Thermal decoupling and the smallest subhalo mass in dark matter models with Sommerfeld-enhanced annihilation rates

Abstract

We consider dark matter consisting of weakly interacting massive particles (WIMPs) and revisit in detail its thermal evolution in the early universe, with a particular focus on models where the annihilation rate is enhanced by the Sommerfeld effect. After chemical decoupling, or freeze-out, dark matter no longer annihilates but is still kept in local thermal equilibrium due to scattering events with the much more abundant standard model particles. During kinetic decoupling, even these processes stop to be effective, which eventually sets the scale for a small-scale cutoff in the matter density fluctuations. Afterwards, the WIMP temperature decreases more quickly than the heat bath temperature, which causes dark matter to reenter an era of annihilation if the cross-section is enhanced by the Sommerfeld effect. Here, we give a detailed and self-consistent description of these effects. As an application, we consider the phenomenology of simple leptophilic models that have been discussed in the literature and find that the relic abundance can be affected by as much two orders of magnitude or more. We also compute the mass of the smallest dark matter subhalos in these models and find it to be in the range of about 10^{-10} to 10 solar masses; even much larger cutoff values are possible if the WIMPs couple to force carriers lighter than about 100 MeV. We point out that a precise determination of the cutoff mass allows to infer new limits on the model parameters, in particular from gamma-ray observations of galaxy clusters, that are highly complementary to existing constraints from g-2 or beam dump experiments.