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

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{sub p} -L{sub p} correlation for SGRBs found by Tsutsui et al. For 53 SGRBs with an observed flux brighter than 4 × 10{sup –6} erg cm{sup –2} s{sup –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 E{sub p} -L{sub p} correlation for SGRBs works well. The minimum event rate at z = 0 is estimated as R{sub on−axis}{sup min}=6.3{sub −3.9}{sup +3.1}× 10{sup −10} events Mpc{sup −3} yr{sup −1}, so that the minimum beaming angle is 0.°6-7.°8 assuming a merging rate of 10{sup –7}- 4 × 10{sup –6} events Mpc{sup –3} yr{sup –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 R{sub all}{sup min}=1.15{sub −0.66}{sup +0.56} × 10{sup −7} events Mpc{sup −3} yr{sup −1}. If SGRBsmore » 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{sub −2.2}{sup +1.8} (146{sub −83}{sup +71}) events yr{sup −1} for an NS-NS (NS-BH) binary, respectively, by a worldwide network with KAGRA, advanced-LIGO, advanced-VIRGO, and GEO.« less