Magnetic field evolution in magnetar crusts through three-dimensional simulations.

Current models of magnetars require extremely strong magnetic fields to explain their observed quiescent and bursting emission, implying that the field strength within the star's outer crust is orders of magnitude larger than the dipole component inferred from spin-down measurements. This presents a serious challenge to theories of magnetic field generation in a proto-neutron star. Here, we present detailed modeling of the evolution of the magnetic field in the crust of a neutron star through 3D simulations. We find that, in the plausible scenario of equipartition of energy between global-scale poloidal and toroidal magnetic components, magnetic instabilities transfer energy to nonaxisymmetric, kilometer-sized magnetic features, in which the local field strength can greatly exceed that of the global-scale field. These intense small-scale magnetic features can induce high-energy bursts through local crust yielding, and the localized enhancement of Ohmic heating can power the star's persistent emission. Thus, the observed diversity in magnetar behavior can be explained with mixed poloidal-toroidal fields of comparable energies.

Hall attractor in axially symmetric magnetic fields in neutron star crusts.

We find an attractor for an axially symmetric magnetic field evolving under the Hall effect and subdominant Ohmic dissipation, resolving the question of the long-term fate of the magnetic field in neutron star crusts. The electron fluid is in isorotation, analogous to Ferraro's law, with its angular velocity being approximately proportional to the poloidal magnetic flux, Ω∝Ψ. This equilibrium is the long-term configuration of a magnetic field evolving because of the Hall effect and Ohmic dissipation. For an initial dipole-dominated field, the attractor consists mainly of a dipole and an octupole component accompanied by an energetically negligible quadrupole toroidal field. The field dissipates in a self-similar way: Although higher multipoles should decay faster, the toroidal field mediates transfer of energy into them from the lower ones, leading to an advection diffusion equilibrium and keeping the ratio of the poloidal multipoles almost constant. This has implications for the structure of the intermediate-age neutron stars, suggesting that their poloidal field should consist of a dipole and an octupole component accompanied by a very weak toroidal quadrupole. For initial conditions that have a higher multipole ℓ structure, the attractor consists mainly of ℓ and ℓ+2 poloidal components.