Magnetohydrodynamic stability of magnetars in the ultrastrong field regime II: The crust

TL;DR

This paper investigates the stability of magnetar crusts under ultrastrong magnetic fields, revealing a field-dependent instability driven by Landau quantization effects that influences magnetic evolution and thermal processes.

Contribution

It introduces a new instability mechanism in magnetar crusts caused by Landau quantization, with implications for magnetic field evolution and thermal modeling.

Findings

Instability growth time is less than 1000 years.

High temperatures can suppress the instability.

Ohmic heating from the instability is insufficient to explain surface temperatures.

Abstract

We study the stability of Hall MHD with strong magnetic fields in which Landau quantization of electrons is important. We find that the strong-field Hall modes can be destabilized by the dependence of the differential magnetic susceptibility on magnetic field strength. This instability is studied using linear perturbation theory, and is found to have typical growth time of order $\lesssim 10^3$ yrs, with the growth time decreasing as a function of wavelength of the perturbation. The instability is self-limiting, turning off following a period of local field growth by a few percent of the initial value. Finite temperature is also shown to limit the instability, with sufficiently high temperatures eliminating it altogether. Alfv\'{e}n waves can show similar unstable behaviour on shorter timescales. We find that Ohmic heating due to the large fields developed via the instability and magnetic domain formation is not large enough to account for observed magnetar surface temperatures. However, Ohmic heating is enhanced by the oscillatory differential magnetic susceptibility of Landau-quantized electrons, which could be important to magneto-thermal simulations of neutron star crusts.