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Magnetic field sustained by the elastic force in neutron star crusts

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 $> 10^{46}$ erg can be stored in the crust, even for a normal surface dipole-field-strength ($<10^{13}$ G). The magnetic energy much exceeds the elastic energy ($ 10^{44} -10^{45}$ 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.