The Luminosity and Angular Distributions of Long GRBs

D. Guetta; T. Piran; E. Waxman

doi:10.1086/423125

paper

The Luminosity and Angular Distributions of Long GRBs

arXiv:astro-ph/0311488 · doi:10.1086/423125

Abstract

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, $L \propto θ^{- 2}$ . 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 $4.4 \times 1 0^{51}$ erg/sec, a typical jet angle of 0.12 rad and a local GRB rate of $0.44 h_{65}^{3}$ Gpc $^{- 3}$ yr $^{- 1}$ . The angular distribution implied by $L \propto θ^{- 2}$ agrees well with the observed one, and implies a correction factor to the local rate due to beaming of $75 \pm 25$ (instead of 500 as commonly used). The inferred overall local GRB rate is $33 \pm 11 h_{65}^{3}$ Gpc $^{- 3}$ yr $^{- 1}$ . The luminosity function and angle distribution obtained within the universal structured jet model, where the angular distribution is essentially $\propto θ$ and hence the luminosity function must be $\propto L^{- 2}$ , deviate from the observations at low peak fluxes and, correspondingly, at large angles. The corresponding correction factor for the universal structure jet is $\sim 20 \pm 10$ .

11 pages, 5 figures, accepted for publication in ApJ

The Luminosity and Angular Distributions of Long GRBs

Abstract

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