PREPRINT
7E7E1614-9D81-451F-B959-6E405EC5D9E5

# Accumulation of elastic strain toward crustal fracture in magnetized neutron stars

Yasufumi Kojima

Submitted on 9 September 2022

## 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.

## Preprint

Comment: 14 pages, 5 figures

Subjects: Astrophysics - High Energy Astrophysical Phenomena; General Relativity and Quantum Cosmology