Thermal and Electric Conductivities of Coulomb Crystals in Neutron Stars and White Dwarfs

Abstract

Thermal and electric conductivities are calculated for degenerate electrons scattered by phonons in a crystal made of atomic nuclei. The exact phonon spectrum and the Debye--Waller factor are taken into account. Monte Carlo calculations are performed for body-centered cubic (bcc) crystals made of C, O, Ne, Mg, Si, S, Ca, and Fe nuclei in the density range from $10^3$ to $10^{11}$ g cm$^{-3}$ at temperatures lower than the melting temperature but higher than the temperature at which the Umklapp processes begin to be "frozen out". A simplified method of calculation is proposed, which makes it possible to describe the results in terms of simple analytic expressions, to extend these expressions to any species of nucleus, and to consider face-centered cubic (fcc) crystals. The kinetic coefficients are shown to depend tangibly on the lattice type. The results are applicable to studies of heat transfer and evolution of the magnetic field in the cores of white dwarfs and in the crusts of neutron stars. The thermal drift of the magnetic field in the crust of a neutron star is discussed.