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Using 72 Short Gamma Ray Bursts (SGRBs) with well determined spectral dataobserved by BATSE, we determine their redshift and the luminosity by applying$E_p$--$L_p$ correlation for SGRBs found by \cite{tsutsui13}. For 53 SGRBs withthe observed flux brighter than $4 \times 10^{-6}~{\rm erg~cm^{-2}s^{-1}}$, thecumulative redshift distribution up to $z=1$ agrees well with that of 22 {\itSwift}~SGRBs. This suggests that the redshift determination by the $E_p$--$L_p$correlation for SGRBs works well. The minimum event rate at $z=0$ is estimatedas $\rho_{SGRB}(0) = 6.3_{-3.9}^{+3.1} \times 10^{-10}~{\rmevents~Mpc^{-3}yr^{-1}}$ so that the minimum beaming angle is$0.6^\circ-7.8^\circ$ assuming the merging rate of $10^{-7}-4\times10^{-6}~{\rm events~Mpc^{-3}yr^{-1}}$ suggested from the binary pulsar data.Interestingly, this angle is consistent with that for SGRB130603B of $\sim4^\circ-8^\circ$\citep{fong13b}. On the other hand, if we assume the beamingangle of $\sim 6^\circ$ suggested from four SGRBs with the observed value ofbeaming angle, the minimum event rate including off-axis SGRBs is estimated as$\rho_{SGRB,all}^{min}(0)=1.15_{-0.71}^{+0.57}\times 10^{-7}~{\rmevents~Mpc^{-3}yr^{-1}}$. If SGRBs are induced by coalescence of binary neutronstars (NSs) and/or black holes (BHs), this event rate leads to the minimumgravitational-wave detection rate of $\rm 3.9_{-2.4}^{+1.9}(152_{-94}^{+75})~events~y^{-1}$ for NS-NS (NS-BH) binary, respectively, by aworldwide network with KAGRA, advanced-LIGO, advanced-Virgo, and GEO.

astrophysical journal/the astrophysical journal

Short Gamma Ray Burst Formation Rate from BATSE data using E_p-L_p  correlation and the minimum gravitational wave event rate of coalescing  compact binary