  The North American Nanohertz Observatory for Gravitational Waves (NANOGrav)
has reported evidence for the presence of an isotropic nanohertz gravitational
wave background (GWB) in its 15 yr dataset. However, if the GWB is produced by
a population of inspiraling supermassive black hole binary (SMBHB) systems,
then the background is predicted to be anisotropic, depending on the
distribution of these systems in the local Universe and the statistical
properties of the SMBHB population. In this work, we search for anisotropy in
the GWB using multiple methods and bases to describe the distribution of the
GWB power on the sky. We do not find significant evidence of anisotropy, and
place a Bayesian $95\%$ upper limit on the level of broadband anisotropy such
that $(C_{l>0} / C_{l=0}) < 20\%$. We also derive conservative estimates on the
anisotropy expected from a random distribution of SMBHB systems using
astrophysical simulations conditioned on the isotropic GWB inferred in the
15-yr dataset, and show that this dataset has sufficient sensitivity to probe a
large fraction of the predicted level of anisotropy. We end by highlighting the
opportunities and challenges in searching for anisotropy in pulsar timing array
data.
