Luminosities and Space Densities of Gamma-Ray Bursts

We use a homogeneous sample of gamma-ray bursts (GRB) extracted from 5.9 years of BATSE DISCLA data (astro-ph/9908190) and a variety of broken power-law luminosity functions to derive GRB luminosities and space densities. Luminosity functions that are narrow or exhibit no density evolution produce expected redshift distributions that are incompatible with the observation of a GRB redshift of 3.4. For q_o=0.1 and density evolution rising to 10 at z=1, we find for a variety of slopes of the luminosity function values of the local space density around 0.18 Gpc^{-3} y^{-1} with a range of only 40%. Characteristic 50--300 keV peak luminosities exhibit a range of a factor of 6 around 6e51 erg/s corresponding to a characteristic total luminosity of 1.2e53 erg in the 10--1000 keV band. For q_o=0.5, densities are higher and luminosities lower, both by a factor of 2.5. The local emissivity of GRBs is 1.0e52 erg Gpc^{-3} y^{-1} in the 10--1000 keV band.