2014MNRAS.441.1408T

Accretion discs are present around both stellar-mass black holes in X-ray binaries and supermassive black holes in active galactic nuclei. A wide variety of circumstantial evidence implies that many of these discs are warped. The standard Bardeen-Petterson model attributes the shape of the warp to the competition between Lense-Thirring torque from the central black hole and viscous angular-momentum transport within the disc. We show that this description is incomplete in many accretion discs, and that torques from the companion star (for X-ray binaries) or the self-gravity of the disc (for active galactic nuclei) can play a major role in determining the properties of the warped disc. Including these effects leads to a rich set of new phenomena. For example, (i) when a companion star is present and the warp arises from a misalignment between the companion's orbital axis and the black hole's spin axis, there is no steady-state solution of the Pringle-Ogilvie equations for a warped disc when the viscosity falls below a critical value, which typically requires a disc aspect ratio ≲ 10^–3 in X-ray binaries; (ii) in AGN accretion discs, the warp can excite short-wavelength bending waves governed by the self-gravity of the disc, which propagate inwards with growing amplitude until they are damped by the disc viscosity. We show that both phenomena can occur for plausible values of the black hole and disc parameters, and briefly discuss their observational implications.