Cosmic Variance in Anisotropy Searches at Pulsar Timing Arrays

Abstract: Recent pulsar timing array (PTA) analyses show evidence for a gravitational wave background (GWB) with angular correlations consistent with the Hellings-Downs curve. Anisotropies are a key discriminator of the origin of this GWB, as they are expected to be at 1--20\% for astrophysical sources, but suppressed for cosmological GWBs. However, contrary to gravitational wave detectors at higher frequencies, PTAs only take a few independent measurements of a GWB and consequently are highly sensitive to cosmic variance, which induces apparent anisotropies in individual realizations of an isotropic GWB. We demonstrate explicitly that statistical inference nevertheless remains robust, i.e., measurements are consistent with the underlying assumption of isotropy. This confirms that searches for anisotropies will be able to robustly discriminate astrophysical from cosmological GWBs. En route, we demonstrate that the maximum multipole constrained by a PTA dataset scales linearly with the number of pulsars $\ell_{\rm max} \sim N_p$.