The Decline of the Source Population of Gamma-Ray Bursts and Their Luminosity Function
The source population of gamma-ray bursts (GRBs) declines towards the present epoch being consistent with the measured decline of the star formation rate. We show this using the brightness distribution of 3255 long BATSE GRBs found in an off-line scan of the BATSE continuous 1.024 s count rate records. The significance of this conclusion is enhanced by the detection of three GRBs with known redshifts brighter than 10^{52} erg/s during the last two years. This is an argument in favor of the generally believed idea that GRBs are strongly correlated with the star production, at least on cosmological time scales, and favors the association of long GRBs with collapses of supermassive stars. However, we still cannot rule out neutron star mergers if the typical delay time for binary system evolution is relatively short. If we assume a steep decline of the GRB population at z>1.5, then their luminosity function can be clearly outlined. The luminosity function is close to a power law, dN/dL ~ L^{-1.4}, for low luminosities over at least 1.7 orders of magnitude. Then the luminosity function breaks to a steeper slope or to an exponential decline around L = 3*10^{51} erg/s in the 50-300 keV range assuming isotropic emission.