Magnetic field sustained by the elastic force in neutron star crusts

Abstract

We investigate the magneto–elastic equilibrium of a neutron star crust and magnetic energy stored by the elastic force. The solenoidal motion driven by the Lorentz force can be controlled by the magnetic elastic force, so that conditions for the magnetic field strength and geometry are less restrictive. For equilibrium models, the minor solenoidal part of the magnetic force is balanced by a weak elastic force because the irrotational part is balanced by the dominant gravity and pressure forces. Therefore, a strong magnetic field may be confined in the interior, regardless of poloidal or toroidal components. We numerically calculated axially symmetric models with the maximum shear–strain, and found that a magnetic energy >1046 erg can be stored in the crust, even for a normal surface dipole-field-strength (<1013 G). The magnetic energy much exceeds the elastic energy (1044 − 1045 erg). The shear–stress spatial distribution revealed that the elastic structure is likely to break down near the surface. In particular, the critical position is highly localized at a depth less than 100 m from the surface.

Evolutionary Deformation toward the Elastic Limit by a Magnetic Field Confined in the Neutron-star Crust

“…where the radial functions x l and k l (l = 1, 3) are determined using Equations ( 24) and (25); (Kojima et al 2022):…”

“…The Lorentz force is comparable in magnitude to the elastic force in the crust. However, only static magneto-elastic equilibria of the crust have been studied thus far (Kojima et al 2021(Kojima et al , 2022Fujisawa et al 2023). These studies demonstrated that neutron-star models with strong magnetic fields are possible owing to the elasticity of the crust.…”

Accumulation of Elastic Strain toward Crustal Fracture in Magnetized Neutron Stars

“…The displacement ξ f is decoupled with respect to the index l, owing to spherical symmetry, i.e., μ(r). Equation ( 15) is reduced to a set of ordinary differential equations for k l (Kojima et al 2022):…”

“…In this study, we consider the crust in a magnetized neutron star. The static magneto-elastic force balance was studied for various magnetic-field configurations (Kojima et al 2021a(Kojima et al , 2022. A variety of magneto-elastic equilibria was demonstrated, and is considerably different from the barotropic equilibrium without a solid crust.…”

Evolutionary deformation toward the elastic limit by a magnetic field confined in the neutron--star crust

“…The Lorentz force is comparable in magnitude to the elastic force in the crust. However, only static magneto-elastic equilibria of the crust have been studied thus far (Kojima et al 2021(Kojima et al , 2022Fujisawa et al 2023). These studies demonstrated that neutron star models with strong magnetic fields are possible owing to the elasticity of the crust.…”