core emission is due to a hot $\sim 10^7$ K) disk wind, then the observed radio/X-ray correlation could be attributed to a common disk origin for the radio (disk wind) and soft X-ray (disk wind + disk blackbody) emission." + It would be interesting to pursue this analogy further in the contest of core enission in quasars aud ACN (although iu this case. ouly the disk wind. aud not the disk blackbody enission. would contribute to the soft X-ray enission) and indeed he extent to which the disk wind. if equatorial as in SS133. plavs the role of the putative obscuring torus.," It would be interesting to pursue this analogy further in the context of core emission in quasars and AGN (although in this case, only the disk wind, and not the disk blackbody emission, would contribute to the soft X-ray emission) and indeed the extent to which the disk wind, if equatorial as in SS433, plays the role of the putative obscuring torus." + Although it is now widely acknowledged that feedback yon AGN is required to reconcile simmlations of ealaxy formation with observations. the details of these Xocesses relmain to be explored (e.g.Nesvadbaetal. 2006).," Although it is now widely acknowledged that feedback from AGN is required to reconcile simulations of galaxy formation with observations, the details of these processes remain to be explored \citep[e.g.\,][]{Nesvadba06}." +. Tn particular. although jets are invoked as a ueans of relocating mass and energev away frou the active ealactic nucleus. a limitation of this picture is hat jets are by their very uaturedirectional and relatively light.," In particular, although jets are invoked as a means of relocating mass and energy away from the active galactic nucleus, a limitation of this picture is that jets are by their very nature and relatively light." + Winds from accretion disks. however. are considerably less directional aud heavier aud may provide a better means of dispersing mass/energv into the ICAL and explaining the observed link between growth of supermassive black holes aud their host galaxy properties (Nine2005).," Winds from accretion disks, however, are considerably less directional and heavier and may provide a better means of dispersing mass/energy into the IGM and explaining the observed link between growth of supermassive black holes and their host galaxy properties \citep{King05}." +. A mass outflow rate CVzMgqa) of hot (Q0 KE) sas may be sufficient to offset cooling in ealaxies.," A mass outflow rate $\Mdotw +\gtapprox \dot M_{\rm Edd}$ ) of hot $\sim 10^7$ K) gas may be sufficient to offset cooling in galaxies." + We have proposed that the radio cores of racdio-quiet quasars are thermal m origin. arising from an accretion disk wind.," We have proposed that the radio cores of radio-quiet quasars are thermal in origin, arising from an accretion disk wind." + This wind uaturally produces flat spectrum radio Cluission Via optically-thin broiisstralilung radiation., This wind naturally produces flat spectrum radio emission via optically-thin bremsstrahlung radiation. + The remarkable sunuilarities i radio core properties of radio-quiet aud Guan) racio-loud quasars sugecsts that a radio-ciitting disk wind is present at some level iu all quasars., The remarkable similarities in radio core properties of radio-quiet and (many) radio-loud quasars suggests that a radio-emitting disk wind is present at some level in all quasars. + The observed luminosities of radio core enuiüssion from quasars Προς that they are accreting at super-Eddineton rates aud that the disk wind expels most of this matter well before it reaches the immer accretion flow. thereby providing an cficicut mechanisi for angular momentum transport and ACN feedback.," The observed luminosities of radio core emission from quasars implies that they are accreting at super-Eddington rates and that the disk wind expels most of this matter well before it reaches the inner accretion flow, thereby providing an efficient mechanism for angular momentum transport and AGN feedback." + We would like to thauk the referee for helpful cohunents on the manuscript., We would like to thank the referee for helpful comments on the manuscript. + ΑΠΟ thanks the Roval Society for a University Research Fellowship aud the Leverluline Trust for their support., KMB thanks the Royal Society for a University Research Fellowship and the Leverhulme Trust for their support. + Zl& acknowledges an Australian Academy. of Scieuce. Scicutific Visits to Europe eraut., ZK acknowledges an Australian Academy of Science Scientific Visits to Europe grant. + Both authors thauk the 1851 Roval Connuission for the support of their research careers. especially most recently for the reception at Buckingham Palace. Loudon. where this work was conceived.," Both authors thank the 1851 Royal Commission for the support of their research careers, especially most recently for the reception at Buckingham Palace, London, where this work was conceived." +The general form of the time dependent statistical equilibrium equation is where v is the velocity. 7; is the population of state 7. and [ij is the transition rate from state { to state 7.,"The general form of the time dependent statistical equilibrium equation is where $v$ is the velocity, $n_i$ is the population of state $i$, and $R_{ij}$ is the transition rate from state $i$ to state $j$." + The forms of Ay; and fj; are standard. and can be found. for example. in Tihalas (1978).," The forms of $ R_{ij}$ and $R_{ji}$ are standard, and can be found, for example, in Mihalas (1978)." + For simplicity we have not distinguished between he different processes (collisional. bound-free. and bound-bound) entering these rates.," For simplicity we have not distinguished between the different processes (collisional, bound-free, and bound-bound) entering these rates." + In massive stars. the winds can be approximated as stationary.," In massive stars, the winds can be approximated as stationary." + In such cases we consider a Eulerian formulation. and take On/OF o be zero.," In such cases we consider a Eulerian formulation, and take $\partial n/\partial t$ to be zero." +" The V.(n;v) term is the advection term. and is usually neglected. however it can become important in the outer regions of he wind. since the ratio of the recombination time. 1 /an,.. to the flow time. fr. scales as the radius. r (here. a is the recombination coefficient)."," The $\nabla.(n_iv)$ term is the advection term, and is usually neglected, however it can become important in the outer regions of the wind, since the ratio of the recombination time, $1/{\alpha n_e}$ , to the flow time, $r/v$, scales as the radius, $r$ (here, $\alpha$ is the recombination coefficient)." + Supernovae are obviously time dependent. and in this case it makes sense to use a Lagrangean formalism.," Supernovae are obviously time dependent, and in this case it makes sense to use a Lagrangean formalism." + Using the continuity equation the statistical equilibrium equations become where 2/DI is the comoving derivative., Using the continuity equation the statistical equilibrium equations become where $D/Dt$ is the comoving derivative. + For a Hubble flow. which is the form we used in these calculations.," For a Hubble flow, which is the form we used in these calculations." + To solve these equations we use implicit first. order differencing in the Lagrangean frame., To solve these equations we use implicit first order differencing in the Lagrangean frame. + Thus the equations to be solved become where &1. & refer to values at consecutive time steps but with the same comoving coordinate.," Thus the equations to be solved become where $k-1$, $k$ refer to values at consecutive time steps but with the same comoving coordinate." + For a Hubble flow. we can simply use the velocity as the Lagrangean co-ordinate.," For a Hubble flow, we can simply use the velocity as the Lagrangean co-ordinate." +" The solution of these equations proceeds in an identical fashion to that used to solve the steady-state statistical equilibrium equations (Hillier 1987: Hillier 1990: Hillier Miller 1998): the only distinction 1s that we have a ""source"" term that comes from the populations at an earlier time step.", The solution of these equations proceeds in an identical fashion to that used to solve the steady-state statistical equilibrium equations (Hillier 1987; Hillier 1990; Hillier Miller 1998); the only distinction is that we have a “source” term that comes from the populations at an earlier time step. +" The energy equation is where c is the internal energy/unit mass. x the opacity. 7j, the emissivity. and ./, the mean intensity. and we have ignored other forms of energy deposition (such as nuclear decay)."," The energy equation is where $e$ is the internal energy/unit mass, $\chi_\nu$ the opacity, $\eta_\nu$ the emissivity, and $J_\nu$ the mean intensity, and we have ignored other forms of energy deposition (such as nuclear decay)." +" e can be written in the form where and In the above. » is the total particle density (excluding electrons). 77, is the electron density. and /7; is the total energy (excitation and ionization) of state /."," $e$ can be written in the form where and In the above, $n$ is the total particle density (excluding electrons), $n_e$ is the electron density, and $E_i$ is the total energy (excitation and ionization) of state $i$." + This equation is solved implicitly. via linearization. and is no more difficult to treat than the regular constraint of radiative equilibrium.," This equation is solved implicitly, via linearization, and is no more difficult to treat than the regular constraint of radiative equilibrium." + Below we examine when the time dependent terms in the statistical equilibrium equations will play an important role in determining he radiative transfer in SN envelopes., Below we examine when the time dependent terms in the statistical equilibrium equations will play an important role in determining the radiative transfer in SN envelopes. + To do this. we need to compare the time it takes to replenish the population of individual evels with the flow time.," To do this, we need to compare the time it takes to replenish the population of individual levels with the flow time." + As noted previously. the flow-time scale is simply r/v. and for a Hubble flow this is fexp. where /exp is the ime since the explosion.," As noted previously, the flow-time scale is simply $r/v$, and for a Hubble flow this is $t_{\hbox{exp}}$, where $t_{\hbox{exp}}$ is the time since the explosion." + We will only examine the ionization equilibrium in detail. since it is the ionization equilibrium that will be most affected by he time-dependent terms — statistical equilibrium of excited levels will generally be satistied because the radiatives rates tend to be arge C1>105 Ly and the transitions have low tor moderate) optical depths.," We will only examine the ionization equilibrium in detail, since it is the ionization equilibrium that will be most affected by the time-dependent terms – statistical equilibrium of excited levels will generally be satisfied because the radiatives rates tend to be large $A> 10^6$ $^{-1}$ ), and the transitions have low (or moderate) optical depths." + The simplest recombination timescale can be found by estimating the time it takes. at fixed electron density. for all ions to recombine.," The simplest recombination timescale can be found by estimating the time it takes, at fixed electron density, for all ions to recombine." + Thus the recombination timescale for hydrogen. /rec is simply given by Using à=ag2.50.10 eem?ss * at 10.000K (Osterbrock197-1.. gives We use ay since in SN conditions every direct recombination to the ground state will generally be followed by an ionization.," Thus the recombination timescale for hydrogen, $t_{\hbox{rec}}$ is simply given by Using $\alpha=\alpha_B=2.59 \times 10^{-13}$ $^{3}$ $^{-1}$ at 10,000K \citep{Osterbrock_1974}, gives We use $\alpha_B$ since in SN conditions every direct recombination to the ground state will generally be followed by an ionization." + The recombination time scale for is very similar to that ofHI., The recombination time scale for is very similar to that of. + Since the comoving density is x1//7. the ratio of recombination time to the flow time. at a given velocity. scales as /7.," Since the comoving density is $\propto 1/t^3$, the ratio of recombination time to the flow time, at a given velocity, scales as $t^2$." + Thus the ionization must eventually become frozen. and first at high velocities.," Thus the ionization must eventually become frozen, and first at high velocities." + The previous discussion refers to the case when we can ignore optical depth effects and the existence of metastable states., The previous discussion refers to the case when we can ignore optical depth effects and the existence of metastable states. + When optical depth effects are important. and/or there exist low lying metastable states. it is more difficult to ascertain the relevant recombination time scale.," When optical depth effects are important, and/or there exist low lying metastable states, it is more difficult to ascertain the relevant recombination time scale." + In such cases. it is the net flow of electronsto the ground state that will set the ionization equilibrium.," In such cases, it is the net flow of electronsto the ground state that will set the ionization equilibrium." + As an illustration consider a two level atom with continuum., As an illustration consider a two level atom with continuum. + The relevant equations are and, The relevant equations are and +The optical images of two galaxies of the sample (namely VCC 1030 and VCC 1535)eae both detected in the VLA images. show the presence of large-scale dusty disks (Cotéetal.2004) that prevent the study and classification of their surface brightness profiles.,"The optical images of two galaxies of the sample (namely VCC 1030 and VCC 1535) both detected in the VLA images, show the presence of large-scale dusty disks \citep{cote04} that prevent the study and classification of their surface brightness profiles." + We then retrieved from theHS7 archive their infrared images where the impact of dust absorption is less severe., We then retrieved from the archive their infrared images where the impact of dust absorption is less severe. + The images were taken withNICMOS/HST through the filter FI60W band) and were processed by the standardHST pipeline., The images were taken with through the filter F160W band) and were processed by the standard pipeline. + The camera NIC] was used. with a pixel size of 070043. for a field of view of ~ «11.," The camera NIC1 was used, with a pixel size of 043, for a field of view of $\sim$ $\times$." + Elliptical isophotes were fit to both images using the IRAF task ‘ellipse’ (Jedrzejewski1987)., Elliptical isophotes were fit to both images using the IRAF task `ellipse' \citep{jedrzejewski87}. +. Although these images are still affected by dust absorption (see Figure 4+ and 6)). there are sufficient dust free regions to derive the SBP after proper masking.," Although these images are still affected by dust absorption (see Figure \ref{sbpfig1} and \ref{sbpfig2}) ), there are sufficient dust free regions to derive the SBP after proper masking." + Since the image of VCC 1535 fills completely the field of view. we extended the radial coverage of the SBP using the band image from the Two Micron All Sky Survey (2MASS).," Since the image of VCC 1535 fills completely the field of view, we extended the radial coverage of the SBP using the band image from the Two Micron All Sky Survey (2MASS)." + The SBP were fit using a Sérrsic law (Sérsic1968) convolved with the appropriate point-spread function before comparison with the data., The SBP were fit using a Sérrsic law \citep{sersic68} convolved with the appropriate point-spread function before comparison with the data. + The SBP of VCC 1030 is reproduced very closely by a Sérrsic model with an effective radius of r.=379 and a Sérrsic index #7=1.7., The SBP of VCC 1030 is reproduced very closely by a Sérrsic model with an effective radius of $r_e = 3\farcs9$ and a Sérrsic index $n=1.7$. + This is not the case of VCC 1535 that shows a strong light deficit in the innermost regions with respect to the Sérrsic that describes the external regions and requires the presence of a flat central core., This is not the case of VCC 1535 that shows a strong light deficit in the innermost regions with respect to the Sérrsic that describes the external regions and requires the presence of a flat central core. +" We therefore fit its SBP with a core-Sérrsic model (Trujilloetal.2004);; the parameters of the best fit are an effective radius r,=106"". an index n=5.2. a core radius r,.=0715. and a inner slope 5=0.06."," We therefore fit its SBP with a core-Sérrsic model \citep{trujillo04}; the parameters of the best fit are an effective radius $r_e = 106\arcsec$, an index $n= 5.2$, a core radius $r_c = +0\farcs15$, and a inner slope $\gamma = 0.06$." + This analysis leads to a classification based on the SBP properties of VCC 1030 as a Sérrsie galaxy and of VCC 1535 as a core-Sérrsic galaxy., This analysis leads to a classification based on the SBP properties of VCC 1030 as a Sérrsic galaxy and of VCC 1535 as a core-Sérrsic galaxy. +V405 Aur owas observed. by the satellite (Jansen 22001: Turner 22001) on 2001 October 5.,V405 Aur was observed by the satellite (Jansen 2001; Turner 2001) on 2001 October 5. + A 30-ks observation was made with the EPLC-AIOS cameras in using the Thin Filter 1: the PN camera was not in operation., A 30-ks observation was made with the EPIC-MOS cameras in using the Thin Filter 1; the PN camera was not in operation. + The source was outside the OAL window. so these data were not. used.," The source was outside the OM window, so these data were not used." + We analysed the data using. the software v5.4.1., We analysed the data using the software v5.4.1. + In the central CCD data is compressed onto a single axis. thus selection is based on columns rather than pixels.," In the central CCD data is compressed onto a single axis, thus selection is based on columns rather than pixels." + Only single or double pixel events with à zero quality [ag were selected from a 4d4-column region centred on the source., Only single or double pixel events with a zero quality flag were selected from a 44-column region centred on the source. + We also removed column 315 from the MOS-2 data. which showed a spurious signal at low energies.," We also removed column 315 from the MOS-2 data, which showed a spurious signal at low energies." + Owing to the limited coverage of the window we used an adjacent chip (CCDS) to estimate the background., Owing to the limited coverage of the window we used an adjacent chip (CCD3) to estimate the background. + The power spectrum of the 0.212 keV. data from the ALOS cameras is given in Fig. 1.., The power spectrum of the 0.2–12 keV data from the MOS cameras is given in Fig. \ref{fig:ft}. + Phis shows prominent peaks at the spin frequeney and its first harmonic (periods 545.5 s and 272.7 s respectively)., This shows prominent peaks at the spin frequency and its first harmonic (periods 545.5 s and 272.7 s respectively). +" We find that the first harmonic is the stronger at energies below 0.7 keV. (hereafter the ""soft band). while the fundamental is the stronger at. energies above 0.7. keV. (hereafter the ""hard! band). as previously reported by Allan ((1996)."," We find that the first harmonic is the stronger at energies below 0.7 keV (hereafter the `soft' band), while the fundamental is the stronger at energies above 0.7 keV (hereafter the `hard' band), as previously reported by Allan (1996)." + The folded lighteurves from the two bands (Fig. 2)), The folded lightcurves from the two bands (Fig. \ref{fig:spin}) ) + confirm these results. showing that the soft. emission has a clouble-peakecl profile whereas the hard. emission has a single-pealked. sawtooth modulation.," confirm these results, showing that the soft emission has a double-peaked profile whereas the hard emission has a single-peaked, sawtooth modulation." + Little data has να been published. and we used. pre-release versions of new quantum ellicieney calibration files and canned. response— matrices (Sembay. private communication)," Little data has yet been published, and we used pre-release versions of new quantum efficiency calibration files and canned response matrices (Sembay, private communication)." + lHlowever. there were clear calibration. discrepancies between the two IEPIC-AIOS instruments below 0.4 keV (Fig. 3)).," However, there were clear calibration discrepancies between the two EPIC-MOS instruments below 0.4 keV (Fig. \ref{fig:system}) )." + We thus adcdec systematic errors of tto the data in this energy range., We thus added systematic errors of to the data in this energy range. + Other than this. we do no make allowance for calibration uncertainties in calculating vvalues.," Other than this, we do not make allowance for calibration uncertainties in calculating values." + The data from the two cameras were Litter simultaneously in the fits reported below., The data from the two cameras were fitted simultaneously in the fits reported below. + The X-ray emission in an LP arises from plasma heat to X-ray temperatures at a stanc-oll aceretion shock. which then cools as it approaches the white chwarl surface. AXizu 1973: Cropper 11999).," The X-ray emission in an IP arises from plasma heated to X-ray temperatures at a stand-off accretion shock, which then cools as it approaches the white dwarf surface Aizu 1973; Cropper 1999)." + The mode reproduces a multi-temperature spectrum. with a power-law distribution of temperatures. based on the plasma model.," The model reproduces a multi-temperature spectrum, with a power-law distribution of temperatures, based on the plasma model." + Fitting our phase-averaged spectrum with a model plus. simple and. partial-covering absorption (as conumonly found. in LPs) gave a poor fit (A2—220). owing to a large soft excess., Fitting our phase-averaged spectrum with a model plus simple and partial-covering absorption (as commonly found in IPs) gave a poor fit 20) owing to a large soft excess. + Adding a blackbody emitter to mocel the soft emission improved the fit hugely to AZ—11.38., Adding a blackbody emitter to model the soft emission improved the fit hugely to 1.38. + We then tried replacing the with two ccomponents and found a significant improvement in [it quality (47—11276. 42-1128) implying that a power-law is a poor description of the temperature. distribution in the plasma column.," We then tried replacing the with two components and found a significant improvement in fit quality 1276, 1.28) implying that a power-law is a poor description of the temperature distribution in the plasma column." + The best-fitting temperatures were 0.2 and 9 keV. The blackbody. component was still necessary, The best-fitting temperatures were 0.2 and 9 keV. The blackbody component was still necessary +Table A lists the polynomial coellicients for all the 10 filters (F225W. F275W and F336W coellicients are [rom Bellini Beclin 2000. reported here lor completeness).,"Table A lists the polynomial coefficients for all the 10 filters (F225W, F275W and F336W coefficients are from Bellini Bedin 2009, reported here for completeness)." +the phase interval B the independent fit with a model provides a large negative value of[. which is very different to that obtained from any other fit.,"the phase interval B the independent fit with a model provides a large negative value of$\Gamma$, which is very different to that obtained from any other fit." + This result can be explained by the large contribution of the component to the total flux. while in the other cases most of the flux is due to the component: in fact. for the phase interval B we can obtain a good fit also using a simple model (2/d.o.f.," This result can be explained by the large contribution of the component to the total flux, while in the other cases most of the flux is due to the component: in fact, for the phase interval B we can obtain a good fit also using a simple model $\chi^{2}_{\nu}$ /d.o.f." + = 1.17/33)., = 1.17/33). + This means that an additional component is required only to fit the high energy end of the spectrum. thus providing a large negative value of the photon index.," This means that an additional component is required only to fit the high energy end of the spectrum, thus providing a large negative value of the photon index." + Before the oobservation of the only X-ray investigation of this source was performed by citepReigRoche99.., Before the observation of the only X–ray investigation of this source was performed by \\citep{ReigRoche99}. + Therefore it is interesting to compare our results with those obtained ten years before., Therefore it is interesting to compare our results with those obtained ten years before. + From the timing analysis. we have obtained a new refined pulse period. = 853.4 + 0.2 s. which is lower than the previous value of 860 + 2 s found byRossiXTE.," From the timing analysis, we have obtained a new refined pulse period, = 853.4 $\pm$ 0.2 s, which is lower than the previous value of 860 $\pm$ 2 s found by." +. This implies à pulsar spin-up during the past ten years. with P=(191-Ε0.58)«10 ss Ll and suggests a momentum transfer to the neutron star.," This implies a pulsar spin–up during the past ten years, with $\dot P = (-1.91\pm0.58)\times10^{-8}$ s $^{-1}$, and suggests a momentum transfer to the neutron star." + Based on the observed source flux. we have estimated a source luninosity Ly~100 erg + in the 2-10 keV energy range (assuming a source distance of 5 kpe). which is one order of magnitude lower than the luminosity level detected byRossiXTE.," Based on the observed source flux, we have estimated a source luminosity $L_{\rm X} \sim 10^{34}$ erg $^{-1}$ in the 2–10 keV energy range (assuming a source distance of 5 kpc), which is one order of magnitude lower than the luminosity level detected by." +. From the spectral analysis. we have obtained a hydrogen column density Ny = (2.8 + 107! 7. which is much lower than the values estimated byRossiXTE:: the lowest result (obtained with a double BB model) was (2.1 + 4107? 