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 ) ∝ ( 1 + z ) 4.47 is found. After removing this evolution, the luminosity function is ( L ) ∝ L 0 − 0.29 0.01 for dim sGRBs and ( L ) ∝ L 0 − 1.07 0.01 for bright sGRBs, with the break point 8.26 × 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.