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

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 pointlike and diffuse 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.