7. which is almost one order of magnitude higher than our result: moreover. using our same model. the ddata provided a best-fit value of (8.2 + 10°? which is ~ 30 times higher than our value.," From the spectral analysis, we have obtained a hydrogen column density $N_{\rm H}$ = (2.8 $\pm$ $\times10^{21}$ $^{-2}$, which is much lower than the values estimated by: the lowest result (obtained with a double BB model) was (2.1 $\pm$ $\times10^{22}$ $^{-2}$, which is almost one order of magnitude higher than our result; moreover, using our same model, the data provided a best–fit value of (8.2 $\pm$ $\times10^{22}$ $^{-2}$, which is $\sim$ 30 times higher than our value." + On this subject. we emphasize that the energy range of the sspectral analysis (above 3 keV) is not well suited for a good estimate of Ny. while the low-energy end of the sspectra (0.2 keV) allows a much more reliable analysis.," On this subject, we emphasize that the energy range of the spectral analysis (above 3 keV) is not well suited for a good estimate of $N_{\rm H}$, while the low–energy end of the spectra (0.2 keV) allows a much more reliable analysis." + Moreover. we also note that LS 1698. the optical counterpart ofJ1037.5-5647.. has a color excess — 0.75 (2): assuming ;ly = 3.1 and the average relation Ay = Nyv5.59«10.72 ? between optical extinction and X-ray absorption (2).. this would predict δη=L16«1073 ?.a value comparable to our result.," Moreover, we also note that LS 1698, the optical counterpart of, has a color excess $\simeq$ 0.75 \citep{Motch+97}; assuming $A_{\rm V}$ = 3.1 and the average relation $A_{\rm V}$ = $N_{\rm H} \times 5.59 \times 10^{-22}$ $^{-2}$ between optical extinction and X–ray absorption \citep{PredehlSchmitt95}, this would predict $N_{\rm H}=4.16\times10^{21}$ $^{-2}$ , a value comparable to our result." + This indicates that in the oobservation the measured absorption is due to the interstellar mecium and not to local matter around the system. which has," This indicates that in the observation the measured absorption is due to the interstellar medium and not to local matter around the system, which has" +heat release (due to magnetic reconnection) near the disk is expected to be more complex than that modeled here.,heat release (due to magnetic reconnection) near the disk is expected to be more complex than that modeled here. +" In the presence of complex magnetic field configurations, the magnetic structure hosting the flaring plasma is expected to confine more efficiently the hot plasma, producing a flare evolution more similar to that described by 1D models."," In the presence of complex magnetic field configurations, the magnetic structure hosting the flaring plasma is expected to confine more efficiently the hot plasma, producing a flare evolution more similar to that described by 1D models." + It is worth emphasizing that our 3D simulation is focused on the effects of the flare on the stability of the disk and does not pretend to describe accurately the evolution of the flaring loop., It is worth emphasizing that our 3D simulation is focused on the effects of the flare on the stability of the disk and does not pretend to describe accurately the evolution of the flaring loop. +" Nevertheless, we show here that, even if the flare evolution is not described accurately, the length, maximum temperature, and peak X-ray luminosity of the flaring loop reproduced by our simulation resemble those derived from the analysis of the brightest X-ray flares observed in young low-mass stars (?))."," Nevertheless, we show here that, even if the flare evolution is not described accurately, the length, maximum temperature, and peak X-ray luminosity of the flaring loop reproduced by our simulation resemble those derived from the analysis of the brightest X-ray flares observed in young low-mass stars \citealt{2005ApJS..160..469F}) )." +" We are confident, therefore, that the flare simulated here is appropriate to investigate the effects of bright flares observed in young stars on the stability of the disk."," We are confident, therefore, that the flare simulated here is appropriate to investigate the effects of bright flares observed in young stars on the stability of the disk." +" During the flare evolution, the injected heat pulse produces an overpressure in the disk at the footpoint of the loop."," During the flare evolution, the injected heat pulse produces an overpressure in the disk at the footpoint of the loop." +" This overpressure travels through the disk and reaches the opposite boundary after ~5 hours, where it pushes the plasma out to form an intense funnel stream."," This overpressure travels through the disk and reaches the opposite boundary after $\approx +5$ hours, where it pushes the plasma out to form an intense funnel stream." +" Figure 5 shows the distributions of density and pressure in (19,2) slices passing through the middle of the stream."," Figure \ref{stream_evol} shows the distributions of density and pressure in $(R,z)$ slices passing through the middle of the stream." + The overpressure wave triggering the stream is evident in the bottom panels., The overpressure wave triggering the stream is evident in the bottom panels. + This new intense stream flows along the dipolar magnetic field lines and impacts onto the stellar surface e25 hours after the injection of the heat pulse., This new intense stream flows along the dipolar magnetic field lines and impacts onto the stellar surface $\approx 25$ hours after the injection of the heat pulse. + The right panels in Fig., The right panels in Fig. + 3 show a cutaway view of the star-disk system (upper panel) after the impact of the stream onto the stellar surface and a schematic view of the system during the stream evolution (lower panel)., \ref{fig1} show a cutaway view of the star-disk system (upper panel) after the impact of the stream onto the stellar surface and a schematic view of the system during the stream evolution (lower panel). +" As a result, the stream accretes substantial mass onto the young star from the side of the disk opposite to the post-flare loop."," As a result, the stream accretes substantial mass onto the young star from the side of the disk opposite to the post-flare loop." +" Our 3D simulation follows the evolution of the accretion stream for additional 23 hours, for a total of 48 hours."," Our 3D simulation follows the evolution of the accretion stream for additional 23 hours, for a total of 48 hours." + In this time lapse the stream gradually approaches a quasi-stationary condition., In this time lapse the stream gradually approaches a quasi-stationary condition. + We analyzed the dynamics of the stream by deriving the forces at work along a fiducial magnetic field line nested within the stream., We analyzed the dynamics of the stream by deriving the forces at work along a fiducial magnetic field line nested within the stream. + Initially the stream is triggered by a strong pressure gradient due to the overpressure wave originating from the flare., Initially the stream is triggered by a strong pressure gradient due to the overpressure wave originating from the flare. + The pressure gradient force drives the material out of the disk and channels it into a funnel flow., The pressure gradient force drives the material out of the disk and channels it into a funnel flow. + Then the gravitational force accelerates the escaped material toward the central star., Then the gravitational force accelerates the escaped material toward the central star. + These forces evolve with time and Fig., These forces evolve with time and Fig. + 6 shows them along the fiducial field line after the stream impacts the stellar surface.," \ref{fig2} + shows them along the fiducial field line after the stream impacts the stellar surface." +" At this stage, the pressure gradient is still effective in pushing the disk material out of the disk, but it acts in the opposite direction (against the free-fall of matter) in most of the accretion stream."," At this stage, the pressure gradient is still effective in pushing the disk material out of the disk, but it acts in the opposite direction (against the free-fall of matter) in most of the accretion stream." +" The pressure gradient becomes the dominant force close to the stellar surface, substantially braking (but not stopping) the accretion flow."," The pressure gradient becomes the dominant force close to the stellar surface, substantially braking (but not stopping) the accretion flow." +" As discussed below, at this stage of evolution, the stream has not yet reached a quasi-stationary condition."," As discussed below, at this stage of evolution, the stream has not yet reached a quasi-stationary condition." +" Later, when the stream stabilizes, the gravitational force dominates the stream evolution and the plasma continuously accelerates toward the star, approaching the free-fall speed ug at the star's photosphere."," Later, when the stream stabilizes, the gravitational force dominates the stream evolution and the plasma continuously accelerates toward the star, approaching the free-fall speed $u\rs{ff}$ at the star's photosphere." + Other forces acting against the free-fall of matter are the centrifugal force and a backward force due to the magnetic mirror effect when the material approaches the star (see also ??)).," Other forces acting against the free-fall of matter are the centrifugal force and a backward force due to the magnetic mirror effect when the material approaches the star (see also \citealt{2002ApJ...578..420R, 2009A&A...508.1117Z}) )." +" However, these forces are much smaller than the others and do not play any relevant role in the stream dynamics (Fig. 6;;"," However, these forces are much smaller than the others and do not play any relevant role in the stream dynamics (Fig. \ref{fig2};" + see also ??)).," see also \citealt{2002ApJ...578..420R, 2009A&A...508.1117Z}) )." + Figure 7 shows the profiles of particle number density and different velocities along the fiducial magnetic field line shown in Fig., Figure \ref{fig4_s} shows the profiles of particle number density and different velocities along the fiducial magnetic field line shown in Fig. + 6 at time t—36 hours., \ref{fig2} at time $t=36$ hours. + The matter flows with poloidal velocity ustr., The matter flows with poloidal velocity $u\rs{str}$. +" The flow is accelerated by gravity and becomes supersonic at a distance of +2x10!! cm from the disk, while the stream density decreases."," The flow is accelerated by gravity and becomes supersonic at a distance of $\approx 2\times 10^{11}$ cm from the disk, while the stream density decreases." +" T'he flow gradually approaches the free-fall velocity ug, reaching a maximum velocity of ustr©200 km s~* at szz10! cm (usuzz 0.8ug)."," The flow gradually approaches the free-fall velocity $u\rs{ff}$, reaching a maximum velocity of $u\rs{str}\approx 200$ km $^{-1}$ at $s\approx +10^{11}$ cm $u\rs{str}\approx 0.8 u\rs{ff}$ )." + Then the flow slightly brakes while the stream density increases again approaching the stellar surface., Then the flow slightly brakes while the stream density increases again approaching the stellar surface. +" As discussed above, the slowdown of the flow is due to the pressure gradient force acting against the free-fall of matter for s ranging between 0.5x10!! and 1x10’! cm (see Fig. 6))."," As discussed above, the slowdown of the flow is due to the pressure gradient force acting against the free-fall of matter for $s$ ranging between $0.5\times 10^{11}$ and $1\times 10^{11}$ cm (see Fig. \ref{fig2}) )." + 'This feature is present until the end of our 3D simulation at t©48 hours., This feature is present until the end of our 3D simulation at $t\approx 48$ hours. +" To further investigate the evolution of the accretion stream, we performed an additional simulation with the same parameters of the 3D simulation discussed above but carried out in 2.5 dimensions (2.5D), that is, in"," To further investigate the evolution of the accretion stream, we performed an additional simulation with the same parameters of the 3D simulation discussed above but carried out in 2.5 dimensions (2.5D), that is, in" +"The mos ""udineutary models of accreion disks orediet. temperatwes at distauces such as hose of interest here (few parsecs) that are 00 low to unply the presence o: jonizecd eas.",The most rudimentary models of accretion disks predict temperatures at distances such as those of interest here (few parsecs) that are too low to imply the presence of ionized gas. + But the ree-[ree abso1TSion shows that such gas is present., But the free-free absorption shows that such gas is present. +" Otler lines of evidence. based on attempts to uxlerstaud op—ical lines. also suggest tha jonized gas ls jresent 'efereucestheri αι,"," Other lines of evidence, based on attempts to understand optical lines, also suggest that ionized gas is present \citep[see][and references therin]{C99}." + Ht dis possible that such gas is not jn tie plane of the ¢isk. but rather in an atmosphere or wind above the disk that is icüzed by &ereetic photous fΟι the cent‘al regious of he system.," It is possible that such gas is not in the plane of the disk, but rather in an atmosphere or wind above the disk that is ionized by energetic photons from the central regions of the system." + Iftus is the case. the coustraius shown iu Figwe | apply to tle Jonlzec atmosphere or wiud. not he neutral core of the cisk.," If this is the case, the constraints shown in Figure \ref{recomb10000} apply to the ionized atmosphere or wind, not the neutral core of the disk." + I£ a wind is iiolvec 1991).. itis l1xey that the the velocity wotld be outside the observed wiudow. providiug a uatural explanation for the lack of an observed recombination ine even if it weren't for the effects of the external radiation.," If a wind is involved \citep[see, for example][]{K94}, it is likely that the the velocity would be outside the observed window, providing a natural explanation for the lack of an observed recombination line even if it weren't for the effects of the external radiation." + A search has been iade for the Πόσα recombination line in the radio source 3C 81 in tl center of NCGCI275., A search has been made for the $\alpha$ recombination line in the radio source 3C 84 in the center of NGC1275. + Observatious of free-Iree absorpion agalust the norhern feature at about ... pe projected distalice row the core of this source suggested that. for a wide range of possiT densities. such rec‘ouiration lines could be observe.," Observations of free-free absorption against the northern feature at about 2.5 pc projected distance from the core of this source suggested that, for a wide range of possible densities, such recombination lines could be observed." + The recombinatio1 lines were only. expect to be observed agaiust he weak nortjern feature whichi is probably the receediug jet ou tle [ar sic ol the source., The recombination lines were only expected to be observed against the weak northern feature which is probably the receeding jet on the far side of the source. + The abiliy ofthe VLBA o separate this feature [roi the 'est of the source spatia was used to relax the oudpass caliration requirenellts and to allow he use of a novel sche to to do ai accurate baudpass calib‘alion based ou the source itself., The ability of the VLBA to separate this feature from the rest of the source spatially was used to relax the bandpass calibration requirements and to allow the use of a novel scheme to to do an accurate bandpass calibration based on the source itself. + Tese advautages alowec much deeper search fo: the recombillaion line to ye]nade than woulc have been possile wi lower spatial resoution., These advantages allowed a much deeper search for the recombination line to be made than would have been possible with lower spatial resolution. + No Πόσα liue was found., No $\alpha$ line was found. + Tje. limi ou the optical depth is approximatly 0.15. deperding on exacly how the 1Jeasture nentsare mace and what 'eglcyt ds Lueastuect.," The limit on the optical depth is approximatly 0.15, depending on exactly how the measurements are made and what region is measured." +" The non-detectio1 is expeced because of sattration and ""adiatiou clamp!he causec by the luteise radio racation {'om the jets.", The non-detection is expected because of saturation and radiation damping caused by the intense radio radiation from the jets. + Therefore coiclusious ca1not be made abou the physica concditious in the the free-[ree asorbiig region uuless that regiou is actually 1nicl furtler [rou he jets that the geonetry WOLld suggest — a bare minimui of twice as [ar expecLed. auc xobady much frther., Therefore conclusions cannot be made about the physical conditions in the the free-free absorbing region unless that region is actually much further from the jets than the geometry would suggest — a bare minimum of twice as far as expected and probably much further. + LrIf sattration aid radiation damping we‘e pot all Issue. 'ecombluatiol ine optical «eptl limi| would Constral ithe [ree-[ree absorbing material to have : 'ombination of ueh liue width aud high densiyo as shown in Figure L.," If saturation and radiation damping were not an issue, the recombination line optical depth limit would constrain the free-free absorbing material to have a combination of high line width and high density, as shown in Figure \ref{recomb10000}." + Alternativels. the absorbine material coulc inve a velocity Sienificantly oIset {rori the systemic value.," Alternatively, the absorbing material could have a velocity significantly offset from the systemic value." + High line widths atd offset. velocities are ofen seen in AGN. inclucing NCC 1275.," High line widths and offset velocities are often seen in AGN, including NGC 1275." + The most extreme velocities aid line widths are in he BLR. wlich is siualler th:ui tlie region of the absorption. but velocities adecuate to hide the 'ecolnujnation liie could occur on the :ippropriate scales.," The most extreme velocities and line widths are in the BLR, which is smaller than the region of the absorption, but velocities adequate to hide the recombination line could occur on the appropriate scales." +contains few objects with large redshifts and no radio fluxes below a certain limit.,contains few objects with large redshifts and no radio fluxes below a certain limit. + These two factors contribute to enhance the population of very luminous radio objects in the simulated data-sets (when an average or large radio flux is associated to a large z). while the region with high redshift and low radio luminosity is still under-populated. leading to steeper slopes. Le. objects more radio-Iuminous than the real ones.," These two factors contribute to enhance the population of very luminous radio objects in the simulated data-sets (when an average or large radio flux is associated to a large z), while the region with high redshift and low radio luminosity is still under-populated, leading to steeper slopes, i.e. objects more radio-luminous than the real ones." + As a last check. we also performed the “scrambling test” for the flux-flux correlations.," As a last check, we also performed the “scrambling test” for the flux-flux correlations." + In this ease. the simulated Spearman correlation coefficients are centered (both for 6 and 20 em) in 0. as expected for random uncorrelated points (see Fig 10)).," In this case, the simulated Spearman correlation coefficients are centered (both for 6 and 20 cm) in 0, as expected for random uncorrelated points (see Fig \ref{scrambling_flux}) )." + Not even a simulated data-set has a correlation coefficient as large as the ones measured in the real data-sets. in agreement with the very low estimated NHP in the latter.," Not even a simulated data-set has a correlation coefficient as large as the ones measured in the real data-sets, in agreement with the very low estimated NHP in the latter." + However. the strong correlation found between the X-ray and radio fluxes in CAIXA may still be implicitly due by distance effects.," However, the strong correlation found between the X-ray and radio fluxes in CAIXA may still be implicitly due by distance effects." + Due to selection effects. X-ray fluxes are tightly linked to redshift.," Due to selection effects, X-ray fluxes are tightly linked to redshift." + This is clearly shown in Fig. 9..," This is clearly shown in Fig. \ref{zdist_fluxbin}," + where we plot the redshift distributions of the sources in CAIXA in four hard X-ray flux bins., where we plot the redshift distributions of the sources in CAIXA in four hard X-ray flux bins. + The evolution of the distributions is evident: faint objects are clustered at high z. while bright sources are peaked at low z. Therefore. although we cannot exclude the presence of a physical correlation between hard X-ray and radio fluxes in CAIXA. we are unable to disentangle it from the selection effects present in the catalogue.," The evolution of the distributions is evident: faint objects are clustered at high z, while bright sources are peaked at low z. Therefore, although we cannot exclude the presence of a physical correlation between hard X-ray and radio fluxes in CAIXA, we are unable to disentangle it from the selection effects present in the catalogue." + In conclusions. the observed correlation between radio and hard X-ray luminosity appears extremely significant on the basis of standard statistical tests (Spearman. correlation coefficients. partial Kendall correlation). but the role of distance effect may be dominant in determining. the significance and functional. relation.," In conclusions, the observed correlation between radio and hard X-ray luminosity appears extremely significant on the basis of standard statistical tests (Spearman correlation coefficients, partial Kendall correlation), but the role of distance effect may be dominant in determining the significance and functional relation." +" In. particular. the scrambling test shows that even the widely used partial Kendall correlation may underestimate the distance effects. thus care must be taken when interpreting the results derived from it,"," In particular, the scrambling test shows that even the widely used partial Kendall correlation may underestimate the distance effects, thus care must be taken when interpreting the results derived from it." + However. random scrambling cannot reproduce the observed slope of the luminosity correlation. and destroys the flux-flux correlation. which is instead observed to be significant.," However, random scrambling cannot reproduce the observed slope of the luminosity correlation, and destroys the flux-flux correlation, which is instead observed to be significant." + Both results may represent the revealing signs of a real underlying correlation. but they can also be induced by the incompleteness of CAIXA.," Both results may represent the revealing signs of a real underlying correlation, but they can also be induced by the incompleteness of CAIXA." + Therefore. although a physical correlation may be present in our data. we conservatively cannot draw any conclusion from the X-ray/radio correlations in CAIXA.," Therefore, although a physical correlation may be present in our data, we conservatively cannot draw any conclusion from the X-ray/radio correlations in CAIXA." + We would like to stress that this is true for CAIXA. which includes upper limits. but it is by no means a flux-limited or volume-limited sample. while distance effects may of course play less important roles in other catalogues or in complete samples.," We would like to stress that this is true for CAIXA, which includes upper limits, but it is by no means a flux-limited or volume-limited sample, while distance effects may of course play less important roles in other catalogues or in complete samples." + In the left panel of Fig. 11..," In the left panel of Fig. \ref{rx_ro}," + we plot the correlation between the two radio-loudness parameters used to exclude the radio-loud objects in CAIXA. one based on the optical fluxes found in literature. the other on the X-ray fluxes measured in this work (see BOY for details).," we plot the correlation between the two radio-loudness parameters used to exclude the radio-loud objects in CAIXA, one based on the optical fluxes found in literature, the other on the X-ray fluxes measured in this work (see B09 for details)." + As expected. a highly significant linear regression between the two parameters is found (see Table 1)).," As expected, a highly significant linear regression between the two parameters is found (see Table \ref{corr}) )." +" The slope of the best fit (0.88+0.06) is perfectly in agreemer= with the ones found by ? and ?.. even if their samples include also radio-loud objects. thus spanning a larger range both for Εν and R,."," The slope of the best fit $0.88\pm0.06$ ) is perfectly in agreement with the ones found by \citet{tw03} and \citet{panessa07}, even if their samples include also radio-loud objects, thus spanning a larger range both for $\mathrm{R_X}$ and $\mathrm{R_o}$." + In the right panel of Fig. Il...," In the right panel of Fig. \ref{rx_ro}," + we show the X-ray radio-loudness parameter versus the Eddington ratio., we show the X-ray radio-loudness parameter versus the Eddington ratio. + ? found an highly significant anti-correlation between these two parameters. suggesting that weakly active nuclei are powered by advection-dominated accretion flows (ADAFs). which give rise to radio-loud spectra.," \citet{ho02} found an highly significant anti-correlation between these two parameters, suggesting that weakly active nuclei are powered by advection-dominated accretion flows (ADAFs), which give rise to radio-loud spectra." + Although this trend seems to be observed in CAIXA. the anti-correlation is not significant (p=—0.14 - NHP=0.19).," Although this trend seems to be observed in CAIXA, the anti-correlation is not significant $\rho=-0.14$ - NHP=0.19)." + However. this is not unexpected. because our catalogue does not include radio-loud objects and. indeed. the large Rx-low Lpo4/Lu4 region is not populated in our plot.," However, this is not unexpected, because our catalogue does not include radio-loud objects and, indeed, the large $\mathrm{R_X}$ -low $\mathrm{L_{bol}/L_{Edd}}$ region is not populated in our plot." + Finally. we note here that no correlation is apparent between the soft to hard X-ray luminosity ratio and the radio luminosity.," Finally, we note here that no correlation is apparent between the soft to hard X-ray luminosity ratio and the radio luminosity." + Apart from the correlations with Hg and the X-ray luminosity ratio. already discussed in Sect. 2.1..," Apart from the correlations with $\beta$ and the X-ray luminosity ratio, already discussed in Sect. \ref{hbeta}," + there are no other significant correlations with the hard X-ray spectral index in CAIXA., there are no other significant correlations with the hard X-ray spectral index in CAIXA. + In particular. in the literature. there are claims of a correlation between DL; and the 2-10 keV luminosity ??).. but there are also several studies that do not find such a correlation (e.g.2?2)..," In particular, in the literature there are claims of a correlation between $\Gamma_h$ and the 2-10 keV luminosity \citep[e.g.][]{dai04,saez08}, but there are also several studies that do not find such a correlation \citep[e.g.][]{rt00,george00,win09}." + In CAIXA. this correlation is not significant confidence level): we note here that this confidence level is not far from the ones quoted by ? and ?.. unless the correlation is calculated in particular bins of (relatively high) redshift.," In CAIXA, this correlation is not significant confidence level): we note here that this confidence level is not far from the ones quoted by \citet{dai04} and \citet{saez08}, unless the correlation is calculated in particular bins of (relatively high) redshift." + In other words. the low significance of the Γη [ινιο correlation in CAIXA 1s in agreement with previous studies. even with those which claim the correlation is real.," In other words, the low significance of the $\Gamma_h$ $L_\mathrm{2-10}$ correlation in CAIXA is in agreement with previous studies, even with those which claim the correlation is real." + Nonetheless. we remind that significant difference," Nonetheless, we remind that significant difference" +broad lines in NGC 4203 was caused bv the ongoing Udal disruption of a red supergiant star which would have made ~ 1.5 orbits in the time span of the$779 observations supergiantstarsexistinSO galaxies)..,broad lines in NGC 4203 was caused by the ongoing tidal disruption of a red supergiant star which would have made ${\sim}$ 1.5 orbits in the time span of the observations \cite[see][for evidence that red supergiant stars exist in S0 galaxies]{Dav10}. + In the tidal disruption scenario. the average densitv of ionized gas responsible lor the double-peaked broad La emission line is likelv to be comparable to the outer atmosphere of Detelgeuse for which n ~ 5 x 10! ? (Raviοἱal.2011).. high enough. perhaps. to explain the anomalous Balmer decrement noted in Section 2.0.4.," In the tidal disruption scenario, the average density of ionized gas responsible for the double-peaked broad ${\alpha}$ emission line is likely to be comparable to the outer atmosphere of Betelgeuse for which n ${\sim}$ 5 ${\times}$ $^{11}$ $^{-3}$ \citep{Rav11}, high enough, perhaps, to explain the anomalous Balmer decrement noted in Section 2.0.4." + The mass of gas can be estimated using equation 2. an effective recombination coefficient aff) = L16 x P em? Land a Iuminositv L(4Ja) = 1.38 x 105 L.. based on the between the broad line flux measured in 2010 and 1999 which should more closely represent. that produced by just the ring in 2010.," The mass of gas can be estimated using equation 2, an effective recombination coefficient ${\alpha^{eff}_{H\alpha}}$ = 1.16 x $^{-13}$ ${^{3}}$ ${^{-1}}$ and a luminosity $L (H{{\alpha}}$ ) = 1.38 x ${^6}$ ${_{\sun}}$, based on the between the broad line flux measured in 2010 and 1999 which should more closely represent that produced by just the ring in 2010." + The resulting of ionized gas corresponds to ~ 2 x > M. and is presumably strewn in a ring shaped contrail marking the trajectory of the supergiant much as envisaged by Scoville&Norman(1995.see(theirFig.1) and Boedanovieetal.