Dark Matter Annihilation Rates with Velocity-Dependent Annihilation
  Cross Sections
  The detection of byproducts 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 for
annihilation. In such models, the cross section 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.
