Electrical conductivity of a warm neutron star crust in magnetic fields

Abstract

We study the electrical conductivity of finite-temperature crust of a warm compact star which may be formed in the aftermath of a supernova explosion or a binary neutron star merger as well as when a cold neutron star is heated by accretion of material from a companion. We focus on the temperature-density regime where plasma is in the liquid state and, therefore, the conductivity is dominated by the electron scattering off correlated nuclei. The dynamical screening of this interaction is implemented in terms of the polarization tensor computed in the hard-thermal-loop effective field theory of QED plasma. The correlations of the background ionic component are accounted for via a structure factor derived from Monte Carlo simulations of one-component plasma. With this input we solve the Boltzmann kinetic equation in relaxation time approximation taking into account the anisotropy of transport due to the magnetic field. The electrical conductivity tensor is studied numerically as a function of temperature and density for carbon and iron nuclei as well as density-dependent composition of zero-temperature dense matter in weak equilibrium with electrons. We also provide accurate fit formulas to our numerical results as well as supplemental tables which can be used in dissipative magneto-hydrodynamics simulations of warm compact stars.