  White dwarfs, the most abundant stellar remnants, provide a promising means
of probing dark matter 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 dark
matter-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 dark matter-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 evaporation, 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.
