Disk accretion onto a magnetized star

An exact solution is found for the interaction of a rotating magnetic field that is frozen into a star with a thin, highly conducting accretion disk. The disk pushes the magnetic-field lines towards the star, compressing the stellar dipole magnetic field. At the corotation radius, where the Keplerian and stellar rotational frequencies are equal, a current loop appears. Electric currents flow in the magnetosphere only along two particular magnetic surfaces, which connect the corotation region and the inner edge of the disk with the stellar surface. It is shown that a closed current surface encloses the magnetosphere. The disk rotation is stopped at some distance from the stellar surface, equal to 0.55 of the corotation radius. The accretion from the disk spins up the stellar rotation. The angular momentum transferred to the star is determined.