Effect of magnetized phonons on electrical and thermal conductivity of neutron star crust

TL;DR

This paper investigates how strong magnetic fields modify phonon spectra in neutron star crusts, significantly increasing electrical and thermal resistivities at certain temperatures, which impacts neutron star thermal evolution models.

Contribution

It introduces a detailed analysis of magnetized phonon effects on conductivity in neutron star crusts, including numerical methods and the impact of soft phonon modes.

Findings

Electrical and thermal resistivities increase at low temperatures due to soft phonon modes.

Magnetic field modifies phonon spectrum, facilitating easier excitation of certain phonons.

Results are relevant for modeling neutron star magneto-thermal evolution.

Abstract

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 three-dimensional 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 $T \lesssim 0.1 T_{\rm p}$ ($T_{\rm p}$ is the ion plasma temperature) in a wide range of chemical compositions and mass densities of matter even for moderately magnetized crystals $\omega_{\rm B} \sim \omega_{\rm p}$ ($\omega_{\rm B}$ and $\omega_{\rm p}$ are the ion cyclotron and plasma frequencies). This effect is due to an appearance of a soft ($\omega \propto k^2$) 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.