Effects of Bound States on Dark Matter Annihilation

We study the impact of bound state formation on dark matter annihilation rates in models where dark matter interacts via a light mediator, the dark photon. We derive the general cross section for radiative capture into all possible bound states, and point out its non-trivial dependence on the dark matter velocity and the dark photon mass. For indirect detection, our result shows that dark matter annihilation inside bound states can play an important role in enhancing signal rates over the rate for direct dark matter annihilation with Sommerfeld enhancement. The effects are strongest for large dark gauge coupling and when the dark photon mass is smaller than the typical momentum of dark matter in the galaxy. As an example, we show that for thermal dark matter the Fermi gamma ray constraint is substantially increased once bound state effects are taken into account. We also find that bound state effects are not important for dark matter annihilation during the freeze out and recombination epochs.