Dynamics Of Accretion Disks Research Articles

Magnetized tori around Kerr black holes: analytic solutions with a toroidal magnetic field

The dynamics of accretion discs around galactic and extragalactic black holes may be influenced by their magnetic field. In this paper, we generalize the fully relativistic theory of stationary axisymmetric tori in Kerr metric of Abramowicz, Jaroszynski & Sikora by including strong toroidal magnetic field and construct analytic solutions for barotropic tori with constant angular momentum. This development is particularly important for the general relativistic computational magnetohydrodynamics that suffers from the lack of exact analytic solutions that are needed to test computer codes.

The dynamics of eccentric accretion discs in superhump systems

We have applied an eccentric accretion disc theory in simplified form to the case of an accretion disc in a binary system, where the disc contains the 3:1 Lindblad resonance. This is relevant to the case of superhumps in SU Ursae Majoris cataclysmic variables and other systems, where it is thought that this resonance leads to growth of eccentricity and a modulation in the light curve due to the interaction of a precessing eccentric disc with tidal stresses. A single differential equation is formulated which describes the propagation, resonant excitation and viscous damping of eccentricity. The theory is first worked out in the simple case of a narrow ring and leads to the conclusion that the eccentricity distribution is locally suppressed by the presence of the resonance, creating a dip in the eccentricity at the resonant radius. Application of this theory to the superhump case confirms this conclusion and produces a more accurate expression for the precession rate of the disc than has been previously accomplished with simple dynamical estimates.

Simple, Accurate, Approximate Orbits in the Logarithmic and a Range of Power-Law Galactic Potentials

Curves in a family derived from powers of the polar-coordinate formula for ellipses are found to provide good fits to bound orbits in a range of power-law potentials. This range includes the well-known 1/r (Keplerian) and logarithmic potentials. These approximate orbits, called p-ellipses, retain some of the basic geometric properties of ellipses. They satisfy and generalize Newton's apsidal precession formula, which is one of the reasons for their surprising accuracy. Because of their simplicity the p-ellipses make very useful tools for studying trends among power-law potentials, and especially the occurrence of closed orbits. The occurrence of closed or nearly closed orbits in different potentials highlights the possibility of period resonances between precessing, eccentric orbits and circular orbits, or between the precession period of multilobed closed orbits and satellite periods. These orbits and their resonances promise to help illuminate a number of problems in galaxy and accretion disk dynamics.

Non-linear bending waves in Keplerian accretion discs

The non-linear dynamics of a warped accretion disc is investigated in the important case of a thin Keplerian disc with negligible viscosity and self-gravity. A one-dimensional evolutionary equation is formally derived that describes the primary non-linear and dispersive effects on propagating bending waves other than parametric instabilities. It has the form of a derivative non-linear Schrodinger (DNLS) equation with coefficients that are obtained explicitly for a particular model of a disc. The properties of this equation are analysed in some detail and illustrative numerical solutions are presented. The non-linear and dispersive effects both depend on the compressibility of the gas through its adiabatic index Γ. In the physically realistic case r 3, non-linearity leads to wave steepening and solitary waves are supported. The effects of a small effective viscosity, which may suppress parametric instabilities, are also considered. This analysis may provide a useful point of comparison between theory and numerical simulations of warped accretion discs.

The Long‐Term Light Curves of X‐Ray Binaries Contain Simultaneous Periodic and Random Components

LMC X-3 and Cyg X-2 show large amplitude X-ray fluctuations that have been attributed to a warped accretion disk. Cyg X-3 displays high amplitude, apparently non-periodic oscillations. We reanalyze these systems using RXTE ASM data and time-frequency decomposition techniques. We find that the long-term variations in Cyg X-2 can be completely characterized by excursions whose durations are integer multiples of the orbital period, including one essentially identical to the reported of 78 days. Cyg X-3 can be characterized in terms of integer multiples of a 71-day fundamental period unrelated to the 4.8 day orbital period, but suggestively close to the approximately equal to greater than 60 day reported precession period of the relativistic jet inferred from recent radio observations. The long-term excursions of LMC X-3 are related to each other by rational fractions, suggesting the characteristic time scale is 10.594 days, shorter than any observed excursion to date. We explore the phase space evolution of the light curves using a natural embedding and find that all three systems possess two rotation centers that organize the phase space trajectories, one of low luminosity and the other of high luminosity. The implications of this repeatable behavior on generic models of accretion disk dynamics and mass transfer variability are explored.

