Dark matter self-annihilation as a hidden energy source in white dwarfs

White dwarfs (WDs) are compact remnants of stars, supported by electron degeneracy pressure, and their structures are generally considered to be well understood. Significant discrepancies exist between the theoretical and observed white dwarf mass-radius (MR) relations, especially for hot Q-branch white dwarfs with unexplained heating sources. In this study, we explore the potential of WDs as a portal to dark matter (DM) physics by investigating the effect of self-annihilating DM (SADM) admixed in WDs, solving the set of two-fluid hydrostatic equilibrium and heat diffusion equations self-consistently. We obtain empirical formulae for the WD luminosity L and effective temperature T eff as functions of the DM mass fraction f d, annihilation cross section σv, and particle mass m χ, as well as the WD's total mass M t. We also compare the WD MR relations for various L, f d, and both Fermionic and Bosonic DM particle statistics, with the observational data. We show that the majority of observed deviations in the WD MR relation can be accounted for by having SADM admixed with f d 10-5 and σv 3 times10-26 cm cubed s-1, the thermal relic cross section. Therefore, our results suggest that WDs can be sensitive DM detectors, and DM self-annihilation could provide additional heating in WDs, accounting for their observed extra luminosities.