  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 anistropy 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 SGWB due to
the distribution of binary orientation angles with respect to the line of
sight.
