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The substructures of the Galactic dark matter halo such as dark mattersubhalos and dwarf galaxies have very low velocity dispersions, which makesthem useful in constraining the scenario of Sommerfeld-enhanced dark matterannihilation. We calculate the velocity distribution of dark matter particlesin dark matter halo substructures using the Eddington's formula with NFWdensity profile. We parametrize the effect of Sommerfeld enhancement of s-wavedark matter annihilation on the gamma-ray flux as the Sommerfeld-enhancedJ-factors, and explicitly calculate their values for 15 known dwarf spheroidalgalaxies. Using the Fermi-LAT 3FGL data on the unassociated point-sources andthe N-body simulation results on the dark matter subhalo distribution, wederive upper limits on the dark matter annihilation cross sections withSommerfeld enhacement. Similar upper limits are derived from the Ferm-LATgamma-ray data on the dwarf spheroidal galaxies. We find that in a wide regionof parameter space, the constraints can be a few orders of magnitude morestringent than that in the case without the Sommerfeld enhancement. For darkmatter annihilation dominantly into $e^+e^-$, $\mu^+\mu^-$, $\tau^{+}\tau^{-}$and $b\bar b$, those constraints can exclude thermal relic dark matter for thedark matter mass below about 1 TeV.

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