Unified Mapmaking For An Anisotropic Stochastic Gravitational Wave Background

A stochastic gravitational wave background (SGWB), created by the superposition of signals from unresolved astrophysical sources, may be detected in the next few years. Several theoretical predictions are being made about the possible nature of anisotropies in the background. Estimating the variation of intensity across the sky can, therefore, play a key role in improving our understanding of astrophysical models. Sky maps have been produced for all the data-taking runs of the advanced ground-based interferometric detectors. While these maps are being produced in pixel and spherical harmonic (SpH) bases, to probe, respectively, localized and diffuse astrophysical and cosmological sources, with algorithms that employ cross-correlation as the common strategy, the underlying algebra and numerical implementation remain different. As a consequence, there was a need for producing sky maps in both bases in those analyses. We show that these manifestly redundant methods could indeed be unified to a single analysis that can probe very different scales and demonstrate it by applying them on real data. We first develop the algebra to show that the results in two different bases are easily transformable. We then incorporate both the schemes in the now-standard analysis pipeline for anisotropic SGWB, PyStoch. This will enable SGWB anisotropy searches in SpH basis also to take full advantage of integrated HEALPix tools and makes it computationally feasible to perform the search in every frequency bin. We, however, follow a different approach for direct estimation of the SpH moments. We show that the results obtained from these different methods match very well; the differences are less than 0.1% for the SpH moments and less than 0.01% for the Fisher information matrices. Thus, we conclude that a single sky map will be sufficient to describe the anisotropies in a stochastic background. The multiple capabilities of PyStoch will be useful for estimating and constraining various measures that characterize an anisotropic background.