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NASA NTRS1990

Wave propagation in gaseous accretion disks

Linear wave propagation is studied in geometrically thin accretion disks where the equilibrium variables, such as density and temperature, are stratified in the direction normal to the plane of the disk, i.e., the vertical direction. Temperature stratification causes refraction such that initially radially propagating waves are deflected in the vertical direction. For moderate temperature contrast between the disk's midplane and its surface, wave transmission into the tenuous upper atmosphere is allowed. In typical astrophysical accretion disks, these two effects inhibit wave propagation through large distances in the radial direction.

Lin, D. N. C.↗

NASA NTRS1993

On the stability of irradiated accretion disks

The effects of external heating on the stability of hot accretion disks are studied in some detail. It is known that geometrically thin, optically thick, nonirradiated accretion disks have two distinct branches in the surface density mass-accretion rate plane: the upper branch is radiation pressure-dominated and is unstable against thermal and secular perturbations, while the lower one is gas-pressure-dominated and is stable. We show quite generally that, even when disks are strongly irradiated, the upper branch remains unstable and the lower branch remains stable; the lower branch, however, can become radiation pressure dominated, if the irradiating flux, F(irr), is kept constant. A stable, radiation pressure dominated state thus appears. If F(irr) changes in proportion to the mass-accretion rate through the disk, the instabilities associated with radiation pressure dominated disks cannot be removed. Some observational implications are discussed in the context of long-term variations of low-mass X-ray binaries.

Mineshige, Shin↗

NASA NTRS1994

Emission lines from X-ray-heated accretion disks in low-mass X-ray binaries

We investigate the structure of accretion disks illuminated by X-rays from a central compact object in a binary system. X-rays can photoionize the upper atmosphere of the disk and form an accretion disk corona (ADC) where emission lines can form. We construct a model to calculate the vertical structure and the emission spectrum of the ADC with parameters appropriate to low-mass X-ray binaries. These models are made by nonlocal thermodynamic equilibrium calculations of ion and level populations and include a large number of atomic processes for 10 cosmically abundant elements. Transfer of radiation is treated by using the escape probability formalism. The vertical temperature profile of the ADC consists of a Compton-heated region and a mid-T zone where the temperature is approximately 10(exp 6) K. A thermal instability occurs close to the disk photosphere and causes the temperature of the ADC to drop abruptly from 10(exp 6) K to several times 10(exp 4) K. The emission spectrum in the optical, ultraviolet, extreme ultraviolet, and X-ray range is discussed and compared with the observations.

Ko, Yuan-Kuen↗

NASA NTRS1994

Dynamics of flux tubes in accretion disks

The study of magnetized plasmas in astrophysics is complicated by a number of factors, not the least of which is that in considering magnetic fields in stars or accretion disks, we are considering plasmas with densities well above those we can study in the laboratory. In particular, whereas laboratory plasmas are dominated by the confining magnetic field pressure, stars, and probably accretion disks, have magnetic fields whose beta (ratio of gas pressure to magnetic field pressure) is much greater than 1. Observations of the Sun suggest that under such circumstances the magnetic field breaks apart into discrete flux tubes with a small filling factor. On the other hand, theoretical treatments of MHD turbulence in high-beta plasmas tend to assume that the field is more or less homogeneously distributed throughout the plasma. Here we consider a simple model for the distribution of magnetic flux tubes in a turbulent medium. We discuss the mechanism by which small inhomogeneities evolve into discrete flux tubes and the size and distribution of such flux tubes. We then apply the model to accretion disks. We find that the fibrilation of the magnetic field does not enhance magnetic buoyancy. We also note that the evolution of an initially diffuse field in a turbulent medium, e.g., any uniform field in a shearing flow, will initially show exponential growth as the flux tubes form. This growth saturates when the flux tube formation is complete and cannot be used as the basis for a self-sustaining dynamo effect. Since the typical state of the magnetic field is a collection of intense flux tubes, this effect is of limited interest. However, it may be important early in the evolution of the galactic magnetic field, and it will play a large role in numerical simulations. Finally, we note that the formation of flux tubes is an essential ingredient in any successful dynamo model for stars or accretion disks.

Vishniac, E. T.↗

NASA NTRS1996

Accretion Disks in Supersoft X-ray Sources

We examine the role of the accretion disk in the steady-burning white dwarf model for supersoft sources. The accretion luminosity of the disk is quite small compared to the nuclear burning luminosity of the central source. Thus, in contrast to standard accretion disks, the main role of the disk is to reprocess the radiation from the white dwarf. We calculate models of accretion disks around luminous white dwarfs and compare the resulting disk fluxes to optical and UV observations of the LMC supersoft sources CAL 83, CAL 87, and RX J0513.9-6951. We find that if the white dwarf luminosity is near the upper end of the steady-burning region, and the flaring of the disk is included, then reprocessing by the disk can account for the UV fluxes and a substantial fraction of the optical fluxes of these systems. Reprocessing by the companion star can provide additional optical flux, and here too the disk plays an important role: since the disk is fairly thick, it shadows a significant fraction of the companion's surface.

