  Spatial extension has been hailed as a "smoking gun" in the gamma-ray search
of dark galactic subhalos, which would appear as unidentified sources for
gamma-ray telescopes. In this work, we study the sensitivity of the Fermi-LAT
to extended subhalos using simulated data based on a realistic sky model. We
simulate spatial templates for a set of representative subhalos, whose
parameters were derived from our previous work with N-body cosmological
simulation data. We find that detecting an extended subhalo and finding an
unequivocal signal of angular extension requires, respectively, a flux 2 to 10
times larger than in the case of a point-like source. By studying a large grid
of models, where parameters such as the WIMP mass, annihilation channel or
subhalo model are varied significantly, we obtain the response of the LAT as a
function of the product of annihilation cross section times the J-factor.
Indeed, we show that spatial extension can be used as an additional filter to
reject subhalos candidates among the pool of unidentified LAT sources, as well
as a "smoking gun" for positive identification. For instance, typical angular
extensions of a few tenths of degree are expected for the considered scenarios.
Finally, we also study the impact of the obtained LAT sensitivity to such
extended subhalos on the achievable dark matter constraints, which are a few
times less constraining than comparable point-source limits.
