Linking the rates of neutron star binaries and short gamma-ray bursts

Abstract

Short gamma-ray bursts are believed to be produced by both binary neutron star (BNS) and neutron star-black hole (NSBH) mergers. We use current estimates for the BNS and NSBH merger rates to calculate the fraction of observable short gamma-ray bursts produced through each channel. This allows us to constrain merger rates of BNS to ${\mathcal{R}}_{\mathrm{BNS}}=384_{-213}^{+431}{\mathrm{Gpc}}^{-3}{\mathrm{yr}}^{-1}$ ($90\%$ credible interval), a $16\%$ decrease in the rate uncertainties from the second LIGO--Virgo Gravitational-Wave Transient Catalog, GWTC-2. Assuming a top-hat emission profile with a large Lorentz factor, we constrain the average opening angle of gamma-ray burst jets produced in BNS mergers to $\approx 15^{\circ }$. We also measure the fraction of BNS and NSBH mergers that produce an observable short gamma-ray burst to be $0.02_{-0.01}^{+0.02}$ and $0.01\pm 0.01$, respectively and find that $\gtrsim 40\%$ of BNS mergers launch jets (90\% confidence). We forecast constraints for future gravitational-wave detections given different modelling assumptions, including the possibility that BNS and NSBH jets are different. With $24$ BNS and $55$ NSBH observations, expected within six months of the LIGO-Virgo-KAGRA network operating at design sensitivity, it will be possible to constrain the fraction of BNS and NSBH mergers that launch jets with $10\%$ precision. Within a year of observations, we can determine whether the jets launched in NSBH mergers have a different structure than those launched in BNS mergers and rule out whether $\gtrsim 80\%$ of binary neutron star mergers launch jets. We discuss the implications of future constraints on understanding the physics of short gamma-ray bursts and binary evolution.

Accepted in Physical Review D: 13 pages, 5 figures

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• Predicting Short-duration GRB Rates in the Advanced LIGO Volume
• Modelling the formation of the first two neutron star-black hole mergers, GW200105 and GW200115: metallicity, chirp masses and merger remnant spins