The Luminosity and Angular Distributions of Long GRBs

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The realization that the total energy of GRBs is correlated with their jet break angles motivates the search for a similar relation between the peak luminosity, L, and the jet break angles, L∝θ⁻². 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. The luminosity function can be approximated by a broken power law with a break peak luminosity of 4.4 × 10⁵¹ erg/sec, a typical jet angle of 0.12 rad and a local GRB rate of 0.44 h₆₅³ Gpc⁻³yr⁻¹. The angular distribution implied by L∝θ⁻² 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 h₆₅³ Gpc⁻³yr⁻¹. The luminosity function and angle distribution obtained within the universal structured jet model, where the angular distribution is essentially ∝ θ and hence the luminosity function must be ∝ L⁻², deviate from the observations at low peak fluxes and, correspondingly, at large angles. The corresponding correction factor for the universal structure jet is 20 ± 10.