Untwisting magnetospheres of neutron stars

Magnetospheres of neutron stars are anchored in the rigid crust and can be twisted by sudden crustal motions ("starquakes"). The twisted magnetosphere does not remain static and gradually untwists, dissipating magnetic energy and producing radiation. The equation describing this evolution is derived, and its solutions are presented. Two distinct regions coexist in untwisting magnetospheres: a potential region where curl(B)=0 ("cavity") and a current-carrying bundle of field lines ("j-bundle"). The cavity has a sharp boundary, which expands with time and eventually erases all of the twist. In this process, the electric current of the j-bundle is sucked into the star. Observational appearance of the untwisting process is discussed. A hot spot forms at the footprints of the j-bundle. The spot shrinks with time toward the magnetic dipole axis, and its luminosity and temperature gradually decrease. As the j-bundle shrinks, the amplitude of its twist can grow to the maximum possible value ~ 1. The strong twist near the dipole axis increases the spindown rate of the star and can generate a broad beam of radio emission. The model explains the puzzling behavior of magnetar XTE J1810-197 -- a canonical example of magnetospheric evolution following a starquake. We also discuss implications for other magnetars. The untwisting theory suggests that the nonthermal radiation of magnetars is preferentially generated on a bundle of extended closed field lines near the dipole axis.