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

We use the formalism of Gould and Raffelt 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 $\alpha$ and $\kappa$ for cross-sections that go as $v_{\rm rel}^2$, $v_{\rm rel}^4$, $v_{\rm rel}^{-2}$, $q^2$, $q^4$ and $q^{-2}$, where $v_{\rm rel}$ is the relative DM-nucleus velocity and $q$ is the momentum transferred in the collision. We find that a $v_{\rm rel}^{-2}$ 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.