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

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. 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 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, which improves rapidly with a decreasing low-frequency cutoff f low in sensitivity. 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. The medium angular resolution of BNS for a network of three detectors of the ET-D or CE type in the US, Europe and Australia is around 10 deg 2 at z = 2. We discuss the implications of our results to multi-messenger astronomy and in particular to 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 deceleration parameter, or ∆w0 = 0.03 and ∆wa = 0.2 for EoS of dark energy, respectively.

Binary neutron star mergers and third generation detectors: Localization and early warning

“…Mills, et al, 2017 [34] consider localization of short transient signals from BNS mergers with a network of both second and three generation detectors. More recently, there has been work considering the long in-band duration and the rotation of the earth [35]. In this latter work the authors have modeled the GW signal using the stationary phase approximation -essentially the leading-order term in an expansion in powers of the small quantity that is the ratio of the radiation-reaction time scale and the orbital period.…”

Localization of binary neutron star mergers with second and third generation gravitational-wave detectors

“…The loudest BNS signals could last hours to days in the detector bandwidth, introducing a time dependence in the detector response. This can be used to improve the localization, particularly when the network is operating with just one, or two, detectors and baseline triangulation is not possible [74,75]. However for the majority of signals this effect will be small.…”

“…There have been previous studies of ET that estimate the detection efficiency and the accuracy of mass measurements [68][69][70]73]. Estimates of the localization ability of various third generation networks were also considered as part of a comprehensive parameter estimation study [66], and in analytical studies focusing on the low frequency benefits of 3G detectors [74] and the implications for cosmology [75]. Furthermore, detailed studies of the optimal location of future detectors have been performed [76][77][78].…”

Improving cosmological parameter estimation with the future gravitational-wave standard siren observation from the Einstein Telescope

“…Some forecast studies on cosmology by using the future GW observations (with short-hard γ-ray bursts or other EM counterparts, as standard sirens) have been performed in the literature (see, e.g., Refs. [20][21][22][23][24][25][26][27][28][29]). For example, in Ref.…”