Thermal Conductivity and Thermal Hall Effect in Dense Electron-Ion Plasma

TL;DR

This paper investigates how thermal conductivity and the thermal Hall effect behave in dense electron-ion plasmas relevant to astrophysical objects, providing analytical relations and formulas for use in simulations of neutron stars and white dwarfs.

Contribution

It offers new analytical scaling relations and fitting formulas for thermal conductivity and the thermal Hall effect in dense plasmas across degenerate and non-degenerate regimes.

Findings

Thermal conductivity increases with density and temperature.

Magnetic fields induce anisotropy and the thermal Hall effect.

A minimum ratio of thermal conductivity to temperature marks the transition between regimes.

Abstract

In this study, we examine thermal conductivity and the thermal Hall effect in electron-ion plasmas relevant to hot neutron stars, white dwarfs, and binary neutron star mergers, focusing on densities found in the outer crusts of neutron stars and the interiors of white dwarfs. We consider plasma consisting of single species of ions, which could be either iron $\isotope[56]{Fe}$ or carbon $\isotope[12]{C}$ nuclei. The temperature range explored is from the melting temperature of the solid $T\sim10^9$~K up to $10^{11}$~K. This covers both degenerate and non-degenerate electron regimes. We find that thermal conductivity increases with density and temperature for which we provide analytical scaling relations valid in different regimes. The impact of magnetic fields on thermal conductivity is also analyzed, showing anisotropy in low-density regions and the presence of the thermal Hall effect characterized by the Righi--Leduc coefficient. The transition from a degenerate to non-degenerate regime is characterized by a minimum ratio of thermal conductivity to temperature, which is analogous to the minimum observed already in the case of electrical conductivity. We provide also formulas fit to our numerical results, which can be used in dissipative magneto-hydrodynamics simulations of warm compact stars.