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The Luminosity and angular distributions of long GRBs

Nov, 2003
15 pages
Published in:
  • Astrophys.J. 619 (2005) 412-419
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Abstract: (arXiv)
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, LL, and the jet break angles, L∝θ−2L\propto\theta^{-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 4.4×10514.4 \times 10^{51} erg/sec, a typical jet angle of 0.12 rad and a local GRB rate of 0.44h6530.44 h_{65}^{3} Gpc−3^{-3}yr−1^{-1}. The angular distribution implied by L∝θ−2L\propto\theta^{-2} agrees well with the observed one, and implies a correction factor to the local rate due to beaming of 75±2575\pm25 (instead of 500 as commonly used). The inferred overall local GRB rate is 33±11h65333\pm11 h_{65}^{3} Gpc−3^{-3}yr−1^{-1}. The luminosity function and angle distribution obtained within the universal structured jet model, where the angular distribution is essentially ∝θ\propto \theta and hence the luminosity function must be ∝L−2\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 ∼20±10\sim 20 \pm 10.
Note:
  • 11 pages, 5 figures, accepted for publication in ApJ Journal-ref: Astrophysical J. 619 (2005) 412-419