The stability of a warped accretion disc

An accretion disk becomes warped when subjected to torque which is misaligned with the disk plane. Such torques may be caused by Lense-Thirring precession near a spinning compact object, or the quadrupole field of a binary star. Here the flow in an adiabatic warped disk is modeled as a two-dimensional shear layer with linear velocity profile and free surface boundary conditions, and is investigated by means of a linear stability analysis. The flow is found to be unstable whenever it contains a critical layer, i.e., a level at which the shear velocity is equal to the phase velocity. The instability occurs over a broad wavenumber range and has a typical dimensionless growth rate of about 0.1 for both the compressible and incompressible cases. These waves grow with a time-scale of about one orbital period, and are likely to have a major effect on the disk viscosity.