Searching for anisotropic gravitational-wave backgrounds using pulsar timing arrays

We present the results of simulated injections testing the first Bayesian search pipeline capable of investigating the angular structure of a gravitational-wave (GW) background influencing pulsar signals. A stochastic background of GWs from the incoherent superposition of many inspiraling supermassive black hole binaries at nHz frequencies is likely to be the dominant GW signal detectable by pulsar timing arrays (PTAs). Even though one might expect a background composed of a high-redshift cosmological population of sources to be fairly isotropic, deviations from isotropy may be indicative of local GW hotspots or some form of continuous anisotropy in the angular distribution of GW power. A gravitational-wave background (GWB) induces time-of-arrival deviations in pulsar signals which are correlated between separated pulsars. In an isotropic background this cross correlation follows a distinctive relationship, known as the Hellings and Downs curve, that depends only on the angular separation of the pulsars. If the background is anisotropic, the cross correlation is different, but predictable, and also depends on the absolute position of the pulsars. By simulating data sets containing GWBs with various anisotropic configurations, we have explored the prospects for constraining anisotropy using near future data. We find that at moderate to high signal to noise ratio the assumption of isotropy is no longer an appropriate description of the simulated background. Furthermore, we can recover the nature of the injected anisotropy in a Bayesian parameter-estimation search, and propose a prior on the anisotropy search space motivated by the physicality of the implied distribution of sources. The Tempo2 plugins used to generate pulsar time-of-arrival data sets influenced by anisotropic GWBs can be freely downloaded from the tempo2-anisotropy-plugins GitHub repository.