Investigating the effect of Milky Way dwarf spheroidal galaxies extension on dark matter searches with Fermi-LAT data

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".