Accumulation of elastic strain toward crustal fracture in magnetized neutron stars

TL;DR

This paper models how magnetic field evolution in magnetized neutron-star crusts causes elastic strain accumulation, leading to crust fractures that release energy comparable to magnetar outbursts.

Contribution

It explicitly calculates the timescales, maximum elastic energy, and stress distribution for crust fractures due to magnetic evolution in neutron stars.

Findings

Breakup time is a few years for magnetars with ~10^{15} G fields.

Elastic energy stored ranges from 10^{41} to 10^{45} erg.

Fracture energy release is comparable to magnetar outbursts.

Abstract

This study investigates elastic deformation driven by the Hall drift in a magnetized neutron-star crust. Although the dynamic equilibrium initially holds without elastic displacement, the magnetic-field evolution changes the Lorentz force over a secular timescale, which inevitably causes the elastic deformation to settle in a new force balance. Accordingly, elastic energy is accumulated, and the crust is eventually fractured beyond a particular threshold. We assume that the magnetic field is axially symmetric, and we explicitly calculate the breakup time, maximum elastic energy stored in the crust, and spatial shear-stress distribution. For the barotropic equilibrium of a poloidal dipole field expelled from the interior core without a toroidal field, the breakup time corresponds to a few years for the magnetars with a magnetic field strength of $\sim 10^{15}$G; however, it exceeds 1 Myr for normal radio pulsars. The elastic energy stored in the crust before the fracture ranges from $10^{41}$ to $10^{45}$ erg, depending on the spatial-energy distribution. Generally, a large amount of energy is deposited in a deep crust. The energy released at fracture is typically $\sim 10^{41}$ erg when the rearrangement of elastic displacements occurs only in the fragile shallow crust. The amount of energy is comparable to the outburst energy on the magnetars.