The transport of angular momentum is the central issue in accretion disk dynamics. We review recent three-dimensional simulations that investigate possible transport mechanisms. Purely hydrodynamic local instabilities and turbulence are ruled out; global spiral waves remain a possibility. MHD turbulence, arising from a local MHD instability, has been shown effective in transporting angular momentum at dynamically important rates. These results establish the basic picture of accretion disk transport.

We review those processes associated with accretion discs that are probably influenced by magnetic fields, specifically, accretiondisc viscosity, energy dissipation and jet formation. We consider how magnetic instabilities in the disc can lead to a self-sustaining dynamical dynamo and how this is manifested as magnetohydrodynamic turbulence in numerical simulations. We show that currently these models do not fit with observational constraints imposed by dwarf-nova outbursts. We also show that the drop in ionisation fraction does not lead to the apparently necessary drop in viscosity in quiescent cataclysmic variable discs. Large-scale magnetic fields are required to launch and collimate jets form discs. We describe an inverse cascade process that can construct sufficient large-scale field from small-scale field generated by a dynamo.

A magnetic alternative to the standard viscous accretion disc is presented. The magnetic field is generated and maintained in the disc by a dynamo mechanism. Magnetic stresses dominate in the advection of angular momentum, and only weak turbulence is needed to generate the required field.

Magnetized objects surrounded by a turbulent and keplerian accretion disk are considered. In such systems, magnetic field lines are embedded into the disk. The magnetic field of the central object is assumed to be dipolar in the absence of the accretion disk. In the presence of a turbulent accretion disk, it is shown that the interaction with the disk stretches magnetic field lines along the disk and that most of the non-magnetospheric magnetic flux is expelled outside the disk.

The shearing box has rapidly become the accepted way to investigate turbulence in Keplerian shear flows. In this paper we discuss to what extent and in which way the outcome of the shearing box is affected by the adopted boundary conditions, and how the shearing box can be modified to capture more of the physics of an accretion disc. The original shearing box model is too symmetric to generate a net accretion flow, but the symmetry can be broken by including the main effects of the cylindrical geometry of the real disc. However the quantitative change in the resulting angular momentum transport is small.

I investigate the hydrodynamics of three-dimensional Bondi-Hoyle-Lyttleton accretion including velocity and density gradients in the incoming flow and determine how much angular momentum is accreted. A medium taken to be an ideal gas with an adiabatic index of 5/3 or 4/3 moves at supersonic speeds (Mach 3 and 10) past a totally absorbing sphere with a radius of 0.1 or 0.02 accretion radii. The velocity within the medium is given a gradient of 3% or 20% (over one accretion radius). I find that a substantial amount (0.1 to 0.7) of the specific angular momentum available within one accretion radius in the upstream flow actually is accreted. The amount is smaller for smaller accretor sizes. The flow is roughly just as unstable as in the previous models without gradients. The unstable flow is best seen in animated sequences.

I consider the angular momentum balance in binaries where the accretor has a significant magnetic field. The ejector AE Aqr provides a counterexample to most simple ideas. In particular it shows that the criterion for disc formation must involve the spin rate of the accretor, and that this rate may be subject to cycles, rather than settling to an equilibrium characterized by the magnetic fieldstrength. Angular momentum loss via magnetized disc winds can never be strong enough to affect the binary evolution significantly, but spinup of the accretor can have a marked effect. Although there is strong spin-orbit coupling in the AM Her systems, this cannot produce the orbital expansion needed to explain the low accretion rate states of these systems. Instead a mechanism intrinsic to the secondary star (such as starspots) probably interrupts mass transfer in all short-period CVs: the results are seen directly in AM Her systems, but masked by the presence of an accretion disc in most other cases.

The boundary layer region, where the accretion disk meets the accreting star, is crucial to understanding the spectra and evolution of accretion disk systems. Recent numerical modeling of the flow of the accreting material and radiation in the boundary layer has provided a better understanding of this region. I will describe the “standard” boundary layer structure predicted by the models for the case where the boundary layer is optically thick and geometrically thin in the vertical direction. Large variations in this structure can occur when the boundary layer becomes optically thin or geometrically thick. Boundary layer models have been applied to cataclysmic variables and accreting pre-main-sequence stars. I will discuss the boundary layer spectra predicted by the models and how well they agree with observations of these objects. The boundary layer also controls the transfer of angular momentum and energy between the disk and star. This can have important effects upon pre-main-sequence stellar evolution.

