Electronic screening and damping in magnetars

TL;DR

This paper investigates how strong magnetic fields in magnetars influence electron screening of ion interactions, revealing anisotropic effects, long-range oscillations, and implications for crust structure and heat transport.

Contribution

It provides the first detailed calculation of electron screening and damping effects in magnetar crusts under intense magnetic fields, highlighting anisotropic and long-range phenomena.

Findings

Screening length can be smaller than inter-ion spacing in magnetar crusts.

Screened potential exhibits Friedel oscillations parallel to magnetic field.

Damping of lattice phonons is highly anisotropic, affecting heat transport.

Abstract

We calculate the screening of the ion-ion potential due to electrons in the presence of a large background magnetic field, at densities of relevance to neutron star crusts. Using the standard approach to incorporate electron screening through the one-loop polarization function, we show that the magnetic field produces important corrections both at short and long distances. In extreme fields, realized in highly magnetized neutron stars called magnetars, electrons occupy only the lowest Landau levels in the relatively low density region of the crust. Here our results show that the screening length for Coulomb interactions between ions can be smaller than the inter-ion spacing. More interestingly, we find that the screening is anisotropic and the screened potential between two static charges exhibits long range Friedel oscillations parallel to the magnetic field. This long-range oscillatory behavior is likely to affect the lattice structure of ions, and can possibly create rod-like structures in the magnetar crusts. We also calculate the imaginary part of the electron polarization function which determines the spectrum of electron-hole excitations and plays a role in damping lattice phonon excitations. We demonstrate that even for modest magnetic fields this damping is highly anisotropic and will likely lead to anisotropic phonon heat transport in the outer neutron star crust.