We calculate for the first time the phonon excitation rate in the outer crust of a neutron star due to scattering from light dark matter (LDM) particles gravitationally boosted into the star. We consider dark matter particles in the sub-GeV mass range scattering off a periodic array of nuclei through an effective scalar-vector interaction with nucleons. We find that LDM effects cause a modification of the net number of phonons in the lattice as compared to the standard thermal result. In addition, we estimate the contribution of LDM to the ion-ion thermal conductivity in the outer crust and find that it can be significantly enhanced at large densities. Our results imply that for magnetized neutron stars the LDM-enhanced global conductivity in the outer crust will tend to reduce the anisotropic heat conduction between perpendicular and parallel directions to the magnetic field.
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