On the Rates of Gamma-Ray Bursts and Type Ib/c Supernovae

Abstract

We measure the local rates of low-luminosity gamma-ray bursts (LL GRBs; i.e., L 1049 ergs s-1) and high-luminosity gamma-ray bursts (HL GRBs). The values are in the range 0 = 100-1800 Gpc-3 yr-1 and 0 = 100-550 Gpc-3 yr-1, respectively, and their ratios to Type Ibc supernovae (SNe Ibc) are ~1%-9% and 0.4%-3%, respectively. These data may suggest the existence of two physically distinct classes of GRBs in which LL GRBs are (intrinsically) more frequent events than HL GRBs. However, with the present data, we cannot exclude the possibility of a single population of GRBs that gives rise to both an isotropic low-luminous emission (LL GRBs: detectable only in nearby GRBs) and to a highly collimated high luminous emission (HL GRBs: detectable preferentially at high z). We also compute the rate of SNe Ibc characterized by broad-lined spectra (hypernovae [HNe]) and find it to be about 1.5 × 10-4 yr-1 per 1010 LB, ☉ (i.e., less than 10% of SNe Ibc occurring in spiral galaxies). This result implies that the ratio of HL GRBs to HNe is smaller than 1, possibly in the range of 0.04-0.3. We have used the ratio between HNe and LL GRBs to constrain their beaming factor to f ~ 10 or less.