2022ApJ...938...91K

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 ∼10¹⁵ G; however, it exceeds 1 Myr for normal radio pulsars. The elastic energy stored in the crust before the fracture ranges from 10⁴¹ to 10⁴⁵ erg, depending on the spatial-energy distribution. Generally, a large amount of energy is deposited in a deep crust. The energy released at a fracture is typically ∼10⁴¹ 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.