Time evolution of relativistic force-free fields connecting a neutron star and its disk

We study the magnetic interaction between a neutron star and its disk by solving the time-dependent relativistic force-free equations. At the initial state, we assumed that the dipole magnetic field of the neutron star connects the neutron star and its equatorial disk, which deeply enters into the magnetosphere of the neutron star. Magnetic fields were assumed to be frozen to the star and the disk. The rotations of the neutron star and the disk were imposed as boundary conditions. We applied the Harten-Lax-van Leer (HLL) method to simulate the evolution of the star-disk system. We carried out simulations for (1) a disk inside the corotation radius, in which the disk rotates faster than the star, and (2) a disk outside the corotation radius, in which the neutron star rotates faster than the disk. The numerical results indicate that for both models, the magnetic field lines connecting the disk and the star inflate as they are twisted by the differential rotation between the disk and the star. When the twist angle exceeds pi radian, the magnetic field lines expand with a speed close to the speed of light. This mechanism can be the origin of the relativistic outflows observed in binaries containing a neutron star.