The Luminosity and Redshift Distributions of Short-Duration GRB

We rederive the short GRBs luminosity function using the BATSE peak flux distribution and compare the predicted redshift distribution with the observed redshift distribution of long bursts. We show that both distributions are compatible with the assumption that the long as well as the short burst follow the star formation rate. In this case the difference between the two observed distributions could be interpreted as arising from the different sensitivity of the detector to long and short bursts and the local rate of short bursts is 0.1 h_{70}^3 Gpc^{-3}yr^{-1}. We also consider the possibility that short GRBs may be associated with binary neutron star mergers and derive the effect of the merging time delay on the luminosity function and the redshift distribution. The luminosity function can be approximated by two broken power laws with a break peak luminosity of 2.2 \times 10^{51}erg/sec, and the local short GRB rate is \sim 0.8 h_{70}^3 Gpc ^{-3} yr^{-1}. Assuming that all binary merging systems lead to short GRBs we find a typical jet opening angle of 1.6^\cir