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

TL;DR

This study analyzes the luminosity function and formation rate of short gamma-ray bursts, revealing strong luminosity evolution, a broken power-law luminosity function, and a rapid decrease in formation rate at low redshifts, with implications for gravitational wave detection.

Contribution

It introduces a new method to derive the luminosity function and formation rate of sGRBs without assumptions, incorporating luminosity evolution and estimating event rates for gravitational wave observatories.

Findings

Luminosity evolution follows $L(z) \\propto (1+z)^{4.47}$.

Broken power-law luminosity function with different slopes for dim and bright sGRBs.

Estimated local sGRB formation rate and predicted detection rate for LIGO/Virgo.

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^{+1152.09}_{-135.54} $ events Gpc$^{-3}$ yr$^{-1}$. We also estimate that the event rate of sGRBs detected by the advanced LIGO and Virgo is $0.85^{+4.82}_{-0.56} $ events yr$^{-1}$ for NS-NS binary.