  In the cold dark matter scenario, galactic dark matter halos are populated
with a large number of smaller subhalos. Previous work has shown that dark
matter annihilations in subhalos can generate a distinctive, non-Poisson signal
in the gamma-ray photon counts probability distribution function (PDF). Here we
show that the gamma-ray PDF also carries information about the velocity
dependence of the dark matter annihilation cross section. After calculating the
PDF assuming $s$-wave and Sommerfeld-enhanced annihilation, we perform a mock
data analysis to illustrate how current and future observations can constrain
the microphysics of the dark matter annihilation. We find that, with current
Fermi data, and assuming a dark matter annihilation cross section roughly at
the limit of current bounds from annihilation in dwarf spheroidal galaxies, one
can potentially distinguish the non-Poissonian fluctuations expected from dark
matter annihilation in subhalos from Poisson sources, as well as from dark
matter models with an incorrect velocity-dependence. We explore how robust
these results are to assumptions about the modeling of astrophysical
backgrounds. We also point out a four-parameter degeneracy between the velocity
dependence of the dark matter annihilation, the minimum subhalo mass, the power
law index of the subhalo mass function, and the normalization of the dark
matter signal. This degeneracy can be broken with priors from N-body
simulations or from observational constraints on the subhalo mass function.
