Thermal conduction and thermopower of inner crusts of magnetized neutron stars

Abstract

We compute the thermal conductivity and thermoelectric power (thermopower) of the inner crust of compact stars across a broad temperature-density domain relevant for proto-neutron stars, binary neutron-star mergers, and accreting neutron stars. The analysis covers the transition from a semi-degenerate to a highly degenerate electron gas and assumes temperatures above the melting threshold of the nuclear lattice, such that nuclei form a liquid. The transport coefficients are obtained by solving the Boltzmann kinetic equation in the relaxation-time approximation, fully incorporating the anisotropies generated by non-quantizing magnetic fields. Electron scattering rates include (i) dynamical screening of the electron-ion interaction in the hard-thermal-loop approximation of QED, (ii) ion-ion correlations within a one-component plasma, and (iii) finite nuclear-size effects. As an additional refinement, we evaluate electron-neutron scattering induced by the coupling of electrons to the anomalous magnetic moment of free neutrons; this contribution is found to be subdominant throughout the parameter range explored. To assess the sensitivity of transport coefficients to the underlying microphysics, we perform calculations for several inner-crust compositions obtained from different nuclear interactions and many-body methods. Across most of the crust, variations in relaxation times and in the components of the anisotropic thermal-conductivity and thermopower tensors reach up to factors 3-4 and 1.5-2, respectively, with the exception of the region where pasta phases are expected. These results provide updated, composition-dependent microphysical inputs for dissipative magneto-hydrodynamic simulations of warm neutron stars and post-merger remnants, where anisotropic heat and charge transport are of critical importance.