Probing the anisotropies of a stochastic gravitational-wave background using a network of ground-based laser interferometers

TL;DR

This paper develops a maximum-likelihood method to map the anisotropies of a stochastic gravitational-wave background using a network of ground-based interferometers, improving sensitivity and generality over existing isotropic and radiometer approaches.

Contribution

It introduces a spherical harmonic decomposition technique for anisotropic background mapping with multiple detectors, extending previous methods and providing detailed statistical and numerical analysis.

Findings

The method accurately estimates multipole moments of the gravitational-wave sky.

Including multiple baselines enhances detection sensitivity.

Numerical tests show effectiveness for both point-like and diffuse sources.

Abstract

We present a maximum-likelihood analysis for estimating the angular distribution of power in an anisotropic stochastic gravitational-wave background using ground-based laser interferometers. The standard isotropic and gravitational-wave radiometer searches (optimal for point sources) are recovered as special limiting cases. The angular distribution can be decomposed with respect to any set of basis functions on the sky, and the single-baseline, cross-correlation analysis is easily extended to a network of three or more detectors-that is, to multiple baselines. A spherical harmonic decomposition, which provides maximum-likelihood estimates of the multipole moments of the gravitational-wave sky, is described in detail. We also discuss: (i) the covariance matrix of the estimators and its relationship to the detector response of a network of interferometers, (ii) a singular-value decomposition method for regularizing the deconvolution of the detector response from the measured sky map, (iii) the expected increase in sensitivity obtained by including multiple baselines, and (iv) the numerical results of this method when applied to simulated data consisting of both point-like and di#use sources. Comparisions between this general method and the standard isotropic and radiometer searches are given throughout, to make contact with the existing literature on stochastic background searches.