The time-dependence of non-planar accretion discs

Abstract

The time dependence of a viscous, tilted accretion disk, such as projected for some binaries, undergoing external torques is investigated analytically. Full hydrodynamic equations are employed, with consideration given to the conservation of angular momentum. An equation linearized in terms of small tilt angle of the disk is obtained, and limiting conditions on the validity of the formulation are defined. The equation of state for the disk is assumed to be barotropic to eliminate shear forces on the disk in the z-direction. It is shown that derivation of a simple diffusion equation for the tilt angle relies on the viscosity parameter of the disk being greater than the opening angle of the disk. The approach presented is only valid in these conditions, or consideration must be given to the proper dynamical modes of the disk.