(2004.anclreferences therein).., The resulting of ionized gas corresponds to ${\sim}$ 2 ${\times}$ ${^{-5}}$ ${_\odot}$ and is presumably strewn in a ring shaped contrail marking the trajectory of the supergiant much as envisaged by \citet[][see their Fig. 1]{Sco95} and \citet[][and references therein]{Bog04}. + More recently Maiolinoetal.(2010). describe objects shaped like comets orbiting aud eclipsing the central N-ray source in NGC 1365., More recently \cite{Mai10} describe objects shaped like comets orbiting and eclipsing the central X-ray source in NGC 1365. + The defining haracteristies of their “comets” — a dense head and low mass tail are intriguingly similar to the those proposed here for the supereiant producing the stellaa-contrail in NGC 4203., The defining characteristics of their “comets” – a dense head and low mass tail – are intriguingly similar to the those proposed here for the supergiant producing the stellar-contrail in NGC 4203. + It was noted in section 4.3 that NGC 4203 suffers [rom an ionizing deficit that. was parlicularly acute in 2010., It was noted in section 4.3 that NGC 4203 suffers from an ionizing deficit that was particularly acute in 2010. + The delicit could be alleviated if the AGN had brightened by a factor of 4 since 2003. but this is unlikely as the amplitude of the UV variability is ~ αἱ the shortest wavelength when it was measured by Maozοἱal.(2005).," The deficit could be alleviated if the AGN had brightened by a factor of 4 since 2003, but this is unlikely as the amplitude of the UV variability is ${\sim}$ at the shortest wavelength when it was measured by \cite{Mao05}." +. Frathermore. one can nol appeal to a boost of N-ravs as no X-ray variability has been detected (Pianοἱal.2010:Porquet.Sabra.&Reeves 2011).," Furthermore, one can not appeal to a boost of X-rays as no X-ray variability has been detected \citep{Pia10, You11}." +. ILowever. the broad Ila line emission observed in 2010 is dominated by the double-peaked broad line component (hat is attributed to the tidal disruption event.," However, the broad ${\alpha}$ line emission observed in 2010 is dominated by the double-peaked broad line component that is attributed to the tidal disruption event." + Thus. it is quite conceivable that ram pressure shock ionization produced by the interaction of the in-falling supergiant star with (he ambient interstellar medium could provide an additionalmechanical source of ionization that would help alleviate the ionizing deficit noted for NGC 4203.," Thus, it is quite conceivable that ram pressure shock ionization produced by the interaction of the in-falling supergiant star with the ambient interstellar medium could provide an additional source of ionization that would help alleviate the ionizing deficit noted for NGC 4203." + Note that ram pressure ionization is a very different mechanism for exciting the contrail than proposed by Rees(1988). which appeals to externalflares eenerated by material as il is accreted onto the DIL (e.g.Gezarietal. 2003).., Note that ram pressure ionization is a very different mechanism for exciting the contrail than proposed by \citet{Rees88} which appeals to external generated by material as it is accreted onto the BH \citep[e.g.][]{Gez03}. . + Ram pressure ionization is producedin-sihu., Ram pressure ionization is produced. + Although ram pressure ionization was discussed previously in (he context of the tail of ionized gas leaving the Galactic Center M supereiant IRS 7 (Serabvn.1991;Yusel-Zacleh&Melia1992) there is a need to explicitly model the tidal disruption of a supergiante star as existinge studies have tended to locus onsolar," Although ram pressure ionization was discussed previously in the context of the tail of ionized gas leaving the Galactic Center M supergiant IRS 7 \citep{Ser91, Yus92} there is a need to explicitly model the tidal disruption of a supergiant star as existing studies have tended to focus onsolar" +cover the ranges 3—45 mJy (at 100 um) and 5.5—72 mJy (at 160 um); the COSMOS field allows upper boundaries to be extended to 142 and 179 mJy.,cover the ranges $3-45$ mJy (at 100 $\mu$ m) and $5.5-72$ mJy (at 160 $\mu$ m); the COSMOS field allows upper boundaries to be extended to 142 and 179 mJy. +" Integrating the counts over the whole flux range, we obtain vI,=6.36+1.67 and 6.58+1.62 [nW m sr-!], within 1.3c and 1.0σ from the reference values at 100 and 160 jum, respectively (Fig. 2))."," Integrating the counts over the whole flux range, we obtain $\nu I_\nu=6.36\pm1.67$ and $6.58\pm1.62$ $[$ nW $^{-2}$ $^{-1}]$, within $\sigma$ and $\sigma$ from the reference values at 100 and 160 $\mu$ m, respectively (Fig. \ref{fig:pep_cib}) )." + These correspond to ~45+12% and ~52+13% of the ? estimate., These correspond to $\sim 45\pm12$ and $\sim52\pm13$ of the \citet{dole2006} estimate. + The derived uncertainty now also includes the effect of Poisson statistics and not only photometric errors., The derived uncertainty now also includes the effect of Poisson statistics and not only photometric errors. +" The bright end of number counts, covered only by COSMOS, gives a small contribution (4— 6%)) to the total CIB surface brightness."," The bright end of number counts, covered only by COSMOS, gives a small contribution $\sim4-6$ ) to the total CIB surface brightness." +" The PACS detection rate of Spitzer 24 um sources (S24 ge220 uJy, is roughly15%.", The PACS detection rate of Spitzer 24 $\mu$ m sources \citep[$S_{24} 20 $\mu$ is roughly. +". It is possible to derive a deeper CIB estimate, through stacking on the PEP maps at the positions of all 24 um objects, including those not detected in the FIR (e.g.?).."," It is possible to derive a deeper CIB estimate, through stacking on the PEP maps at the positions of all 24 $\mu$ m objects, including those not detected in the FIR \citep[e.g.][]{dole2006}." + Uncertainties on the stacked fluxes are computed via a simple bootstrap procedure., Uncertainties on the stacked fluxes are computed via a simple bootstrap procedure. +" The CIB surface brightness produced by 24 um sources is 7.39+0.48 and 9.57+0.71 [nW m sr-!] at 100 and 160 jm, consistent with ?,, and providing ~51% and ~75% of the total background, within 1.1c and 0.5c from ?.."," The CIB surface brightness produced by 24 $\mu$ m sources is $7.39\pm0.48$ and $9.57\pm 0.71$ $[$ nW $^{-2}$ $^{-1}]$ at 100 and 160 $\mu$ m, consistent with \citet{bethermin2010}, and providing $\sim$ and $\sim$ of the total background, within $\sigma$ and $\sigma$ from \citet{dole2006}." +" In the attempt to reproduce the observed ISO and Spitzer number counts, several authors built “backward” evolutionary models, including luminosity and/or density evolution, as well as different galaxy populations."," In the attempt to reproduce the observed ISO and Spitzer number counts, several authors built “backward” evolutionary models, including luminosity and/or density evolution, as well as different galaxy populations." +" In Fig. 1,,"," In Fig. \ref{fig:pep_counts}," + we overlay recent models onto the observed PACS counts., we overlay recent models onto the observed PACS counts. +" We include in this collection also the ? A-CDM semi-analytical model (SAM), complemented with radiative transfer dust reprocessing."," We include in this collection also the \citet{lacey2009} $\Lambda$ -CDM semi-analytical model (SAM), complemented with radiative transfer dust reprocessing." +" The most successful models are the ?,, including luminosity-dependent distribution functions for the galaxy IR SEDs and their AGN contribution, and ?,, employing analytic evolutionary functions without discontinuities and 4 galaxy populations."," The most successful models are the \citet{valiante2009}, including luminosity-dependent distribution functions for the galaxy IR SEDs and their AGN contribution, and \citet{rowanrobinson2009}, employing analytic evolutionary functions without discontinuities and 4 galaxy populations." +" Gruppioni and ? overestimate the amplitude of the number counts peak in both bands, while ? and ? reproduce the counts fairly well only in one channel (100 and 160 um, respectively)."," Gruppioni and \citet{lagache2004} overestimate the amplitude of the number counts peak in both bands, while \citet{franceschini2009} and \citet{leborgne2009} reproduce the counts fairly well only in one channel (100 and 160 $\mu$ m, respectively)." +" It is worth recalling that to date most of these models have been fine-tuned to reproduce mid-IR and sub-mm statistics, while a big gap in wavelength was affecting far-IR predictions."," It is worth recalling that to date most of these models have been fine-tuned to reproduce mid-IR and sub-mm statistics, while a big gap in wavelength was affecting far-IR predictions." +" Most include a luminosity evolution ος(1+z)?9-9, but the redshift limit for this slope, the details of density evolution, or the adopted galaxy zoo vary significantly from author to author."," Most include a luminosity evolution $\propto(1+z)^{3.0-3.5}$, but the redshift limit for this slope, the details of density evolution, or the adopted galaxy zoo vary significantly from author to author." +" Besides spanning a much wider range of observational data (UV, optical, near-IR luminosity functions, galaxy sizes, metallicity, etc.),"," Besides spanning a much wider range of observational data (UV, optical, near-IR luminosity functions, galaxy sizes, metallicity, etc.)," +" the SAM approach suffers here for a limited flexibility in the choice of parameters, and significantly overestimates the bright end of PACS counts."," the SAM approach suffers here for a limited flexibility in the choice of parameters, and significantly overestimates the bright end of PACS counts." +" Moreover, it cannot reproduce the peak, especially in the green band."," Moreover, it cannot reproduce the peak, especially in the green band." +" Thanks to the rich ancillary dataset in GOODS-N, we split the far-IR number counts into redshift bins (Fig. 3))."," Thanks to the rich ancillary dataset in GOODS-N, we split the far-IR number counts into redshift bins (Fig. \ref{fig:pep_counts_redshift}) )." + This elaboration offers a remarkable chance to set detailed constraints on the evolution of the galaxy populations adopted in current recipes., This elaboration offers a remarkable chance to set detailed constraints on the evolution of the galaxy populations adopted in current recipes. + This view highlights some new features and the main problems of the models under discussion., This view highlights some new features and the main problems of the models under discussion. +" First, in the lowest redshift bin, 0.0«z<0.5, the differential number counts, normalized to the Euclidean slope, monotonically increase as a function of flux, resembling the trend expected for a non-evolving population of galaxies."," First, in the lowest redshift bin, $0.0 would0.25. making up a total of 1911uiobjects.,"galaxies (RSGs) are chosen to be those with U–B $\geq$ 0.25, making up a total of 1941 objects." + Ideally. we also like to select galaxies on edss of morpholosx. but we uufortunatelv lack that information for the saluple uuder analysis.," Ideally, we would also like to select galaxies on the basis of morphology, but we unfortunately lack that information for the sample under analysis." + Therefore. iu order to minimize contanunation bv stronely reddened late-tvpe sealaxies we mupose another cut. based on the equivalent width (EW) of [OT] 3727 (see definition by Fisher 1998).," Therefore, in order to minimize contamination by strongly reddened late-type galaxies we impose another cut, based on the equivalent width (EW) of [OII] 3727 (see definition by Fisher 1998)." + This is illustrated in the right panel of Figure 1.. where a histogram of [ΟΠ EWs is shown for all RSCs In our seuple.," This is illustrated in the right panel of Figure \ref{fig1}, where a histogram of [OII] EWs is shown for all RSGs in our sample." + Strong cmissiou-lne RSGs have very negative values of ΕΑΝΟΠ while the zero of [OT] clnission is at ~ 3.7 A (Nouidaris in preparation)., Strong emission-line RSGs have very negative values of EW[OII] while the zero of [OII] emission is at $\sim$ 3.7 ${\rm\AA}$ (Konidaris in preparation). + The distribution is strouely peaked at very low [OTT] emission values with a loug tail towards galaxies with strong ΟΤΙ emission., The distribution is strongly peaked at very low [OII] emission values with a long tail towards galaxies with strong [OII] emission. +" Contamination by reddened late-type galaxies is likely to be more importaut in the strone-ciuuission line regime. so that we remove from our sample all galaxies with [OM] EW < 5 A,"," Contamination by reddened late-type galaxies is likely to be more important in the strong-emission line regime, so that we remove from our sample all galaxies with [OII] EW $\leq$ –5 ${\rm\AA}$." + This euissiou-line cut aciuittedly leaves in our sample a large nuniber of galaxies in the low-ciission Ime regia., This emission-line cut admittedly leaves in our sample a large number of galaxies in the low-emission line regime. + These are mostly ACN on the basis of the ratios between [OTI] and residual Daliner line eiissiou (Schiavon in preparation. IKonidaris iu preparation). as has been also found for low redshift RSCs(Phillips 1986. Riuupazzo 2005. and Yan 2006).," These are mostly AGN on the basis of the ratios between [OII] and residual Balmer line emission (Schiavon in preparation, Konidaris in preparation), as has been also found for low redshift RSGs (Phillips 1986, Rampazzo 2005, and Yan 2006)." + The color aud emission-line cuts leave us with a sample of 1160 salaxies., The color and emission-line cuts leave us with a sample of 1160 galaxies. + We create six subsaniples out of this set of galaxies. three with varving colors but the same redshift range. aud three with wirviug redshifts. but consistent colors aud luminosities.," We create six subsamples out of this set of galaxies, three with varying colors but the same redshift range, and three with varying redshifts, but consistent colors and luminosities." + The color aud redshift limits of cach bin are listed in Table 1.., The color and redshift limits of each bin are listed in Table \ref{tbl1}. + In au attempt to conrpare objects with simular masses. galaxies iu tle color and redshift sub-seunnples were further selected within l maes-wide Ag intervals where the central magnitude was chosen to be cousisteut with passive evolution from the age and ietallicity of the lieh-: sample.," In an attempt to compare objects with similar masses, galaxies in the color and redshift sub-samples were further selected within 1 mag-wide $M_B$ intervals where the central magnitude was chosen to be consistent with passive evolution from the age and metallicity of the $z$ sample." + However. adopting the exact same Mp interval for each + bin docs not change the results.," However, adopting the exact same $M_B$ interval for each $z$ bin does not change the results." + The umubers of galaxies in cach bin are listed in Table 1, The numbers of galaxies in each bin are listed in Table \ref{tbl1}. + The 1160 ealaxy spectra were visually inspected iu order to clean the sample from ai few misclassified stars. ealaxics with wrong redshifts. aud zero-S/N spectra.," The 1160 galaxy spectra were visually inspected in order to clean the sample from a few misclassified stars, galaxies with wrong redshifts, and zero-S/N spectra." + A rough relative fluxiug was achieved by dividing cach spectra by the normalized throughput of the DEIMOS spectrograph with the 1200 l/nuu erating., A rough relative fluxing was achieved by dividing each spectrum by the normalized throughput of the DEIMOS spectrograph with the 1200 l/mm grating. + Before coaddition. the spectra were brought to restfraune and then nonualized through division bv the average (o-clipped) counts within the AA 39001100. A interval," Before coaddition, the spectra were brought to restframe and then normalized through division by the average $\sigma$ -clipped) counts within the $\lambda\lambda$ 3900--4100 ${\rm\AA}$ interval." + Coaddition was performed adopting a a-clipping procedure to cliuinate sky-subtraction residuals. zero-count pixels due to CCD gaps. and other spectral blemishes.," Coaddition was performed adopting a $\sigma$ -clipping procedure to eliminate sky-subtraction residuals, zero-count pixels due to CCD gaps, and other spectral blemishes." + After several tests the best results were obtained when a sinele 3-0 clipping iteration was adopted., After several tests the best results were obtained when a single $\sigma$ clipping iteration was adopted. + On average more than of all galaxies in a eiven bin coutribute to the stacked spectruu at any given wavelength., On average more than of all galaxies in a given bin contribute to the stacked spectrum at any given wavelength. + No clipping was performed in the region of the [ΟΠ A 3727 A linc., No clipping was performed in the region of the [OII] $\lambda$ 3727 ${\rm\AA}$ line. + Tn Figure 2aa we compare one of our stacked spectra with a SSP model from Scliavou (2006)., In Figure \ref{fig2}a a we compare one of our stacked spectra with a SSP model from Schiavon (2006). + In order to match the overall fus distribution of the theoretical xpectiiun. the observed spectrua was cereddened by E(BVW)=0.2.," In order to match the overall flux distribution of the theoretical spectrum, the observed spectrum was dereddened by E(B–V)=0.2." + Since the observations were not properly flux-calibrated. this E(B-V) value does not reflect the average reddening im the sample galaxies and this correction has the sole purpose of bringing observations and theory to a common relative scale so as to highlisht the outstanding agreciment between line streugths in the observed aud svuthetic spectra.," Since the observations were not properly flux-calibrated, this E(B-V) value does not reflect the average reddening in the sample galaxies and this correction has the sole purpose of bringing observations and theory to a common relative scale so as to highlight the outstanding agreement between line strengths in the observed and synthetic spectra." +" All Lick iudices in the AA 1000.L500 Α reeion were measured in the stacked spectra. but we focus here ou the Hép and Fe1383 indices. which are chiefly scusitive to age and [Fe/T]]. respectively,"," All Lick indices in the $\lambda\lambda$ 4000–4500 ${\rm\AA}$ region were measured in the stacked spectra, but we focus here on the $H\delta_F$ and Fe4383 indices, which are chiefly sensitive to age and [Fe/H], respectively." + The spectra were first broadened to the Lick resolution as given by Wortley Ottaviani (1997). and the indices were measured following definitions bv those authors aud bv Wortley (1991).," The spectra were first broadened to the Lick resolution as given by Worthey Ottaviani (1997), and the indices were measured following definitions by those authors and by Worthey (1994)." + Velocity dispersious (0) were measured m the stacked spectra through Fourier cross correlation using the IRAF routine., Velocity dispersions $\sigma$ ) were measured in the stacked spectra through Fourier cross correlation using the IRAF routine. + The template adopted was a model spectrin from Schiavon (2006) for a SSP with solar metallicity and an age of 2 Cyr., The template adopted was a model spectrum from Schiavon (2006) for a SSP with solar metallicity and an age of 2 Gyr. + The same model spectrin was used to infer corrections to the Ime iudices for the effect of e-broadenius., The same model spectrum was used to infer corrections to the line indices for the effect of $\sigma$ -broadening. + The iudices were all corrected to σ=0 km/s using the σ deternüned for cach stacked spectrum., The indices were all corrected to $\sigma =0$ km/s using the $\sigma$ determined for each stacked spectrum. + The latter are listed in Table 1, The latter are listed in Table \ref{tbl1}. + We do not attempt to convert the line iudices to the Lick system. aside from smoothing them to the Lick/IDS resolution.," We do not attempt to convert the line indices to the Lick system, aside from smoothing them to the Lick/IDS resolution." + ILowever. zero-point differences should be very snall. flusedgiven that the Scluavon (2006) models are based on spectra and the DEEP2 spectra are corrected from instrumental throughput.," However, zero-point differences should be very small, given that the Schiavon (2006) models are based on fluxed spectra and the DEEP2 spectra are corrected from instrumental throughput." + Finally. Daliner lues were corrected for cuussiou-line infill. which was estimated from EWOT]. adopting Ufa) = ο (Yan 2006) and ΤΠ) = 0.13 (la).," Finally, Balmer lines were corrected for emission-line in-fill, which was estimated from EW[OII], adopting $H\alpha$ ) = 6 (Yan 2006) and $H\delta$ ) = 0.13 $H\alpha$ )." + The correction to fap is smaller than 0.2 A. corresponding to less than 1 Cor in age.," The correction to $H\delta_F$ is smaller than 0.2 ${\rm\AA}$, corresponding to less than 1 Gyr in age." + Calaxy evolution is better assessed when distant aud local samples of simular objects are contrasted using evolutionary iodels., Galaxy evolution is better assessed when distant and local samples of similar objects are contrasted using evolutionary models. + Moreover. it is vital that the nearby and distaut samples are defined as cousisteutlv as possible. to eusure that the two samples represent objects of the same class.," Moreover, it is vital that the nearby and distant samples are defined as consistently as possible, to ensure that the two samples represent objects of the same class." + For a local counterpart to the distaut, For a local counterpart to the distant +experiment. where we study the evolution of the angular momentum/spin distributions within a relatively smal cosmological volume.,"experiment, where we study the evolution of the angular momentum/spin distributions within a relatively small cosmological volume." + We find that the spin. clistribution shows some clear deviations from a lognormal. ancl does not seem to relax towards the latter. above statistica uncertainty.," We find that the spin distribution shows some clear deviations from a lognormal, and does not seem to relax towards the latter, above statistical uncertainty." + These deviationshalo... a east for the underlying LODAL mocel stucied in this paper.," These deviations, at least for the underlying LCDM model studied in this paper." + We also perform a possible check on the role of possible systematics in our analysis bv comparing with the results of wo cillerent. simulations: the GIE2 (?).. and a simulation recently perfomed by. ο," We also perform a possible check on the role of possible systematics in our analysis by comparing with the results of two different simulations: the GIF2 , and a simulation recently perfomed by ." +"ν, Both these works adopted. a Spherical Overcdensity (SO)finder. slightly clilfercn rom our chosen halo finder (the Amiga Lalo Finder. ΤΗ), recenthy introduced by ο"," Both these works adopted a Spherical Overdensity (SO), slightly different from our chosen halo finder (the Amiga Halo Finder, ), recently introduced by ." +"ν, We address the problem of the origin of these deviations by exploiting an exact resul rom statistics to demonstrate tha he deviations from a lognormal distribution are induce rom between the total energy. and. mass of ialoes. as should be expected for not completely: virialisec The plan of the paper is as follows: In section 2. we esent the details of the simulations we have performed. strictly describing the code adopted. the initial conditions and the halo finder."," We address the problem of the origin of these deviations by exploiting an exact result from statistics to demonstrate that the deviations from a lognormal distribution are induced from between the total energy and mass of haloes, as should be expected for not completely virialised The plan of the paper is as follows: In section \ref{sec:sims} we present the details of the simulations we have performed, briefly describing the code adopted, the initial conditions and the halo finder." + We then describe the main results concerning JA relationship (section 3.1))., We then describe the main results concerning $J-M$ relationship (section \ref{sec:jm}) ). + In section 4 we concentrate on the spin. probability distribution. and we show that the deviations from a lognormal shape are dependent on halo mass.," In section \ref{sec:diss:spin} we concentrate on the spin probability distribution, and we show that the deviations from a lognormal shape are dependent on halo mass." + We. trace the origin of these deviations to the presence of correlations among the quantities. entering its definition. by applying the Ixendall test.," We trace the origin of these deviations to the presence of correlations among the quantities entering its definition, by applying the Kendall test." +" We discuss our findings in the Conclusion (section 5)). 