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 .