  White dwarfs, the most abundant stellar remnants, provide a promising means
of probing dark matter (DM) interactions, complimentary to terrestrial
searches. The scattering of dark matter from stellar constituents leads to
gravitational capture, with important observational consequences. In
particular, white dwarf heating occurs due to the energy transfer in the dark
matter capture and thermalisation processes, and the subsequent annihilation of
captured dark matter. We consider the capture of dark matter by scattering on
either the ion or the degenerate electron component of white dwarfs. For ions,
we account for the stellar structure, the star opacity, realistic nuclear form
factors that go beyond the simple Helm approach, and finite temperature effects
pertinent to sub-GeV dark matter. Electrons are treated as relativistic,
degenerate targets, with Pauli blocking, finite temperature and multiple
scattering effects all taken into account. We also estimate the dark matter
evaporation rate. The DM-nucleon/electron scattering cross sections can be
constrained by comparing the heating rate due to dark matter capture with
observations of cold white dwarfs in dark matter-rich environments. We apply
this technique to observations of old white dwarfs in the globular cluster
Messier 4, which we assume to be located in a DM subhalo. For DM-nucleon
scattering, we find that white dwarfs can probe the sub-GeV mass range
inaccessible to direct detection searches, with the low mass reach limited only
by either evaporation or dominant DM annihilation to neutrinos, and can be
competitive with direct detection in the $1-10^4$ GeV range. White dwarf limits
on dark matter-electron scattering are found to outperform current electron
recoil experiments over the full mass range considered, and extend well beyond
the $\sim 10$ GeV mass regime where the sensitivity of electron recoil
experiments is reduced.
