Revisiting the event rate of short GRBs and estimating their detectable number within the Advanced LIGO horizon

The redshift and luminosity distributions of 36 Swift short gamma-ray bursts (GRBs) are fitted by connecting their event rates with cosmic star formation rates using power-law distributed delay times f(τ )\propto {τ }^-1, where a broken-power-law luminosity function is assumed and some empirical observational selection effects are taken into account. As a result, the most-likely model parameters are constrained to be {ν }₁=0.91, {ν }₂=1.66 as power-law indices, with a break at {L}_b=2.51× {10}⁵¹ erg s^-1 for the luminosity function and {τ }_c=6.0 Gyr for a typical gravitational wave decay timescale of the binary orbit. The corresponding local rate of short GRBs is found to be ∼ (3-4) {Gpc}}^-3 {yr}}^-1. With these parameters, the detectable numbers of short GRBs are estimated within the horizon of Advanced LIGO.