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تسجيل مستخدم جديدShort 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
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Using 72 Short Gamma Ray Bursts (SGRBs) with well determined spectral data observed 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 with the observed flux brighter than $4 times 10^{-6}~{rm erg~cm^{-2}s^{-1}}$, the cumulative redshift distribution up to $z=1$ agrees well with that of 22 {it Swift}~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 estimated as $rho_{SGRB}(0) = 6.3_{-3.9}^{+3.1} times 10^{-10}~{rm events~Mpc^{-3}yr^{-1}}$ so that the minimum beaming angle is $0.6^circ-7.8^circ$ assuming the merging rate of $10^{-7}-4times 10^{-6}~{rm events~Mpc^{-3}yr^{-1}}$ suggested from the binary pulsar data. Interestingly, this angle is consistent with that for SGRB130603B of $sim 4^circ-8^circ$citep{fong13b}. On the other hand, if we assume the beaming angle of $sim 6^circ$ suggested from four SGRBs with the observed value of beaming angle, the minimum event rate including off-axis SGRBs is estimated as $rho_{SGRB,all}^{min}(0)=1.15_{-0.71}^{+0.57}times 10^{-7}~{rm events~Mpc^{-3}yr^{-1}}$. If SGRBs are induced by coalescence of binary neutron stars (NSs) and/or black holes (BHs), this event rate leads to the minimum gravitational-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 a worldwide network with KAGRA, advanced-LIGO, advanced-Virgo, and GEO.
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