2016MNRAS.458.2840B

We study electrical and thermal conductivities of degenerate electrons emitting and absorbing phonons in a strongly magnetized crystalline neutron star crust. We take into account modification of the phonon spectrum of a Coulomb solid of ions caused by a strong magnetic field. Boltzmann transport equation is solved using a generalized variational method. The ensuing 3D integrals over the transferred momenta are evaluated by two different numerical techniques, the Monte Carlo method and a regular integration over the first Brillouin zone. The results of the two numerical approaches are shown to be in a good agreement. An appreciable growth of electrical and thermal resistivities is reported at quantum and intermediate temperatures T <= 0.1T_p (T_p is the ion plasma temperature) in a wide range of chemical compositions and mass densities of matter even for moderately magnetized crystals ω_B ∼ ω_p (ω_B and ω_p are the ion cyclotron and plasma frequencies). This effect is due to an appearance of a soft (ω ∝ k²) phonon mode in the magnetized ion Coulomb crystal, which turns out to be easier to excite than acoustic phonons characteristic of the field-free case. These results are important for modelling magneto-thermal evolution of neutron stars.