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 ( 37 ) .
For 53 SGRBs with the observed flux brighter than 4 \times 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 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 } ~ { } { 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 } -4 \times 10 ^ { -6 } ~ { } { 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 } ( 13 ) .
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 } ~ { } { 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 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 .