Localization accuracy of compact binary coalescences detected by the third-generation gravitational-wave detectors and implication for cosmology

TL;DR

This study assesses the localization accuracy of third-generation gravitational-wave detectors for binary neutron star and neutron star-black hole mergers, highlighting implications for cosmology and the measurement of fundamental parameters.

Contribution

It provides a detailed analysis of the angular resolution and distance uncertainties for 3G GW detectors, considering Earth's rotation and detector networks, and discusses cosmological measurement implications.

Findings

Median angular resolution ~150 deg² at z=0.1 for a single ET-D detector.

Network of two CE detectors achieves ~20 deg² resolution at z=0.2.

Detection of 10 BNSs at z=0.1 can measure H₀ with 0.9% accuracy.

Abstract

We use the Fisher information matrix to investigate the angular resolution and luminosity distance uncertainty for coalescing binary neutron stars (BNSs) and neutron star-black hole binaries (NSBHs) detected by the third-generation (3G) gravitational-wave (GW) detectors. Our study focuses on an individual 3G detector and a network of up to four 3G detectors at different locations including the US, Europe, China and Australia for the proposed Einstein Telescope (ET) and Cosmic Explorer (CE) detectors. We in particular examine the effect of the Earth's rotation, as GW signals from BNS and low mass NSBH systems could be hours long for 3G detectors. We find that, a time-dependent antenna beam-pattern function can help better localize BNS and NSBH sources, especially those edge-on ones. The medium angular resolution for one ET-D detector is around 150 deg$^2$ for BNSs at a redshift of $z=0.1$. The medium angular resolution for a network of two CE detectors in the US and Europe respectively is around 20 deg$^2$ at $z=0.2$ for the simulated BNS and NSBH samples. While for a network of two ET-D detectors, the similar angular resolution can be achieved at a much higher redshift of $z=0.5$. The angular resolution of a network of three detectors is mainly determined by the baselines between detectors regardless of the CE or ET detector type. We discuss the implications of our results to constrain the Hubble constant $H_0$, the deceleration parameter $q_0$ and the equation-of-state (EoS) of dark energy. We find that in general, if 10 BNSs or NSBHs at $z=0.1$ with known redshifts are detected, $H_0$ can be measured with an accuracy of $0.9\%$. If 1000 face-on BNSs at $z<2$ are detected with known redshifts, we are able to achieve $\Delta q_0=0.002$, or $\Delta w_0=0.03$ and $\Delta w_a=0.2$ for dark energy.(Abridged version).