Pulsar timing array sensitivity to anisotropies in the gravitational wave background

Pulsar Timing Array (PTA) observations have recently gathered substantial evidence for the existence of a gravitational wave background in the nHz frequency band. Searching for anisotropies in this signal is key to determining its origin, and in particular to distinguish possible astrophysical from cosmological sources. In this work, we assess the sensitivity of current and future pulsar timing arrays to such anisotropies using the full covariance matrix of pulsar timing delays. While current day pulsar timing arrays can only set mildly informative constraints on the dipole and quadrupole, we show that percent level accuracy for several low multipoles can be achieved in the near future. Moreover, we demonstrate that anisotropies in the gravitational wave background and the Hellings-Downs angular correlation, indicating the presence of GWs, are approximately uncorrelated, and can hence be reconstructed independently. These results can be reproduced with \href{https://github.com/Mauropieroni/fastPTA}{\texttt{fastPTA}}, a publicly available Python code to forecast the constraining power of PTA configurations.