Bayesian parameter estimation for targeted anisotropic gravitational-wave background

TL;DR

This paper introduces a Bayesian formalism for analyzing anisotropic stochastic gravitational-wave backgrounds, enabling parameter estimation and model selection, and applies it to LIGO-Virgo data to set upper limits on pulsar populations.

Contribution

The paper presents a novel Bayesian approach for parameter estimation and model selection in anisotropic gravitational-wave background analysis, improving upon conventional spherical harmonics methods.

Findings

Developed a Bayesian method for anisotropic background analysis.

Applied the method to LIGO-Virgo data, setting upper limits on pulsar signals.

Provided a systematic way to determine angular scale cut-offs using Bayes factors.

Abstract

Extended sources of the stochastic gravitational backgrounds have been conventionally searched on the spherical harmonics bases. The analysis during the previous observing runs by the ground-based gravitational wave detectors, such LIGO and Virgo, have yielded the constraints on the angular power spectrum $C_\ell$, yet it lacks the capability of estimating model parameters. In this paper, we introduce an alternative Bayesian formalism to search for such stochastic signals with a particular distribution of anisotropies on the sky. This approach provides a Bayesian posterior of model parameters and also enables selection tests among different signal models. While the conventional analysis fixes the highest angular scale \textit{a priori}, here we show a more systematic and quantitative way to determine the cut-off scale based on a Bayes factor, which depends on the amplitude and the angular scale of observed signals. Also, we analyze the third observing runs of LIGO and Virgo for the population of milli-second pulsars and obtain the 95 % constrains of the signal amplitude, $\epsilon < 2.7\times 10^{-8}$.