Constraining the Sommerfeld enhancement with Cherenkov telescope observations of dwarf galaxies

The presence of dark matter in the halo of our galaxy could be revealed through indirect detection of annihilation products. Dark matter annihilation is one of the possible interpretations of the recent measured excesses in positron and electron fluxes, once boost factors of the order of 10 or more are taken into account. Such boost factors are actually achievable through the velocity-dependent Sommerfeld enhancement of the annihilation cross-section. Here we study the expected γ-ray flux from two local dwarf galaxies for which air Cerenkov measurements are available, namely Draco and Sagittarius. We use velocity dispersion measurements to model the dark matter halos of the dwarfs, and the results of numerical simulations to model the presence of an associated population of subhalos. We incorporate the Sommerfeld enhancement of the annihilation cross-section. We compare our predictions with observations of Draco and Sagittarius performed by MAGIC and HESS, respectively. We also compare our results with the sensitivities of Fermi and of the future Cherenkov Telescope Array. We find that the boost factor due to the Sommerfeld enhancement is already constrained by the MAGIC and HESS data, with enhancements greater than 5× 10 being excluded. While Fermi will not be able to detect γ-rays from the dwarf galaxies s even with the most optimistic Sommerfeld effect, we show that the Cherenkov Telescope Array will be able to test enhancements greater than 1.5× 10.