The Luminosity and Angular Distributions of Long GRBs

The realization that the total energy of GRBs is related to their jet break angles suggests a similar relation between the peak luminosity, L, and the jet break angles, L ∝ θ. Such a relation implies that the GRB luminosity function determines the angular distribution. 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 erg/sec, a typical jet angle of 0.12 rad and a local GRB rate of 0.44 Gpcyr. The angular distribution implied by L ∝ θ agrees well with the observed one, and implies a correction factor to the local rate due to beaming of 75±25 (instead of 500 as commonly used). The inferred overall local GRB rate is 33 ± 11 Gpcyr. The luminosity function and angle distribution obtained within the standard jet model, where the angular distribution is essentially ∝ θ and hence the luminosity function must be ∝ L, deviate from the observations at low peak fluxes and, correspondingly, at large angles. Subject headings: cosmology:observations-gamma rays:bursts