Extension of the Bayesian searches for anisotropic stochastic gravitational-wave background with non-tensorial polarizations

Abstract: The recent announcement of strong evidence for a stochastic gravitational-wave background (SGWB) by various pulsar timing array collaborations has highlighted this signal as a promising candidate for future observations. Despite its non-detection by ground-based detectors such as Advanced LIGO and Advanced Virgo, Callister \textit{et al.}~\cite{tom_nongr_method} developed a Bayesian formalism to search for an isotropic SGWB with non-tensorial polarizations, imposing constraints on signal amplitude in those components that violate general relativity using LIGO's data. Since our ultimate aim is to estimate the spatial distribution of gravitational-wave sources, we have extended this existing method to allow for anisotropic components in signal models. We then examined the potential benefits from including these additional components. Using injection campaigns, we found that introducing anisotropic components into a signal model led to more significant identification of the signal itself and violations of general relativity. Moreover, the results of our Bayesian parameter estimation suggested that anisotropic components aid in breaking down degeneracies between different polarization components, allowing us to infer model parameters more precisely than through an isotropic analysis. In contrast, constraints on signal amplitude remained comparable in the absence of such a signal. Although these results might depend on the assumed source distribution on the sky, such as the Galactic plane, the formalism presented in this work has laid a foundation for establishing a generalized Bayesian analysis for an SGWB, including its anisotropies and non-tensorial polarizations.