Magneto-elastic equilibrium of a neutron star crust

We examine the equilibrium of a magnetized neutron-star-crust. We calculate axially symmetric models in which an elastic force balances solenoidal motion driven by a Lorentz force. A large variety of equilibrium models are allowed by incorporating the elastic shear deformation; in addition, toroidal-magnetic-field dominated models are available. These results remarkably differ from those in barotropic fluid stars. We demonstrate some models wherein the magnetic energy exceeds the elastic energy. The excess comes from the fact that a large amount of magnetic energy is associated with the irrotational part of the magnetic force, which is balanced with gravity and pressure. It is sufficient for equilibrium models that the minor solenoidal part is balanced by a weak elastic force. We find that the elasticity in the crust plays an important role on the magnetic-field confinement. Further, we present the spatial distribution of the shear-stress at the elastic limit, by which the crust-fracture location can be identified. The result has useful implications for realistic crust-quake models.