We study two magnetised accretion – outflow problems: the slow rotator and the propeller. In the former case, we show that the funnel flow does not result in the accretion of a significant amount of matter angular momentum, contrary to what is assumed in the standard Ghosh and Lamb model. Implications of this finding are investigated, particularly in relation to the fastness parameter. We also argue that magnetospheric mass ejection (the magnetospheric streamer model) is a viable mechanism for the ejection of mass and angular momentum from a magnetic star-disc system in the propeller regime.

Properties of the quasi-coherent oscillations in the extreme ultraviolet flux of the dwarf nova SS Cygni are described.

X-ray pulsars are the only accreting magnetic stars where rotation torques induced by accretion are large enough to be measured on short timescales ~ days. They are thus unique laboratories for studying the interaction between an accretion disk and a stellar magnetosphere. We describe 5 years of continuous pulsar timing observations by the BATSE instrument on GRO which paint a strikingly different picture of pulsar spin behavior than understood from the previous 20 years of sparse observations. In particular, we find that more than half of the persistent pulsars we observe undergo dramatic torque reversals, switching suddenly between extended periods of steady spin-up and steady spin-down. Moreover, variations in pulsed flux are anticorrelated with torque in at least one system undergoing secular spin-down, GX1+4. This behavior contradicts standard accretion torque theory (Ghosh and Lamb 1979). A simple – albeit unconventional – hypothesis which naturally explains these observations is that the disks in these systems somehow alternate between epochs of prograde and retrograde rotation.

Instabilities of accretion disks in cataclysmic variable stars are reviewed in relation to dwarf nova outbursts. Two different kinds of instabilities of accretion disks are now known: the thermal instability and the tidal instability. The thermal instability is produced by hydrogen ionization-recombination transition, which gives rises to a thermal limit-cycle oscillation in accretion disks and it is thought to be responsible for outbursts of U Gem-type dwarf novae. The tidal instability is produced by the tidal effects of the secondary star on accretion disks, by which the disk is deformed to eccentric form and it slowly precesses in the inertial frame of reference. The tidal instability is thought to be responsible for the superhump phenomenon observed during superoutbursts of SU UMa-type dwarf novae. There is a rich variety in outburst behaviors of non-magnetic cataclysmic variables, starting from non-outbursting nova-like stars to various sub-classes of dwarf novae. A unification model for dwarf nova outbursts is then proposed based on these two instabilities. In this model, the non-magnetic cataclysmic variables are classified in the orbital-period versus mass-transfer-rate diagram into four regions depending on different combination to these two instabilities, and their observed outburst behaviors are basically understood on this diagram.

We present a model for the dwarf nova WZ Sge which does not imply an unusually – and unexplained – low value of the viscosity during low states. We propose that the inner parts of the accretion disc are disrupted by either a magnetic field or evaporation, so that the disc is stable (or very close to being stable) in quiescence, as the mass transfer rate is very low, and the disc can sit on the cool, lower branch of the thermal equilibrium curve. Outbursts are triggered by an increase of mass transfer, causing a standard disc instability, and are strongly enhanced by illumination effects. Both the recurrence time, and the characteristics of the light curve in outburst can be accounted for.

The mass transfer process in low mass close binaries is reviewed. The driving mechanisms and the stability properties are discussed by means of general, simple formulations. A model in terms of mass transfer instabilities is suggested to explain the outbursts of GRO J1655–40 in 1994.

