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Short Gamma-Ray Burst (SGRB) progenitors have long been thought to becoalescing binary systems of two Neutron Stars (NSNS) or a Neutron Star and aBlack Hole (NSBH). The August 17$^{\rm th}$, 2017 detection of the GW170817gravitational-wave signal by Advanced LIGO and Advanced Virgo in coincidencewith the electromagnetic observation of the SGRB GRB 170817A confirmed thisscenario and provided new physical information on the nature of theseastronomical events. We use SGRB observations by the Neil Gehrels SwiftObservatory Burst Alert Telescope and GW170817/GRB 170817A observational datato estimate the detection rate of coincident gravitational-wave andelectromagnetic observations by a gravitational-wave detector network andconstrain the physical parameters of the SGRB jet structure. We estimate therate of gravitational-wave detections coincident with SGRB electromagneticdetections 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 designsensitivity. Assuming a structured model with a uniform ultra-relativistic jetsurrounded by a region with power-law decay emission, we find the jethalf-opening angle and the power-law decay exponent to be $\theta_c\sim7\,{}^\circ$ -- $22\,{}^\circ$ and $s\sim 5$ -- $30$ at 1$\sigma$ confidencelevel, respectively.

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