Simulation of energy transport by dark matter scattering in stars

Asymmetric dark matter (ADM) that is captured in stars can act as an efficient conductor of heat. Small ADM-induced changes in a star's temperature gradient are known to alter neutrino fluxes and asteroseismological signatures, erase convective cores and modify a star's main sequence lifetime. The Sun's proximity to us makes it an ideal laboratory for studying these effects. However, the two formalisms commonly used to parametrize such heat transport were developed over 30 years ago, and calibrated with a single set of simulations. What's more, both are based on assumptions that break down at the Knudsen transition, where heat transport is maximized. We construct a Monte Carlo simulation to exactly solve the Boltzmann collision equation, determining the steady-state distribution and luminosity carried in stars by ADM with cross sections that depend on velocity and momentum. We find that, although the established (Gould and Raffelt) formalism based on local thermal equilibrium does well for constant cross sections, the isothermal (Spergel and Press) method actually performs better across all models with a simple, universal rescaling function. Based on simulation results, we provide recommendations on the parametrization of DM heat transport in stellar evolution models.