Impact of Evaporation Barriers on Solar-Captured Dark Matter Distributions and Evaporation Mass

We study the non-thermal distributions of dark matter captured by the Sun by solving the linear Boltzmann equation with a Markov-chain Monte Carlo scheme in the space of orbital energy and angular momentum. From the resulting steady-state distribution, we derive the capture rate, the evaporation rate, and the effective annihilation volume, and provide compact fitting formulas across the studied mass ranges for several values of the potential-depth parameter beta. The presence of an in-medium potential deepens the total solar potential and raises the local escape speed, compressing the phase space toward lower specific energy and angular momentum. As a result, the capture rate increases, the evaporation rate is exponentially suppressed, the effective annihilation volume is mildly reduced, and the evaporation mass shifts to smaller values. Maps in the plane of dark-matter mass and scattering cross section quantify these trends, with the evaporation mass indicated on the maps. The results are presented in a form directly applicable to solar-neutrino flux calculations and related dark-matter phenomenology.