Exploring short gamma-ray bursts as gravitational-wave standard sirens

Recent observations support the hypothesis that a large fraction of "short-hard" gamma-ray bursts (SHBs) are associated with the inspiral and merger of compact binaries. Since gravitational-wave (GW) measurements of well-localized inspiraling binaries can measure absolute source distances, simultaneous observation of a binary's GWs and SHB would allow us to directly and independently determine both the binary's luminosity distance and its redshift. Such a "standard siren" (the GW analog of a standard candle) would provide an excellent probe of the nearby (z ≲ 0.3) universe's expansion, independent of the cosmological distance ladder, thereby complementing other standard candles. Previous work explored this idea using a simplified formalism to study measurement by advanced GW detector networks, incorporating a high signal-to-noise ratio limit to describe the probability distribution for measured parameters. In this paper, we eliminate this simplification, constructing distributions with a Markov Chain Monte Carlo technique. We assume that each SHB observation gives source sky position and time of coalescence, and we take non-spinning binary neutron star and black hole-neutron star coalescences as plausible SHB progenitors.We examine how well parameters (particularly distance) can be measured from GW observations of SHBs by a range of ground-based detector networks. We find that earlier estimates overstate how well distances can be measured, even at fairly large signal-to-noise ratio. The fundamental limitation to determining distance proves to be a degeneracy between distance and source inclination. Overcoming this limitation requires that we either break this degeneracy, or measure enough sources to broadly sample the inclination distribution.