The Luminosity and Angular Distributions of Long GRBs
Abstract
The realization that the total energy of GRBs is related to their jet break angles suggests a similar relation between the peak luminosity and the jet break angles. Such a relation implies that the GRB luminosity function determines the angular distribution. Alternatively, within the standard jet model, where the angular distribution is essentially ~theta^2, the luminosity function must be ~L^{-2}. We re-derive the GRB luminosity function using the BATSE peak flux distribution and compare the predicted distribution with the observed redshift distribution. We find that a GRB rate that follows the Rowan-Robinson SFR is preferred. The luminosity function can be approximated by two broken power laws with a break peak luminosity of 4.4*10^{51} erg/sec and a corresponding local GRB rate of 0.44/Gpc^3 yr. The implied angular distribution agrees well with the observed one. We also find that the luminosity function derived from a standard jet deviates from the observations at low peak fluxes and, correspondingly, the angle distribution deviates from the observed one at large angles. We find that the correction to the local rate due to beaming is a factor of 75+-25 (instead of 500 as commonly used). The implied overall local GRB rate is 33+-11/Gpc^3 yr.Keywords
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