Long-term evolution of the force-free twisted magnetosphere of a magnetar

Abstract

We study the long-term quasi-steady evolution of the force-free magnetosphere of a magnetar coupled to its internal magnetic field. We find that magnetospheric currents can be maintained on long time-scales of the order of thousands of years. Meanwhile, the energy, helicity and twist stored in the magnetosphere all gradually increase over the course of this evolution, until a critical point is reached, beyond which a force-free magnetosphere cannot be constructed. At this point, some large-scale magnetospheric rearrangement, possibly resulting in an outburst or a flare, must occur, releasing a large fraction of the stored energy, helicity and twist. After that, the quasi-steady evolution should continue in a similar manner from the new initial conditions. The time-scale for reaching this critical point depends on the overall magnetic field strength and on the relative fraction of the toroidal field. The energy stored in the force-free magnetosphere is found to be up to ∼30 per cent larger than the corresponding vacuum energy. This implies that for a 1014 G field at the pole, the energy budget available for fast magnetospheric events is of the order of a few 1044 erg. The spin-down rate is estimated to increase by up to ∼60 per cent, since the dipole content in the magnetosphere is enhanced by the currents present there. A rough estimate of the braking index n reveals that it is systematically n < 3 for the most part of the evolution, consistent with actual measurements for pulsars and early estimates for several magnetars.