Thermal conduction and thermopower of a warm neutron star crust in magnetic fields
We compute the thermal conductivity and thermopower of the inner crust of compact stars over a broad temperature-density domain relevant to proto-neutron stars, binary neutron-star mergers, and accreting neutron stars, spanning the transition from a semi-degenerate to a highly degenerate electron gas above the lattice melting temperature, where nuclei form a liquid. Nuclear composition is fixed by selected zero-temperature inner-crust models as temperature varies. Transport coefficients follow from the Boltzmann equation in the relaxation-time approximation, including anisotropies from non-quantizing magnetic fields. Electron scattering rates incorporate (i) dynamical screening of electron-ion interactions via the hard-thermal-loop QED approximation, (ii) ion-ion correlations in a one-component plasma, and (iii) finite nuclear-size effects. We also evaluate electron-neutron scattering from coupling to the neutron anomalous magnetic moment, finding it subdominant throughout. To test sensitivity to microphysics, we compare several inner-crust compositions from different nuclear interactions and many-body methods. Across most of the crust, relaxation times and the anisotropic thermal-conductivity and thermopower tensor components vary by factors of 3 to 4 and 1.5 to 2, respectively, except near the pasta-phase region. Within this single-component, fixed-composition approximation, these results offer composition-dependent microphysical inputs for dissipative magneto-hydrodynamic simulations of warm neutron stars and post-merger remnants, where anisotropic heat and charge transport are critical.