Transport In Accretion Discs Research Articles

Global Three‐dimensional Magnetohydrodynamic Simulations of Accretion Disks and the Surrounding Magnetosphere

We present the results of global three-dimensional numerical simulations of magnetized accretion disks which have been performed in order to study the evolution of an accretion disk and its surrounding corona within the framework of ideal magnetohydrodynamics. A self-consistent study of this coupled system is a necessary step toward gaining an understanding of both the production and structure of outflows and the angular momentum transport in accretion disks. We study model disks that are initially threaded by a uniform, homogenous magnetic field parallel to the rotational axis. The evolution of these disks is examined under the assumption of an adiabatic equation of state. When the disk is threaded with a weak initial magnetic field, we observe new, intrinsically three-dimensional nonaxisymmetric phenomena that do not occur in the two-dimensional axisymmetric approximation. Our three-dimensional simulations show that in the weak field case MHD waves are generated at the surface of the disk and subsequently propagate into the corona, possibly contributing to coronal heating. To investigate the nature and the origin of these waves, we have performed a series of exploratory simulations with different rotation profiles of the corona and different density relations between disk and corona, as well as simulations with a purely toroidal initial magnetic field. When the simulations are computed with a strong initial field, we find that there is very little difference between two-dimensional and three-dimensional evolution. In both the weak field and strong field cases, in agreement with previous two-dimensional simulations, the disk collapses on orbital timescales. Disk collapse arises from angular momentum transport by the Balbus-Hawley instability in the weak field case and by the external torque of an outflow in the strong field case. We observe the generation of winds in all our simulations. In the weak field case, these winds are unsteady, and they do not collimate within the time frame of the simulation.

Tidally-driven transport in accretion disks in close binary systems

The effects of binary tidal forces on transport within an accretion disk are studied with a time-dependent hydrodynamical model of a two-dimensional isothermal accretion disk. Tidal forces quickly truncate the accretion disk to radii of order half the average radius of the Roche lobe, and excite a two-armed spiral wave that remains stationary in the rotating reference frame of the binary system. We measure an effective α of order 0.1 near the outer edge of the disk in all of our models, independent of the mass ratio of the binary system, the Mach number of the orbital motion in the disk, and the radial density profile of the disk. The value of α drops with decreasing radius, implying that steady-state models (constant mass accretion rate at all radii) do not exist. In cold disks with high Mach number, the effective α drops so rapidly that it falls below our threshold of measurement (∼10 −3) at a radius of only one third the tidal radius. In warmer disks where the Mach numbers remain below 20, we can measure an effective α down to radii 10 times smaller than the maximum size of the disk.

Transport in accretion disks

Astrophysical accretion disks are powered by the release of gravitational potential energy as gas spirals down onto a compact star or black hole. The dynamics and evolution of accretion disks depend upon how angular momentum is transported outward from one fluid element to another. The nature of this process was unclear for many years. Since the early 1990s, however, considerable progress has been made in understanding how turbulence arises and transports angular momentum in astrophysical accretion disks. Accretion disks are generally highly conducting plasmas; the equations governing their evolution are those of ideal magnetohydrodynamics. Although a hydrodynamical disk would be locally stable, the combination of a weak subthermal magnetic field and outwardly decreasing differential rotation rapidly generates magnetohydrodynamical turbulence via a remarkably simple linear instability. Thus, turbulent accretion disks are fundamentally magnetohydrodynamical in nature.

Instability, turbulence, and enhanced transport in accretion disks

Recent years have witnessed dramatic progress in our understanding of how turbulence arises and transports angular momentum in astrophysical accretion disks. The key conceptual point has its origins in work dating from the 1950s, but its implications have been fully understood only in the last several years: the combination of a subthermal magnetic field (any nonpathological configuration will do) and outwardly decreasing differential rotation rapidly generates magnetohydrodynamic (MHD) turbulence via a remarkably simple linear instability. The result is a greatly enhanced effective viscosity, the origin of which had been a long-standing problem. The MHD nature of disk turbulence has linked two broad domains of magnetized fluid research: accretion theory and dynamos. The understanding that weak magnetic fields are not merely passively acted upon by turbulence, but actively generate it, means that the assumptions of classical dynamo theory break down in disks. Paralleling the new conceptual understanding has been the development of powerful numerical MHD codes. These have taught us that disks truly are turbulent, transporting angular momentum at greatly enhanced rates. We have also learned, however, that not all forms of disk turbulence do this. Purely hydrodynamic turbulence, when it is imposed, simply causes fluctuations without a significant increase in transport. The interplay between numerical simulation and analytic arguments has been particularly fruitful in accretion disk theory and is a major focus of this article. The authors conclude with a summary of what is now known of disk turbulence and mention some knotty outstanding questions (e.g., what is the physics behind nonlinear field saturation?) for which we may soon begin to develop answers.

