Dark matter annihilation rates with velocity-dependent annihilation cross sections

The detection of by-products from particle annihilations in galactic halos would provide important information about the nature of the dark matter. Observational evidence for a local excess of high-energy positrons has motivated recent models with an additional interaction between dark matter particles that can result in a Sommerfeld enhancement to the cross section. In such models, the cross section for annihilation becomes velocity-dependent and may enhance the dark matter annihilation rate in the solar neighborhood relative to the rate in the early Universe sufficiently to source observed fluxes of high-energy positrons. We demonstrate that, for particle interaction cross sections that increase with decreasing velocity, the kinematical structures of dark matter halos with interior density profiles shallower than isothermal, such as Navarro-Frenk-White or Einasto halos, may induce a further enhancement owing to the position-dependent velocity distribution. We provide specific examples for the increase in the annihilation rate with a cross section enhanced by the Sommerfeld effect. In dark matter halos like that of the Milky Way and Local Group dwarf galaxies, the effective cross section at the halo center can be significantly larger than its local value. The additional enhancement owing to halo kinematics depends upon the parameters of any model, but is a prediction of certain models aimed at explaining measured positron fluxes and can exceed an order of magnitude.