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Anisotropies in the nanohertz gravitational-wave background are a compellingnext target for pulsar timing arrays (PTAs). Measurements or informative upperlimits to the anisotropies are expected in the near future and can offerimportant clues about the origin of the background and the properties of thesources. Given that each source is expected (in the simplest scenario ofcircular inspirals) to emit at a fixed frequency, the anisotropy will mostgenerally vary from one frequency to another. The main result presented in thiswork is an analytical model for the anisotropies produced by a population ofinspiralling supermassive black-hole binaries (SMBHBs). This model can beimmediately connected with parametrizations of the SMBHB mass function and canbe easily expanded to account for new physical processes taking place withinthe PTA frequency band. We show that a variety of SMBHB models predictsignificant levels of anistropy at the highest frequencies accessible to PTAobservations and that measurements of anisotropies can offer new informationregarding this population beyond the isotropic component. We also model theimpact of additional dynamical effects driving the binary towards merger andshow that, if these processes are relevant within the PTA band, thedetectability of anisotropies relative to the isotropic background will beenhanced. Finally, we use the formalism presented in this work to predict thelevel anisotropy of the circular and linear polarizations of the SGWB due tothe distribution of binary orientation angles with respect to the line ofsight.

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