# Magnetic-field evolution in a plastically-failing neutron-star crust

## TL;DR

This paper models the plastic failure and magnetic-field evolution in neutron-star crusts, revealing surface motions and magnetic field weakening, with implications for understanding magnetar activity.

## Contribution

It introduces a coupled model of plastic flow and magnetic evolution in neutron-star crusts, highlighting the role of plasticity in magnetic stress release and surface motion.

## Key findings

- Surface motions of 10-100 cm/year occur after crust yields.
- Plastic flow viscosity must be around 10^{36}-10^{37} g cm^{-1}s^{-1}.
- Localized magnetic fields are weaker with plastic flow than without.

## Abstract

Under normal conditions in a neutron-star crust, ions are locked in place in the crustal lattice and only electrons are mobile, and magnetic-field evolution is thus directly related to the electron velocity. The evolution, however, builds magnetic stresses that can become sufficiently large for the crust to exceed its elastic limit, and to flow plastically. We consider the nature of this plastic flow and the back-reaction on the crustal magnetic field evolution. We formulate a plane-parallel model for the local failure, showing that surface motions are inevitable once the crust yields, in the absence of extra dissipative mechanisms. We perform numerical evolutions of the crustal magnetic field under the joint effect of Hall drift and Ohmic decay, tracking the build-up of magnetic stresses, and diagnosing crustal failure with the von Mises criterion. Beyond this point we solve for the coupled evolution of the plastic velocity and magnetic field. Our results suggest that to have a coexistence of a magnetar corona with small-scale magnetic features, the viscosity of the plastic flow must be roughly $10^{36}-10^{37}\ \textrm{g cm}^{-1}\textrm{s}^{-1}$. We find significant motion at the surface at a rate of $10-100$ centimetres per year, and that the localised magnetic field is weaker than in evolutions without plastic flow. We discuss astrophysical implications, and how our local simulations could be used to build a global model of field evolution in the neutron-star crust.