Abstract
Gravitational waves from the coalescence of compact binaries, together with an associated electromagnetic counterpart, are ideal probes of cosmological models. As demonstrated with GW170817, such multimessenger observations allow one to use the source as a standard siren, analog of standard candles in conventional astronomy, in order to measure cosmological parameters such as the Hubble constant. No cosmological ladder is needed to estimate the source luminosity distance from the detected gravitational waves. The error on the luminosity distance plays a crucial r\^ole in the error budget for the inference of the Hubble constant. In this paper, we provide analytic expressions for the statistical errors on the luminosity distance inferred from gravitational wave data as a function of the sky position and the detector network. In particular, we take into account degeneracy in the parameter space of the gravitational waveform showing that in certain conditions on the gravitational-wave detector network and the source sky position it may not be possible to estimate the luminosity distance of the source. Our analytic approximants shows a good agreement with the uncertainties measured with Bayesian samplers and simulated data. We also present implications for the estimation error on the Hubble constant.
Highlights
The first direct observations of gravitational waves (GWs) by the LIGO and Virgo collaborations [1, 2] has opened the possibility of studying astrophysical compact objects and gravity in the strong-field regime
The LIGO and Virgo collaborations have reported the firm detection of eleven compact binary coalescences (CBC) including ten binary black hole mergers (BBH) [2] and one binary neutron star (BNS) merger [4] during the first two scientific runs
In this paper we focus on the distance measurement uncertainty for a given BNS event, and study how it varies as a function of the properties of the source — including its sky location and orientation — and of the network of gravitational-wave detectors — including the number and sensitivity of detectors in the network, and their relative alignment
Summary
The first direct observations of gravitational waves (GWs) by the LIGO and Virgo collaborations [1, 2] has opened the possibility of studying astrophysical compact objects and gravity in the strong-field regime (see e.g., [3]). The best GW measurement of the Hubble constant is given by the joint electromagnetic and GWs observation of the BNS GW170817, combined with with binary black hole GW detections and galaxy catalogues. This measurement is H0 = 68+−174.0.0 km s−1 Mpc−1 at 1σ confidence level [13]. This paper revisits and extends the seminal calculations done by Cutler and Flanagan in [19] that provides first-order (or “Gaussian”) as well as higherorder (or “beyond Gaussian”) approximations of the estimation errors Those estimates are applied to binary mergers at any source sky position, detector network, etc. VI we apply the uncertainty estimates to the specific case of GW170817 and to the Hubble constant estimate obtained from this observation
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