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

We measure the local rates of ``low-luminosity'' (LL-GRBs, i.e. L<10⁴⁸⁻⁻⁴⁹erg/sec) and ``high-luminosity'' Gamma-ray Bursts (HL-GRBs). The values are in the range n0=100--1800 Gpc^(-3)yr^(-1) and n0=100--550 Gpc^(-3) yr^(-1), respectively, and the ratios to SNe-Ibc \~ 1%-9% and 0.4% -3%. 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 which give 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 compute also the rate of SNe-Ibc characterized by broad-lined spectra (Hypernovae) and found it to be about 1.5\× 10^(-4)HNe yr^(-1) 10^(10) L_(B\) (i.e less than 10% of SNe-Ibc occurring in Spirals). This result implies that the ratio HL-GRBs/HNe is smaller than 1, possibly in the range 0.04--0.3. We have used the ratio between Hypernovae and LL-GRBs to constrain their beaming factor to f_b^(-1)\~ 10 or less.