  Dark matter with momentum- or velocity-dependent interactions with nuclei has
shown significant promise for explaining the so-called Solar Abundance Problem,
a longstanding discrepancy between solar spectroscopy and helioseismology. The
best-fit models are all rather light, typically with masses in the range of 3-5
GeV. This is exactly the mass range where dark matter evaporation from the Sun
can be important, but to date no detailed calculation of the evaporation of
such models has been performed. Here we carry out this calculation, for the
first time including arbitrary velocity- and momentum-dependent interactions,
thermal effects, and a completely general treatment valid from the optically
thin limit all the way through to the optically thick regime. We find that
depending on the dark matter mass, interaction strength and type, the mass
below which evaporation is relevant can vary from 1 to 4 GeV. This has the
effect of weakening some of the better-fitting solutions to the Solar Abundance
Problem, but also improving a number of others. As a by-product, we also
provide an improved derivation of the capture rate that takes into account
thermal and optical depth effects, allowing the standard result to be smoothly
matched to the well-known saturation limit.