Diagnostics of Neutron Star and Black Hole X‐Ray Binaries with X‐Ray Shot Widths

A statistic, w, the differential coefficient of the mean absolute difference of an observed light curve, is proposed for timescale analysis of shot widths. The shortest width of random shots can be measured by the position of the lower cutoff in the timescale spectrum of w. We use the statistic to analyze X-ray light curves from a sample of neutron star and black hole binaries, and the results show that the timescale analysis can help us distinguish between neutron star binaries and black hole binaries. The analysis can further reveal the structure and dynamics of accretion disks around black holes.

Long Term Simulations of Astrophysical Jets

We have performed self-consistent 2.5-dimensional nonsteady MHD numerical simulations of jet formation, including the dynamics of accretion disks. Although the previous nonsteady MHD simulations for astrophysical jets revealed that the characteristics of nonsteady jets are very similar to those of steady jets, the calculation time of these simulations is very short compared with the time scale of observed jets. Thus we have investigated long term evolutions of the mass accretion rate (M a ), mass outflow rate (M w ), and energy of the toroidal magnetic field (E m g t ). We found that the jet is ejected intermittently with a period of around 2π which is similar to the growth time of the magnetorotational instability (MRI).

Local Three‐dimensional Simulations of Magnetorotational Instability in Radiation‐dominated Accretion Disks

We examine the small-scale dynamics of black hole accretion disks in which radiation pressure exceeds gas pressure. Local patches of disk are modeled by numerically integrating the equations of radiation MHD in the flux-limited diffusion approximation. The shearing-box approximation is used, and the vertical component of gravity is neglected. Magnetorotational instability (MRI) leads to turbulence in which accretion stresses are due primarily to magnetic torques. When radiation is locked to gas over the length and timescales of fluctuations in the turbulence, the accretion stress, density contrast, and dissipation differ little from those in the corresponding calculations, with radiation replaced by extra gas pressure. However, when radiation diffuses each orbit a distance that is comparable to the rms vertical wavelength of the MRI, radiation pressure is less effective in resisting squeezing. Large density fluctuations occur, and radiation damping of compressive motions converts P dV work into photon energy. The accretion stress in calculations having a net vertical magnetic field is found to be independent of opacity over the range explored and approximately proportional to the square of the net field. In calculations with zero net magnetic flux, the accretion stress depends on the portion of the total pressure that is effective in resisting compression. The stress is lower when radiation diffuses rapidly with respect to the gas. We show that radiation-supported Shakura-Sunyaev disks accreting via internal magnetic stresses are likely to have radiation marginally coupled to turbulent gas motions in their interiors.

Chaos in turbulence driven by the magnetorotational instability

Chaotic flow is studied in a series of numerical magnetohydrodynamical simulations that use the shearing box formalism. This mimics important features of local accretion disc dynamics. The magnetorotational instability gives rise to flow turbulence, and quantitative chaos parameters, such as the largest Lyapunov exponent, can be measured. Linear growth rates appear in these exponents even when the flow is fully turbulent. The extreme sensitivity to initial conditions associated with chaotic flows has practical implications, the most important of which is that hundreds of orbital times are needed to extract a meaningful average for the stress. If the evolution time in a disc is less than this, the classical α formalism will break down.

A laboratory plasma experiment for studying magnetic dynamics of accretion discs and jets

This work describes a laboratory plasma experiment and initial results which should give insight into the magnetic dynamics of accretion discs and jets. A high-speed multiple-frame CCD camera reveals images of the formation and helical instability of a collimated plasma, similar to MHD models of disc jets, and also plasma detachment associated with spheromak formation, which may have relevance to disc winds and flares. The plasmas are produced by a planar magnetized coaxial gun. The resulting magnetic topology is dependent on the details of magnetic helicity injection, namely the force-free state eigenvalue αgun imposed by the coaxial gun.

