On the rates of gamma-ray bursts and Type Ib/c supernovae

We measure the local rates of "low-luminosity" gamma-ray bursts (LL GRBs; i.e., L less than or similar to 10(49) ergs s(-1)) and "high-luminosity" gamma-ray bursts (HL GRBs). The values are in the range (n) over dot (0) G = 100-1800 Gpc(-3) yr(-1) and (n) over dot (0) = 100-550 Gpc(-3) yr(-1), respectively, and their ratios to Type Ibc supernovae (SNe Ibc) are similar to 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 x 10(-4) yr(-1) per 10(10) L-B,L-. (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 f(b)(-1) similar to 10to or less.