Constraints on short, hard gamma-ray burst beaming angles from gravitational wave observations

The first detection of a binary neutron star merger, GW170817, and an associated short gamma-ray burst confirmed that neutron star mergers are responsible for at least some of these bursts. The prompt gamma-ray emission from these events is thought to be highly relativistically beamed. We present a method for inferring limits on the extent of this beaming by comparing the number of short gamma-ray bursts (SGRBs) observed electromagnetically with the number of neutron star binary mergers detected in gravitational waves. We demonstrate that an observing run comparable to the expected Advanced LIGO (aLIGO) 2016–2017 run would be capable of placing limits on the beaming angle of approximately $\theta \in (2\buildrel{\circ}\over{.} 88,14\buildrel{\circ}\over{.} 15)$, given one binary neutron star detection, under the assumption that all mergers produce a gamma-ray burst, and that SGRBs occur at an illustrative rate of ${{ \mathcal R }}_{\mathrm{grb}}=10\,{\mathrm{Gpc}}^{-3}\,{\mathrm{yr}}^{-1}$. We anticipate that after a year of observations with aLIGO at design sensitivity in 2020, these constraints will improve to $\theta \in (8\buildrel{\circ}\over{.} 10,14\buildrel{\circ}\over{.} 95)$, under the same efficiency and SGRB rate assumptions