  Several Pulsar Timing Array (PTA) collaborations have recently found evidence
for a gravitational wave background (GWB) permeating our galaxy. The origin of
this background is still unknown. Indeed, while the gravitational wave emission
from inspiraling supermassive black hole binaries (SMBHB) is the primary
candidate for its origin, several cosmological sources have also been proposed.
One distinctive feature of SMBHB-generated backgrounds is the presence of GWB
anisotropies stemming from the binaries distribution in the local Universe.
However, none of the anisotropy searches performed to date reported a
detection. In this work, we show that the lack of anisotropy detection is not
currently in tension with a SMBHB origin of the background. We accomplish this
by calculating the anisotropy detection probability of present and future PTAs.
We find that a PTA with the noise characteristics of the NANOGrav 15-year data
set had only a $~2\%-11\%$ probability of detecting SMBHB-generated
anisotropies, depending on the properties of the SMBHB population. However, we
estimate that for the IPTA DR3 data set these probabilities will increase to
$~4\%-28\%$, putting more pressure on the SMBHB interpretation in case of a
null detection. We also identify SMBHB populations that are more likely to
produce detectable levels of anisotropies. This information could be used
together with the spectral properties of the GWB to characterize the SMBHB
population.
