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 th
e 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.
In this study, we examine the magnetic field evolution occurring in a neutron star crust. Beyond the elastic limit, the lattice ions are assumed to act as a plastic flow. The Ohmic dissipation, Hall drift, and bulk fluid velocity driven by the Lorent
z force are considered in our numerical simulation. A magnetically induced quadrupole deformation is observed in the crust during the evolution. Generally, the ellipticity decreases as the magnetic energy decreases. In a toroidal-field-dominated model, the sign of the ellipticity changes. Namely, the initial prolate shape tends to become oblate. This occurs because the toroidal component decays rapidly on a smaller timescale than the poloidal dipole component. We find that the magnetic dipole component does not change significantly on the Hall timescale of $sim 1$Myr for the considered simple initial models. Thus, a more complex initial model is required to study the fast decay of surface dipoles on the abovementioned timescale.
We examine the propagation of collisionless particles emitted from a spherical shell to infinity. The number distribution at infinity, calculated as a function of the polar angle, exhibits a small deviation from uniformity. The number of particles mo
ving from the polar region toward the equatorial plane is slightly larger than that of particles in the opposite direction, for an emission radius $ > 4.5M$ in extreme Kerr space-time. This means that the black hole spin exerts an anti-collimation effect on the particles stream propagating along the rotation axis. We also confirm this property in the weak field limit. The quadrupole moment of the central object produces a force toward the equatorial plane. For a smaller emission radius $r<4.5M$, the absorption of particles into the black hole, the non-uniformity and/or the anisotropy of the emission distribution become much more important.
Nonlinear growth of the bar-mode deformation is studied for a differentially rotating star with supercritical rotational energy. In particular, the growth mechanism of some azimuthal modes with odd wave numbers is examined by comparing a simplified m
athematical model with a realistic simulation. Mode coupling to even modes, i.e., the bar mode and higher harmonics, significantly enhances the amplitudes of odd modes, unless they are exactly zero initially. Therefore, other modes which are not axially symmetric cannot be neglected at late times in the growth of the unstable bar-mode even when starting from an almost axially symmetric state.
We investigate the nonlinear behaviour of the dynamically unstable rotating star for the bar mode by three-dimensional hydrodynamics in Newtonian gravity. We find that an oscillation along the rotation axis is induced throughout the growth of the uns
table bar mode, and that its characteristic frequency is twice as that of the bar mode, which oscillates mainly along the equatorial plane. A possibility to observe Faraday resonance in gravitational waves is demonstrated and discussed.
