The search for anisotropy in the gravitational-wave background with
  pulsar-timing arrays
  Pulsar-timing arrays (PTAs) are seeking gravitational waves from
supermassive-black-hole binaries, and there are prospects to complement these
searches with stellar-astrometry measurements. Theorists still disagree,
however, as to whether the local gravitational-wave background will be
statistically isotropic, as arises if it is the summed contributions from many
SMBH binaries, or whether it exhibits the type of statistical anisotropy that
arises if the local background is dominated by a handful (or even one) bright
source. Here we derive, using bipolar spherical harmonics, the optimal PTA
estimators for statistical anisotropy in the GW background and simple estimates
of the detectability of this anisotropy. We provide results on the smallest
detectable amplitude of a dipole anisotropy (and several other low-order
multipole moments) and also the smallest detectable amplitude of a "beam" of
gravitational waves. Results are presented as a function of the signal-to-noise
with which the GW signal is detected and as a function of the number of pulsars
(assuming uniform distribution on the sky and equal sensitivity per pulsar). We
provide results first for measurements with a single time-domain window
function and then show how the results are augmented with the inclusion of
time-domain information. The approach here is intended to be conceptually
straightforward and to complement the results of more detailed (but
correspondingly less intuitive) modeling of the actual measurements.
