Short gamma-ray bursts as a possible probe of binary neutron star mergers

We study the properties of short gamma-ray bursts (GRBs), based on the assumption that they are all connected to binary neutron star mergers, whose mechanism contains a large amount of uncertainty. In particular, the merger time distribution, which is essential for short GRB rate estimation, is focused on; we parametrize it simply as P-m(t) proportional to t(alpha) with a lower cut-off timescale tau. The short GRB rate, calculated using such a parametrization with a specific model of the cosmic star formation rate, is found to be quite insensitive to the value of tau, but very sensitive to alpha. With such formation rate models, the peak flux distribution observed by BATSE is fitted. In the fitting process, the local short GRB rate rho(0) is treated as one of the free parameters, giving the best fit when rho(0) = 0.1-2 yr(-1) Gpc(-3), depending on the other free parameters as well as the formation rate model represented by (tau, alpha). We also discuss several implications for the intrinsic properties of possible sources of short GRBs, such as jet structure, intrinsic luminosity function, and intrinsic duration distribution.