Rotating twisted magnetosphere of magnetars: approximate analytical solutions

Abstract: An approximate analytical solution for the rotating twisted magnetosphere of magnetars is presented. The poloidal flux is approximated by the self-similar twisted dipole field. The toroidal field is obtained by the minimum torque model. Under this approximation, it is found that: (1) The Y-point radius decreases with the increase of twist of the magnetic field. (2) The polar cap is larger for larger twist. (3) The particle outflow luminosity is larger for larger twist. (4) The maximum acceleration potential, pulse width of magnetar radio emission etc all increase with the twist. (5) For an untwisting magnetosphere, the physical properties general evolves towards that of the normal pulsars. The above findings are consistent with previous analytical and numerical results. The larger polar cap may corresponds to the hot spot during magnetar outburst. In general, a rotating twisted magnetosphere has larger open field line regions. The radio emission of magnetars and fast radio burst may both originates in the larger and evolving open field line regions of magnetars.