Torque Exerted on an Oblique Rotator by a Magnetically Threaded Accretion Disk

Abstract

Simple analytical expressions are derived for the torque exerted by an accretion disk on a star whose magnetic dipole axis is inclined to the rotation axis. Spin-down stresses are transmitted to the star by the field lines that penetrate the disk beyond the corotation radius R c. As the dipole inclination angle increases, the vertical magnetic flux through the disk decreases, and the spin-down contribution to the torque weakens. For inclinations exceeding some limiting value c in the range of approximately 54-67, the braking component is unable to offset the spin-up resulting from the accretion of matter, even when the inner radius of the Keplerian disk, R 0 , is located very close to R c , so that the fastness parameter (R 0 /R c) 3/2 approaches unity. Thus, for large tilt angles, there can be no steady equilibrium state in which the net torque on the accreting star vanishes, unless some of the material is simultaneously expelled by centrifugal forces or accumulates within the disk.