1n the following. we will denote the natural logarithn using the svmbol ""In. and the decimal logarithm as ""log (or ""Log"")."," We discuss our findings in the Conclusion (section \ref{sec:concl}) In the following, we will denote the natural logarithm using the symbol $\ln$ ”, and the decimal logarithm as $\log$ ” (or “Log”)." +" As underlving cosmological model we have chosen the fiducial 5-vear WMAP LOCDAM cosmology(7).. with. Llubble constant: df,71.9. and. the cosmological parameters:(Q5...Qa.QO,.. ni. ox)) = 0.044.0.742.0.258.0.963.0.7986]. Our main target was that of producing a statistically significant number of DAL haloes. thus we tried to adopt a softening length sullicientIy small to ensure that the smallest haloes we want to resolve have a size large enough at the initial recshilt of the simulation."," As underlying cosmological model we have chosen the fiducial 5-year WMAP LCDM cosmology, with Hubble constant: $H_{0} = 71.9\,$, and the cosmological parameters:, ) = $[0.044, 0.742, 0.258, 0.963, 0.7986]$ Our main target was that of producing a statistically significant number of DM haloes, thus we tried to adopt a softening length sufficiently small to ensure that the smallest haloes we want to resolve have a size large enough at the initial redshift of the simulation." + In order to do this. we define at first an initial instability raclius τω. Lor which we refer to the τους radius presented in eq. (," In order to do this, we define at first an initial instability radius $r_{initial}$, for which we refer to the ${\rm r}_{200}$ radius presented in eq. (" +"1) ofPs: rog=IOA5/Q,,)°C|2) kpe (where Mo is defined as M10AZ. ).","1) of: $r_{200}~= 2.98\times 10^{2}(M_{9}/\Omega_{m})^{1/3}/(1+z)\,$ kpc (where $M_{9}$ is defined as $M/10^{9}M_{\odot}$ )." + For the initial redshift of our simulations. their formula. gives: τρίτηroug(2=50.M)zz10.36 kpe.," For the initial redshift of our simulations, their formula gives: $r_{initial}=r_{200}(z=50,M_{m}) \approx 10.36\,$ kpc." +" Moreover. as we explain later. we consider only haloes having. a lower mass threshold AZ,=144.10(0M..."," Moreover, as we explain later, we consider only haloes having a lower mass threshold $M_{m} \geq 1.44\times 10^{9} \rm{M}_{\sun}$." + WeH then choose a softening length /=12.5 kpe. thus allowing the linear density field to become eravitationally unstable on this spatial scale at the beginning of the runs.," We then choose a softening length $l = 12.5\,$ kpc, thus allowing the linear density field to become gravitationally unstable on this spatial scale at the beginning of the runs." + Note that OUL USC Pyaar ds circumscribed only to the initial instability criterion., Note that our use $r_{initial}$ is circumscribed only to the initial instability criterion. +" We have chosen a box with size L,=70h+Alpe. not large enough to minimise cosmic variance elfects."," We have chosen a box with size $L_{b} = 70\, h^{-1}\, \rmn{Mpc}$, not large enough to minimise cosmic variance effects." + Within this box. we have performed. two runs. dillering only for the number of particles used: run 32M. was performed: using 320° particles. and run 500M with S007.," Within this box, we have performed two runs, differing only for the number of particles used: run 32M was performed using $320^{3}$ particles, and run 500M with $800^{3}$." + Thus. the particles masses for runs 32M and SOOM are. respectively. 7.49107 and 4.59.10 b+ ALL. We have generated the initial conditions using a parallel version of the package by2.. that we developed ourselves.," Thus, the particles masses for runs 32M and 500M are, respectively, $7.49\times 10^{8}$ and $4.79\times 10^{7}\,$ $h^{-1}\,$ $_{\sun}$ We have generated the initial conditions using a parallel version of the package by, that we developed ourselves." + We started all the simulations from a redshift >=50., We started all the simulations from a redshift $z=50$. + The latter is chosen in such a wav to ensure that the linear modes are linear within the chosen box4., The latter is chosen in such a way to ensure that the linear modes are linear within the chosen box. +1).. Reeent work suggests however that. for the mass range of interest to this work. the starting redshift has little influence on the average final properties of the Our main simulation tool isΕΙ... a parallel AIPL N-bods cosmological simulation code implementing a parallel version of the Barnes-Llut octal tree algorithm(?7).," Recent work suggests however that, for the mass range of interest to this work, the starting redshift has little influence on the average final properties of the Our main simulation tool is, a parallel MPI N-body cosmological simulation code implementing a parallel version of the Barnes-Hut octal tree algorithm." +. adopts an ellicient parallelization scheme: domain decomposition is applied to distribute. particles. and. workload decomposition is. further applied το ensure. load balancing128D.," adopts an efficient parallelization scheme: domain decomposition is applied to distribute particles, and workload decomposition is further applied to ensure load balancing." + The availability of large samples of DAL haloes. obtained from state-oFthe art N-body simulations. means we can obtain statistics such as the mass function with very small poissonian errors.," The availability of large samples of DM haloes, obtained from state-of-the art N-body simulations, means we can obtain statistics such as the mass function with very small poissonian errors." + However. in order to extract a significant amount of cosmological information from these statistics. one should have a control on the systematic. elfects.," However, in order to extract a significant amount of cosmological information from these statistics, one should have a control on the systematic effects." + The of DM halo is one possible source of svstematies., The of DM halo is one possible source of systematics. + Presentlv. halo definition. algorithms fall into two broad categories: those based on the (LOL) algorithm. anc those based on some criterion. both of which are usually supplemented by some recursive scheme to eliminate outliers (Le. eravitationally unbotnel particles).," Presently, halo definition algorithms fall into two broad categories: those based on the (FOF) algorithm, and those based on some criterion, both of which are usually supplemented by some recursive scheme to eliminate outliers (i.e. gravitationally unbound particles)." + Dilferent definitions mostly affect small haloes and the outer. low-density regions of more massive haloes(?).," Different definitions mostly affect small haloes and the outer, low-density regions of more massive haloes." +. For this reason. we have chosen to restrict. our attention to haloes described by a relatively large. (300) minimum number of We have decided to adopt for our analysis a group finder which has only one threshold. parameter. i.e. the recently introduced(?72).," For this reason, we have chosen to restrict our attention to haloes described by a relatively large (300) minimum number of We have decided to adopt for our analysis a group finder which has only one threshold parameter, i.e. the recently introduced." +. In haloes are defined using the commonly used virialization criterion. Le. first computing Isodensity contours. and then including only those particles whose average density is larger than the critical overscdensity:," In haloes are defined using the commonly used virialization criterion, i.e. first computing isodensity contours, and then including only those particles whose average density is larger than the critical oversdensity:" + , +Nevertheless Podsiadlowskietal(2003)— restrict accretion. iuto the black hole to the Eddinetou linüt.,Nevertheless \citet{Pod03} restrict accretion into the black hole to the Eddington limit. +" With this same assuniption they were able to ect CRS 1915] 105 up to a spin paramcter a,=0.9.", With this same assumption they were able to get GRS $+$ 105 up to a spin parameter $a_\star=0.9$. +" owever. AleClintocketal.(2006) measured its spin parameter to be a,~O980.99."," However, \citet{McC06} measured its spin parameter to be $a_\star\sim0.98-0.99$." + We were able to get the spin paranueter up to the measured αν2(0.98 with lypercritical accretion (Brownetal.2007) (sec the discussion on P.355., We were able to get the spin parameter up to the measured $a_\star>0.98$ with hypercritical accretion \citep{BLMM07} (see the discussion on P.355. + of Betheetal. (2003)])., of \citet{Bet03}) ). +" If we suppress the assuuption that the rate of accretion is lanited to the Eddiustou limit we observe that the Παν (νο dom Podsiaclowskictal.(2003) would v0 able to transter up to 30A, during the first tlermal nuescale (assunuue there is that mich mass in the system). aud another few solar masses afterwards. during he period where the black hole aud the secondary star are detached. before the secondary fills again its Roche obe during the red giant stage."," If we suppress the assumption that the rate of accretion is limited to the Eddington limit we observe that the binary Cyg $-$ 1 in \citet{Pod03} would be able to transfer up to $\sim30\msun$ during the first thermal timescale (assuming there is that much mass in the system), and another few solar masses afterwards, during the period where the black hole and the secondary star are detached, before the secondary fills again its Roche lobe during the red giant stage." + Cre 1. Vl1611 Ser aud GRS 1915] 105 are similar in that the donors iu all cases were more massive han the black hole at the time the black hole was ormed.," Cyg $-$ 1, V4641 Sgr and GRS $+$ 105 are similar in that the donors in all cases were more massive than the black hole at the time the black hole was formed." +" The hvpereritical accretion for GRS | 105 Is necessary to bring e, up to e,>0.98 (Brownctal. 2007).", The hypercritical accretion for GRS $+$ 105 is necessary to bring $a_\star$ up to $a_\star>0.98$ \citep{BLMM07}. +. For the purposes of discussing Cre X 1 including the hvpercertical nature of the accretion the detailed. evolution of Podsiadlowskietal.(2003) 1 useful., For the purposes of discussing Cyg $-$ 1 including the hypercritical nature of the accretion the detailed evolution of \citet{Pod03} is useful. + Caven hvpercritical accretion. M33. 7 can be straightforwardly discussed ii a similar wav as we show in the next sections.," Given hypercritical accretion, M33 $-$ 7 can be straightforwardly discussed in a similar way as we show in the next sections." + Iu Sec. ??..," In Sec. \ref{M33X7}," + we discuss what would be the cousequeuces if the current spin of M33. N-7. were natal., we discuss what would be the consequences if the current spin of M33 X-7 were natal. + We discuss a few problems in this scenario., We discuss a few problems in this scenario. + In Sec., In Sec. + 2? πο discuss the case for lypercritical accretion in M32. Ντ as an alternative way of making high spin of black hole in M33 N-7., \ref{Evol} we discuss the case for hypercritical accretion in M33 X-7 as an alternative way of making high spin of black hole in M33 X-7. +" We stuuarize our conclusion in Sec. 77,", We summarize our conclusion in Sec. \ref{Conc}. + Iu this section. we ask for M39 XN 7 what the consequences would be were the currently observed spin of the black hole all natal.," In this section, we ask for M33 $-$ 7 what the consequences would be were the currently observed spin of the black hole all natal." +" Most important for the binary evolution is that the heliuui-star (progenitor of the black hole) is spun up bx the secondary star so that these ""helimu-stars will be fully svuchrouized with their orbital motion throughout them core-heliuui buius: re. there is tidal locking of the οτιστα with the secondary star (WandenIHeuvel&Yoon 2007)."," Most important for the binary evolution is that the helium-star (progenitor of the black hole) is spun up by the secondary star so that these “helium-stars will be fully synchronized with their orbital motion throughout their core-helium burning""; i.e., there is tidal locking of the helium-star with the secondary star \citep{Heu07}." +. Hence. the spin of Ποιαμίαν aud the orbital motion of binary being locked together. aud the aueular momentum of He-star is transferred to that of black hole as the heliun star falls iuto the latter (Leeet 2002))).," Hence, the spin of helium-star and the orbital motion of binary being locked together, and the angular momentum of He-star is transferred to that of black hole as the helium star falls into the latter \citep{Lee02}) )." +" Iu that case. with the currently measured spin parameter a,= 0.77. the preexplosiou orbital period of \I33 N-7 would be esseutially the same as for Nova Sco. which Leeetal.(2002) predicted to be 0.£ days with spin paralcter ~0.75 (see Figure 12 of Leeetal. (2002)))."," In that case, with the currently measured spin parameter $a_\star=0.77$ , the preexplosion orbital period of M33 X-7 would be essentially the same as for Nova Sco, which \citet{Lee02} predicted to be 0.4 days with spin parameter $\sim0.75$ (see Figure 12 of \citet{Lee02}) )." +" This prediction was confirmed by Shafeeetal.(2006) with the measurement of &,=(0.65—0.75) for Nova Sco.", This prediction was confirmed by \citet{Sha06} with the measurement of $a_\star=(0.65-0.75)$ for Nova Sco. + Tere we sunuuarize a few problems with this scenario., Here we summarize a few problems with this scenario. + Tn the case of Nova Sco. the explosiou involved a lass loss of several solar masses (Nelemansetal.1999).," In the case of Nova Sco, the explosion involved a mass loss of several solar masses \citep{Nel99}." +. The heliocentric radial svsteià velocity of Nova Sco is 150-191nis 3., The heliocentric radial system velocity of Nova Sco is $-150\pm19$ km $^{-1}$ . + After correction for peculiar motion of the stun and differcutial Galactic rotation. the magnitude of the velocity stands out as beiug higher than aux other dvuamically identified Calactic black hole caudidate (Brandtetal.1995).," After correction for peculiar motion of the sum and differential Galactic rotation, the magnitude of the velocity stands out as being higher than any other dynamically identified Galactic black hole candidate \citep{Bra95}." +. Caven the donor mass of ~2M. and the black hole mass of (5.1.5.7)AL... at lost nearly half of its syste mass in the explosion (Nelemansctal. 1999).," Given the donor mass of $\sim2\msun$ and the black hole mass of $(5.1-5.7)\msun$, it lost nearly half of its system mass in the explosion \citep{Nel99}." +. The reason why Nova Sco is the most energetic explosion among the soft X-ray transient sources is that the explosion eucrgy las to be big enough to expel nearly half of its svstem mass., The reason why Nova Sco is the most energetic explosion among the soft X-ray transient sources is that the explosion energy has to be big enough to expel nearly half of its system mass. + We believe that this cucrey was provided bv the black hole spin., We believe that this energy was provided by the black hole spin. + The present remaiming rotational energy is 130 bethes (1 bethe =10°! eres)., The present remaining rotational energy is $430$ bethes (1 bethe $=10^{51}$ ergs). + Leeetal.(2002) found that iu Nova Sco most of the rotational cucrey is natal., \citet{Lee02} found that in Nova Sco most of the rotational energy is natal. + Given the same spin parameter in the natal spin of AD)3 7. it would have ~3 times more rotational enerev than Nova Sco. because of the ~3 times more massive black hole. about half of AZ?!," Given the same spin parameter in the natal spin of M33 $-$ 7, it would have $\sim 3$ times more rotational energy than Nova Sco, because of the $\sim 3$ times more massive black hole, about half of $\msun c^2$!" + In between the explosion and the present time. no forces act ou the binary assuming the (negligible) sub-Eddingtou rate of accretion.," In between the explosion and the present time, no forces act on the binary assuming the (negligible) sub-Eddington rate of accretion." + Iu other words. the explosion must couvert the originally 0.1 day period into the present one of3.15 days.," In other words, the explosion must convert the originally $0.4$ day period into the present one of $3.45$ days." + We take the black holemass after the explosion to be the present one. since accretion at the Eddington limit changes its mass negligiblv iu2-3 million years.," We take the black holemass after the explosion to be the present one, since accretion at the Eddington limit changes its mass negligibly in2-3 million years." + Iu the Blaaww-Bocrsima explosion. assunüng rapid circularization. EIS2p," In the Blaauw-Boersma explosion, assuming rapid circularization, )^2 P_1" +raises the possiblity that DAZs may be caused. by hitherto unseen stellar or substellar companions that deposit material through a stellar wind onto the surfaces of the white dwarls.,raises the possiblity that DAZs may be caused by hitherto unseen stellar or substellar companions that deposit material through a stellar wind onto the surfaces of the white dwarfs. + The evidence for apparently single DAZs with unknown companions is thin., The evidence for apparently single DAZs with unknown companions is thin. + Only two known substellar companions to white cwarls exist. in widely separated binaries (??)..," Only two known substellar companions to white dwarfs exist, in widely separated binaries \citep{zuckerman92,farihi04}." + This is despite wide searches for unresolved stellar or substellar objects in close orbits (????)..," This is despite wide searches for unresolved stellar or substellar objects in close orbits \citep{probst82,zuckerman92,dobbie05,farihi05}." + Furthermore. concerted searches of DAZs themselves show that stelar companions are ruled oul al all separations aud substellar companions ruled out for all but. the closest orbital separations (?7?7)..," Furthermore, concerted searches of DAZs themselves show that stellar companions are ruled out at all separations and substellar companions ruled out for all but the closest orbital separations \citep{debes05a,debes05b,debes05c}." + AI Def stellar wind mass loss rates are poorly understood and hard (ο studyupper imis can only be placed on the nearby M5.5 Proxima Centauri based ou X-ray and Ly a studies with upper limits of 6x10.TAL. /vr (3 M.)and 4x10.AL. /vr (0.2 M.) respectively (27)..," M Dwarf stellar wind mass loss rates are poorly understood and hard to study–upper limits can only be placed on the nearby M5.5 Proxima Centauri based on X-ray and Ly $\alpha$ studies with upper limits of $\times 10^{-14}M_{\odot}$ /yr (3 $\dot{M}_\odot$ ) and $\times 10^{-15} M_\odot$ /yr (0.2 $\dot{M}_{\odot}$ ) respectively \citep{wargelin02,wood01}." + Raclio observations wilh marginal detections and spectroscopic observations of coronal nass ejections [from low mass stus have been used to propose verv high mass loss rates rom clwarl stars. which has a theoretical motivation (???)..," Radio observations with marginal detections and spectroscopic observations of coronal mass ejections from low mass stars have been used to propose very high mass loss rates from dwarf stars, which has a theoretical motivation \citep{mullan92,foing90,badalyan92}." + These results are controversial. j0wever. and depend on (he model assumptions made (?)..," These results are controversial, however, and depend on the model assumptions made \citep{lim96}." + The recent results lor Proxima Centauri suggest that perhaps M dwarl stars have winds comparable to or smaller (han solar ivpevpe stars. rather than thanthe larger rates.," The recent results for Proxima Centauri suggest that perhaps M dwarf stars have winds comparable to or smaller than solar type stars, rather than the larger rates." + The strength ofvoung M chwarldwarl winds can affectallect (1the lifetiifelime of ggaseousus material materialin disks thatthal are important lor planet formationFormation andlimit limit t1the presence of clusty disks (22)..," The strength of young M dwarf winds can affect the lifetime of gaseous material in disks that are important for planet formation and limit the presence of dusty disks \citep{laughlin05,plavchan05}." + In orbit around white dwarls. M dwarl winds are important for the origin of cataclysmic variables (?)..," In orbit around white dwarfs, M dwarf winds are important for the origin of cataclysmic variables \citep{g03}." + Under the assumption that the cause of the metal lines in DAZs is due to Al dwarl companions. the stellar wind rates for known DAZ+\I dwarf systems can be calculated.," Under the assumption that the cause of the metal lines in DAZs is due to M dwarf companions, the stellar wind rates for known DAZ+M dwarf systems can be calculated." + These calculations require the known orbits of the M. dwarl companions., These calculations require the known orbits of the M dwarf companions. + Three of the known DAZ--M systems have well known orbital periods and masses since thev are detached transiting svstems., Three of the known DAZ+M systems have well known orbital periods and masses since they are detached transiting systems. + The other three have recent HST Advanced Camera for Survevs (ACS) images (hat allow orbital information to be estimated., The other three have recent HST Advanced Camera for Surveys (ACS) images that allow orbital information to be estimated. + In this paper I infer Cie stellar wind mass loss rates of the M dwarl companions to six DAZ-M dwarl binaries., In this paper I infer the stellar wind mass loss rates of the M dwarf companions to six DAZ+M dwarf binaries. + In Section 2. I estimate the orbital semi-major axis for each binary., In Section \ref{s1} I estimate the orbital semi-major axis for each binary. + In Section 3. I use the semi-major axes ancl white dwarf diffusion coefficients to infer the nass accretion rate onto the white dwarls ancl thus the mass loss rate of the companion M cdwarls., In Section \ref{s2} I use the semi-major axes and white dwarf diffusion coefficients to infer the mass accretion rate onto the white dwarfs and thus the mass loss rate of the companion M dwarfs. + Finally. in Section 4. I discuss mv results.," Finally, in Section \ref{s3} I discuss my results." +demonstrates that the galaxy templates describe the vast majority of galaxies very well.,demonstrates that the galaxy templates describe the vast majority of galaxies very well. + The galaxy redshift’ histogram of all objects in the different patches is shown in Fig. 13.., The galaxy redshift histogram of all objects in the different patches is shown in Fig. \ref{histo_galaxies}. + The mean galaxy, The mean galaxy +Although much has been learned about gamma-ray busts (GRBs) in the last several vears. (he nature of the central exploding object remains uncertain (see Piran. 2000: van Paraclijs et al.,"Although much has been learned about gamma-ray busts (GRBs) in the last several years, the nature of the central exploding object remains uncertain (see Piran, 2000; van Paradijs et al." + 2000: Meszaros. 