Substructure boosts to dark matter annihilation from Sommerfeld enhancement

The recently introduced Sommerfeld enhancement of the dark matter annihilation cross section has important implications for the detection of dark matter annihilation in subhalos in the Galactic halo. In addition to the boost to the dark matter annihilation cross section from the high densities of these subhalos with respect to the main halo, an additional boost caused by the Sommerfeld enhancement results from the fact that they are kinematically colder than the Galactic halo. If we further believe the generic prediction of the cold dark matter paradigm that in each subhalo there is an abundance of substructure which is approximately self-similar to that of the Galactic halo, then I show that additional boosts coming from the density enhancements of these small substructures and their small velocity dispersions enhance the dark matter annihilation cross section even further. I find that very large boost factors (${10}^5$ to ${10}^9$) are obtained in a large class of models. The implications of these boost factors for the detection of dark matter annihilation from dwarf spheroidal galaxies in the Galactic halo are such that, generically, they outshine the background gamma-ray flux and are detectable by the Fermi Gamma-ray Space Telescope.