Mapping Anisotropies in the Stochastic Gravitational-Wave Background with space detector networks

TL;DR

This work develops and tests a maximum-likelihood map-making pipeline for the anisotropic stochastic gravitational-wave background using a network of space-based detectors (TianQin, LISA, Taiji). By modeling the SGWB as Gaussian, unpolarized, and with a directional dependence expanded in spherical harmonics, the authors derive a cross-correlation statistic across detector baselines and recover the sky distribution via a deconvolved clean map, regularized with singular-value decomposition to handle an ill-conditioned Fisher matrix. Through data simulations with Gaussian noise and two spectral shapes, they demonstrate that the TianQin–LISA–Taiji network can reconstruct the angular power spectrum up to $l=14$ (with reliable fidelity up to $l\le10$) for $\alpha=3$, achieving substantial gains over single detectors. The results underscore the benefits of multi-detector networks in reducing degeneracies, increasing SNR, and enabling more robust anisotropy studies of the SGWB, while also outlining practical limitations and directions for future work on more realistic noise models and non-separable signals.

Abstract

Future space-based gravitational-wave detectors such as TianQin, LISA, and Taiji are expected to conduct joint observations. Such a multi-detector network will provide complementary viewing angles for the anisotropic stochastic gravitational-wave background (SGWB), thereby significantly enhancing the capability to reconstruct and localize its spatial distribution. In this paper, we have established the first dedicated data analysis pipeline for the anisotropic stochastic gravitational-wave background using a joint network of TianQin, LISA, and Taiji. Our analysis incorporates both Gaussian, stationary, and unpolarized point sources from diverse sky locations as well as a random sky map. We have performed full-sky map reconstruction in pixel space using maximum likelihood estimation to extract the angular distribution of the SGWB. The results demonstrate that, when considering the detector noise, the TianQin+LISA+Taiji detector network can reconstruct the angular power spectrum of the stochastic background up to a maximum multipole moment of $l = 14 $, which can provide valuable information for studies on the spatial distribution of galactic compact binaries and physical imprints from the early Universe.

Figures (10)

• Figure 1: The noise PSD for the A, E, and T channels of different detectors, where the A and E channels exhibit identical noise levels
• Figure 2: The condition numbers for various detector network configurations (TianQin, Taiji, and LISA in different combinations). The value of “counts” represents how many leading eigenvalues we retain. The spectral index in Eq. (\ref{['eq:spectrum index']}) is set to $\alpha = 2/3$.
• Figure 3: Relative error characteristics of the AA and EE correlation channels in the TQ+LS and TQ+TJ detector networks. The segment duration is set to 3600 seconds.
• Figure 4: Normalized sky map recovery of gravitational-wave detector networks, assuming a power-law index of $\alpha = 3$. The top-left panel displays the injected SGWB sky map in ecliptic coordinates, centered at $[\lambda, \beta] = [5\pi/3, \pi/6]$, which is expanded in spherical harmonics with coefficients retained up to $l \leq 16$.
• Figure 5: The residual maps between the injected sky map and the sky reconstructions obtained from different detector networks in Fig. \ref{['fig:alpha3 map']}