Prospects and Limitations of PTAs Anisotropy Searches -- The Frequentist Case

Abstract

Recent findings from several Pulsar Timing Array (PTA) collaborations point to the existence of a Gravitational Wave Background (GWB) at nanohertz frequencies. A key next step towards characterizing this signal and identifying its origin is to map the sky distribution of its power. Several strategies have been proposed to reconstruct this distribution using PTA data. In this work, we compare these different strategies to determine which one is best suited to detect GWB anisotropies of different topologies. We find that, for both localized and large-scale anisotropies, reconstruction methods based on pixel and radiometer maps are the most promising. However, in both scenarios, even the optimistically large anisotropic signals discussed in this work remain challenging to detect with near-future PTA sensitivities. For example, we find that for a GWB hotspot contributing to $80\%$ of the GWB power in the second frequency bin, detection probabilities reach at most $\mathcal{O}(10\%)$ for a PTA with noise properties comparable with the ones of the upcoming IPTA third data release. Finally, we consider the fundamental limitations that cosmic variance poses to these kinds of searches by deriving the smallest deviations from isotropy that could be detected by an idealized PTA with no experimental or pulsar noise.