High‐Resolution Simulations of the Plunging Region in a Pseudo‐Newtonian Potential: Dependence on Numerical Resolution and Field Topology

New three-dimensional magnetohydrodynamic simulations of accretion disk dynamics in a pseudo-Newtonian Paczynski-Wiita potential are presented. These have finer resolution in the inner disk than any previously reported. Finer resolution leads to increased magnetic field strength, greater accretion rate, and greater fluctuations in the accretion rate. One simulation begins with a purely poloidal magnetic field, the other with a purely toroidal field. Compared to the poloidal initial field simulation, a purely toroidal initial field takes longer to reach saturation of the magnetorotational instability and produces less turbulence and weaker magnetic field energies. For both initial field configurations, magnetic stresses continue across the marginally stable orbit; measured in units corresponding to the Shakura-Sunyaev α-parameter, the stress grows from ~0.1 in the disk body to as much as ~10 deep in the plunging region. Matter passing the inner boundary of the simulation has ~10% greater binding energy and ~10% smaller angular momentum than it did at the marginally stable orbit. Both the mass accretion rate and the integrated stress fluctuate widely on a broad range of timescales.

Study of magnetic helicity injection via plasma imaging using a high-speed digital camera

The evolution of a plasma generated by a novel planar coaxial gun is photographed using a state-of-the-art digital camera, which captures eight time-resolved images per discharge. This experiment is designed to study the fundamental physics of magnetic helicity injection, which is an important issue in fusion plasma confinement, as well as solar and astrophysical phenomena such as coronal mass ejections and accretion disk dynamics. The images presented in this paper are not only beautiful but provide a powerful way to understand the global dynamics of the plasma.

2.5‐dimensional Nonsteady Magnetohydrodynamic Simulations of Magnetically Driven Jets from Geometrically Thin Disks

We have performed self-consistent 2.5-dimensional nonsteady MHD numerical simulations of jets from geometrically thin disks including the dynamics of accretion disks. For the initial rotational velocity of the disk, we consider two cases, the Keplerian case and the sub-Keplerian case. We compare our results with the thick-disk case in detail. The characteristics of nonsteady jets from geometrically thin disks in our Keplerian case are similar to those of the steady theory and thick-disk cases: (1) The ejection point of the jets corresponds to the slow magnetosonic point, which is determined by the effective potential made by the gravitational and centrifugal forces along the magnetic field. (2) The dependences of the velocity (Vjet) and the mass outflow rate (w) on the initial magnetic field strength (B0) are w ∝ B0 and Vjet ∝ 1/3, therefore Vjet ∝ B, where ΩF is the angular velocity of a field line. Although this dependence of the velocity corresponds to Michel's scaling law, the velocity of our simulated jets still does not reach the fast magnetosonic velocity. In the sub-Keplerian case, the relation Vjet ∝ B is satisfied, but the other dependences are not necessarily equal to those of the Keplerian case. The velocity of the jets is larger when the initial rotational velocity of the disk is smaller. The initial acceleration force on the jets is the magnetic pressure when the initial magnetic field is weak, while the centrifugal force is dominant when the initial magnetic field is strong. Finally, we found two interesting phenomena in the sub-Keplerian cases: one is knotlike structures around the rotational axis, and the other is outflow along the disk surface.

Radiation Hydrodynamics of 2-D Accretion Disks

To examine the structure and dynamics of thick accretion disks, we use a two-dimensional viscous hydrodynamic code coupled with radiation transport. The -model and the full viscous stress-tensor description for the kinematic viscosity are used. The radiation transport is treated in the gray, flux-limited diffusion approximation. The finite difference methods used are based on an explicit-implicit method. We apply the numerical code to the Super-Eddington black-hole model for SS 433.@The result for a very small viscosity parameter a reproduces well the characteristic features of SS 433, such as the relativistic jets with 0.26c, the small collimation degree of the jets, the mass-outflow rate of , and the formation of the X-ray iron emission lines.

Thermal stability of self-gravitating, optically thin accretion disks

In the dynamics of accretion disks, the presence of collective eects associated with the self-gravity of the disk is expected to aect not only the momentum transport, but also the relevant energy balance equations, which could dier substantially from the non-self-gravitating case. Here we follow the model that, when the disk is suciently cold, the stirring due to Jeans-related instabilities acts as a source of eective heating. The corresponding reformulation of the energy equations allows us to: (i) demonstrate how self-regulation can be established, so that the stability parameter Q is maintained close to a threshold value, with weak dependence on radius; (ii) rediscuss the opacity properties in the self-gravitating regime. In particular, we show that, if cooling is dominated by bremsstrahlung, an optically thin stationary accretion solution is thermally stable, even in the non-advective case, provided the disk is self-gravitating. The details of the cooling function have little eect on the structure of such accretion disk, which is in any case induced by self-gravity to self-regulate. This condition of self-gravitating accretion is expected to be appropriate for the outer regions of many disks of astrophysical interest. With the reformulation of the energy equations described in this paper, we have also secured: (iii )a starting point for the study of the emission properties of self-gravitating accretion disks; (iv) a tool to analyze the structure of the transition region, where the disk becomes self-gravitating.

