On the time evolution of giant radio galaxies
  A time evolution of giant lobe-dominated radio galaxies (with projected linear size $D>1$ Mpc) is analysed on the basis of dynamical evolution of the entire FRII-type population. Two basic physical parameters, namely the jet power $Q_{0}$ and central density of the galaxy nucleus $\rho_{0}$ are derived for a sample of giants with synchrotron ages reliably determined, and compared with the relevant parameters in a comparison sample of normal-size sources consisting of 3C, B2, and other sources. Having apparent luminosity (power) $P$ and linear size $D$ of each sample source, $Q_{0}$ and $\rho_{0}$ are fitted using the dynamical model of Kaiser et al. (1997) but modified by allowing an evolution of the cocoon axial ratio with time as suggested by Blundell et al. (1999). In a result, we found that: (i) there is not a unique factor governing the source size; giants are old sources with high enough jet power evolved in a relatively low-density environment. The size is dependent, in order of decreasing partial correlation coefficients, on age; then on $Q_{0}$; next on $\rho_{0}$, (ii) a number of the sample sources, having similar $Q_{0}$ and $\rho_{0}$ but different ages and axial ratios (called a `clan'), fit very well the evolutionary luminosity-size ($P$-$D$) and energy density-total energy tracks derived from the model for a `fiducial' source with $Q_{0}$ and $\rho_{0}$ equal to the means of relevant values obtained for the `clan' members. Therefore, these sources can be considered as `the same' source observed at different epochs of its lifetime, and hence very useful for an observational constraint of evolutionary models of the source dynamics, (iii) in some cases a slow acceleration of the average expansion speed of the cocoon along the jet axis seems to be present. 
J. Machalski, K. T. Chyzy, M. Jamrozy (Astronomical Observatory of the   Jagiellonian Univerity, Krakow)