Thermal conduction by dark matter with velocity and momentum-dependent cross-sections

Abstract

We use the formalism of Gould and Raffelt [1] to compute the dimensionless thermal conduction coefficients for scattering of dark matter particles with standard model nucleons via cross-sections that depend on the relative velocity or momentum exchanged between particles. Motivated by models invoked to reconcile various recent results in direct detection, we explicitly compute the conduction coefficients α and κ for cross-sections that go as vrel2, vrel4, vrel−2, q2, q4 and q−2, where vrel is the relative DM-nucleus velocity and q is the momentum transferred in the collision. We find that a vrel−2 dependence can significantly enhance energy transport from the inner solar core to the outer core. The same can true for any q-dependent coupling, if the dark matter mass lies within some specific range for each coupling. This effect can complement direct searches for dark matter; combining these results with state-of-the-art solar simulations should greatly increase sensitivity to certain DM models. It also seems possible that the so-called Solar Abundance Problem could be resolved by enhanced energy transport in the solar core due to such velocity- or momentum-dependent scatterings.