d Axisymmetric force-free magnetosphere in the exterior of a neutron star

Magnetar magnetospheres gradually become twisted due to shearing by footpoint motion. The axisymmetric solutions for the force-free field with a power-law current model are calculated by taking into account general relativistic effects. Here we show how the magnetic energy and helicity are accumulated along a sequence of equilibria. In a strongly twisted case, a magnetic flux rope, in which a large amount of toroidal field is confined, detaches in the vicinity of the star. It is found that this kind of magnetic field-line structure is easily produced due to strong relativistic effects compared with the results in flat space-time. Although the structure is not inherent to the relativity, the confinement is possible even for a smaller power-law index. There is an upper bound on the energy and helicity stored in the magnetosphere. When the helicity is further accumulated, a catastrophic event such as a giant flare may occur.