2014ApJ...789...65Y

Using 72 short gamma-ray bursts (SGRBs) with well determined spectral data observed by BATSE, we determine their redshift and luminosity by applying the E_p-L_p correlation for SGRBs found by Tsutsui et al. For 53 SGRBs with an observed flux brighter than 4x10^–6 erg/cm2/s, the cumulative redshift distribution up to z = 1 agrees well with that of 22 Swift SGRBs. This suggests that the redshift determination by the E_p-L_pcorrelation for SGRBs works well. The minimum event rate at z = 0 is estimated as R_on–axis^min = 6.3_-3.9^+3.1 x 10^–10 events/Mpc3/yr, so that the minimum beaming angle is 0.°6-7.°8 assuming a merging rate of 10^–7- 4x10^–6 events/Mpc3/yr suggested from the binary pulsar data. Interestingly, this angle is consistent with that for SGRB 130603B of ∼4°-8°. On the other hand, if we assume a beaming angle of ∼6° suggested from four SGRBs with the observed beaming angle value, then the minimum event rate including off-axis SGRBs is estimated as R_all^min = 1.15_–.66^+0.56 x 10^–7 events/Mpc3/yr. If SGRBs are induced by the coalescence of binary neutron stars (NSs) and/or black holes (BHs), then this event rate leads to a minimum gravitational-wave detection rate of 3.8_–2.2^+1.8 (146_–83⁺⁷¹ events/Mpc3/yr for an NS-NS (NS-BH) binary, respectively, by a worldwide network with KAGRA, advanced-LIGO, advanced-VIRGO, and GEO.