Abstract:
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, 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 thin warped disc when the viscosity falls below a critical value; (ii) in AGN accretion discs, the warp can excite short-wavelength bending waves that propagate inward 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.

Abstract:
Warped, precessing accretion discs appear in a range of astrophysical systems, for instance the X-ray binary Her X-1 and in the active nucleus of NGC4258. In a warped accretion disc there are horizontal pressure gradients that drive an epicyclic motion. We have studied the interaction of this epicyclic motion with the magnetohydrodynamic turbulence in numerical simulations. We find that the turbulent stress acting on the epicyclic motion is comparable in size to the stress that drives the accretion, however an important ingredient in the damping of the epicyclic motion is its parametric decay into inertial waves.

Abstract:
Warped accretion discs in Active Galactic Nuclei (AGN) exert a torque on the black hole that tends to align the rotation axis with the angular momentum of the outer disc. We compute the magnitude of this torque by solving numerically for the steady state shape of the warped disc, and verify that the analytic solution of Scheuer and Feiler (1996) provides an excellent approximation. We generalise these results for discs with strong warps and arbitrary surface density profiles, and calculate the timescale on which the black hole becomes aligned with the angular momentum in the outer disc. For massive holes and accretion rates of the order of the Eddington limit the alignment timescale is always short (less than a Myr), so that jets accelerated from the inner disc region provide a prompt tracer of the angular momentum of gas at large radii in the disc. Longer timescales are predicted for low luminosity systems, depending on the degree of anisotropy in the disc's hydrodynamic response to shear and warp, and for the final decay of modest warps at large radii in the disc that are potentially observable via VLBI. We discuss the implications of this for the inferred accretion history of those Active Galactic Nuclei whose jet directions appear to be stable over long timescales. The large energy deposition rate at modest disc radii during rapid realignment episodes should make such objects transiently bright at optical and infrared wavelengths.

Abstract:
We study the radiation-driven warping of accretion discs in the context of X-ray binaries. The latest evolutionary equations are adopted, which extend the classical alpha theory to time-dependent thin discs with non-linear warps. We also develop accurate, analytical expressions for the tidal torque and the radiation torque, including self-shadowing. We investigate the possible non-linear dynamics of the system within the framework of bifurcation theory. First, we re-examine the stability of an initially flat disc to the Pringle instability. Then we compute directly the branches of non-linear solutions representing steadily precessing discs. Finally, we determine the stability of the non-linear solutions. Each problem involves only ordinary differential equations, allowing a rapid, accurate and well resolved solution. We find that radiation-driven warping is probably not a common occurrence in low-mass X-ray binaries. We also find that stable, steadily precessing discs exist for a narrow range of parameters close to the stability limit. This could explain why so few systems show clear, repeatable `super-orbital' variations. The best examples of such systems, Her X-1, SS 433 and LMC X-4, all lie close to the stability limit for a reasonable choice of parameters. Systems far from the stability limit, including Cyg X-2, Cen X-3 and SMC X-1, probably experience quasi-periodic or chaotic variability as first noticed by Wijers & Pringle. We show that radiation-driven warping provides a coherent and persuasive framework but that it does not provide a generic explanation for the long-term variabilities in all X-ray binaries.

Abstract:
The non-linear fluid dynamics of a warped accretion disc was investigated in an earlier paper by developing a theory of fully non-linear bending waves in a thin, viscous disc. That analysis is here extended to take proper account of thermal and radiative effects by solving an energy equation that includes viscous dissipation and radiative transport. The problem is reduced to simple one-dimensional evolutionary equations for mass and angular momentum, expressed in physical units and suitable for direct application. This result constitutes a logical generalization of the alpha theory of Shakura & Sunyaev to the case of a time-dependent warped accretion disc. The local thermal-viscous stability of such a disc is also investigated.