2001 [or recent reviews).," 2000; Meszaros, 2001 for recent reviews)." +" The possible detection of x-ray lines in GRD alterglows is very important in this connection since the lines provide strong constraints on models,", The possible detection of x-ray lines in GRB afterglows is very important in this connection since the lines provide strong constraints on models. + Piro et al. (, Piro et al. ( +"2000) claimed to detect an Fe Ix,, line and (he corresponding recombination edge in GRB 991216.",2000) claimed to detect an Fe $_\alpha$ line and the corresponding recombination edge in GRB 991216. + The line was seen about 1.5 days (in the observer frame) after the initial burst., The line was seen about 1.5 days (in the observer frame) after the initial burst. + There have been claims for iron lines also in a few other bursts (GRB 970508: Piro et al., There have been claims for iron lines also in a few other bursts (GRB 970508: Piro et al. + 1999: GRB 970823: Yoshida et al., 1999; GRB 970828: Yoshida et al. + 1999: GRD 000214: Antonelli et al., 1999; GRB 000214: Antonelli et al. + 2000)., 2000). + Recently. Reeves et al. (," Recently, Reeves et al. (" +"2002) reported the detection of x-ray Ix, lines of Mg XI (or XII). Si XIV. S XVI. Ar XVIII and Ca XX in GRD 011211.","2002) reported the detection of x-ray $_\alpha$ lines of Mg XI (or XII), Si XIV, S XVI, Ar XVIII and Ca XX in GRB 011211." + The presence of multiple lines al apparently the same redshift makes this detection particularly interesting., The presence of multiple lines at apparently the same redshift makes this detection particularly interesting. + If the lines are emitted isotropicallv. GRD 011211 must have emitted over LO eres in each line as measured in (he source frame.," If the lines are emitted isotropically, GRB 011211 must have emitted over $10^{48}$ ergs in each line as measured in the source frame." + The emission occurred a few hours after the GRB and continued [or about half an hour in the source frame., The emission occurred a few hours after the GRB and continued for about half an hour in the source frame. + Since the lines are blue-shifted by /e~0.1 with respect to the GRD. the emission must have occurred within a sub-relativistic outflow from (he source.," Since the lines are blue-shifted by $v/c\sim0.1$ with respect to the GRB, the emission must have occurred within a sub-relativistic outflow from the source." + We show in (his paper that it is quite challengimg to come up with a viable theoretical model to explain the lines seen in GRD 011211., We show in this paper that it is quite challenging to come up with a viable theoretical model to explain the lines seen in GRB 011211. + Recently. Borozdin Trudolvubov. (2002) have suggested that the lines may be an instrumental artifact. which would of course solve the theoretical problems.," Recently, Borozdin Trudolyubov (2002) have suggested that the lines may be an instrumental artifact, which would of course solve the theoretical problems." + In the rest of (he paper we derive constraints on some of the popular models that have been proposed so far for the line emission., In the rest of the paper we derive constraints on some of the popular models that have been proposed so far for the line emission. + The constraints apply to GRB 011211 and also to any other GRB [or which a line with an energy output of about 10 eres is detected: (his level of line emission roughly corresponds to the detection threshold of the current. generation of instruments for a high redshilt GRB., The constraints apply to GRB 011211 and also to any other GRB for which a line with an energy output of about $^{48}$ ergs is detected; this level of line emission roughly corresponds to the detection threshold of the current generation of instruments for a high redshift GRB. + We also propose in this paper a new model for line production. which we believe suffers [rom fewer problems than ihe previous models.," We also propose in this paper a new model for line production, which we believe suffers from fewer problems than the previous models." + Two broad classes of models have been proposed to explain the x-ray lines., Two broad classes of models have been proposed to explain the x-ray lines. + In one model. it is assumed that the GRB is associated with a long-lived engine. with a duration of several hours to a dav (Meszaros Rees 2000).," In one model, it is assumed that the GRB is associated with a long-lived engine, with a duration of several hours to a day (Meszaros Rees 2000)." +" Part of the long-duration emission from (he engine is intercepted by a funnel that has been carved out of the supernova ejecta,", Part of the long-duration emission from the engine is intercepted by a funnel that has been carved out of the supernova ejecta. + The intercepted raciation is reprocessed into x-ray line photons by (he photoionized gas in the surface lavers ol the funnel., The intercepted radiation is reprocessed into x-ray line photons by the photoionized gas in the surface layers of the funnel. + Lazzati. Ramirez-Ruiz Rees (2002) have shown that this model is ruled out in the ease of GRD 011211. the reason being that the radiation [rom the central engine," Lazzati, Ramirez-Ruiz Rees (2002) have shown that this model is ruled out in the case of GRB 011211, the reason being that the radiation from the central engine" +(2) If the absorber is more ionized. for example αἱ log£=2.6. (hen an absorber velocity ol 0 kins |1 (with respect to the source) is needed to predict features al 7.0 8.0 keV and 6.42 keV. Here then. this may be just a high £ component to WAL rather than a clilferent absorber with a different velocity.,"(2) If the absorber is more ionized, for example at $\log\xi=2.6$, then an absorber velocity of $\sim 0$ km $^{-1}$ (with respect to the source) is needed to predict features at $7.0$ $8.0$ keV and $6.42$ keV. Here then, this may be just a high $\xi$ component to WA1 rather than a different absorber with a different velocity." + Again we require a column density of Nyy~1075 7. (, Again we require a column density of $N_{\rm H}\sim10^{23}$ $^{-2}$. ( +3) For ionizations log£. between1.7 and 2.6. the velocity shift. will be somewhere between —6000 km land O km |.,"3) For ionizations $\log\xi$, between$1.7$ and $2.6$, the velocity shift will be somewhere between $-6000$ km $^{-1}$ and $0$ km $^{-1}$." + Again. column densities need to be high. 7. to produce strong absorption features. or there is a super-solar abundance of Fe.," Again, column densities need to be high, $N_{\rm H}\sim10^{23}$ $^{-2}$, to produce strong absorption features, or there is a super-solar abundance of Fe." + lligh velocity dispersion could also help explain the broad trough., High velocity dispersion could also help explain the broad trough. + From situations (1)-(3). we present the possible parameters (that do well al explaining the hard X-ray. (>5 keV) spectrum in Table 4..," From situations (1)-(3), we present the possible parameters that do well at explaining the hard X-ray $>5$ keV) spectrum in Table \ref{abs2}." + We are not able to deduce from the soft N-rav (<2 keV) spectrum which absorber is the best lor the following reason., We are not able to deduce from the soft X-ray $<2$ keV) spectrum which absorber is the best for the following reason. + The higher ionizalion models. ionization similar to that of (2). (which preclict few soft. X-ray lines) cdo nol incorrectly predict strong lines in the soft X-ray but may incorrectly predict weak ones (the strength of predicted lines are less (han noise in spectrum) where none is observed. while the lower ionization models. ionization similar to that of (1). with redshilt and ionization parameter similar to WAL end up predicting many of the same lines as WAL. although not as well (partially due to the hieh column density requirecl to predict strong absorption in the hard. X-ray).," The higher ionization models, ionization similar to that of (2), (which predict few soft X-ray lines) do not incorrectly predict strong lines in the soft X-ray but may incorrectly predict weak ones (the strength of predicted lines are less than noise in spectrum) where none is observed, while the lower ionization models, ionization similar to that of (1), with redshift and ionization parameter similar to WA1 end up predicting many of the same lines as WA1, although not as well (partially due to the high column density required to predict strong absorption in the hard X-ray)." + It could be possible (hat there is only a single warm absorber component (WAL) with a super-solar abundance of Fe: if we increase Fe to about 10 times the solar abundance WAL shows strong absorption to explain the features in the vicinity of the Fe Ix edee., It could be possible that there is only a single warm absorber component (WA1) with a super-solar abundance of Fe: if we increase Fe to about $10$ times the solar abundance WA1 shows strong absorption to explain the features in the vicinity of the Fe K edge. + However. a verv high Fe abundance would imply lots of Fe L lines at lower energies. which are not seen.," However, a very high Fe abundance would imply lots of Fe L lines at lower energies, which are not seen." + Additionally. the strength of the Fe IX emission line does not support a sienificantly high Fe abundance in the surrounding absorber. (," Additionally, the strength of the Fe K emission line does not support a significantly high Fe abundance in the surrounding absorber. (" +4) We also investigated the possibility that the absorption is due to absorption by the interstellar medium.,4) We also investigated the possibility that the absorption is due to absorption by the interstellar medium. + In this case. we fixed the ISM absorber (SMABS) redshift at z=0. and varied photoionization and column densitwv to describe absorption al 6.42 keV aud 7.0 8.0 keV. However. again we find that we require a high column density (Njc1075 em7. larger (han what would be expected if we are looking through interstellar medium of the Galaxy). and so absorption around (he source is preferred insteac. (," In this case, we fixed the ISM absorber ) redshift at $z=0$, and varied photoionization and column density to describe absorption at $6.42$ keV and $7.0$ $8.0$ keV. However, again we find that we require a high column density $N_{\rm H}\sim10^{23}$ $^{-2}$, larger than what would be expected if we are looking through interstellar medium of the Galaxy), and so absorption around the source is preferred instead. (" +5) We investigated the case that the features are due to a redshifted warm absorber as well.,5) We investigated the case that the features are due to a redshifted warm absorber as well. + We are unable to find reasonable parameters to predict strong absorption at 7.0 8.0 keV. The 6.42 keV absorption feature can be explained. accounted for with redshilted warm absorber models with log£>2.9 that are highly redshifted with respect to the source (relative velocity of >5000 km +) (see Fig. 6)).," We are unable to find reasonable parameters to predict strong absorption at $7.0$ $8.0$ keV. The $6.42$ keV absorption feature can be explained, accounted for with redshifted warm absorber models with $\log\xi\geq 2.9$ that are highly redshifted with respect to the source (relative velocity of $>5000$ km $^{-1}$ ) (see Fig. \ref{5300}) )." + Such a model could also explain the ambiguous absorption at 2.54 keV mentioned in ??.. which would mean that (he 2.54 keV is possibly real ancl is not due to a gap in the detection. however (he model also incorrectly," Such a model could also explain the ambiguous absorption at $2.54$ keV mentioned in \ref{NarrowAbsorptionLines}, , which would mean that the $2.54$ keV is possibly real and is not due to a gap in the detection, however the model also incorrectly" +beyond the scope of this Letter. we focus on validating the ring geometry.,"beyond the scope of this Letter, we focus on validating the ring geometry." + We compare a radial cut along the midplane averaged over 5 pixels (Fig. 3)).," We compare a radial cut along the midplane averaged over 5 pixels (Fig. \ref{fig:radcut}) )," + artificially lowering the model intensity on the faint side by a factor of 1.3., artificially lowering the model intensity on the faint side by a factor of 1.3. + Indeed. models with an offset Oo=a:e of 2.75+0.85 AAU. where « is the semi-major axis for the peak density (61.25+0.85 AAU) and e the eccentricity (0.045+ 0.015). still provide a decent match after reduction with LOCI.," Indeed, models with an offset $o = a \cdot e$ of $2.75 \pm 0.85$ AU, where $a$ is the semi-major axis for the peak density $ 61.25\pm 0.85$ AU) and $e$ the eccentricity $0.045 \pm 0.015$ ), still provide a decent match after reduction with LOCI." + Models without offset are worse particularly out to ~63 AU for each ring side because the shift in peak intensity is missing., Models without offset are worse particularly out to $\sim$ 63 AU for each ring side because the shift in peak intensity is missing. + Therefore the offset does not appear to be an artifact of the data reduction., Therefore the offset does not appear to be an artifact of the data reduction. + Model comparison suggests an inner surface density power-law slope of ~7. but a fit is difficult because reduction artifacts differ for nodels and observations.," Model comparison suggests an inner surface density power-law slope of $\sim$ 7, but a fit is difficult because reduction artifacts differ for models and observations." + The outer slope (fixed to -4) is uncertain because we do not model the ISM interaction., The outer slope (fixed to $-4$ ) is uncertain because we do not model the ISM interaction. + In any case. the inner rim appears to be significantly steeper than the outer rim.," In any case, the inner rim appears to be significantly steeper than the outer rim." + From the brightness asymmetry between the upper and lower are we estimate the asymmetry parameter to |g] ~0.3., From the brightness asymmetry between the upper and lower arc we estimate the asymmetry parameter to $|g| \sim$ 0.3. + This value is uncertain because the weak are is strongly contaminated by reduction residuals., This value is uncertain because the weak arc is strongly contaminated by reduction residuals. + Additionally. the HG phase function is a simplistic model for scattering in debris disks.," Additionally, the HG phase function is a simplistic model for scattering in debris disks." + A positive. g-value. assuming that the brighter side is the front. would indicate forward scattering grams.," A positive $g$ -value, assuming that the brighter side is the front, would indicate forward scattering grains." + This may not always be the case e.g. ?).., This may not always be the case \citep[see e.g.][]{min10}. . + In our full image (Fig. 2)), In our full image (Fig. \ref{fig:bgobjects}) ) + we detect six point sources at r>3., we detect six point sources at $r > 3\arcsec$. + These are seen in the ? data as well., These are seen in the \citet{hines07} data as well. + Astrometric tests show that their relative proper motion 1s consistent with all objects being background sources refsec:astrometry))., Astrometric tests show that their relative proper motion is consistent with all objects being background sources \\ref{sec:astrometry}) ). + In the LOCI image reduced with the smaller minimum rotation. we search for closer companions., In the LOCI image reduced with the smaller minimum rotation we search for closer companions. + After convolving the resulting image with an aperture of 5 pixels diameter. we calculate the noise level at a given separation as the standard deviation in a concentric annulus.," After convolving the resulting image with an aperture of 5 pixels diameter, we calculate the noise level at a given separation as the standard deviation in a concentric annulus." + To determine the flux loss from partial self-subtraction we implant artifical sources in the raw data., To determine the flux loss from partial self-subtraction we implant artifical sources in the raw data. + The measured contrast curve is corrected for this flux loss to yield the final 5c detectable constrast curve (Fig. 4))., The measured contrast curve is corrected for this flux loss to yield the final $5\sigma$ detectable constrast curve (Fig. \ref{fig:masslimit}) ). + We translate the contrast to à mass limit using the COND evolutionary models by ?.., We translate the contrast to a mass limit using the COND evolutionary models by \citet{baraffe03}. + We assume an age of MMyr., We assume an age of Myr. + We do not detect any companion candidates. but are able to set limits well below the deuterium burning limit.," We do not detect any companion candidates, but are able to set limits well below the deuterium burning limit." + The high-resolution image enables us to distinguish the actual debris ring from the material that appears to be streaming away from the system., The high-resolution image enables us to distinguish the actual debris ring from the material that appears to be streaming away from the system. + The results reveal a ring center offset of ~3 AAU and an additional brightness asymmetry suggesting density variations., The results reveal a ring center offset of $\sim$ AU and an additional brightness asymmetry suggesting density variations. + The eccentricity of the debris ring could be shaped by gravitational interaction. with a companion on an eccentric orbit., The eccentricity of the debris ring could be shaped by gravitational interaction with a companion on an eccentric orbit. + A similar system is Fomalhaut with a belt eccentricity of 0.11 (2).., A similar system is Fomalhaut with a belt eccentricity of 0.11 \citep{kalas05b}. + Mass constraints were discussed for Fomalhaut b by ?.., Mass constraints were discussed for Fomalhaut b by \citet{chiang09}. +" A rough adaptation of their result to HD 61005 shows that a planet below our detection limit of M, located beyond ~40 AU at maximum angular separation could perturb the ring.", A rough adaptation of their result to HD 61005 shows that a planet below our detection limit of $\sim$ $M_\mathrm{J}$ located beyond $\sim$ 40 AU at maximum angular separation could perturb the ring. + Because of the high inclination a planet of higher mass and lower semi-major axis could also hide withir the residuals at smaller projected separation from the star., Because of the high inclination a planet of higher mass and lower semi-major axis could also hide within the residuals at smaller projected separation from the star. + Models of the spectral energy distribution by ? suggestec that the debris required multiple temperature components., Models of the spectral energy distribution by \citet{hillenbrand08} suggested that the debris required multiple temperature components. +" This could be fitted by either an extended debris model (Ri,«10 AU and Raj; 740 AU) or more likely an inner warm ring anc an outer cool ring. which could coincide with the dust detectec in the scattered light images."," This could be fitted by either an extended debris model $R_\mathrm{inner} < 10$ AU and $R_\mathrm{outer} > $ 40 AU) or more likely an inner warm ring and an outer cool ring, which could coincide with the dust detected in the scattered light images." + To explain the structure of the interacting material. ? explored several scenarios. and proposed that a low-density cloud is perturbing grain orbits because of ram pressure.," To explain the structure of the interacting material, \citet{maness09} explored several scenarios, and proposed that a low-density cloud is perturbing grain orbits because of ram pressure." + The streamers would be barely bound. sub-micron sized grains on highly eccentric orbits. consistent with the observed blue color and the brightness profile.," The streamers would be barely bound, sub-micron sized grains on highly eccentric orbits, consistent with the observed blue color and the brightness profile." + Their model currently cannot reproduce the sharpness of the streamers. but the observed geometry of the parent body ring might help improve the models to validate this theory.," Their model currently cannot reproduce the sharpness of the streamers, but the observed geometry of the parent body ring might help improve the models to validate this theory." + These might then answer whether the ring offset could also be caused by the ISM interaction rather than a planet., These might then answer whether the ring offset could also be caused by the ISM interaction rather than a planet. + Obtaining colors of the ring through high-resolution imaging at other wavelengths could indicate if a grain size difference exists between parent body ring and swept material., Obtaining colors of the ring through high-resolution imaging at other wavelengths could indicate if a grain size difference exists between parent body ring and swept material. + As a solar-type star. and with a debris ring at a radius not much larger than that of the Kuiper belt. the HD 61005 system provides an interesting comparison to models of the young solar system.," As a solar-type star, and with a debris ring at a radius not much larger than that of the Kuiper belt, the HD 61005 system provides an interesting comparison to models of the young solar system." + ? calculate the infrared excess of the solar system as a function of time based onstrong assumptions consistent with the Nice model., \citet{booth09} calculate the infrared excess of the solar system as a function of time based onstrong assumptions consistent with the Nice model. + At ~90 MMyr the calculated um excess ratio Fyo/Fyo4 1s about four times lower than that, At $\sim$ Myr the calculated $\mu$ m excess ratio $F_{70}$ $F_{70\star}$ is about four times lower than that +Wlüle the measures of the burst duration axl Loy in the hard X-ray band are neslieible affected by the operating iu a spiuniug modo. hiuks to the almost all-sky FoV of the MCAL. we cau just put a lower nuit at 119 s on the duration of the CteV. emission since the CRB weut out of the CRID FoV at ~ty125 s and its eniüssion was fainter than the mstrumenut seusitivitv when he burst was back iuside. on ty|£10 s (1. 6. 285 s later).,"While the measures of the burst duration and $T_{90}$ in the hard X-ray band are negligibly affected by the operating in a spinning mode, thanks to the almost all-sky FoV of the MCAL, we can just put a lower limit at 119 s on the duration of the GeV emission since the GRB went out of the GRID FoV at $\simeq t_0 + +125$ s and its emission was fainter than the instrument sensitivity when the burst was back inside, on $t_0 + 410$ s (i. e. 285 s later)." + For this reason we cannot draw any serious coiclusion about the duration O| the GRDB in gamma ravs from the data., For this reason we cannot draw any serious conclusion about the duration of the GRB in gamma rays from the data. + The cross-correlation of the liehiteurves of CRB 101210 wihout backeround subtraclon and iu various ΟΠΟΥ ranecs (0.3 1 MeV .1 5 MeV. 5. so MeV. aud 22 Moev 3.5 GeV) shows two pecuju characteristics: the sinultaneous onset of the eunumnia rav and lard X-IAV OLudsslols all the coincidence of the peak position in the fiue seriesο," The cross-correlation of the lightcurves of GRB 100724B without background subtraction and in various energy ranges (0.3 – 1 MeV, 1 – 5 MeV, 5 – 80 MeV, and 22 MeV – 3.5 GeV) shows two peculiar characteristics: the simultaneous onset of the gamma ray and hard X-ray emissions and the coincidence of the peak position in the time series." + This is demonstrated by the absence of spec‘tral lag between the AICAL lightcurves at differeut onere swith a bin size of1Οδ Ες (see fie. 2 ))," This is demonstrated by the absence of spectral lag between the MCAL lightcurves at different energies, with a bin size of 1.024 s (see fig. \ref{fig:MCAL_cross-cor}) )" +" aud between t16 GRID lighteurve and the MCAL ones in three euerev langes. with a bin size of 2.5 s, mainly limited by the Satistics of the €(RID data (see fig. 3))."," and between the GRID lightcurve and the MCAL ones in three energy ranges, with a bin size of 2.5 s, mainly limited by the statistics of the GRID data (see fig. \ref{fig:MCAL-GRID_cross-cor}) )." + Moreover. he first photou is deected by the ACILE/CRID at 10.9 s after trigger. diving the rise of the burst Cluission iu the MeV baud.," Moreover, the first photon is detected by the AGILE/GRID at 10.9 s after trigger, during the rise of the burst emission in the MeV band." + The MCAL aud GRID nue series read siauultaneous also if we accumulate he deita from the whole αιαον intervals of cach instrument. showing tlat the position of the main bunyps is he same. without sienifi‘aut time lacs.," The MCAL and GRID time series remain simultaneous also if we accumulate the data from the whole energy intervals of each instrument, showing that the position of the main bumps is the same, without significant time lags." + The absence of time lag makes GRE1)) 110721B unusual ainone the events observed so far iu. eiua ravs., The absence of time lag makes GRB 100724B unusual among the events observed so far in gamma rays. + In fact. sole similarities in the lighteurve can be found in CRB 000217A (?).. but in that case the fs ~3 s in the eaniuna rav ighteurve are considerably fainter than in hard N-ravs. aud iun CRB 080916C ο]. ln tits Gana rav enudssk DIESarts at tje second peak. -~ 5.68 after trigecr.," In fact, some similarities in the lightcurve can be found in GRB 090217A \citep{Ackermann_et_al_090217A}, but in that case the first $\simeq 3$ s in the gamma ray lightcurve are considerably fainter than in hard X-rays, and in GRB 080916C \citep{Abdo_et_al_080916C}, but its gamma ray emission starts at the second peak, $\simeq 3.6$ s after trigger." +"ao The lack of gala ravs diwing the first pedk at MeV of CRB WOOLGC ancl the presence of them in the second one anda afOY IS use as an argument by ? to sugeest tha the Wo pxks nma orieiu roni spatially distinct regions or frou two pairs of colliding shels that are cdiffereu lupIvica conditiois and harcluess,", The lack of gamma rays during the first peak at MeV of GRB 080916C and the presence of them in the second one and after is used as an argument by \citet{Abdo_et_al_080916C} to suggest that the two peaks may origin from spatially distinct regions or from two pairs of colliding shells that are different in physical conditions and hardness. + Followine the same TOSOLLδρ We Call OUSe that he CieV aud Me* Olissions of CRB ]00721D may originate in a conou spatial regiou or. 1 ithe iternalshock secnario. from the οςdlixion of the siue]vay of shells.," Following the same reasons, we can argue that the GeV and MeV emissions of GRB 100724B may originate in a common spatial region or, in the internal-shock scenario, from the collision of the same pair of shells." + Simuüilarvy. 2? consider the siuultaneitv of tre GeV and MeV. emission ai the siuele spectral shape across the wide euergv band as a more definite arelmeut iu favour of the iuterual shock origin of the eanmua ray component. assumed as a spectral exteusion to lower energies of the MeV. emission.," Similarly, \citet{Maxham_Zhang_Zhang_2011} consider the simultaneity of the GeV and MeV emission and the single spectral shape across the wide energy band as a more definite argument in favour of the internal shock origin of the gamma ray component, assumed as a spectral extension to lower energies of the MeV emission." + CRB 100721D is characterised by au evident spectral evolu10ion in the MeV. energy. baud., GRB 100724B is characterised by an evident spectral evolution in the MeV energy band. + Iu fact. a significant hared-ο-πο νιwiation iu the the spectrum from the first (ty ty|Ws) to the second bump (ty|578. ty|90s) is cletecος by the AGILE/MCAL (see fig.," In fact, a significant hard-to-soft variation in the the spectrum from the first $t_0$ – $t_0 + 40$ s) to the second bump $t_0 + 57$ s – $t_0 + 90$ s) is detected by the AGILE/MCAL (see fig." + E: and Table 1)). while the statistics iu the eiunnia ray. band docs not allow appreciation «Moa simular evolutio1," \ref{fig:MCAL_spectra} and Table \ref{table:MCAL_spectra}) ), while the statistics in the gamma ray band does not allow appreciation of a similar evolution." + The burst spectra evolution10 app‘ars stronger if we loxds at the Ionus-Wi (?) in the 1δ 1160 keV baud. in which the seco broad. bump ty|50s fy|85 5) is brighter than the first one (ty fy|25 s) and there is also a soft bunip. extending approximately from ty|1Os until fy|Llosa AC visible only beow TO keV. energy. therefore not detected by AICAL.," The burst spectral evolution appears stronger if we look at the Konus-Wind \citep{GCN_10981} in the 18 – 1160 keV band, in which the second broad bump $t_0 + 50$ s – $t_0 + 85$ s) is brighter than the first one $t_0$ – $t_0 + 25$ s) and there is also a soft bump, extending approximately from $t_0 + 100$ s until $t_0 + 140$ s and visible only below 70 keV energy, therefore not detected by MCAL." + The sune feature is also detected by CDM below 200 keV (?).., The same feature is also detected by GBM below 200 keV \citep[][]{Guiriec_et_al_2011}. + The protovindes of 2.13αι obtained from the fit of the time-incerated MCAL spectrum (see Table 1)) is iu good agreenent with the highest energy photon mdoex from the Bare function. measured at :2.00!0.00.09 bY Wind in the 20 keV — 10 MeV energy range (?).. although ou a longer time interval (from ty|6 s to fy|235 s). and with the value of =1.99+£0.01 measured by 7? from he FermifC@BAL data.," The photon index of $-2.13^{+0.05}_{-0.04}$ obtained from the fit of the time-integrated MCAL spectrum (see Table \ref{table:MCAL_spectra}) ) is in good agreement with the highest energy photon index from the Band function measured at $-2.00^{+0.07}_{-0.09}$ by Konus-Wind in the 20 keV – 10 MeV energy range \citep{GCN_10981}, although on a longer time interval (from $t_0 + 6$ s to $t_0 + 235$ s), and with the value of $-1.99 +\pm 0.01$ measured by \citet{Guiriec_et_al_2011} from the Fermi/GBM data." + For this burst the peak energy is nensured at 369|E keV by Konuus-Wiud (2?) and at 6 keV by Ferui/CDM 7..," For this burst the peak energy is measured at $369_{-37}^{+42}$ keV by Konus-Wind \citep{GCN_10981} and at $352 +\pm 6$ keV by Fermi/GBM \citet{Guiriec_et_al_2011}." + Tn this analvsis of the Feruü/OGDM data. ?/ fiud hat the fit of the spectra in tho 8 keV LO MeV energv band significantly improves by iucluding a thermal component of AT=38.1140.57 keV. Ii this case. the Hel-cuerey photon index? of the Band fnction 1s softer. 