Luminosities and Space Densities of Gamma-Ray Bursts

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Abstract
We use a homogeneous sample of gamma-ray bursts (GRBs) extracted from 5.9 yr of BATSE DISCLA data and a variety of assumed 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 q0 = 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 yr-1 with a range of only 40%. Characteristic 50-300 keV peak luminosities exhibit a range of a factor of 6 around 6 × 1051 ergs s-1, corresponding to a characteristic total luminosity of 1.2 × 1053 ergs in the 10-1000 keV band. For q0 = 0.5, densities are higher and luminosities lower, both by a factor of 2.5. The local emissivity of GRBs is 1.0 × 1052 ergs Gpc-3 yr-1 in the 10-1000 keV band.
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