Abstract
We studied the dark matter induced Mikheyev-Smirnov-Wolfenstein e ect on neutrino oscillations in the Sun and the core-collapse supernovae. However, to have sizable e ect, we found that the dark matter cannot self-annihilate, for instance, the asymmetric dark matter. From the solar neutrino data, we found strong constraint on the interaction between dark matter and neutrino for asymmetric dark matter with mass less than 40 GeV. For supernovae, we found that the additional e ect would be detectable only if the supernova sits close to the Galactic center or the interaction between dark matter and neutrinos is strong enough.