The LISA-Taiji Network: Precision Localization of Coalescing Massive Black Hole Binaries

Abstract

We explore a potential LISA-Taiji network to fast and accurately localize the coalescing massive black hole binaries. For an equal-mass binary located at redshift of 1 with a total intrinsic mass of 105M⊙, the LISA-Taiji network may achieve almost four orders of magnitude improvement on the source localization region compared to an individual detector. The precision measurement of sky location from the gravitational-wave signal may completely identify the host galaxy with low redshifts prior to the final black hole merger. Such identification of the host galaxy is vital for the follow-up variability in electromagnetic emissions of the circumbinary disc when the binary merges to a new black hole and enables the coalescing massive black hole binaries to be used as a standard siren to probe the expansion history of the Universe.

Hubble parameter estimation via dark sirens with the LISA-Taiji network

“…In order to simplify the calculation, we adopt the restricted post-Newtonian (PN) approximation of the GW waveform for the non-spinning MBHB [ 37 ]. For a non-spinning MBHB at a luminosity distance d L , with component masses m 1 and m 2 , total mass M = m 1 + m 2 , symmetric mass ratio η = m 1 m 2 / M 2 and chirp mass M c = η 3/5 M , the frequency-domain version of the strain is given by [ 22 , 38 ], \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}\begin{eqnarray*} \tilde{h}(f)&=&-\bigg (\frac{5\pi }{24}\bigg )^{1/2}\bigg (\frac{GM_c}{c^3}\bigg )\bigg (\frac{GM_c}{c^2 D_{{\rm eff}}}\bigg )\nonumber\\ &&\times\,\,\bigg (\frac{GM_c}{c^3}\pi f\bigg )^{-7/6}e^{-i\Psi (f\,\,M_c,\eta )},\\ \end{eqnarray*}\end{document} where D eff is the effective luminosity distance to the source, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}\begin{equation*} D_{{\rm eff}}=d_L \bigg [F^{2}_{+}\bigg (\frac{1+{\rm cos}^2 \iota }{2}\bigg )^2+F^{2}_{\times } {\rm cos}^2 \iota \bigg ]^{-1/2} \end{equation*}\end{document} …”

“…The response functions F + , F × depend on the sky direction of source (α, δ) and the polarization angle ψ. For a space-based GW detector such as LISA and Taiji, F + and F × are functions of frequency [ 22 ]. In the calculation, the response functions of LISA and Taiji are obtained from previous work [ 40 ] with a stationary phase approximation [ 41 ].…”

“…Taiji [ 21 ] is a gravitational wave space facility proposed by the Chinese Academy of Sciences, with a separation distance of 3 million kilometres in a heliocentric orbit ahead of the Earth by about 20°. The LISA-Taiji network [ 20 , 21 ] will be able to localize the CBC events with unprecedented accuracy [ 22 ]. As demonstrated previously, this advantage could help improve the Hubble constant determination.…”

A fully-automated end-to-end pipeline for massive black hole binary signal extraction from LISA data

“…There have also been papers addressing the simultaneous analysis of MBHBs with LISA and other space-based detectors [e.g. [49][50][51].…”

Space-borne atom interferometric gravitational wave detections. Part II. Dark sirens and finding the one

“…The specific form of the phase Ψ in the waveform can be found in the appendix of [51]. We expand Ψ to the second PN order as in [57]. For every merger, the SNR is calculated from ρ = (h, h).…”