Angular Resolution of the Spherical Harmonics Decomposition Search for the Stochastic Gravitational-Wave Background with Terrestrial Detectors

We consider an anisotropic search for the stochastic gravitational-wave (GW) background using terrestrial detectors 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 harmonics modes is optimal for initially detecting GW sources, those sources which are detectable are most effectively localized with higher-order spherical harmonics than what is suggested by the diffraction limit. Additionally, we discuss how our ability to recover simulated GW sources is affected by the number of detector baselines in our network, the frequency range over which we perform our search, and the method by which we regularize the covariance matrix of our GW skymap. Finally, we consider future analysis methods and parameter estimation schemes intended to avoid covariance matrix regularization and reduce assumptions regarding the statistical properties of the angular power spectra.