Accelerations of Water Masers in NGC 4258

The water masers in NGC 4258 delineate the structure and dynamics of a subparsec-diameter accretion disk around a supermassive black hole. Very Long Baseline Array (VLBA) observations provide precise information about the positions in the plane of the sky and the three-dimensional velocity vectors for the maser emission, but the positions along the line of sight must be inferred from models. Previous measurements placed an upper limit on the accelerations of the high-velocity spectral features of 1 km s-1 yr-1, suggesting that they are located near the midline (the diameter perpendicular to the line of sight), where they would have exactly zero acceleration. From similar measurements, the accelerations of the systemic velocity spectral features have been estimated to be about 9 km s-1 yr-1, indicating that they lie toward the front of the disk where the acceleration vector points directly away from the line of sight. We report acceleration measurements for 12 systemic velocity spectral features and 19 high-velocity spectral features using a total of 25 epochs of observations from Effelsberg (five epochs), the Very Large Array (15 epochs), and the VLBA (five epochs) spanning the years 1994-1997. The measured accelerations of the systemic velocity features are between 7.5 and 10.4 km s-1 yr-1, and there is no evidence for a dip in the spectrum at the systemic velocity. Such a dip has been attributed in the past to an absorbing layer of noninverted H2O. The accelerations of the high-velocity features, measured here for the first time, range from -0.77 to 0.38 km s-1 yr-1. From the line-of-sight accelerations and velocities, we infer the positions of these high-velocity masers with a simple edge-on disk model. The resulting positions fall between -136 and 93 in azimuth (measured from the midline). A model that suggests a spiral shock origin of the masers, in which changes in maser velocity are due to the outward motion of the shock wave, predicts apparent accelerations of -0.05(θp/25) km s-1 yr-1, where θp is the pitch angle of the spiral arms. Our data are not consistent with these predictions. We also discuss the physical properties of the high-velocity masers. Most notably, the strongest high-velocity masers lie near the midline, where the velocity gradient is smallest, thereby providing the longest amplification path lengths.

An alpha theory of time-dependent warped accretion discs

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 extended here 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.

The ZEUS code for astrophysical magnetohydrodynamics: new extensions and applications

A brief review of the numerical methods implemented in the widely used ZEUS code for astrophysical magnetohydrodynamics (MHD) is given. Extensions of the numerical methods to treat problems in nonideal MHD in a variety of regimes are discussed. In particular, methods for treating Ohmic dissipation, and methods for studying partially ionized plasmas in which the ion and neutral components are weakly coupled through a collisional drag term are considered. Recent application of the methods to the study of the dynamics of accretion disks is described.

The non-linear fluid dynamics of a warped accretion disc

The dynamics of a viscous accretion disc subject to a slowly varying warp of large amplitude is considered. Attention is restricted to discs in which self-gravitation is negligible, and to the generic case in which the resonant wave propagation found in inviscid Keplerian discs does not occur. The equations of fluid dynamics are derived in a coordinate system that follows the principal warping motion of the disc. They are reduced using asymptotic methods for thin discs, and solved to extract the equation governing the warp. In general, this is a wave equation of parabolic type with non-linear dispersion and diffusion, which describes fully non-linear bending waves. This method generalizes the linear theory of Papaloizou & Pringle (1983) to allow for an arbitrary rotation law, and extends it into the non-linear domain, where it connects with a generalized version of the theory of Pringle (1992). The astrophysical implications of this analysis are discussed briefly.

Stream overflow and dwarf nova eruptions

We consider the effects of accretion stream overflow on the viscous dynamics of accretion discs in dwarf novae. If the stream from the secondary star is geometrically thick enough, some fraction of its material can flow over and under the disc. The mass and specific angular momentum of the stream are then deposited not only at the point of collision with the outer disc, but also at those radii in the inner disc with geometric heights that are large enough to intercept the residual stream, or near the radius where the disc has the same specific angular momentum as the stream. The overflowing stream can alter the behaviour of heating fronts and cooling fronts in the disc. If the mass fraction of the overflowing stream is of order tens of per cent, the deposition of mass in the inner parts of the disc is sufficient to change the character of the eruption light curves significantly.