Gamma-Ray Burst Luminosity Functions Based on Luminosity Criteria

We review five studies of the gamma-ray burst (GRB) luminosity function that are based on one or more of the proposed luminosity criteria, i.e., variability, spectral lag and spectral hardness. A comparison between the resulting luminosity functions at redshift zero shows considerable divergence. We derive for each of the luminosity functions the expected source counts and the Euclidean value of <V/Vmax>. The source counts exhibit large differences from the observed counts. In most cases the value of <V/Vmax> differs substantially from the observed value of 0.34 for BATSE-based samples, with offsets ranging from 6-24 sigmas. Given that the value of <V/Vmax> is well established and that it is a cosmological distance indicator, we recommend that any study of the GRB luminosity function take its value into account.