Thermal conduction and thermopower of inner crusts of magnetized neutron stars

TL;DR

This paper calculates the thermal conductivity and thermopower of the inner crust of magnetized neutron stars, considering various microphysical effects and anisotropies, to improve models of heat and charge transport in these extreme environments.

Contribution

It provides detailed, composition-dependent calculations of transport coefficients in the neutron star crust, including magnetic field effects and microphysical refinements, for the first time across a broad parameter range.

Findings

Transport coefficients vary by factors of 3-4 with composition.

Electron-neutron scattering is subdominant in the crust.

Results are crucial for magneto-hydrodynamic simulations of 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.