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

Abstract

In this paper, we study the luminosity function and formation rate of short gamma-ray bursts (sGRBs). Firstly, 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 $L(z)\propto (1+z{)}^{4.47}$ is found. After removing this evolution, the luminosity function is $\Psi (L)\propto L_0^{-0.29\pm 0.01}$ for dim sGRBs and $\psi (L)\propto L_0^{-1.07\pm 0.01}$ for bright sGRBs, with the break point $8.26\times 10^{50}$ erg s${}^{-1}$. We also find that the formation rate decreases rapidly at $z<1.0$, which is different with 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 NS-NS binary.

arXiv comment30 pages, 8 figures, 2 tables, proofed version, several references added

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