Magnetic energy stored in relativistic force-free magnetosphere

A magnetar is one of variable sources, whose activity is supplied by huge magnetic energy. Magnetar magnetosphere is gradually twisted due to shearing motion at the surface. At the same time, the energy is stored there. When it exceeds a threshold, the energy is abruptly released on a dynamical timescale as observed in energetic flares. Here, static and axially symmetric force-free magnetospheres are calculated in the exterior of non-rotating relativistic star. The magnetic energy increases along a sequence characterized by the twist degree. In a highly twisted case, a magnetic flux rope, in which large amount of toroidal field is confined, is detached in vicinity of the star. It is found that larger amount of energy is capable to be stored in the relativistic magnetosphere. In an extreme case, the magnetic energy in presence of current flow increases up to a few times larger than that of current-free dipole. There is an upper limit in any model, and a catastrophic event like a giant flare would occur, when the field is further twisted.