Sensitivity to anisotropic gravitational-wave background with space-borne detector networks

Single gravitational-wave detectors face inherent limitations in detecting the anisotropy of the stochastic background. In this work, we explore the sensitivity to anisotropic backgrounds with a network of space-borne detectors. We find that the separation between detectors plays an important role in determining the sensitivity. For the first time, we observe as large as three orders of magnitude enhancement in detection sensitivity for multipoles with $l=5$ and 6, compared to coinciding detectors. Coordinating and optimizing the separation between two space-borne detectors can significantly enhance the network's sensitivity to the multipole components of the stochastic background. For the $\mathrm{TianQin}+\text{Laser}$ Interferometer Space Antenna (LISA) network, benefiting from detector separation, it is possible to achieve sensitivity levels of 2--3 orders of magnitude better than those when using the TianQin or LISA detector alone. These findings pave the way to uncover the underlying physics of anisotropy through gravitational-wave detections.