Instability, Turbulence, and Enhanced Transport in Accretion Disks

AbstractThe nature of MHD and hydrodynamical turbulence in accretion disks is discussed. Comparison is made with planar Couette flow, a classical system prone to nonlinear shear instability resulting in enhanced turbulent transport. Both Keplerian and non-Keplerian hydrodynamical disks are studied, and it is found that only constant angular momentum disks are unstable to nonlinear disturbances and develop enhanced turbulent transport. Convective instabilities do not lead to enhanced turbulent transport. Hydrodynamical Keplerian disks are quite stable to nonlinear disturbances. Several lines of argument are presented which all lead to this conclusion, but the key to disk turbulence is the interaction between the stress tensor and the mean flow gradients. The nature of this coupling is found to determine completely the stability properties of disks (hydrodynamics and magnetic), and the nature of turbulent transport. The weak field MHD instability, which is of great astrophysical importance, displays the same type of stress tensor – mean flow coupling that all classical local shear instabilities exhibit. Hydrodynamical Keplerian disks, on the other hand, do not. Accretion disk turbulence is MHD turbulence.

Angular Momentum Transport in Accretion Disks via Convection

Angular Momentum Transport in Accretion Disks via Convection

Magnetohydrodynamic instabilities and turbulence in accretion disks

In this paper we review the possibilities for magnetohydrodynamic processes to handle the angular momentum transport in accretion disks. Traditionally the angular momentum transport has been considered to be the result of turbulent viscosity in the disk, although the Keplerian flow in accretion disks is linearly stable towards hydrodynamic perturbations. It is on the other hand linearly unstable to some magnetohydrodynamic (MHD) instabilities. The most important instabilities are the Parker and Balbus-Hawley instabilities that are related to the magnetic buoyancy and the shear flow, respectively. We discuss these instabilities not only in the traditional MHD framework, but also in the context of slender flux tubes, that reduce the complexity of the problem while keeping most of the stability properties of the complete problem. In the non-linear regime the instabilities produce turbulence. Recent numerical simulations describe the generation of magnetic fields by a dynamo in the resulting turbulent flow. Eventually such a dynamo may generate a global magnetic field in the disk. The relation of the MHD-turbulence to observations of accretion disks is still obscure. It is commonly believed that magnetic fields can be highly efficient in transporting the angular momentum, but emission lines, short-time scale variability and non-thermal radiation, which a stellar astronomer would take as signs of magnetic variability, are more commonly observed during periods of low accretion rates.

Keplerian Complexity: Numerical Simulations of Accretion Disk Transport

Supercomputer simulations have been used in conjunction with analytic studies to investigate the central issue of astrophysical accretion-disk dynamics: the nature of the angular momentum transport. Simulations provide the means to investigate and experiment with candidate mechanisms, including global hydrodynamic instabilities, spiral shock waves, and local magnetohydrodynamic (MHD) instabilities. Simulations have demonstrated that accretion disks are generally MHD turbulent. These results suggest that the fundamental physical mechanism for angular momentum transport in accretion disks has now been identified.

Dynamics of the magnetic shearing instability and magnetohydrodynamic turbulence in accretion disks. 1: Vertical magnetic field

Recently, the magnetic shearing instability (MSI) has been proposed as a dynamical mechanism for angular momentum transport in accretion disks (Balbus & Hawley 1991; Hawley & Balbus 1991). In this paper, the nonlinear dynamics of MSI modes in the presence of a vertical magnetic field B(sub 0) is discussed. In particular, the saturation levels of the fluctuating fields, the angular momentum flux, and the energy dissipation mechanism, are examined in detail. It is shown that MSI induces strong magnetohydrodynamic (MHD) turbulence in a range of wavenumbers 1/H is less than K is less than or equal to Omega/V(sub A)(sub 0)), where H is the thickness, Omega is the rotation frequency of the disk, and V(sub A)(sub 0) is the Alfven velocity. Despite the fact that the linear growth rate of MSI is maximal at small-scale (i.e., k is approximately Omega/V(sub A(sub 0)), angular momentum transport due to MSI turbulence is dominated by the magnetic Reynolds stress driven by large-scale modes (k is approximately 1/H). It is shown that the amplitude of low k(sub r) MSI eddies is limited primarily by subscale shear flow instability. Thus, dominant MSI cells are quasi-isotropic. In a stationary state, the effective Shakura-Sunyaev 'alpha' value is predicted to be of order V(sub A)(sub 0)0/C(sub s). In addition, the veritcal magnetic-field-induced MSI cells convert vertical magnetic field B(sub 0) into azimuthal magnetic field B(sub theta) in the disk. The generation of azimuthal magnetic field in turn introduces new physical processes, such as dynamo activity and azimuthal MSI turbulence. We conclude that it is not possible to decouple vertical MSI saturation from azimuthal MSI evolution. Low-frequency MSI cells are shown to co-exist with high-frequency radial buoyancy or internal waves. We show that modulational interaction between waves on these two frequency ranges is usually weak in the case when mean magnetic field is vertical. Thus, MSI and internal wave dynamics must be treated on an equal footing.

