Gamma Ray Bursts from the First Stars: Neutrino Signals
  If the first (PopIII) stars were very massive, their final fate is to collapse into very massive black holes. Once a proto-black hole has formed into the stellar core, accretion continues through a disk. It is widely accepted, although not confirmed, that magnetic fields drive an energetic jet which produces a burst of TeV neutrinos by photon-meson interaction, and eventually breaks out of the stellar envelope appearing as a Gamma Ray Burst (GRB). Based on recent numerical simulations and neutrino emission models, we predict the expected neutrino diffuse flux from these PopIII GRBs and compare it with the capabilities of present and planned detectors as AMANDA and IceCube. If beamed into 1% of the sky, we find that the rate of PopIII GRBs is $\le 4 \times 10^6$ yr$^{-1}$. High energy neutrinos from PopIII GRBs could dominate the overall flux in two energy bands [$10^4 - 10^5$] GeV and [$10^5 - 10^6$] GeV of neutrino telescopes. The enhanced sensitivities of forthcoming detectors in the high-energy band (AMANDA-II, IceCube) will provide a fundamental insight on the characteristic explosion energies of PopIII GRBs and will constitute a unique probe of the the Initial Mass Function (IMF) of the first stars and of the redshift $z_f$ marking the metallicity-driven transition from a top-heavy to a normal IMF. The current upper limit set by AMANDA-B10 implies that such transition must have occurred not later than $z_f =9.2$ for the most plausible jet energies. Based on such results, we speculate that PopIII GRBs, if not chocked, could be associated with a new class of events detected by BeppoSax, the Fast X-ray Transient (FXTs), which are bright X-ray sources, with peak energies in the 2-10 keV band and durations between 10-200 s. 
Raffaella Schneider, Dafne Guetta & Andrea Ferrara (OAArcetri)