Galactic center excess in γ rays from annihilation of self-interacting dark matter

Observations by the Fermi Large-Area Telescope have uncovered a significant γ-ray excess directed toward the Milky Way Galactic Center. There has been no detection of a similar signal in the stacked population of Milky Way dwarf spheroidal galaxies. Additionally, astronomical observations indicate that dwarf galaxies and other faint galaxies are less dense than predicted by the simplest cold dark matter models. We show that a self-interacting dark matter model with a particle mass of roughly 50 GeV annihilating to the mediator responsible for the strong self-interaction can simultaneously explain all three observations. The mediator is necessarily unstable, and its mass must be below about 100 MeV in order to decrease the dark matter density of faint galaxies. If the mediator decays to electron-positron pairs with a cross section on the order of the thermal relic value, then we find that these pairs can up-scatter the interstellar radiation field in the Galactic center and produce the observed γ-ray excess.