  Satellite galaxies of the Milky Way with high mass-to-light ratios and little
baryon content, i.e. dwarf spheroidal galaxies (dSphs), are among the most
promising targets to detect or constrain the nature of dark matter (DM) through
its final annihilation products into high-energy photons. Previously, the
assumption that DM emission from dSphs is point-like has been used to set
strong constraints on DM candidates using data from the Fermi Large Area
Telescope (LAT). However, due to their high DM densities and proximity, dSphs
actually have sufficient angular extension to be detected by the Fermi-LAT.
Here, we assess, for the first time, the impact of accounting for angular
extension in the search for gamma-ray DM signals towards known dSphs with
Fermi-LAT. We show that, depending on the dSph under consideration, limits on
the DM cross section can be weakened by up to a factor of 2-2.5, while the
impact on the stacked, i.e. combined, limits is at most 1.5-1.8 depending on
the annihilation channel. This result is of relevance when comparing dSphs
limits to other multi-messenger DM constraints and for testing the DM
interpretation of anomalous "excesses".
