The Evolution of Viscous Inclined Disks in Axisymmetric and Triaxial Galaxies

We have used a set of equations developed by Pringle to follow the evolution of a viscous twisted disk in a galaxy-like potential that is stationary or tumbling relative to inertial space. In an axisymmetric potential, the disk settles to the equatorial plane at a rate largely determined by the coefficient ν2, associated with shear perpendicular to the local disk plane. If the disk is initially close to the galaxy equator, then the rate at which the inclination decays is well described by the analytic formula of Steiman-Cameron & Durisen; in a highly inclined disk, “breaking waves” of curvature steepen as they propagate through the disk, rendering the numerical treatment untrustworthy. In a triaxial potential that is stationary in inertial space, settling is faster than in an oblate or prolate galaxy, since the disk twists simultaneously about two perpendicular axes. If the figure of the potential tumbles about one of its principal axes, the viscous disk can settle into a warped state in which gas at each radius follows a stable tilted orbit, which precesses in such a way as to remain stationary relative to the underlying galaxy.