Short gamma-ray burst formation rate from batse data using Ep -Lp correlation and the minimum gravitational-wave event rate of a coalescing compact binary

Abstract

Using 72 short gamma-ray bursts (SGRBs) with well determined spectral data observed by BATSE, we determine their redshift and luminosity by applying the Ep -Lp correlation for SGRBs found by Tsutsui et al. For 53 SGRBs with an observed flux brighter than 4 × 10-6 erg cm-2 s-1, the cumulative redshift distribution up to z = 1 agrees well with that of 22 Swift SGRBs. This suggests that the redshift determination by the Ep -Lp correlation for SGRBs works well. The minimum event rate at z = 0 is estimated as , so that the minimum beaming angle is 0.°6-7.°8 assuming a merging rate of 10-7- 4 × 10-6 events Mpc-3 yr-1 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 . 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 for an NS-NS (NS-BH) binary, respectively, by a worldwide network with KAGRA, advanced-LIGO, advanced-VIRGO, and GEO. © 2014. The American Astronomical Society. All rights reserved.