Mapping Anisotropies in the Stochastic Gravitational-Wave Background with TianQin

TL;DR

This paper analyzes TianQin's ability to detect and characterize anisotropies in the stochastic gravitational-wave background, revealing its potential and limitations compared to LISA, and suggesting optimal data channel combinations for future analysis.

Contribution

First theoretical assessment of TianQin's capability to recover anisotropy moments in the stochastic background, including analysis of detector-specific features and data channel optimization.

Findings

TianQin can recover anisotropy moments up to l=4 with SNR=16 in one year.

Identified mirror symmetry feature in the stochastic background sky map.

Certain data channel combinations improve map-making due to singularity differences.

Abstract

In the milli-Hertz frequency band, stochastic gravitational-wave background can be composed of both astronomical and cosmological sources, both can be anisotropic. Numerically depicting these anisotropies can be critical in revealing the underlying properties of their origins. For the first time, we perform a theoretical analysis of the constraining ability of TianQin on multiple moments of the stochastic background. First, we find that with a one-year operation, for a background with a signal-to-noise ratio of 16, TianQin can recover the multiple moments up to $l=4$. We also identified a unique feature of the stochastic background sky map, which is the mirror symmetry along the fixed orbital plane of TianQin. Thirdly, we explain the difference in anisotropy recovering ability between TianQin and LISA, by employing the criteria of the singularity of the covariance matrix (which is the condition number). Finally, we find that since the different data channel combinations correspond to different singularities, certain combinations might have an advantage in stochastic background map-making. We believe that the findings of this work can provide an important reference to future stochastic background analysis pipelines. It can also serve as a guideline for designing better gravitational-wave detectors aiming to decipher anisotropies in the stochastic background.