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

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 United States, Europe, China, and Australia for the proposed Einstein Telescope (ET) and Cosmic Explorer (CE) detectors. In particular, we 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. In this case, an individual detector can be effectively treated as a detector network with long baselines formed by the trajectory of the detector as it rotates with the Earth. Therefore, a single detector or two-detector networks could also be used to localize the GW sources effectively. We find that a time-dependent antenna beam-pattern function can help better localize BNS and NSBH sources, especially 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, which improves rapidly with a decreasing low-frequency cutoff f₋₎ₖ in sensitivity. The medium angular resolution for a network of two CE detectors in the United States 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. The medium angular resolution of BNS for a network of three detectors of the ET-D or CE type in the United States, Europe, and Australia is around 10 deg^2 at z=2. We discuss the implications of our results for multimessenger astronomy and, in particular, for using GW sources as independent tools to constrain the Hubble constant H₀, the deceleration parameter q₀, 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 by 3G networks consisting of two ET-like detectors, H₀ 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 q₀=0. 002 for the deceleration parameter, or w₀=0. 03 and w₀=0. 2 for EoS of dark energy, respectively.