Low Luminosity Gamma-Ray Bursts as a Unique Population: Luminosity Function, Local Rate, and Beaming Factor

The newly discovered GRB 060218 is a nearby event with low luminosity, resembling GRBs 980425 and 031203. The fact that it was discovered by Swift slightly over 1-year operation suggests that the GRB rate of these low luminosity GRBs (LL-GRBs) should be much higher than previous expected, and that they form a distinct new class of GRBs with respect to the conventional high luminosity GRBs (HL-GRBs). We characterize the LF of each class by a smoothed broken power law, $\\Phi(L)\\propto [(L/L_b)^{\\alpha_1}+(L/L_b)^{\\alpha_2}]^{-1}$, and investigate the constraints to the LF parameters by the following two criteria: (1) The absolute GRB numbers predicted by the LFs for both LL-GRBs and HL-GRBs should be consistent with the Swift detections for the two classes, respectively; and (2) at 3 sigma significance level, the 2-dimensional GRB distributions in the luminosity-redshift plane derived from the LFs should be consistent with the data of GRBs with known redshifts detected by Swift and other missions. We obtain alpha_1~0.2, alpha_2~3.0, and L_b~5\\times 10^{51} erg s^{-1} for HL-GRBs and alpha_1~0.1, alpha_2~4.0, and L_b~2\\times 10^{47}erg s^{-1} for LL-GRBs. The inferred local GRB rates \\rho_0 are 1.5 and 522 Gpc^{-3} yr^{-1} for HL-GRBs and LL-GRBs, respectively. The observed (on-beam) LL-GRB rate is ~1% of the local Type Ib/c supernovae (SNe). Combining with the fact that less than 10% of Type Ib/c SNe are associated with off-beam GRBs, our results suggest that the LL-GRBs have a beaming factor typically less than 10, or a jet angle typically wider than 37 degrees.