Nuclear and dark matter heating in massive white dwarf stars

Recently, Cheng et al. identified a number of massive white dwarfs (WD) that appear to have an additional heat source providing a luminosity near $\approx 10^{-3}L_\odot$ for multiple Gyr. In this paper we explore heating from electron capture and pycnonuclear reactions. We also explore heating from dark matter annihilation. WD stars appear to be too small to capture enough dark matter for this to be important. Finally, if dark matter condenses to very high densities inside a WD this could ignite nuclear reactions. We calculate the enhanced central density of a WD in the gravitational potential of a very dense dark matter core. While this might start a supernova, it seems unlikely to provide modest heating for a long time. We conclude that electron capture, pycnonuclear, and dark matter reactions are unlikely to provide significant heating in the massive WD that Cheng considers.