J factors for velocity-dependent dark matter annihilation

Abstract

If dark matter annihilates with a velocity-dependent cross section within a subhalo, then the magnitude and angular distribution of the resulting photon signal will change. These effects are encoded in the J-factor. In this work we compute the J-factor for a variety of choices for the cross section velocity dependence, and for a variety of choices for the dark matter profile, including generalized Navarro-Frenk-White, Einasto, Burkert and Moore. Interestingly, we find that for a density profile with an inner slope power law steeper than 4/3, Sommerfeld-enhanced annihilation in the Coulomb limit leads to a divergence at the center, requiring a more detailed treatment of departure from the Coulomb limit.