Luminosities, space densities and redshift distributions of gamma-ray bursts

We use the BD2 sample of gamma-ray bursts (GRBs) based on 5.9 years of BATSE DISCLA data with a variety of models of the luminosity function to derive characteristic GRB luminosities, space densities and redshift distributions. Previously published results for an open universe and modest density evolution of the GRBs showed characteristic peak luminosities around 5×10^51 ergs s^–1 in the 50–300 keV band if the emission is isotropic, and local space densities around 0.2 Gpc^–3 y^–1. In this paper, we illustrate for several luminosity function models the predicted distributions of peak flux, luminosity and redshifts. We use the luminosity function models also to address the connection between supernovae and GRB. If all supernovae of type Ib/c harbor a GRB, the beaming fraction would have to be in the range 10^–5–10*–3.5. We find that GRB 980425, if correctly identified with SN 1998bw, has to be part of a population different from that of the bulk of GRBs.