Description
In this paper, we study the luminosity function and formation rate of short gamma-ray bursts (sGRBs). First, we derive the Ep-Lp 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){propto}(1+z)^4.47^ is found. After removing this evolution, the luminosity function is {Psi}(L){propto}L_0_^-0.29+/-0.01^ for dim sGRBs and {psi}(L){propto}L_0_^-1.07+/-0.01^ for bright sGRBs, with the break point 8.26x10^50^erg/s. 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. 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. 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.
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