A new look at the dynamics of twisted accretion disks

The dynamic response of a thin, viscous accretion disk to twisting torques is reexamined, taking into consideration the earlier work of Bardeen and Patterson (1975). Several corrections are made to the earlier work, and a new version of the twist equations, consistent with the physical assumptions stated in it, is presented. The distortion disk is described in terms of Cartesian direction cosines, and the twist equations are transformed into a single, linear, complex equation. Formulas for the external twisting torques, which might be encountered in astrophysics, are derived, and it is shown that even with the driving torques the twist equation remains linear. Exact analytic solutions are found for the steady-state structure of a disk subject to Lense-Thirring torques by a nonaligned central Kerr black hole, and for the time-dependent problem of the structure of a slaved disk with its oscillating boundary conditions. The stability of disks against twisting modes is discussed, and it is shown that undriven disks and disks subject to time-independent driving torques are stable.