2.11£0.02.," In this analysis of the Fermi/GBM data, \citet{Guiriec_et_al_2011} + find that the fit of the spectra in the 8 keV – 40 MeV energy band significantly improves by including a thermal component of $kT = 38.14 \pm 0.87$ keV. In this case, the high-energy photon index $\beta$ of the Band function is softer, $-2.11 \pm 0.02$." + With an cenerev threshold of 300 keV. he adcitional spectral component found w Fernu/GBA at AD=διcOT keV cannot be detected by the ACILE/AICAL.," With an energy threshold of $ \sim 300$ keV, the additional spectral component found by Fermi/GBM at $kT = 38.14 \pm 0.87$ keV cannot be detected by the AGILE/MCAL." + Moreover. the reduced chi square value of 0.92 from the MCAL inteerated spectruii implies tha a siniple powerlaw is an adequate model aud docs no allow us to add other components.," Moreover, the reduced chi square value of 0.92 from the MCAL integrated spectrum implies that a simple powerlaw is an adequate model and does not allow us to add other components." + Nevertheless. we tried to introduce a thermal component in the spectra. bu it does not affect the flux above 500 keV and does no iuprove the reduced chi square (that in fact increases fron 0.92 to 0.95).," Nevertheless, we tried to introduce a thermal component in the spectrum, but it does not affect the flux above 500 keV and does not improve the reduced chi square (that in fact increases from 0.92 to 0.95)." + For these reasons we can couclude that the MCAL spectu is adequately fit by a sime powerlaw., For these reasons we can conclude that the MCAL spectum is adequately fit by a simple powerlaw. +" The time-resolved spectral analysis by ? also shows substantial variations iu the E: parue ιο Daud Muction from ~90 keV up to —1100 ke he first idf of our interval A. Ej, is higher ΙΟ keV) and then decreases clown to 500 keV iji the P) aud C ine iutervals."," The time-resolved spectral analysis by \citet{Guiriec_et_al_2011} + also shows substantial variations in the $E_{peak}$ parameter of the Band function from $\sim 90$ keV up to $\sim 1100$ keV. In the first half of our interval A, $E_{peak}$ is higher $\sim 1100$ keV) and then decreases down to $\sim 500$ keV in the B and C time intervals." + In the AGILE/MCAL ceneLev raice. the spectimun cau only be fitted with a powerlav. hus the Enea parauneter cannot be directly measured.," In the AGILE/MCAL energy range, the spectrum can only be fitted with a powerlaw, thus the $E_{peak}$ parameter cannot be directly measured." + However. he MCAL spectrum is harder (with a lower absolute value of the powerlaw photon iudex) in the A interval aud," However, the MCAL spectrum is harder (with a lower absolute value of the powerlaw photon index) in the A interval and" + e~2 (Backman&1996).. (Ixearns&Lerbst1998).. (Winnetal.2006).. (Trullols&J," $\epsilon$$\sim 2$ \citep{b85, l96}. \citep{kh}, \citep{w06}. \citep{tj}," +ordi1997).. (Luhmanetal.1993," \citep{h98} \citep{lrll}," +ordi1997).. (Luhmanetal.1993)," \citep{h98} \citep{lrll}," +ordi1997).. (Luhmanetal.1993).," \citep{h98} \citep{lrll}," +ordi1997).. (Luhmanetal.1993)..," \citep{h98} \citep{lrll}," +The problem. of the transfer of euergyv. momentum. and information frou sub-photospheric solar regions to both the corona aud the solar wincl is one of the most difficult iu solar aud stellar physics.,"The problem of the transfer of energy, momentum, and information from sub-photospheric solar regions to both the corona and the solar wind is one of the most difficult in solar and stellar physics." +" \laguetolhydrodvuamic (ATID) waves are believed to play a kev role because the waves are natural carriers of chcrev. momentum. aud information (οιο,, Erdéllyi 2006 for a recent review)."," Magnetohydrodynamic (MHD) waves are believed to play a key role because the waves are natural carriers of energy, momentum, and information (e.g., Erdéllyi 2006 for a recent review)." + In addition. the euided nature of the wave propagation opens up very interesting perspectives for fixing and tracing the energy transfer channels liehhehted by the waves.," In addition, the guided nature of the wave propagation opens up very interesting perspectives for fixing and tracing the energy transfer channels highlighted by the waves." + In general. MUD waves can be guided by inhomogeneities iu the characteristic MIED speeds (Alfvéun. fast and slow} as well as the maeguetic field itself. which are fouud in all regions of the solar atinosphliere.," In general, MHD waves can be guided by inhomogeneities in the characteristic MHD speeds (Alfvénn, fast and slow) as well as the magnetic field itself, which are found in all regions of the solar atmosphere." + At. the chromospheric level. one of the most pronounceoc wave phenomena are the annm oscillations over sunspots (sec. ce. Bogdan Judge 2006 for a recent review). usually detected as intensity oscillations in visible ight. UV. aud EUW spectral lines. as well as du nücrowave band (e.g. Shibasaki 2001. Colfreikh et al.," At the chromospheric level, one of the most pronounced wave phenomena are the 3-min oscillations over sunspots (see, e.g. Bogdan Judge 2006 for a recent review), usually detected as intensity oscillations in visible light, UV, and EUV spectral lines, as well as in microwave band (e.g., Shibasaki 2001, Gelfreikh et al." + 1999. Nindos et al.," 1999, Nindos et al." + 2002) iux in the du-racdio flux records (Mésszárrosová ot al., 2002) and in the dm-radio flux records (Mésszárrosová et al. + 2006)., 2006). + Threc-nunute oscillations ia sunspots are believed to boe associated with slow maguetoacoustic waves (c.e.. Zhuezlda 2008).," Three-minute oscillations in sunspots are believed to be associated with slow magnetoacoustic waves (e.g., Zhugzhda 2008)." + Outwardly propagating compressible waves of the same yeriodicity are also secu in both the EUV aand ybandpasses in the magnetic fan structures situated over sunspots (ee. De Moortel. 2006 for a review).," Outwardly propagating compressible waves of the same periodicity are also seen in both the EUV and bandpasses in the magnetic fan structures situated over sunspots (e.g., De Moortel 2006 for a review)." + The xojected phase speed of these waves is subsonic. aud the waves are seen to propagate along the plasma chiauncls clongated along the coronal magnetic field lines. aud icuce are interpreted as slow maguctoacoustic waves.," The projected phase speed of these waves is subsonic, and the waves are seen to propagate along the plasma channels elongated along the coronal magnetic field lines, and hence are interpreted as slow magnetoacoustic waves." + Compressible 3-unin waves observed at the same location in both EUV bandpasses show a high degree of correlation (Ising ct al., Compressible 3-min waves observed at the same location in both EUV bandpasses show a high degree of correlation (King et al. + 2003)., 2003). + The relationship between these waves and ο oscillations iu sunspots remains unclear., The relationship between these waves and 3-min oscillations in sunspots remains unclear. + The nuderstanding of the propagation of 3aniu oscillations through the solar atuosphere is oue of the most important problems of solar physics., The understanding of the propagation of 3-min oscillations through the solar atmosphere is one of the most important problems of solar physics. + Its understanding will probably indicate the nature aud properties of the plasma chauncls that transfer these waves iuto the corona. aud hence the connectivity of different livers of the atmosphere.," Its understanding will probably indicate the nature and properties of the plasma channels that transfer these waves into the corona, and hence the connectivity of different layers of the atmosphere." + The role plaved by 3-uuin oscillations iu the corona is also of interest. iu particular. the relationship between Sain oscillations iu sunspots and the faring activity in the active regious (AR) above the sunspots.," The role played by 3-min oscillations in the corona is also of interest, in particular, the relationship between 3-min oscillations in sunspots and the flaring activity in the active regions (AR) above the sunspots." + A possible indication of such a relationship was uentioned iu Celfveikh (2002)., A possible indication of such a relationship was mentioned in Gelfreikh (2002). + Wave and oscillatory phenomena im various parts ofthe solar atmosphere cau trigger and modulate bursty cherey releases. e.g.àY solar flares.," Wave and oscillatory phenomena in various parts of the solar atmosphere can trigger and modulate bursty energy releases, e.g., solar flares." + Iu this case. the periodicity of the oscillations will be evideut i the flaring ight curves as quasi-periodic pulsations (QPP).," In this case, the periodicity of the oscillations will be evident in the flaring light curves as quasi-periodic pulsations (QPP)." + This can be achieved by several mechanisins., This can be achieved by several mechanisms. + Iu the scenario proposed by Nahudakov et al. (, In the scenario proposed by Nakariakov et al. ( +2006). energv of transverse (liuk OY Sausage} oscillatious of coronal loops cau periodicallv leak to a magnetic ueutral point or line situated nearby.,"2006), energy of transverse (kink or sausage) oscillations of coronal loops can periodically leak to a magnetic neutral point or line situated nearby." + The incoming fast magnetoacoustic wave retracts towards the neutral poiut. experiencing focussing aud steepeniug.," The incoming fast magnetoacoustic wave refracts towards the neutral point, experiencing focussing and steepening." + This periodically eeuerates very sharp spikes of electric current density iu the vicinity of the neutral poiut. which in turn can be affected by current driven plasma miucro-instabilities.," This periodically generates very sharp spikes of electric current density in the vicinity of the neutral point, which in turn can be affected by current driven plasma micro-instabilities." + The instabilities can cause the ouset of nuicro-turbuleuce aud heuce culance the plasiuna resistivity bv several orders of magnitude., The instabilities can cause the onset of micro-turbulence and hence enhance the plasma resistivity by several orders of magnitude. + This would lead to periodic trigeeriug of maguctic reconnection aud hence the manifestation of the loop oscillations as periodic variation in the faving lieht curve., This would lead to periodic triggering of magnetic reconnection and hence the manifestation of the loop oscillations as periodic variation in the flaring light curve. + A compressible wave can periodically trigecrao maguctic reconnection not oulv by periodic current deusitv splkes. but also bv the variation in the plasma densitv iu the vicinity. of he reconnection site.," A compressible wave can periodically trigger magnetic reconnection not only by periodic current density spikes, but also by the variation in the plasma density in the vicinity of the reconnection site." + This possibility was modelled immerically by Chen&Pricst(2006) in, This possibility was modelled numerically by \cite{2006SoPh..238..313C} in + This possibility was modelled immerically by Chen&Pricst(2006) inu, This possibility was modelled numerically by \cite{2006SoPh..238..313C} in +The resulting plot of the significance and depth of a secondary eclipse as a function of the orbital phase is given in Fig. 3..,The resulting plot of the significance and depth of a secondary eclipse as a function of the orbital phase is given in Fig. \ref{fig:fig_phase}. + The highest peak in this diagram appears close to phase 0.5. corresponding to a depth of about 6x 1077.," The highest peak in this diagram appears close to phase 0.5, corresponding to a depth of about $\times$ $^{-5}$." + To make sure that any of the corrections explained above did not add or remove some signal of the secondary eclipse. we inserted a secondary eclipse in phase 0.5 to the raw light curve. and performed the same analysis on this data.," To make sure that any of the corrections explained above did not add or remove some signal of the secondary eclipse, we inserted a secondary eclipse in phase 0.5 to the raw light curve, and performed the same analysis on this data." + The whole procedure. using the same filtering and repeating the pre-whitening of the curve. was performed on the data.," The whole procedure, using the same filtering and repeating the pre-whitening of the curve, was performed on the data." + The results are plotted in Fig. 3..," The results are plotted in Fig. \ref{fig:fig_phase}," + along with the results of the real data., along with the results of the real data. + The highest peak in this case is also centered at 0.5. ana the fitted depth is of about 1.6x 107. i.e.. the sum of the inserted eclipse and the signal present in the data.," The highest peak in this case is also centered at 0.5, and the fitted depth is of about $\times$ $^{-5}$, i.e., the sum of the inserted eclipse and the signal present in the data." + We thus suggest that the whole preparation of the curve before performing the secondary search does not significantly alter the signal we want to measure., We thus suggest that the whole preparation of the curve before performing the secondary search does not significantly alter the signal we want to measure. + The phase-folded light curve during the phases of expected secondary eclipse is plotted in Fig. 4..," The phase-folded light curve during the phases of expected secondary eclipse is plotted in Fig. \ref{fig:fig4}," + together with the best fitted trapezoids., together with the best fitted trapezoids. + We explored the goodness-of-fit through function around phase 0.5. in a grid of secondary eclipse centers and depths.," We explored the goodness-of-fit through function around phase 0.5, in a grid of secondary eclipse centers and depths." + The nodel used for the secondary was a trapezoid with duration and shape fixed to those of the transit., The model used for the secondary was a trapezoid with duration and shape fixed to those of the transit. + The observed secondary eclipse was binned into bins of 0.001 in phase (72.5 min). and we estimated the error of each bin as the standard deviation of the measurements inside the bin divided by the square root of the number of points inside the bin.," The observed secondary eclipse was binned into bins of 0.001 in phase $\sim$ 2.5 min), and we estimated the error of each bin as the standard deviation of the measurements inside the bin divided by the square root of the number of points inside the bin." + We plot the resulting dependence and the formal sigma contours in Fig. 5.., We plot the resulting dependence and the formal sigma contours in Fig. \ref{fig:chisq}. + A secondary eclipse with a depth of 0.006040.0020% is detected in the CoRoT light curve at an orbital phase of 0.494-0.006., A secondary eclipse with a depth of $\pm$ is detected in the CoRoT light curve at an orbital phase of $\pm$ 0.006. + To estimate the significance of the secondary eclipse detection. we performed the following test. which preserved the presence of correlated noise in the data.," To estimate the significance of the secondary eclipse detection, we performed the following test, which preserved the presence of correlated noise in the data." + From the data we subtracted the fitted secondary eclipse and shifted the residuals circularly. and then fitted a trapezoid with the phase and shape expected from the primary eclipse.," From the data we subtracted the fitted secondary eclipse and shifted the residuals circularly, and then fitted a trapezoid with the phase and shape expected from the primary eclipse." + Again. the only parameter was the secondary eclipse depth.," Again, the only parameter was the secondary eclipse depth." + All our 1000 trials resulted in depths less than0.006%.. the depth derived from the real data.," All our 1000 trials resulted in depths less than, the depth derived from the real data." + The mean fitted depth was 0.000120.00085c.. consistent with zero.," The mean fitted depth was $\pm$, consistent with zero." + Additionally. we checked the uncertainties in the depth measurement by two different methods.," Additionally, we checked the uncertainties in the depth measurement by two different methods." + In the first one. we reinserted the fitted secondary eclipse after the residual curves of the previous test were constructed and evaluated the fitted depths.," In the first one, we reinserted the fitted secondary eclipse after the residual curves of the previous test were constructed and evaluated the fitted depths." + We estimated the 1-c uncertainty from the standard deviation of the depths that were fitted during this test., We estimated the $\sigma$ uncertainty from the standard deviation of the depths that were fitted during this test. + The result of this test gave a depth of 0.005940., The result of this test gave a depth of $\pm$. +0008%.. As a second method. we fitted two Gaussian functions to (1) the," As a second method, we fitted two Gaussian functions to (1) the" +strategy was adopted by. tsaak et al. (,strategy was adopted by Isaak et al. ( +2002: 102) the SCUBA Bright Quasar Survey (SBQS) (Paper L) with the xincipal aim of definingὃν a statistically-significantC sample of submm sources. bright enough. to permit a range of follow-up study.,2002: I02)— the SCUBA Bright Quasar Survey (SBQS) (Paper I)— with the principal aim of defining a statistically-significant sample of submm sources bright enough to permit a range of follow-up study. + Roughly a quarter. of the targets: were brighter than the 36.~ lO0mJw limit. suggesting that a substantial fraction of high-redshift) quasars have [zu-infrared. luminosities comparable to their blue luminosities.," Roughly a quarter of the targets were brighter than the $3\sigma\sim10$ mJy limit, suggesting that a substantial fraction of high-redshift quasars have far-infrared luminosities comparable to their blue luminosities." + A natural question is whether this ubiquitous. subnim activity discovered at » dis typical of high-redshift AGN in general: is the optically-luminous quasar phase. always accompanied by a clust-rich submillimetre source. or does this only occur at the highest redshifts?," A natural question is whether this ubiquitous submm activity discovered at $z>4$ is typical of high-redshift AGN in general: is the optically-luminous quasar phase always accompanied by a dust-rich submillimetre source, or does this only occur at the highest redshifts?" + In the current paper we present the results of a comparative survey designed to address this question. targetting the “AGN epoch” at 2~2. the era at which the space density of quasars reaches its maximum. and by which most (2SO percent) of the matter that will ever be accreted onto supermassive black holes has already. served as fuel for AGN.," In the current paper we present the results of a comparative survey designed to address this question, targetting the “AGN epoch” at $z\sim2$, the era at which the space density of quasars reaches its maximum, and by which most $>80$ percent) of the matter that will ever be accreted onto supermassive black holes has already served as fuel for AGN." +" A presentation of rese results. along with brief analysis. is the purpose of the ""urrent. paper: a more detailed ancl wide-ranging studs. in 16 context of all the recent mm ancl submam quasar surveys in this series (M99: 102: Omont et al."," A presentation of these results, along with brief analysis, is the purpose of the current paper: a more detailed and wide-ranging study, in the context of all the recent mm and submm quasar surveys in this series (M99; I02; Omont et al.," + 2001: Omont et al.," 2001; Omont et al.," + 002). will be given in a forthcoming work (Priddev et al.," 2002), will be given in a forthcoming work (Priddey et al.," + in prep.)., in prep.). + We assume the currently-favouredl «dominated cosmology £24; 20.3. O 40.7. Ly | (X).," We assume the currently-favoured $\Lambda$ -dominated cosmology $\Omega_M$ =0.3, $\Omega_{\Lambda}$ =0.7, $H_0$ $^{-1}$ $\Lambda$ )." + For continuity with previous work. we will eive alternatives in an Linsteinde Sitter cosmology. OQ j;=1. O\y=0. with 4/2550 + (dS).," For continuity with previous work, we will give alternatives in an Einstein–de Sitter cosmology, $\Omega_M$ =1, $\Omega_{\Lambda}$ =0, with $H_0$ $^{-1}$ (EdS)." + Our aim was to find a sample of bright. mecitum-redshift quasars well-matchee to the z4 sample observed. by Isaak et al. (," Our aim was to find a sample of bright, medium-redshift quasars well-matched to the $z>4$ sample observed by Isaak et al. (" +2002) (Figure 1).,2002) (Figure 1). + To avoid too heterogeneous a sample. we restricted the input catalogues to a few Iarge. homogeneous surveys.," To avoid too heterogeneous a sample, we restricted the input catalogues to a few large, homogeneous surveys." + Ehe final target list comprises quasars preselected. from the Large Bright Quasar Survey (LBOS: Llewett. Foltz Challee. 1995) and the Hamburg Quasar Survey (LIS: Engels et al.," The final target list comprises quasars preselected from the Large Bright Quasar Survey (LBQS: Hewett, Foltz Chaffee, 1995) and the Hamburg Quasar Survey (HS: Engels et al." + 1998: Hagen ct al., 1998; Hagen et al. + 1999)., 1999). + The first selection criterion is based on optical luminosity represented bv absolute P-band magnitude (Mg)., The first selection criterion is based on optical luminosity represented by absolute $B$ -band magnitude $M_B$ ). + At 2=2. the J photometric band samples very close to rest-framoe D. and Lf starts to do so towards higher redshifts.," At $z=2$, the $J$ photometric band samples very close to rest-frame $B$, and $H$ starts to do so towards higher redshifts." + Using a combination of these bands therefore gives an absorption-free assessment of the rest-frame optical magnitude. minimizing the error due extrapolation of the continuum.," Using a combination of these bands therefore gives an absorption-free assessment of the rest-frame optical magnitude, minimizing the error due extrapolation of the continuum." + This overcomes many of the problems encountered: when deriving Mg for 4 quasars— e.g. contamination of the 77 band. by strong emission andabsorption features (as detailed in Paper I)., This overcomes many of the problems encountered when deriving $M_B$ for $z>4$ quasars— e.g. contamination of the $R$ band by strong emission andabsorption features (as detailed in Paper I). + Similarly. at z22. observed-frame D becomes compromised by the strong CIV and Ly-a emission lines.," Similarly, at $z\approx2$, observed-frame $B$ becomes compromised by the strong CIV and $\alpha$ emission lines." + llence. to obtain a sample of luminous z2 quasars all with J and Jf magnitudes. we erossecorrelated catalogues of bright. mecitun-recdshift quasars with the 23LASS near-infrared catalogue through the web-based interface at LPAC (http://wwwipac.caltech.ecdu).," Hence, to obtain a sample of luminous $z\approx2$ quasars all with $J$ and $H$ magnitudes, we cross-correlated catalogues of bright, medium-redshift quasars with the 2MASS near-infrared catalogue through the web-based interface at IPAC (http://www.ipac.caltech.edu)." + Counting sources out to a radius of 60 aresee enabled us to determine a maximum association radius of 5 arcsec. within which the probability of a chance association is «0.5 percent.," Counting sources out to a radius of 60 arcsec enabled us to determine a maximum association radius of 5 arcsec, within which the probability of a chance association is $<$ 0.5 percent." + Absolute D- band magnitudes were calculated from apparent J ancl // magnitudes thereby obtained (all our targets were detected in both bands) weighted according to the proximity of the band to D in the redshifted spectrum., Absolute $B$ -band magnitudes were calculated from apparent $J$ and $H$ magnitudes thereby obtained (all our targets were detected in both bands) weighted according to the proximity of the band to $B$ in the redshifted spectrum. + They have been corrected for Galactic extinction. though in most cases this is negligible (κ: 0.05mag).," They have been corrected for Galactic extinction, though in most cases this is negligible $<0.05$ mag)." +" We have assumed an optical spectral index eia0.5 (where f, xv""). though. as noted. the extrapolation error is small."," We have assumed an optical spectral index $\alpha_{\rm opt}=-0.5$ (where $f_{\nu}\propto\nu^{\alpha}$ ), though, as noted, the extrapolation error is small." + Photometric errors in -/ ancl Lf are typically 0.1.0.2mag., Photometric errors in $J$ and $H$ are typically 0.1–0.2mag. + In order to match optical luminosity with the zc4 sample. objects with ALE4+ sample’.," In order to match optical luminosity with the $z>4$ sample, objects with $M_B^{\rm EdS}<-27.5$ were initially selected— i.e. adopting the same cosmology as per the selection of the $z>4$ ." + A wide redshift range 1.50<23.00 was chosen to maximize the potential number of targets (Figure 1), A wide redshift range $1.50—0.1 since we are interested in constraining models which have sufficient amount of dark energy at early times."," In analyzing the data, we keep $w_m \geq -0.1$ since we are interested in constraining models which have sufficient amount of dark energy at early times." +" The true ACDM model cannot be exactly reproduced by the EDE class of models since w,,#—1, but in the limit wo2—1,a;—0(z;0 these models ACDM-like behavior."," The true $\Lambda$ CDM model cannot be exactly reproduced by the EDE class of models since $w_m \neq -1$, but in the limit $w_0 += -1, a_t \rightarrow 0 \ (z_t \rightarrow \infty), \Delta_t +\rightarrow 0$ these models replicate $\Lambda$ CDM-like behavior." +" As shown in replicatefigure 7, CMB + cluster count analysis can constrain the ΕΡΕ parameters to wot£-—09,az0.2(%>4,4,0.3, which implies that cluster counts + CMB can constrain deviation from ACDM behavior upto at least z=4."," As shown in figure \ref{fig:SPT_mcmc}, CMB + cluster count analysis can constrain the EDE parameters to $w_0 \lleq -0.9, a_t \lleq 0.2 +(z_t \ggeq 4), \Delta_t \lleq 0.3$, which implies that cluster counts + CMB can constrain any deviation from $\ld$ CDM behavior upto at least z=4." +" For the SZ anypower spectrum data, we find that the EDE parameters are constrained to Wo€—0.85,a,z,0.15(z,>5.5),A,z0.15 (see figure 8))."," For the SZ power spectrum data, we find that the EDE parameters are constrained to $w_0 \lleq -0.85, a_t \lleq 0.15 (z_t \ggeq 5.5), +\Delta_t \lleq 0.15$ (see figure \ref{fig:SZ_mcmc}) )." + SZ power spectrum provide complementary information about dark energy parameters compared to cluster counts., SZ power spectrum provide complementary information about dark energy parameters compared to cluster counts. +" For example, SZ power spectrum put tighter constraints on the dark energy transition parameters compared to cluster counts."," For example, SZ power spectrum put tighter constraints on the dark energy transition parameters compared to cluster counts." + The matter density is reasonably reconstructed for both the cluster counts and SZ power spectrum., The matter density is reasonably reconstructed for both the cluster counts and SZ power spectrum. +" In this work, we have studied early dark energy models in light of future galaxy cluster data."," In this work, we have studied early dark energy models in light of future galaxy cluster data." +" We study two EDE models, both of which are allowed within the current observational constraints."," We study two EDE models, both of which are allowed within the current observational constraints." +" The first model (EDE1) transits from ΕΡΕ, behavior at redshift z>5 to ACDM-like behavior at present, while the second model (EDE2) transits at a higher redshift (z~9) to an equation of state wo=—0.9, which is close to but not identical to ACDM."," The first model (EDE1) transits from EDE behavior at redshift $z \ggeq 5$ to $\ld$ CDM-like behavior at present, while the second model (EDE2) transits at a higher redshift $z \simeq 9$ ) to an equation of state $w_0 = -0.9$, which is close to but not identical to $\ld$ CDM." +" For both the models, as well as for the fiducial ACDM cosmology, we show the predictions for cluster abundance and SZ power spectrum."," For both the models, as well as for the fiducial $\ld$ CDM cosmology, we show the predictions for cluster abundance and SZ power spectrum." +" For that purpose, we consider two instruments — eROSITA for X-ray surveys, and ACT/SPT for SZ effect."," For that purpose, we consider two instruments – eROSITA for X-ray surveys, and ACT/SPT for SZ effect." +" We also do a likelihood analysis of data simulated replicating the SPT and eRosita survey specifications, along with the simulated Planck CMB data, to obtain the constraints on the EDE parameters from future surveys, and find that future galaxy cluster counts and SZ power spectrum can put competitive constraints on these parameters."," We also do a likelihood analysis of data simulated replicating the SPT and eRosita survey specifications, along with the simulated Planck CMB data, to obtain the constraints on the EDE parameters from future surveys, and find that future galaxy cluster counts and SZ power spectrum can put competitive constraints on these parameters." +" It is worth noting some apparent differences between our work here, and some other recent works on EDE signatures."," It is worth noting some apparent differences between our work here, and some other recent works on EDE signatures." +" For example, Fedeli et al. ("," For example, Fedeli et al. (" +"2009) also considered several EDE models, but their cluster counts are higher than for the fiducial ACDM model, although og for EDE models are commonly lower in their work (as it is the case here as well).","2009) also considered several EDE models, but their cluster counts are higher than for the fiducial $\Lambda$ CDM model, although $\sigma_8$ for EDE models are commonly lower in their work (as it is the case here as well)." +" That is because for their choice of EDE models Hubble parameters, E(z) differs significantly from the ACDM model."," That is because for their choice of EDE models Hubble parameters, $E(z)$ differs significantly from the corresponding $\ld$ CDM model." +" This affects minimum observablecorresponding mass as a function of redshift; their EDE models have much lower mass threshold than ACDM, thus resulting in higher observable cluster counts."," This affects minimum observable mass as a function of redshift; their EDE models have much lower mass threshold than $\Lambda$ CDM, thus resulting in higher observable cluster counts." +" In contrast, we have chosen models which have E(z) similar to that of the corresponding ACDM model, to highlight the difference coming from the perturbations rather than the background expansion."," In contrast, we have chosen models which have $E(z)$ similar to that of the corresponding $\ld$ CDM model, to highlight the difference coming from the perturbations rather than the background expansion." +" Similar difference from this work, due to the radical departure of E(z) from ACDM, can be seen in Waizmann Bartelmann (2009), for the effects of EDE on SZ power "," Similar difference from this work, due to the radical departure of $E(z)$ from $\Lambda$ CDM, can be seen in Waizmann Bartelmann (2009), for the effects of EDE on SZ power spectrum." +"In some other cases differences can arise depending whether spectrum.one uses low-k, CMB normalization of the power spectrum as done here, or og normalization as in Sadeh et al. ("," In some other cases differences can arise depending whether one uses low-k, CMB normalization of the power spectrum as done here, or $\sigma_8$ normalization as in Sadeh et al. (" +"2007), although it is clear that a successful model has to fulfill both constraints.","2007), although it is clear that a successful model has to fulfill both constraints." +" We show that the inclusion of dark energy perturbations has a major effect on the matter power spectrum, therefore increasing the possibility of discriminating EDE models from ACDM using large scale structure probes."," We show that the inclusion of dark energy perturbations has a major effect on the matter power spectrum, therefore increasing the possibility of discriminating EDE models from $\ld$ CDM using large scale structure probes." + Neglecting the leads to severe underestimation of the imprint which the sharp transition in dark energy equation of state leaves on the and therefore on the matter power spectrum., Neglecting the leads to severe underestimation of the imprint which the sharp transition in dark energy equation of state leaves on the and therefore on the matter power spectrum. + We show that the models considered here which are allowed by the current observations can be ruled out using the future galaxy cluster probes., We show that the models considered here which are allowed by the current observations can be ruled out using the future galaxy cluster probes. + It is also that both the cluster counts and the SZ power spectrum are interestingsensitive to the redshift at which the transition between early and present day dark energy occurs., It is also interesting that both the cluster counts and the SZ power spectrum are sensitive to the redshift at which the transition between early and present day dark energy occurs. + We expect to put strong constraints on the equation, We expect to put strong constraints on the equation +and instead is (he main route.,and instead is the main route. + This result has consequences for the chemistry., This result has consequences for the chemistry. + ?. found that the new branching ratios do not affect (he calculated abundances in gas phase only. models. but do have significant effects in models that include freezeout.," \citet{roberts03} found that the new branching ratios do not affect the calculated abundances in gas phase only models, but do have significant effects in models that include freezeout." + At low temperatures when Ireezeout is included. the destruction of by reaction with CO becomes less significant as the CÓ is depleted. aud so Reaction 1 gains in importance.," At low temperatures when freezeout is included, the destruction of by reaction with CO becomes less significant as the CO is depleted, and so Reaction \ref{eq:n2h+} gains in importance." + The formation of NII [rom reaction 1 results in the removal of nitrogen from the gas in cold regions. since any NIE that aceretes onto the erains will be rapidly hydrogenated to form Nils. a molecule with a hieh binding enerev (hat is therefore not easily desorbed. unlike No which is verv volatile.," The formation of NH from reaction \ref{eq:n2h+} results in the removal of nitrogen from the gas in cold regions, since any NH that accretes onto the grains will be rapidly hydrogenated to form $_3$, a molecule with a high binding energy that is therefore not easily desorbed, unlike $_2$ which is very volatile." + Consequently. the new reaction pathways can reduce the abundance of nitrogen.bearing molecules in the eas.," Consequently, the new reaction pathways can reduce the abundance of nitrogen–bearing molecules in the gas." + This reduction is less significant in regions where (he grain temperature is higher (han about 20 IX. where NII can be thermally desorbed before reacting. and hence the lormation of NII4 ice is less efficient.," This reduction is less significant in regions where the grain temperature is higher than about 20 K, where NH can be thermally desorbed before reacting, and hence the formation of $_3$ ice is less efficient." + In disks. ? showed that No is an important means of controlling the degree of deuteration.," In disks, \citet{cd05} showed that $_2$ is an important means of controlling the degree of deuteration." + The presence of No will prevent (he transfer of deuteration along the chain of isotopes from to and reduce the abundance of by destroving the less deuterated isolopomers before they have a chance to form., The presence of $_2$ will prevent the transfer of deuteration along the chain of isotopes from to and reduce the abundance of by destroying the less deuterated isotopomers before they have a chance to form. +. The new reaction pathway means that the abundance of No will be reduced in the midplane. and hence the degree of deuteration of will be higher.," The new reaction pathway means that the abundance of $_2$ will be reduced in the midplane, and hence the degree of deuteration of will be higher." + Given (he hieh densities and cold temperatures found in much of the outer disk. molecules that hit a grain are likely to stick to it efficiently.," Given the high densities and cold temperatures found in much of the outer disk, molecules that hit a grain are likely to stick to it efficiently." + We assume that all species Ireezeout at the same rate with a temperature independent sticking coefficient of 0.3., We assume that all species freezeout at the same rate with a temperature independent sticking coefficient of 0.3. + For positive ions the Ireezeout rate is increased slightly. since grains are likely to have a negative charge (?) and therefore there could be a stronger attraction between (he positive ious and (the negatively charged grains.," For positive ions the freezeout rate is increased slightly, since grains are likely to have a negative charge \citep{un80} and therefore there could be a stronger attraction between the positive ions and the negatively charged grains." +" The freezeout. rate of positive ions is assumed to increase by a [actor C = L4-16.71x10.!/(aT,,.) where e is the grain radius and T,, is the grain temperature (?)..", The freezeout rate of positive ions is assumed to increase by a factor $C$ = $1 + 16.71 \times 10^{-4}/(a T_{gr})$ where $a$ is the grain radius and $T_{gr}$ is the grain temperature \citep{un80}. + lons are assumed to recombine on the grain surfaces in the same wav that thev do when reacling wilh electrons in the gas. iin the gas phase and on the grain," Ions are assumed to recombine on the grain surfaces in the same way that they do when reacting with electrons in the gas, in the gas phase and on the grain" +estimates alone.,estimates alone. +" Assuming a more precise estimate of M, (or equivalently R,), fixing the limb darkening parameters, or assuming fixed decorrelation coefficients for in-transit data based upon their solution from out-of-transit data, will all result in higher precision for the system parameters, but such procedures may result in less accuracy."," Assuming a more precise estimate of $M_{\star}$ (or equivalently $R_{\star}$ ), fixing the limb darkening parameters, or assuming fixed decorrelation coefficients for in-transit data based upon their solution from out-of-transit data, will all result in higher precision for the system parameters, but such procedures may result in less accuracy." + Comparing the quality of light curves should not be done out of context., Comparing the quality of light curves should not be done out of context. +" For example, with comparable quality data, the precision for a transit model analysis using fixed limb darkening coefficients should not be directly compared to the precision that results from a transit modeling analysis that allows the limb darkening coefficients to vary."," For example, with comparable quality data, the precision for a transit model analysis using fixed limb darkening coefficients should not be directly compared to the precision that results from a transit modeling analysis that allows the limb darkening coefficients to vary." +" Recently, Tinettietal.(2010) analyzed the same observations of tto measure the transmission spectrum of the atmosphere ofXO-lb."," Recently, \citet{TIN10} analyzed the same observations of to measure the transmission spectrum of the atmosphere of." +". Although their analysis focused on individual spectral channels across the G141 grism, their independent analysis techniques share some similarities with the approach adopted in this study."," Although their analysis focused on individual spectral channels across the G141 grism, their independent analysis techniques share some similarities with the approach adopted in this study." + The 7 state correction described in this study is closely related to their correction for “channel-to-channel” correlations (Swainetal.2008)., The 7 state correction described in this study is closely related to their correction for “channel-to-channel” correlations \citep{SWA08}. +". The gain-like variations associated with the 7 states, which appear to be wavelength independent, would coherently affect the relative flux residuals averaged over all wavelength channels, and be removed through the “channel-to-channel” corrections."," The gain-like variations associated with the 7 states, which appear to be wavelength independent, would coherently affect the relative flux residuals averaged over all wavelength channels, and be removed through the ``channel-to-channel'' corrections." +" The *channel-to-channel"" correction of Swainetal. cannot be applied to the broad-band photometry, (2008)since by definition the broad-band photometry has a single channel."," The “channel-to-channel” correction of \citet{SWA08} cannot be applied to the broad-band photometry, since by definition the broad-band photometry has a single channel." +" The study by Tinettietal.(2010) analyzed only the second HST visit to ((yellow and blue points in Figure 4)), as the first visit (green and red points in Figure 4)) was deemed too photometrically unstable."," The study by \citet{TIN10} analyzed only the second HST visit to (yellow and blue points in Figure ), as the first visit (green and red points in Figure ) was deemed too photometrically unstable." +" By treating orbits in different filter wheel positions separately, we are able to provide reliable model fits (reduced x?~ 1) using data from both HST visits to constrain the properties of the ssystem."," By treating orbits in different filter wheel positions separately, we are able to provide reliable model fits (reduced $\chi^{2}\sim 1$ ) using data from both HST visits to constrain the properties of the system." +" Analysis of more NICMOS observations are warranted, but it indicates our methodology enables a coherent procedure to help analyze NICMOS datasets of transiting planets that were previously thought to be too photometrically unstable to provide useful results."," Analysis of more NICMOS observations are warranted, but it indicates our methodology enables a coherent procedure to help analyze NICMOS datasets of transiting planets that were previously thought to be too photometrically unstable to provide useful results." + The light curve analysis assumes the stellar surface is described by the limb darkening function., The light curve analysis assumes the stellar surface is described by the limb darkening function. +" However, the presence of dark spots or bright faculae on the surface of the star violate this assumption (e.g.,Pontetal. 2008)."," However, the presence of dark spots or bright faculae on the surface of the star violate this assumption \citep[e.g., ][]{PON08}." +. The discovery photometry precision) and slow rotation (vsini«3km indicate that iis not an active star (McCulloughs)etal.2006)., The discovery photometry precision) and slow rotation $v\sin i < 3$ ) indicate that is not an active star \citep{MCC06}. +. There is a apparent flux difference in the measured counts between HST visits; aappears brighter during visit 2., There is a apparent flux difference in the measured counts between HST visits; appears brighter during visit 2. +" The photometric stability of the NICMOS cameras is of order ~1% (Thatteetal.2009),, and orbit to orbit differences of in flux within a single visit are present."," The photometric stability of the NICMOS cameras is of order $\sim 1$ \citep{THA09}, and orbit to orbit differences of in flux within a single visit are present." +" Thus, it is not clear whether the flux difference between the first and second visit is due to intrinsic variability in oor due to instrumental photometric instability."," Thus, it is not clear whether the flux difference between the first and second visit is due to intrinsic variability in or due to instrumental photometric instability." +" If the η=0.006 decrease in flux results from the appearance of an unocculted dark spot, then the R,/R, as measured for the transit when the dark spot is present needs to be reduced by a factor of /l1—7=0.997 to compare to the measured R,/R, when the spot was absent (ie., the transit depth is deeper when more unocculted dark spots are present)."," If the $\eta=0.006$ decrease in flux results from the appearance of an unocculted dark spot, then the $R_{p}/R_{\star}$ as measured for the transit when the dark spot is present needs to be reduced by a factor of $\sqrt{1-\eta}=0.997$ to compare to the measured $R_{p}/R_{\star}$ when the spot was absent (i.e., the transit depth is deeper when more unocculted dark spots are present)." +" The expected change in R,/R, between visits due to the presence of a hypothetical dark spot, is smaller than our precision with which we currently measure R,/R,."," The expected change in $R_{p}/R_{\star}$ between visits due to the presence of a hypothetical dark spot, is smaller than our precision with which we currently measure $R_{p}/R_{\star}$." +" To verify this expectation, we added a free parameter to our model allowing each visit to have its own R,/R,."," To verify this expectation, we added a free parameter to our model allowing each visit to have its own $R_{p}/R_{\star}$." +" The resulting model negligibly improves the fit, Ax?«1, however ARy,/R,=—0.0003+0.0009, or lower Rp/Ry for the second visit."," The resulting model negligibly improves the fit, $\Delta \chi^2<1$, however $\Delta R_{p}/R_{\star}=-0.0003\pm0.0009$, or lower $R_{p}/R_{\star}$ for the second visit." +" This agrees in size and direction as the expectation, however it is within the statistical uncertainty, and thus we don’t formally adjust the results in Table1."," This agrees in size and direction as the expectation, however it is within the statistical uncertainty, and thus we don't formally adjust the results in Table." +. The likelihood used in the Bayesian posterior assumes the residuals are independent and can result in underestimated parameter uncertainties if the residuals are not independent (Pontetal.2006;Carter&Winn2009)..," The likelihood used in the Bayesian posterior assumes the residuals are independent and can result in underestimated parameter uncertainties if the residuals are not independent \citep{PON06,CAR09A}." +" We analyze the sample autocorrelation function (Boxetal.2008) to verify that the correction for systematics removes the temporal correlations present in the raw data, and that our use of the likelihood that assumes independence is valid (Figure 5))."," We analyze the sample autocorrelation function \citep{BOX08} to verify that the correction for systematics removes the temporal correlations present in the raw data, and that our use of the likelihood that assumes independence is valid (Figure )." +" To reliably determine the sample autocorrelation especially for large lags, the sample autocorrelation is calculated on the vector of residuals that are ordered by image number rather than time."," To reliably determine the sample autocorrelation especially for large lags, the sample autocorrelation is calculated on the vector of residuals that are ordered by image number rather than time." + The smooth upper and lower curves in Figure shows the 380 limits as to the expectation of the sample autocorrelation statistic if the underlying population of residuals are independent &Wang, The smooth upper and lower curves in Figure shows the $\sigma$ limits as to the expectation of the sample autocorrelation statistic if the underlying population of residuals are independent \citep{KAN10}. +" The sample autocorrelation quickly(Kan dies off by lag 1, 2010)..αι=—0.067, but a few of the lags spike above the 3c expectation."," The sample autocorrelation quickly dies off by lag 1, $a_{1}=-0.067$, but a few of the lags spike above the $\sigma$ expectation." + We further explore the assumption of independence in the likelihood through Monte Carlo simulation of the raw data and subsequent retrieval of the system parameters., We further explore the assumption of independence in the likelihood through Monte Carlo simulation of the raw data and subsequent retrieval of the system parameters. + We generate a red noise vectorthat has the same variance and autocorrelation function as the model residuals., We generate a red noise vectorthat has the same variance and autocorrelation function as the model residuals. +" 'To ensure the sample autocorrelation function does not underestimate the true autocorrelation function, the simulated red noise has an autocorrelation for all lags (2 1) 1.5 times the sample autocorrelation shown in Figure5."," To ensure the sample autocorrelation function does not underestimate the true autocorrelation function, the simulated red noise has an autocorrelation for all lags $\geq 1$ ) 1.5 times the sample autocorrelation shown in Figure." +". In addition to the transit model with red noise, we add correlations with external parameters and 7 state offsets."," In addition to the transit model with red noise, we add correlations with external parameters and 7 state offsets." +" By comparing the scatter of parameter estimates derived from a x? minimization of the simulated light curves and compare to the uncertainty estimates of an MCMC analysis of the actual data for fixed stellar mass, we find the uncertainties agree within for all the transit model parameters except for the uncertainty in R,, which is larger."," By comparing the scatter of parameter estimates derived from a $\chi^2$ minimization of the simulated light curves and compare to the uncertainty estimates of an MCMC analysis of the actual data for fixed stellar mass, we find the uncertainties agree within for all the transit model parameters except for the uncertainty in $_{\star}$, which is larger." +" However, the larger uncertainty in R, is negligibe compared to the much larger uncertainty in R, that results from the uncertainty in M,."," However, the larger uncertainty in $_{\star}$ is negligible compared to the much larger uncertainty in $_{\star}$ that results from the uncertainty in $_{\star}$ ." + These tests show that the use of a likelihood assuming independence does not result in a significant underestimate in the parameter uncertainties., These tests show that the use of a likelihood assuming independence does not result in a significant underestimate in the parameter uncertainties. +The existence of Population Η1 is related to many inportant issues.,The existence of Population III is related to many important issues. + This population of stars could play an important role in the reionization of the universe (Miralda-EscudéGnedin2000:Fanetal.2000) compensating for the [act that the known populations of quasars and star-forming galaxies are not sufficient to account [or the required number of ionizing photons at z>5.," This population of stars could play an important role in the reionization of the universe \citep{mir98, gne00, fan00} compensating for the fact that the known populations of quasars and star-forming galaxies are not sufficient to account for the required number of ionizing photons at $z\geq 5$." + Alternatively. massive remnants (black holes) as the end-products of these primordial stars could have been the progenitors of the current active galactie nuclei. while the less massive remnants (ancient white dwarls) could have mace a contribution to the NLACIIO population found in the halo of our galaxy. (MéndezAleock.C.etal.2000:Laserre2000) although this contribution is stronely limited by the observed white-dwarl luminosity finetion as well as by energetic argumentis (Isernοἱal.1998.1999).," Alternatively, massive remnants (black holes) as the end-products of these primordial stars could have been the progenitors of the current active galactic nuclei, while the less massive remnants (ancient white dwarfs) could have made a contribution to the MACHO population found in the halo of our galaxy \citep{men00, alc00, las00} although this contribution is strongly limited by the observed white-dwarf luminosity function as well as by energetic arguments \citep{ise98, ise99}." +. Obviously. the real significance of Population II stars in the above issues is determined by the nature of the initial mass function (IME) of the first generation of stars.," Obviously, the real significance of Population III stars in the above issues is determined by the nature of the initial mass function (IMF) of the first generation of stars." +" The idea of a pregalactic metal enrichment has become increasingly important in recent vears because of the discoverv of intergalactic metals in Ly-a forest clouds (NGZII)<108 7) al 2=3—3.5 showingmetal abundances of Z~10?—2Z, (Sonegaila1997:Cowie&Songaila1998:Ellisonetal. 2000)."," The idea of a pregalactic metal enrichment has become increasingly important in recent years because of the discovery of intergalactic metals in $\alpha$ forest clouds $N(H I)\leq 10^{17}$ $^{-2}$ ) at $z= 3 - 3.5$ showingmetal abundances of $Z\sim 10^{-3}-10^{-2} Z_\odot$ \citep{son97, cow98, ell00}." +. Sargentetal.(1980) were the first to identify the La-a forest with a population of primordial hydrogen clouds in pressure equilibrium with a hotter. expanding intergalactic medium (GAL).," \citet{sar80} were the first to identify the $\alpha$ forest with a population of primordial hydrogen clouds in pressure equilibrium with a hotter, expanding intergalactic medium (IGM)." + This picture. however. has changed recently (o one in which the Ly-a [orest is. in fact. the IGM at very early epochs.," This picture, however, has changed recently to one in which the $\alpha$ forest is, in fact, the IGM at very early epochs." + Therefore. these high redshifted clouds are believed to be essentially composed of unprocessed material from which the galaxies were formed.," Therefore, these high redshifted clouds are believed to be essentially composed of unprocessed material from which the galaxies were formed." + However. (he gas producing the Ly-a forest is not pristine since a significant [raction of the detected lines are associated with C IV absorptions at AAI548.1550 (Tytleretal.1995:CowieSongaila&Cowie 1900).," However, the gas producing the $\alpha$ forest is not pristine since a significant fraction of the detected lines are associated with C IV absorptions at $\lambda\lambda 1548, 1550$ \citep{tyl95, cow95, son96}." + The carbon abundance implied by these detections is ος —2.5. although with an important dispersion within (he forest (see e.g. Dorksemberg et al.," The carbon abundance implied by these detections is $\sim -2.5$ , although with an important dispersion within the forest (see e.g. Borksemberg et al." + 1998)., 1998). +panels) is above the Oo I sequence.,panels) is above the Oo I sequence. + With one exception. his is also true for variables with irregular period changes shown in the right-hand. panels.," With one exception, this is also true for variables with irregular period changes shown in the right-hand panels." + The exception is V7s. a Blazhko variable with a pulsation amplitude corresponding o the Ool sequence but with relatively bright. Vi=15.572 mag mean brightness.," The exception is V78, a Blazhko variable with a pulsation amplitude corresponding to the OoI sequence but with relatively bright, $V_\mathrm{i}=15.572$ mag mean brightness." + Phe inspection of SDSS images (Yorketal.2000) has revealed that V7S has a companion at 09 separation with r=18.495 mae brightness (Anοἱal. 