GRO J1744–28 is the first known X-ray source to display both bursts and periodic pulsations. This source may thus provide crucial clues that will lead to an understanding of the differences in the nature of the X-ray variability among accreting neutron stars. We deduce that the magnetic field of the neutron star is relatively weak (~ 8 × 1010 G) but, nevertheless, sufficiently strong to funnel the accretion flow onto the magnetic polar caps and suppress the thermonuclear flashes that would otherwise give rise to type I X-ray bursts. We also present a series of interrelated arguments which demonstrate that the observed bursts are of type II and probably result from an instability associated with the interaction of the neutron-star magnetic field with the inner edge of the accretion disk. From these results, we infer that X-ray pulsars, GRO J1744–28, the Rapid Burster, and the type I X-ray bursters may form a sequence of possible behaviors among accreting neutron stars, with the strength of the magnetic field serving as the crucial parameter that determines the mode of X-ray variability. The companion star in the GRO J1744–28 binary system is probably a very low-mass (~ 0.2 M⊙) giant that is in the final stages of losing its hydrogen-rich envelope. We have carried out binary evolution calculations which show that (1) if the mass of the giant was ~ 1 M⊙ when mass transfer onto the neutron star commenced, then the orbital period and the core mass of the giant have increased from ~ 1 to ~ 11.8 days and from ~ 0.15 to ~ 0.21 M⊙, respectively, during the mass-transfer epoch, which has lasted for ~ 8 × 108 yr, (2) the present long-term average X-ray luminosity is ~ 4 × 1036 ergs s−1, which is at least two orders of magnitude lower than the luminosity at the peak of the transient outburst, and (3) the predicted long-term equilibrium rotation rate of the neutron star is remarkably close to the observed pulse rate. The transient nature of GRO J1744–28 may well be related to the final stages of dissipation of the envelope of the giant companion.

We will summarize results of relativistic calculations of the eigenfunctions and eigenfrequencies of modes of oscillation trapped within the inner region of thin accretion disks by non-Newtonian gravitational properties of a black hole (or a compact, weakly-magnetized neutron star). The focus will be on the most observable, robust, and best-studied class: the analogue of (internal) gravity modes in stars. The frequencies of the corresponding peaks in the power spectrum of the resulting luminosity modulations depend almost entirely upon only the mass and angular momentum of the black hole. The frequency width also depends upon the viscosity parameter of the disk. Searches for such features are being carried out by the RXTE satellite.

A geometrically thin, optically thick, warped accretion disk with a central source of luminosity is subject to non-axisymmetric forces due to radiation pressure; the resulting torque acts to modify the warp. Initially planar accretion disks are unstable to warping driven by radiation torque, as shown in a local analysis by Pringle (1996) and a global analysis of the stable and unstable modes by Maloney, Begelman, & Pringle (1996). In general, the warp also precesses.

We discuss the nature of this instability, and its possible implications for accretion disks in X-ray binaries and active galactic nuclei. Specifically, we argue that this effect provides a plausible explanation for the misalignment and precession of the accretion disks in X-ray binaries such as SS 433 and Her X–l; the same mechanism explains why the maser disk in NGC 4258 is warped.

Recent discoveries of planets around other stars suggest that planets are ubiquitous and their dynamical properties are diverse. We reviewed the formation mechanism for protoplanets and the post-formation planet-disk tidal interaction which may have led the short-period planets to their present configuration. We suggest that these planets may be the survivors of a populations of similar planets which have plunged into and contaminated the stellar convection zone. In the context of the solar system, the mass of the giant planets and the present distribution of the minor planets may be used to infer the structure and evolution for the primordial solar nebula. The large eccentricity of 70 Vir and HD 114762 may be due to cohesive collisions in planetary systems which become unstable during their long term orbital evolution.

Flickering is a phenomenon associated with all known accretion powered processes. Yet despite its energetic importance and universality, our understanding of flickering remains elementary. Only recently has the flickering itself become a topic of serious investigation. This paper briefly addresses two fundamental observational questions: “Where is the flickering coming from?” and “What is the spectrum of the flickering?”.

A two-dimensional time-dependent spectral code is used for the study of tidal effects in accretion discs. A cool disc around a white dwarf (characteristic of CV systems) is modeled under the assumption of a polytropic equation of state and a standard alpha viscosity prescription. For a mass ratio q < 0.1 (considered here) and under the assumption of a reflective inner boundary, tidal effects induce an eccentric (m=l azimuthal) mode in the disc together with an elliptic (m=2 azimuthal) mode in the inner disc.