Low Luminosity Gamma-Ray Bursts as a Unique Population: Luminosity   Function, Local Rate, and Beaming Factor
  Swift/BAT has detected ~ 200 long-duration GRBs, with redshift measurements for ~50 of them. We derive the luminosity function (Phi^{HL}) and the local event rate (rho_0^{HL}) of the conventional high luminosity (HL) GRBs by using the z-known Swift GRBs. Our results are generally consistent with that derived from the CGRO/BATSE data. However, the fact that Swift detected a low luminosity (LL) GRB, GRB 060218, at z=0.033 within ~ 2 year of operation, together with the previous detection of the nearby GRB 980425, suggests a much higher local rate for these LL-GRBs. We explore the possibility that LL-GRBs as a distinct GRB population from the HL-GRBs. We find that rho_0^{LL} is 325_{-177}^{+352} Gpc^{-3} yr^{-1}, which is much higher than rho_0^{HL}(1.12_{-0.20}^{+0.43} Gpc^{-3} yr^{-1}). This rate is ~ 0.7% of the local Type Ib/c SNe. Our results, together with the finding that less than 10% of Type Ib/c SNe are associated with off-beam GRBs, suggest that LL-GRBs have a beaming factor typically less than 14, or a jet angle typically wider than 31^{o}. The high local GRB rate, the small beaming factor, and low luminosity make the LL-GRBs distinct from the HL-GRBs. Although the current data could not fully rule out the possibility that both HL- and LL-GRBs are the same population, our results suggest that LL-GRBs are likely a unique GRB population and the observed low redshift GRB sample is dominated by the LL-GRBs. 
Enwei Liang, Bing Zhang, Francisco Virgili, and Z. G. Dai