A Powerful Local Shear Instability in Weakly Magnetized Disks. IV. Nonaxisymmetric Perturbations

view Abstract Citations (299) References (8) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS A Powerful Local Shear Instability in Weakly Magnetized Disks. IV. Nonaxisymmetric Perturbations Balbus, Steven A. ; Hawley, John F. Abstract In this paper, we continue our study of a powerful axisymmetric MHD instability recently put forward by the authors as the underlying cause of anomalous transport in accretion disks. The theory of local nonaxisymmetric perturbations in weakly magnetized disks is presented. Such disturbances are of interest for several reasons, most notably in the context of a dynamo magnetic field amplification scheme. The most volatile disturbances are those associated with the presence of a poloidal field, which grow by tens of orders of magnitude with e-folding times measured in fractions of an orbital period. We also examine the stability of a purely azimuthal field configuration and find that nonaxisymmetric instability is present, but with a growth time measured in tens of orbital periods. In general, the most rapid growth occurs for very small radial and azimuthal wavenumbers, leading to coherent magnetic field structure in planes parallel to the disk. We suggest that this instability will prove to be a key ingredient for the generation of magnetic fields in disks. Publication: The Astrophysical Journal Pub Date: December 1992 DOI: 10.1086/172022 Bibcode: 1992ApJ...400..610B Keywords: ACCRETION; ACCRETION DISKS; INSTABILITIES; MAGNETOHYDRODYNAMICS: MHD full text sources ADS | Related Materials (3) Part 1: 1991ApJ...376..214B Part 2: 1991ApJ...376..223H Part 3: 1992ApJ...400..595H

Dynamos and angular momentum transport in accretion disks

The transport of angular momentum in astrophysical disks is one of the major issues in modern astrophysics. Here, recent work [Astrophys. J. 347, 435 (1989); 365, 648 (1990)] will be reviewed that suggests that internal waves, analogous to deep ocean waves, play a critical role in transporting angular momentum in neutral disks and generating a magnetic dynamo in ionized disks. Previously, it was shown that low-frequency, slightly nonaxisymmetric (‖m‖=1) waves in thin accretion disks could penetrate to small radii with a unique amplitude because of nonlinear saturation. Here, the ability of these waves to drive an α-Ω dynamo in a disk of thickness H and radius r and keplerian rotational frequency Ω(r)∝r−3/2 is examined. The asymmetry in the wave distribution that creates a nonzero helicity follows from the fact that the fundamental waves all have a positive angular momentum flux. As a result, there will be a large-scale magnetic field driven by an α-Ω dynamo. It is also likely that small-scale fields, driven by higher-order wave modes, will contribute significantly to the local value of BrBφ. It is argued that the magnetic field saturates when its pressure is comparable to the thermal pressure and a crude model of the nonlinear transfer of power to small-scale turbulence is presented. The dynamo process creates a large-scale, axisymmetric toroidal field with Br∼(H/r)3/2Bφ. Smaller-scale waves create small-scale fields with a maximum brbφ∼(H/r)6/5P. In this model, viscous and thermal instabilities in radiation pressure dominated, and electron scattering regions in accretion disks appear to be substantially suppressed.

A self-consistent model of mass and angular momentum transport in accretion disks

view Abstract Citations (62) References (47) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS A Self-consistent Model of Mass and Angular Momentum Transport in Accretion Disks Vishniac, Ethan T. ; Diamond, Patrick Abstract The nature of linear perturbations to a thin, shearing accretion disk composed of compressible material is reexamined. Modes that can carry angular momentum throughout the disk are identified, and it is shown how the subsequent dissipation of these waves through nonlinear processes can form the basis of a viscosity mechanism for realistic accretion disks. It is suggested that the impact of accreting material at the outer edge of the disk provides a natural source of excitation for waves that drive angular momentum transport within the disk. Publication: The Astrophysical Journal Pub Date: December 1989 DOI: 10.1086/168131 Bibcode: 1989ApJ...347..435V Keywords: Accretion Disks; Angular Momentum; Computational Astrophysics; Internal Waves; Sound Waves; Stellar Mass Accretion; Astronomical Models; Energy Dissipation; Optical Thickness; Perturbation Theory; Viscosity; Wave Packets; Astrophysics; STARS: ACCRETION; WAVE MOTIONS full text sources ADS |