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

TL;DR

This paper investigates the potential of using short gamma-ray bursts as standard sirens for measuring cosmic distances through gravitational-wave observations, highlighting limitations and methods to improve distance estimates.

Contribution

It introduces a Markov Chain Monte Carlo approach to assess how well GW observations of SHBs can determine distances, addressing previous overestimations and the impact of degeneracies.

Findings

Distance measurement accuracy is limited by degeneracy with source inclination.

Breaking degeneracy or sampling multiple sources can improve distance estimates.

Ground-based detectors can measure SHB distances but face fundamental limitations.

Abstract

Recent observations support the hypothesis that a large fraction of "short-hard" gamma-ray bursts (SHBs) are associated with compact binary inspiral. 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 independently determine both its luminosity distance and redshift. Such a "standard siren" (the GW analog of a standard candle) would provide an excellent probe of the relatively nearby universe's expansion, complementing other standard candles. In this paper, we examine binary measurement using a Markov Chain Monte Carlo technique to build the probability distributions describing measured parameters. We assume that each SHB observation gives both sky position and the time of coalescence, and we take both binary neutron stars 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. (Abridged)