Constraining dark matter interactions mediated by a light scalar with white dwarfs

Observations of white dwarfs in dark matter-rich environments can provide strong limits on the strength of dark matter interactions. Here we apply the recently improved formalism of the dark matter capture rate in white dwarfs to a general model in which dark matter interacts with the white dwarf ion components via a light scalar mediator. We compute the dark matter capture rate in the optically thin limit in a cold white dwarf from the globular cluster Messier. We then estimate the threshold cross-section, which significantly varies as a function of the light scalar mediator mass $m_\phi$ in the range of $0.05\, m_\chi<m_\phi<m_\chi$ and becomes constant when $m_\phi>m_\chi$. We also show that the bounds obtained from the dark matter capture in a white dwarf from the globular cluster Messier 4 are complementary to direct detection experiments and particularly strong in the sub-GeV regime.