Constraints on the Sommerfeld-enhanced dark matter annihilation from the gamma rays of subhalos and dwarf galaxies

Abstract: The substructures of the Galactic dark matter halo such as dark matter subhalos and dwarf galaxies have very low velocity dispersions, which makes them useful in constraining the scenario of Sommerfeld-enhanced dark matter annihilation. We calculate the velocity distribution of dark matter particles in dark matter halo substructures using the Eddington's formula with NFW density profile. We parametrize the effect of Sommerfeld enhancement of s-wave dark matter annihilation on the gamma-ray flux as the Sommerfeld-enhanced J-factors, and explicitly calculate their values for 15 known dwarf spheroidal galaxies. Using the Fermi-LAT 3FGL data on the unassociated point-sources and the N-body simulation results on the dark matter subhalo distribution, we derive upper limits on the dark matter annihilation cross sections with Sommerfeld enhacement. Similar upper limits are derived from the Ferm-LAT gamma-ray data on the dwarf spheroidal galaxies. We find that in a wide region of parameter space, the constraints can be a few orders of magnitude more stringent than that in the case without the Sommerfeld enhancement. For dark matter annihilation dominantly into $e^+e^-$, $\mu^+\mu^-$, $\tau^{+}\tau^{-}$ and $b\bar b$, those constraints can exclude thermal relic dark matter for the dark matter mass below about 1 TeV.