Exploring the spectrum of stochastic gravitational-wave anisotropies with pulsar timing arrays

Anisotropies in the nanohertz gravitational-wave background are a compelling next target for pulsar timing arrays (PTAs). Measurements or informative upper limits to the anisotropies are expected in the near future and can offer important clues about the origin of the background and the properties of the sources. Given that each source is expected (in the simplest scenario of circular inspirals) to emit at a fixed frequency, the anisotropy will most generally vary from one frequency to another. The main result presented in this work is an analytical model for the anisotropies produced by a population of inspiralling supermassive black-hole binaries (SMBHBs). This model can be immediately connected with parametrizations of the SMBHB mass function and can be easily expanded to account for new physical processes taking place within the PTA frequency band. We show that a variety of SMBHB models predict significant levels of anisotropy at the highest frequencies accessible to PTA observations and that measurements of anisotropies can offer new information regarding this population beyond the isotropic component. We also model the impact of additional dynamical effects driving the binary towards merger and show that, if these processes are relevant within the PTA band, the detectability of anisotropies relative to the isotropic background will be enhanced. Finally, we use the formalism presented in this work to predict the level anisotropy of the circular and linear polarizations of the stochastic gravitational-wave background due to the distribution of binary orientation angles with respect to the line of sight.