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

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}${\rm{BNS}}=384^{+431}{-213}{\rm{Gpc}^{-3} \rm{yr}^{-1}}$($90%$credibleinterval),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 $10\mathrm{\%}$ 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 $\gtrsim 80\mathrm{\%}$ 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.