Electron conduction in magnetized neutron star envelopes

TL;DR

This paper derives practical formulas for calculating electrical and thermal conductivities, thermopower, and tensor components of degenerate electrons in magnetized neutron star envelopes, considering complex scattering effects and providing analytic fits for various conditions.

Contribution

It introduces new analytic expressions for electron transport coefficients in neutron star envelopes that incorporate detailed scattering mechanisms and magnetic field effects.

Findings

Calculated tensor components of conductivities and thermopower.

Provided analytic fitting formulas for relaxation times.

Computed transport coefficients across relevant neutron star conditions.

Abstract

Practical expressions are derived for evaluation of electrical and thermal conductivities and thermopower of degenerate electrons in the outer envelopes of neutron stars with magnetic fields. All tensor components of the kinetic coefficients are calculated (those related to conduction along and across magnetic field and to the Hall currents). The kinetic coefficients are presented as energy averages of expressions containing energy dependent effective relaxation times of two types, associated either with longitudinal or with transverse currents. The calculation is based on the effective scattering potential proposed in the previous paper (astro-ph/9903127), which describes the electron-ion and electron-phonon scattering, taking into account correlation effects in strongly coupled Coulomb liquid and multi-phonon scattering in Coulomb crystal, respectively. Analytic fitting formulae are devised for the effective relaxation times at arbitrary field strength. Basing on these results, we calculate the transport coefficients at various temperatures, densities, and magnetic fields pertinent to the neutron star envelopes.