The formation rate of short gamma-ray bursts and gravitational waves

In this paper, we study the luminosity function and formation rate of short gamma-ray bursts (sGRBs). First, we derive the E-p-L-p correlation using 16 sGRBs with redshift measurements and determine the pseudo redshifts of 284 Fermi sGRBs. Then, we use the Lynden-Bell c(-) method to study the luminosity function and formation rate of sGRBs without any assumptions. A strong evolution of luminosity L(z) proportional to (1 + z)(4.47) is found. After removing this evolution, the luminosity function is Psi(L) proportional to L-0(-0.29 +/- 0.01) for dim sGRBs and psi(L) proportional to L-0(-1.07 +/- 0.01) for bright sGRBs, with the break point 8.26 x 10(50) erg s(-1). We also find that the formation rate decreases rapidly at z < 1.0, which is different from previous works. The local formation rate of sGRBs is 7.53 events Gpc(-3) yr(-1). Considering the beaming effect, the local formation rate of sGRBs including off-axis sGRBs is 203.31(-135.54)(+1152.09) events Gpc(-3) yr(-1). We also estimate that the event rate of sGRBs detected by the advanced LIGO and Virgo is 0.85(-0.56)(+4.82) events yr(-1) for an NS-NS binary.