Impact of sub-MeV dark matter on the cooling of pulsating white dwarfs

In our galaxy, white dwarfs inevitably undergo scattering and capture processes with the interstellar diffuse dark matter. The captured dark matter forms a dark halo that eventually evaporates or annihilates. Theoretical pulsation modes and observations of pulsating white dwarfs provide predictions about their evolution. This motivates us to study the impact of sub-MeV interstellar dark matter on the cooling processes of white dwarfs. In this work, we consider the collisions between dark matter and relativistic degenerate electrons inside white dwarfs, numerically calculating the energy input and output results from scattering, capture, evaporation, and annihilation processes. Based on observational data from G117-B15, we conclude that the maximum cooling luminosity of the interstellar sub-MeV dark matter is approximately $\ensuremath{\sim}{10}^{22}\text{ }\text{ }\mathrm{erg}/\mathrm{s}$, which is insufficient to provide an effective cooling mechanism for white dwarfs. Finally, if future observations detect a pulsating white dwarf in the Galactic center, the potential sensitivity of this scenario could extend to the region ${10}^{\ensuremath{-}3}\text{ }\text{ }\mathrm{MeV}<{m}_{\ensuremath{\chi}}<10\text{ }\text{ }\mathrm{MeV}$ and $6.02\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}38}\text{ }\text{ }{\mathrm{cm}}^{2}>{\ensuremath{\sigma}}_{0}\ensuremath{\ge}1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}40}\text{ }\text{ }{\mathrm{cm}}^{2}$.