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, Φ(L) ∝ [(L/Lb) α1 +(L/Lb) α2 ], 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 3σ 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 α1 = 0.2, α2 = 3.0, and Lb = 5× 10 erg s for HL-GRBs and α1 = 0.1, α2 = 4.0, and Lb = 2× 10 erg s for LL-GRBs. The inferred local GRB rates (ρ0) are 1.5 and 522 Gpc −3 yr 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. Subject headings: gamma-rays: bursts—method: statistics—individuals: GRB 980425, GRB 031203, GRB060218