Size Dependence of the Sommerfeld Enhancement for Puffy Dark Matter

We examine the size effects in the Sommerfeld enhancement factor for puffy dark matter annihilation. First, we use the partial-wave method to study the case of puffy dark matter for which only a charge density distribution is given without specifying its internal structure. We find that by using two dimensionless parameters, we can provide a characterization of the resonance structure of the Sommerfeld enhancement. Using this approach, we demonstrate that the finite size of dark matter particle is another fundamental factor, in addition to low velocity, that affects the Sommerfeld enhancement. Then, as an example of puffy dark matter with nontrivial internal structures, we perform the analysis for the nugget-type dark matter, whose Sommerfeld enhancement factor is found to exhibit a resonant behavior similar to that of point-like particles.