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.

30 pages, 8 figures, 2 tables, proofed version, several references added

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• Statistical properties magnetar bursts and FRB 121102
• Cosmological Evolution of the Formation Rate of Short Gamma-ray Bursts With and Without Extended Emission
• Multi-messenger Detection Rates and distributions of Binary Neutron Star Mergers and Their Cosmological Implications
• Double Neutron Star Formation: Merger Times, Systemic Velocities, and Travel Distances
• Linking the rates of neutron star binaries and short gamma-ray bursts
• A Comparative Study of Luminosity Functions and Event Rate Densities of Long GRBs with Non-parametric Method
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• The short gamma-ray burst population in a quasi-universal jet scenario
• The jet structure and the intrinsic luminosity function of short gamma-ray bursts
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• Discovery of a Universal Correlation For Long and Short GRBs and Its Application on the Study of Luminosity Function and Formation Rate
• New evidence of multiple channels for the origin of gamma-ray bursts with extended emission
• Luminosity Function of collapsar Gamma-Ray Bursts:the Progenitor of Long Gamma-Ray Bursts Is Not Singular
• Comparison of the Origin of Short Gamma-Ray Bursts with or without Extended Emission
• The Formation Rate and Luminosity Function of Fast X-ray transients from Einstein probe
• Bright siren without electromagnetic counterpart by LISA-Taiji-TianQin network
• On the Feasibility of Deriving Pseudo-Redshifts of Gamma-ray Bursts from Two Phenomenological Correlations
• Kilonova rates from spherical and axisymmetrical models
• Hubble constant measurement from QPEs as electromagnetic counterparts to extreme mass ratio inspirals
• Mass function of stellar black holes as revealed by the LIGO-Virgo-KAGRA observations
• The redshift evolution of the luminosity function of type II GRBs
• Peak energy--Isotropic Luminosity Correlation and Jet Opening Angle Evolution in Swift-BAT Short GRBs with Soft Tail Emission
• Constraining the Luminosity Function and Delay-Time Distribution of Short Gamma-Ray Bursts for Multimessenger Gravitational-Wave Detection Rate Estimation
• The apparent and cosmic rates of short gamma-ray bursts
• Searching for the Signature of Fast Radio Burst by Swift/XRT X-ray Afterglow Light Curve