Angular distribution of gamma-ray emission from velocity-dependent dark matter annihilation in subhalos

We consider the effect of velocity-dependent dark matter annihilation on the angular distribution of gamma rays produced in dark matter subhalos. We assume that the dark matter potential is spherically symmetric, characterized by a scale radius and scale density, and the velocity distribution is isotropic. We find that the effect of velocity-dependent dark matter annihilation is largely determined by dimensional analysis; the angular size of gamma-ray emission from an individual subhalo is rescaled by a factor which depends on the form of the dark matter distribution, but not on the halo parameters, while the relative normalization of the gamma-ray flux from different mass subhalos is rescaled by a factor which depends on the halo parameters, but not on the form of the dark matter distribution. We apply our results to a Navarro-Frenk-White profile for the case of an individual subhalo and comment on the application of these results to a distribution of subhalos.