Heavy dark matter in white dwarfs: multiple-scattering capture and thermalization
We present an improved treatment for the scattering of heavy dark matter from the ion constituents of a white dwarf. In the heavy dark matter regime, multiple collisions are required for the dark matter to become gravitationally captured. Our treatment incorporates all relevant physical effects including the dark matter trajectories, nuclear form factors, and radial profiles for the white dwarf escape velocity and target number densities. Our capture rates differ by orders of magnitude from previous estimates, which have typically used approximations developed for dark matter scattering in the Earth. We also compute the time for the dark matter to thermalize in the center of the white dwarf, including in-medium effects such as phonon emission and absorption from the ionic lattice in the case where the star has a crystallized core. We find much shorter thermalization timescales than previously estimated, especially if the white dwarf core has crystallized. We illustrate the importance of our improved approach by determining the cross section required for accumulated asymmetric dark matter to self-gravitate.