Singularities in the gravitational capture of dark matter through long-range interactions

We re-examine the gravitational capture of dark matter (DM) through long-range interactions. We demonstrate that neglecting the thermal motion of target particles, which is often a good approximation for short-range capture, results in parametrically inaccurate results for long-range capture. When the particle mediating the scattering process has a mass that is small in comparison to the momentum transfer in scattering events, correctly...