Jet Geometry and Rate Estimate of Coincident Gamma Ray Burst and Gravitational Wave Observations

Abstract: Short Gamma-Ray Burst (SGRB) progenitors have long been thought to be coalescing binary systems of two Neutron Stars (NSNS) or a Neutron Star and a Black Hole (NSBH). The August 17$^{\rm th}$, 2017 detection of the GW170817 gravitational-wave signal by Advanced LIGO and Advanced Virgo in coincidence with the electromagnetic observation of the SGRB GRB 170817A confirmed this scenario and provided new physical information on the nature of these astronomical events. We use SGRB observations by the Neil Gehrels Swift Observatory Burst Alert Telescope and GW170817/GRB 170817A observational data to estimate the detection rate of coincident gravitational-wave and electromagnetic observations by a gravitational-wave detector network and constrain the physical parameters of the SGRB jet structure. We estimate the rate of gravitational-wave detections coincident with SGRB electromagnetic detections by the Fermi Gamma-ray Burst Monitor to be between $\sim$ 0.1 and $\sim$ 0.6 yr$^{-1}$ in the third LIGO-Virgo observing run and between $\sim$ 0.3 and $\sim$ 1.8 yr$^{-1}$ for the LIGO-Virgo-KAGRA network at design sensitivity. Assuming a structured model with a uniform ultra-relativistic jet surrounded by a region with power-law decay emission, we find the jet half-opening angle and the power-law decay exponent to be $\theta_c\sim 7\,{}^\circ$ -- $22\,{}^\circ$ and $s\sim 5$ -- $30$ at 1$\sigma$ confidence level, respectively.