2008).," The inspection of SDSS images \citep{sdss} has revealed that V78 has a companion at 0.09"" separation with $r=18.495$ mag brightness \citep{sdss2}." +. Most. probably. this companion was not resolved in any of the used photometries.," Most probably, this companion was not resolved in any of the used photometries." + Lf the magnitude of. V78S is corrected for the contamination of the companion. the mean magnitude is about 0.06 mag fainter. in agreement with the Ool classification of the stars based on its aniplitucle (see the right. panels of Fig. 13)).," If the magnitude of V78 is corrected for the contamination of the companion, the mean magnitude is about 0.06 mag fainter, in agreement with the OoI classification of the stars based on its amplitude (see the right panels of Fig. \ref{p-ampv}) )." + The ~0.04 mag decrease of the amplitude caused by the companion does not influence the Oo classification., The $\sim 0.04$ mag decrease of the amplitude caused by the companion does not influence the Oo classification. + The period-change rates of 40 non-Blazhko variables with regular and euasi-regular period variations on the Ool sequence are in the 25 ray emitting plasma is E10 or the TeV 5 ray emitting region is a much larger distances. we are forced to conclude that the accretion rate in this object has mτς107."," Therefore unless either Mrk 421 harbours a black hole of mass $\approxlt +10^6 M_{\odot}$ or the Lorentz factor of the $\gamma$ –ray emitting plasma is $\Gamma\gg 10$ or the TeV $\gamma$ –ray emitting region is at much larger distances, we are forced to conclude that the accretion rate in this object has $\dot m \approxlt 10^{-2}-10^{-3}$." + On the other hand. observations on VLBI scales lez o estimates of the power emitted. in the form. of. je kinetic Luminositw exceeding ~10 “ore s+ (ee. Colotti. 'adovani Chisellini 1097). suggesting that indeed. Alrk 421 is harboring a much higher mass object.," On the other hand, observations on VLBI scales lead to estimates of the power emitted in the form of jet kinetic luminosity exceeding $\sim 10^{46}$ erg $^{-1}$ (e.g. Celotti, Padovani Ghisellini 1997), suggesting that indeed Mrk 421 is harboring a much higher mass object." + This coul »' reconciled. with the low radiative (quasithermal) power if any accreting disc is racdiativelv inellicient., This could be reconciled with the low radiative (quasi–thermal) power if any accreting disc is radiatively inefficient. + Phe deduce imits on m are then consistent with the accretion occurring in the advection.dominated regime., The deduced limits on $\dot m$ are then consistent with the accretion occurring in the advection–dominated regime. + The constraints derived. in this section. imply that if a region comparable in size to the TeV production site £- is pervaded by a radiation field of intensity comparable with the observed one. then an extremely high bulk Lorentz factor. D& 107. is required in order to overcome the limits from photon opacity.," The constraints derived in this section imply that if a region comparable in size to the TeV production site $R_{\gamma}$ is pervaded by a radiation field of intensity comparable with the observed one, then an extremely high bulk Lorentz factor, $\Gamma\approxgt 10^3$ , is required in order to overcome the limits from photon–photon opacity." + l]lowever. one can casily envisage alternative," However, one can easily envisage alternative" +Spiral arma pitch aneles are measured using the sale technique cuiploved by Seigar et ((2005).,Spiral arm pitch angles are measured using the same technique employed by Seigar et (2005). + A two-dimensional fast-Fouricr decomposition technique is used. which employs a program described by Schrodder et al. (," A two-dimensional fast-Fourier decomposition technique is used, which employs a program described by Schrödder et al. (" +1991).,1994). + Logarithmic spirals are assumed im the decomposition., Logarithmic spirals are assumed in the decomposition. + The resulting pitch aneles are listed iu Tables 1. 2 and 3.," The resulting pitch angles are listed in Tables 1, 2 and 3." +After commissioning on the Mercator telescope in April 2009. HERMES immediately became the work-horse instrument.,"After commissioning on the Mercator telescope in April 2009, HERMES immediately became the work-horse instrument." + During the first year of operations. this instrument obtained about 7300 spectra on the sky. which makes clear that HERMES also fulfills its robust operational requirements.," During the first year of operations, this instrument obtained about 7300 spectra on the sky, which makes clear that HERMES also fulfills its robust operational requirements." + HERMES is open to the community at large through collaboration with the consortium members and through the Spanish CAT time allocation programme. available for all telescopes at the Roque de los Muchachos observatory.," HERMES is open to the community at large through collaboration with the consortium members and through the Spanish CAT time allocation programme, available for all telescopes at the Roque de los Muchachos observatory." + Table Al summarises the ZEMAX data of all optical surfaces of the HERMES spectrograph., Table \ref{tab:surface_data} summarises the ZEMAX data of all optical surfaces of the HERMES spectrograph. + The optical system has been optimised by considering the measured values of the refractive indices of the optical glasses., The optical system has been optimised by considering the measured values of the refractive indices of the optical glasses. + This means that the use of standard refractive index values results in a slightly suboptimal image quality for the system that is described here., This means that the use of standard refractive index values results in a slightly suboptimal image quality for the system that is described here. +"so we use a fiducial limiting radius of r=2r,.",so we use a fiducial limiting radius of $r=2r_g$. +" Using equation (6)). we have calculated relations connecting Mj, and A‘, for all three limiting radii and plotted them as dotted lines in Figure 2.."," Using equation \ref{rth}) ), we have calculated relations connecting $M_H$ and $M_\star$ for all three limiting radii and plotted them as dotted lines in Figure \ref{fig2}." + The mass of the black hole in NGC 5905 is not verv well constrained. but it is believed io be in the range Mg~10*—10. (IKomossa2001).. based on the correlation between bulee blue huninosity and black hole mass for spiral galaxies (Saluceietal.2000). and on the correlation between bulge velocity dispersionaud black hole mass lor ellipticals aud spirals (Gebharcltetal.2000:Merritt&Ferrarese2001).," The mass of the black hole in NGC 5905 is not very well constrained, but it is believed to be in the range $M_H \sim 10^7 - 10^8 M_\odot$ \citep{kom01}, based on the correlation between bulge blue luminosity and black hole mass for spiral galaxies \citep{sal00} and on the correlation between bulge velocity dispersionand black hole mass for ellipticals and spirals \citep{geb00,mer01}." +. This information is sufficient to constrain (he mass of the disrupted star fairly üghtly: (he mass must be either in the range 0.01—0.0237. in the case of à SSO or 0.6—LM. in the case of a LMS., This information is sufficient to constrain the mass of the disrupted star fairly tightly: the mass must be either in the range $0.01-0.02 M_\odot$ in the case of a SSO or $0.6-1M_\odot$ in the case of a LMS. + The result. however. depends sensitüivelv on the choice we make for the (dal spin-up parameter A discussed in 822.," The result, however, depends sensitively on the choice we make for the tidal spin-up parameter $k$ discussed in 2." + Figure 2. has been calculated [or 75=3. a reasonable ancl possibly likely value. but in principle 7: could be as small as 1.," Figure \ref{fig2} has been calculated for $k=3$, a reasonable and possibly likely value, but in principle $k$ could be as small as 1." + Figure 2. shows how the mass constraints change when we use the latter value., Figure \ref{fig3} shows how the mass constraints change when we use the latter value. + We see that the allowed range of models is limited to somewhat lower black hole masses. unless the black hole spins very rapidly and allows tidal disruptions down to ry~ rj. We do not discuss the =1 case further.," We see that the allowed range of models is limited to somewhat lower black hole masses, unless the black hole spins very rapidly and allows tidal disruptions down to $r_T\sim r_g$ We do not discuss the $k=1$ case further." + (Frou equations (13)) and (1)) we infer that where / is the fraction of the mass of the star that returns as fallback debris., >From equations \ref{rees_lum}) ) and \ref{lum2}) ) we infer that where $f$ is the fraction of the mass of the star that returns as fallback debris. + The dashed lines in Figure 2. correspond to f=0.0005. 0.012. and 0.12 respectively.," The dashed lines in Figure \ref{fig2} correspond to $f = 0.0005$, $0.012$, and $0.12$ respectively." + We see that. for the case of a LAIS. f must be < 0.0005. which means that an unusually small fraction of the star must have participated in the fallback.," We see that, for the case of a LMS, $f$ must be $< 0.0005$ , which means that an unusually small fraction of the star must have participated in the fallback." + For the case of a SSO. somewhat larger values Lf are obtained (but still rather small).," For the case of a SSO, somewhat larger values of $f$ are obtained (but still rather small)." +" In Figures 4 and 5 we plot the huninosities given by equation (13)) for different values of Ady. M,. and f. where the disrupted object is assumed to be a LAIS (Fig. 4))"," In Figures \ref{fig4} and \ref{fig5} we plot the luminosities given by equation \ref{rees_lum}) ) for different values of $M_H$, $M_\star$, and $f$, where the disrupted object is assumed to be a LMS (Fig. \ref{fig4}) )" + and a SSO (Fig. 5)).," and a SSO (Fig. \ref{fig5}) )," + respectively. aud the disruption time is taken to be /;;=1990.36 vr.," respectively, and the disruption time is taken to be $t_D = 1990.36$ yr." +" We have chosen values of (Mj.M,) from the shaded regions in Figure 2. so that equation (15)) and the condition rp>2r, ave satisfied. and chosen f such that LyZ447x101 eig ! where Ly=LUtp+Al) is the peak luminosity."," We have chosen values of $(M_H, M_\star)$ from the shaded regions in Figure \ref{fig2} so that equation \ref{t1l}) ) and the condition $r_T > 2 +r_g$ are satisfied, and chosen $f$ such that $L_{\rm peak} \ga 4.47 +\times 10^{42}$ erg $^{-1}$ where $L_{\rm peak} \equiv L(t = t_D + +\Delta t_1)$ is the peak luminosity." + We confirm that. in order for the models to fit the observational data. a very small f (κ 0.0003) is required for the case of a LATS (Fig. 4)).," We confirm that, in order for the models to fit the observational data, a very small $f$ $<0.0003$ ) is required for the case of a LMS (Fig.\ref{fig4}) )." + For the case ofà SSO (Fig. 5)), For the case ofa SSO (Fig. \ref{fig5}) ) +" a fairly «mall f (< 0.04) is again required if Mj,>2x10M...", a fairly small $f$ $\la 0.04$ ) is again required if $M_H \ga 2\times 10^7 M_\odot$. + A laveish f (> 0.1) can be obtained only if the black hole has a verv small mass: Mg«4x 10M..., A largish $f$ $> 0.1$ ) can be obtained only if the black hole has a very small mass: $M_H < 4 \times 10^6 M_\odot$ . +Here. Qup.ENSD] represents the injection rate of secondary relativistic electrons. and positrons generated during the collisions between the accelerated relativistic protons with the thermal protons in the LOCAL (Sect.,"Here $Q_e[p,t;N_p(p,t)]$ represents the injection rate of secondary relativistic electrons and positrons generated during the collisions between the accelerated relativistic protons with the thermal protons in the ICM (Sect." + 3.3)., 3.3). + A similar equation can be written for protons (Paper Land references therein): The evolution of the spectrum of the Alfvénn waves is deseribed through a cliffusion equation in the wavenumber space (IXilek. 1979): where Dy 1s the dillusion coellicient due to wave-wave coupling (Sect., A similar equation can be written for protons (Paper I and references therein): The evolution of the spectrum of the Alfvénn waves is described through a diffusion equation in the wavenumber space (Eilek 1979): where $D_{\rm kk}$ is the diffusion coefficient due to wave-wave coupling (Sect. + 3.2.2). E is the damping rate of the Alfvénn waves with particles (Sect.," 3.2.2), $\Gamma$ is the damping rate of the Alfvénn waves with particles (Sect." + 3.2.1) and £i is the injection rate of the Alfvénn waves (Sect., 3.2.1) and $I_k$ is the injection rate of the Alfvénn waves (Sect. + 3.2.3)., 3.2.3). + In I58.(12)) we use the assumption. commonly mace. that wave interaction is just local in the wave number space.," In \ref{turbulence}) ) we use the assumption, commonly made, that wave–wave interaction is just local in the wave number space." + Alb the relevant processes related ο wave-particle interactions. wave-wave interactions and injection of Alfvénn waves in the ICM are described in detail in Paper EL. Here we only provide the reader with a brief overview of the main processes that we include in our calculations.," All the relevant processes related to wave-particle interactions, wave-wave interactions and injection of Alfvénn waves in the ICM are described in detail in Paper I. Here we only provide the reader with a brief overview of the main processes that we include in our calculations." + In the case of nearly. parallel wave propagation (i.e. ky<< mp. kc kj) and isotropic distribution of the velocities of the particles. the evelotron resonant damping rates for Alfvénn waves with particles of species a are given by Melrose (1968): where. in the relativistic case one has: and in the non relativistic case: The upper and lower signs in Eqs. 14-," In the case of nearly parallel wave propagation (i.e., $k_{\perp} << m \Omega/p$ , $k\simeq k_{\Vert}$ ) and isotropic distribution of the velocities of the particles, the cyclotron resonant damping rates for Alfvénn waves with particles of species $\alpha$ are given by Melrose (1968): where, in the relativistic case one has: and in the non relativistic case: The upper and lower signs in Eqs. \ref{damping_1}-" +15 — are for negative and. positive charged: particles respectively.," \ref{damping_2} + are for negative and positive charged particles respectively." + Iq., Eq. + can also be used to evaluate the damping rate in the case of isotropic Alfvénn waves with an approximation which is within a factor of ~3 (Lacombe 1977)., \ref{damping} can also be used to evaluate the damping rate in the case of isotropic Alfvénn waves with an approximation which is within a factor of $\sim 3$ (Lacombe 1977). + Wave-wave interactions cause the spectrum of the waves to cascade. namely to broaden toward larger values of &.," Wave-wave interactions cause the spectrum of the waves to cascade, namely to broaden toward larger values of $k$." + This isa cilfusive process. with cilfusion coellicient Dy=2τε.," This is a diffusive process, with diffusion coefficient $D_{\rm kk} = k^2/\tau_s$." +" The time 7, is the spectral energy. transfer time and can be written as To)τνιτι (Zhou Matthaeus 1990). where Tx,=Afoe ds the non-linear eddy-turnover time (de is the rms velocity [uctuation at wavelength A) and 75 is the time over which this Uuctuation interacts with other luctuations of similar size."," The time $\tau_s$ is the spectral energy transfer time and can be written as $\tau_s \sim \tau_{NL}^2/\tau_3$ (Zhou Matthaeus 1990), where $\tau_{NL}=\lambda/\delta v$ is the non-linear eddy-turnover time $\delta v$ is the rms velocity fluctuation at wavelength $\lambda$ ) and $\tau_3$ is the time over which this fluctuation interacts with other fluctuations of similar size." + In the context of the Kolmogorov phenomenology. the Alfvénn crossing time τι=Afr exceeds ry; and the Iuctuations of comparable size interact in one turnover time. namely 74τν.," In the context of the Kolmogorov phenomenology, the Alfvénn crossing time $\tau_{A}=\lambda/v_A$ exceeds $\tau_{NL}$ and the fluctuations of comparable size interact in one turnover time, namely $\tau_3 \sim +\tau_{NL}$." + Since the velocity Ductuation. Oe. is related to the rms wave field. 03. by deten=ap. the diffusion coellicient can be written as (Miller Roberts 1995): Given a spectrum of injection of waves per unit time. £i. one simple possibility to estimate the cascade time scale is to use the spectum of the waves in Eq.," Since the velocity fluctuation, $\delta v$, is related to the rms wave field, $\delta B$, by $\delta v^2 / v_A^2 = \delta B^2 /B^2$, the diffusion coefficient can be written as (Miller Roberts 1995): Given a spectrum of injection of waves per unit time, $I_k$, one simple possibility to estimate the cascade time scale is to use the spectum of the waves in Eq." + 10 as obtained from. Eq., \ref{dkk} as obtained from Eq. + 12. under stationary conditions ancl without damping processes.," \ref{turbulence} + under stationary conditions and without damping processes." + In Paper L we found: While the physies involved in the process of energy. transfer between waves and. particles for a given spectrum of waves is relatively well understood. the transformation of the wave spectrum starting from. some injection at large scales is rather poorly known.," In Paper I we found: While the physics involved in the process of energy transfer between waves and particles for a given spectrum of waves is relatively well understood, the transformation of the wave spectrum starting from some injection at large scales is rather poorly known." + The waves are expected to. couple with relativistic particles when the turbulence. has been enriched. of short wavelength modes. so that the cascacding is implicitely required to be rather ellicient if the injection occurs on Macroscopic scales.," The waves are expected to couple with relativistic particles when the turbulence has been enriched of short wavelength modes, so that the cascading is implicitely required to be rather efficient if the injection occurs on macroscopic scales." + LE however this is the case. it was shown (Yan Lazarian 2004 and refs.," If however this is the case, it was shown (Yan Lazarian 2004 and refs." + therein) that the Alfvénn waves reach the high-k part of the spectrum with a highly anisotropic spectrum. and the efficiency. of particle acceleration is likely to be therefore drastically rectuced.," therein) that the Alfvénn waves reach the high-k part of the spectrum with a highly anisotropic spectrum, and the efficiency of particle acceleration is likely to be therefore drastically reduced." +"'""hroughout this work we have used a screen model to quantify extinction by dust.",Throughout this work we have used a screen model to quantify extinction by dust. + This assumes that all of the dust responsible for the extinction Is distributed within Arp 220 between the SSCs and the observer. along our line of sight.," This assumes that all of the dust responsible for the extinction is distributed within Arp 220 between the SSCs and the observer, along our line of sight." + This model is inadequate if the SSCs themselves. possess significant amount of dust. and we investigate this possibility using the onion-skin mocel of Surace Sanders (1999).," This model is inadequate if the SSCs themselves possess significant amount of dust, and we investigate this possibility using the onion-skin model of Surace Sanders (1999)." +" In that model. to model the clleet of mixed. stars and dust. a distribution of the unreddened luminosity £4, obscured by a given linc-of-sight extinction ely is assumed to be à power-law form: La,=-oClo|1)""."," In that model, to model the effect of mixed stars and dust, a distribution of the unreddened luminosity $L_{A_V}$ obscured by a given line-of-sight extinction $A_V$ is assumed to be a power-law form; $L_{A_V} = L_{A_V=0} (A_V+1)^\alpha$." + The amount of internal extinction from within the SSC is therefore parameterised bv two numbers: ομως which is a maximum value of ον. and o. which is à parameter modeling the distribution of dust. within the SSCs (the case a=0 corresponds to à scenario in which the dust and stars are well mixed: this is the case that we are worried about here).," The amount of internal extinction from within the SSC is therefore parameterised by two numbers: $A_{V,{\rm max}}$, which is a maximum value of $A_V$, and $\alpha$, which is a parameter modeling the distribution of dust within the SSCs (the case $\alpha=0$ corresponds to a scenario in which the dust and stars are well mixed; this is the case that we are worried about here)." + Figure Al shows the SEDs of SSCs [or some of these models: the relevant parameters are presented in Table AL., Figure A1 shows the SEDs of SSCs for some of these models; the relevant parameters are presented in Table A1. + Here shy. ds the extinction from a screen component unassociated with the SSCs that is superimposed on the internal extinction.," Here $A_{V,s}$ is the extinction from a screen component unassociated with the SSCs that is superimposed on the internal extinction." + The most important thing that we infer from the figure is that the shape of the SED is determined. primarily by the foreground extinction., The most important thing that we infer from the figure is that the shape of the SED is determined primarily by the foreground extinction. + Were extinction from dust within the clusters to be the more important. we would expect a far higher visible-to-near-infrared. [lux ratio than is observed.," Were extinction from dust within the clusters to be the more important, we would expect a far higher visible-to-near-infrared flux ratio than is observed." + Our use of the screen model in the SED fitting is therefore reasonable., Our use of the screen model in the SED fitting is therefore reasonable. + Lt is important to note. however. that. although the shapes of the SEDs are similar (compare the model 4 with the screen miocel). the flux of the well-mixed|screen model is smaller than that of the pure-screen model.," It is important to note, however, that, although the shapes of the SEDs are similar (compare the model 4 with the screen model), the flux of the well-mixed+screen model is smaller than that of the pure-screen model." + “Phis is because the stars with a large local ον clo not contribute o the global SED of the SSC at visible and near-infrared wavelengths., This is because the stars with a large local $A_V$ do not contribute to the global SED of the SSC at visible and near-infrared wavelengths. + Therefore the SSC) luminosities evaluated in he main body of the paper are formally lower limits because of this danger of there existing very heavily obscured regions, Therefore the SSC luminosities evaluated in the main body of the paper are formally lower limits because of this danger of there existing very heavily obscured regions +ealaxies.,galaxies. + Here. we quantily how angular momentum flow refills the capture ancl inspiral’ loss cone in a (riaxial potential and allows compact objects to be more efficiently. captured onto orbits that emit signilieant. gravitational radiation.," Here, we quantify how angular momentum flow refills the 'capture and inspiral' loss cone in a triaxial potential and allows compact objects to be more efficiently captured onto orbits that emit significant gravitational radiation." + We demonstrate this mechanism in section 3 aud determine the Iraction of orbits that ean stochastically participate in refilling the capture and inspiral loss cone in an N-body generated triaxial galaxy model., We demonstrate this mechanism in section 3 and determine the fraction of orbits that can stochastically participate in refilling the capture and inspiral loss cone in an N-body generated triaxial galaxy model. + We also explore (he astrophysical consequences of this aneular momentum flow on the EMBI rate. the SMDII growth rate. and the final parsee problem in sections 4-6.," We also explore the astrophysical consequences of this angular momentum flow on the EMRI rate, the SMBH growth rate, and the final parsec problem in sections 4-6." + We find that this process alone can replenish the capture and inspiral loss cone as fast as it empties. resulting in an EMBI rate in the Milkv. Way that is LOO times larger than the canonical estimate for a spherical. isotropic Milky Wax. bulge moclel.," We find that this process alone can replenish the capture and inspiral loss cone as fast as it empties, resulting in an EMRI rate in the Milky Way that is 100 times larger than the canonical estimate for a spherical, isotropic Milky Way bulge model." + Though we first consider angular momentum flow for all orbits in a triaxial potential. more (racitionally diffusive processes can refil] a loss cone as well.," Though we first consider angular momentum flow for all orbits in a triaxial potential, more traditionally diffusive processes can refill a loss cone as well." + We include dvnamical friction (the first order Fokker-Planek term) ancl kicks’ (2nd-order Fokker-Plank diffusion) using a hivbrid SCE/Fokker-Planck code in our next paper., We include dynamical friction (the first order Fokker-Planck term) and 'kicks' (2nd-order Fokker-Plank diffusion) using a hybrid SCF/Fokker-Planck code in our next paper. + We are also generating a live 10° particle triaxial model to study the time-dependent. non-equilibrium loss cone velilling rate. and we are using these models to explore the decay of binary supermassive black holes explicitly.," We are also generating a live $10^7$ particle triaxial model to study the time-dependent, non-equilibrium loss cone refilling rate, and we are using these models to explore the decay of binary supermassive black holes explicitly." + Most previous studies of the loss cone have assumed that the (vpical change in angular monmenutum is small compared to the total angular momentum., Most previous studies of the loss cone have assumed that the typical change in angular momenutum is small compared to the total angular momentum. + Assuming AS<