Angular resolution of the search for anisotropic stochastic gravitational-wave background with terrestrial gravitational-wave detectors

We perform an anisotropic search for the stochastic gravitational-wave (GW) background by decomposing the gravitational-wave sky into its spherical harmonics components. Previous analyses have used the diffraction limit to define the highest-order spherical harmonics components used in this search. We investigate whether the angular resolution of this search is indeed diffraction-limited by testing our ability to detect and localize simulated GW signals. We show that while using low-order spherical harmonic modes is optimal for initially detecting GW sources, the detected sources can be better localized with higher-order spherical harmonics than expected based on the diffraction limit argument. Additionally, we discuss how the ability to recover simulated GW sources is affected by the number of detectors in the network, the frequency range over which the search is performed, and the method by which the covariance matrix of the GW skymap is regularized. While we primarily consider point-source signals in this study, we briefly apply our methodology to spatially extended sources and discuss potential future modifications of our analysis for such signals.