Astrophysical motivation for directed searches for a stochastic gravitational wave background

The nearby Universe is expected to create an anisotropic stochastic gravitational-wave background (SGWB). Different algorithms have been developed and implemented to search for isotropic and anisotropic SGWBs. The aim of this paper is to quantify the advantage of an optimal anisotropic search, specifically comparing a point source with an isotropic background. Clusters of galaxies appear as point sources to a network of ground-based laser-interferometric detectors. The optimal search strategy for these sources is a "directed radiometer search." We show that the flux of SGWBs created by the millisecond pulsars in the Virgo cluster produces a significantly stronger signal than the nearly isotropic background of unresolved sources of the same kind. We compute their strain power spectra for different cosmologies and the distribution of populations over redshifts. We conclude that a localized source, like the Virgo cluster, can be resolved from the isotropic background with very high significance using the directed-search algorithm. For backgrounds dominated by nearby sources, up to a redshift of about 3, we show that the directed search for a localized source can have a signal-to-noise ratio that is greater than that for the all-sky integrated isotropic search.