Electron-ion scattering in dense multi-component plasmas: application to the outer crust of an accreting neutron star

Abstract

The thermal conductivity of a dense {\it multi-component} plasma is critical to the modeling of accreting neutron stars. To this end, we perform large-scale molecular dynamics simulations to calculate the static structure factor of the dense multi-component plasma in the neutron star crust from near the photosphere-ocean boundary to the vicinity of the neutron drip point. The structure factors are used to validate a microscopic linear mixing rule that is valid for arbitrarily complex plasmas over a wide range of Coulomb couplings. The microscopic mixing rule in turn implies and validates the linear mixing rule for the equation of state properties and also the linear mixing rule for the electrical and thermal conductivities of dense multi-component plasmas. To make our result as useful as possible, for the specific cases of electrical and thermal conductivities, we provide a simple analytic fit that is valid for arbitrarily complex multi-component plasmas over a wide range of Coulomb couplings. We compute the thermal conductivity for a representative compositional profile of the outer crust of an accreting neutron star in which hundreds of nuclear species can be present. We utilize our results to re-examine the so-called impurity parameter formalism as used to characterize impure plasmas.