Abstract:
Standard, planar accretion discs operate through a dissipative mechanism, usually thought to be turbulent, and often modelled as a viscosity. This acts to take energy from the radial shear, enabling the flow of mass and angular momentum in the radial direction. In a previous paper we discussed observational evidence for the magnitude of this viscosity, and pointed out discrepancies between these values and those obtained in numerical simulations. In this paper we discuss the observational evidence for the magnitude of the dissipative effects which act in non--planar discs, both to transfer and to eliminate the non--planarity. Estimates based on the model by Ogilvie (1999), which assumes a small--scale, isotropic viscosity, give alignment timescales for fully ionized discs which are apparently too short by a factor of a few compared with observations, although we emphasize that more detailed computations as well as tighter observational constraints are required to verify this conclusion. For discs with low temperature and conductivity, we find that the timescales for disc alignment based on isotropic viscosity are too short by around two orders of magnitude. This large discrepancy suggests that our understanding of viscosity in quiescent discs is currently inadequate.

Abstract:
Flourescent iron line profiles currently provide the best diagnostic for active galactic nuclei (AGN) engine geometries. Here we construct a method for calculating the relativistic iron line profile from an arbitrarily warped accretion disc, illuminated from above and below by hard X-ray sources. This substantially generalises previous calculations of reprocessing by accretion discs by including non-axisymmetric effects. We include a relativistic treatment of shadowing by ray-tracing photon paths along Schwarzchild geodesics. We apply this method to two classes of warped discs, and generate a selection of resulting line profiles. New profile features include the possibility of sharper red, and softer blue fall-offs, a time varying line profile if the warp precesses about the disc, and some differences between `twisted' and `twist-free' warps. We discuss some qualitative implications of the line profiles in the context of Type I and II Seyfert AGN.

Abstract:
Precessing accretion discs have long been suggested as explanations for the long periods observed in a variety of X-ray binaries, most notably Her X-1/HZ Her. We show that an instability of the disc's response to the radiation reaction force from the illumination by the central source can cause the disc to tilt out of the orbital plane and precess in something like the required manner. The rate of precession and disc tilt obtained for realistic values of system parameters compare favourably with the known body of data on X-ray binaries with long periods. We explore other possible types of behaviour than steadily precessing discs that might be observable in systems with somewhat different parameters. At high luminosities, the inner disc tilts through more than 90 degrees, i.e. it rotates counter to the usual direction, which may explain the torque reversals in systems such as 4U 1626-67.

Abstract:
The broad Balmer emission-line profiles resulting from the reprocessing of UV/X-ray radiation from a warped accretion disc induced by the Bardeen-Petterson effect are studied. We adopt a thin warped disc geometry and a central ring-like illuminating source in our model. We compute the steady-state shape of the warped disc numerically, and then use it in the calculation of the line profile. We find that, from the outer radius to the inner radius of the disc, the warp is twisted by an angle of $\sim\pi$ before being flattened efficiently into the equatorial plane. The profiles obtained depend weakly on the illuminating source radius in the range from $3r_{g}$ to $10r_g$, but depend strongly on this radius when it approaches the marginally stable orbit of an extreme Kerr black hole. Double- or triplet-peaked line profiles are present in most cases when the illuminating source radius is low. The triplet-peaked line profiles observed from the Sloan Digital Sky Survey may be a {"}signature" of a warped disc.

Abstract:
We aim to examine the detailed disc structure that arises in a misaligned binary system as a function of the disc aspect ratio h, viscosity parameter alpha, disc outer radius R, and binary inclination angle gamma_F. We also aim to examine the conditions that lead to an inclined disc being disrupted by strong differential precession. We use a grid-based hydrodynamic code to perform 3D simulations. This code has a relatively low numerical viscosity compared with the SPH schemes that have been used previously to study inclined discs. This allows the influence of viscosity on the disc evolution to be tightly controlled. We find that for thick discs (h=0.05) with low alpha, efficient warp communication in the discs allows them to precess as rigid bodies with very little warping or twisting. Such discs are observed to align with the binary orbit plane on the viscous evolution time. Thinner discs with higher viscosity, in which warp communication is less efficient, develop significant twists before achieving a state of rigid-body precession. Under the most extreme conditions we consider (h=0.01, alpha=0.005 and alpha=0.1), we find that discs can become broken or disrupted by strong differential precession. Discs that become highly twisted are observed to align with the binary orbit plane on timescales much shorter than the viscous timescale, possibly on the precession time. We find agreement with previous studies that show that thick discs with low viscosity experience mild warping and precess rigidly. We also find that as h is decreased substantially, discs may be disrupted by strong differential precession, but for disc thicknesses that are significantly less (h=0.01) than those found in previous studies (h=0.03).