Popham, Robert↗

NASA NTRS1987

Generation of a dynamo magnetic field in a protoplanetary accretion disk

A new computational technique is developed that allows realistic calculations of dynamo magnetic field generation in disk geometries corresponding to protoplanetary and protostellar accretion disks. The approach is of sufficient generality to allow, in the future, a wide class of accretion disk problems to be solved. Here, basic modes of a disk dynamo are calculated. Spatially localized oscillatory states are found to occur in Keplerain disks. A physical interpretation is given that argues that spatially localized fields of the type found in these calculations constitute the basic modes of a Keplerian disk dynamo.

Stepinski, T.↗

NASA NTRS1979

Lightman-Eardley instabilities and accretion disk thickening

After reviewing the role of Compton scattering in accretion disks around black holes, it is discussed whether Lightman-Eardley (LE) secular instabilities can trigger and maintain Pringle-Rees (PR) thermal instabilities. The radiative-transfer-equation and equation-of-state criteria for LE stability in alpha-viscosity-law disk models and dynamic viscosity criteria for more general situations is derived. On the basis of these considerations the LE instability is insufficient for inducing PR instabilities and hot thick inner regions important in accretion-disk models of compact hard X-ray sources. The density thinning due to radial velocity gradients in the accretion flow is suggested as a more likely and satisfactory mechanism.

Stoeger, W. R.↗

NASA NTRS1997

Self-Consistent Thermal Accretion Disk Corona Models for Compact Objects: Application to Cygnus X-1 - II

We apply our self-consistent accretion disk corona (ADC) model, with two different geometries, to the broadband X-ray spectrum of the black hole candidate Cygnus X-1. As shown in a companion paper, models in which the Comptonizing medium is a slab surrounding the cold accretion disk cannot have a temperature higher than about 140 keV for optical depths greater than 0.2, resulting in spectra that are much softer than the observed 10-30 keV spectrum of Cyg X-1. In addition, the slab-geometry models predict a substantial "soft excess" at low energies, a feature not observed for Cyg X-1, and Fe K-alpha fluorescence lines that are stronger than observed. Previous Comptonization models in the literature have invoked a slab geometry with optical depth tau(sub T) approx. greater than 0.3 and coronal temperature T(sub c) approx. 150 keV, but they are not self-consistent. Therefore, ADC models with a slab geometry are not appropriate for explaining the X-ray spectrum of Cyg X-1. Models with a spherical corona and an exterior disk, however, predict much higher self-consistent coronal temperatures than the slab-geometry models. The higher coronal temperatures are due to the lower amount of reprocessing of coronal radiation in the accretion disk, giving rise to a lower Compton cooling rate. Therefore, for the sphere-plus-disk geometry, the predicted spectrum can be hard enough to describe the observed X-ray continuum of Cyg X-1 while predicting Fe fluorescence lines having an equivalent width of approx. 40 eV. Our best-fit parameter values for the sphere-plus-disk geometry are tau(sub T) approx. equal to 1.5 and T(sub c) approx. equal to 90 keV.

Dove, James B.↗

NASA NTRS1995

Accretion disk boundary layers in cataclysmic variables. 1: Optically thick boundary layers

We develop numerical models of accretions disks in cataclysmic variables (CVs), including and emphasizing the boundary layer region where the accretion disk meets the accreting white dwarf. We confine ourselves to solutions where the boundary layer region is vertically optically thick, and find that these solutions share several common features. The angular and radial velocities of the accreting material drop rapidly in a dynamical boundary layer, which has a radial width approximately 1%-3% of the white dwarf radius. The energy dissipated in this region diffuses through the inner part of the disk and is radiated from the disk surface in a thermal boundary layer, which has a radial width comparable to the disk thickness, approximately 5%-15% of the white dwarf radius. We examine the dependence of the boundary layer structure on the mass accretion rate, the white dwarf mass and rotation rate, and the viscosity parameter alpha. We delineate the boundary between optically thick and optically thin boundary layer solutions as a function of these parameters and suggest that by means of a careful comparison with observations it may be possible to estimate alpha in CVs. We derive an expression for the total boundary layer luminosities as a function of the parameters and show that it agrees well with the luminosites of our numerical solutions. Finally, we calcuate simple blackbody continuum spectra of the boundary layer and disk emission for our solutions and compare these to soft X-ray, EUV, and He II emission-line observations of CVs. We show that, through such comparisons, it may be possible to determine the rotation rates of the accreting stars in CVs, and perhaps also the white dwarf masses and the accretion rates. The spectra are quite insensitive to alpha, so the uncertainty in this parameter does not affect such comparisons.

Popham, Robert↗

NASA NTRS1996

Ion Viscosity Mediated by Tangled Magnetic Fields: An Application to Black Hole Accretion Disks

We examine the viscosity associated with the shear stress exerted by ions in the presence of a tangled magnetic field. As an application, we consider the effect of this mechanism on the structure of black hole accretion disks. We do not attempt to include a self-consistent description of the magnetic field. Instead, we assume the existence of a tangled field with coherence length lambda(sub coh), which is the average distance between the magnetic 'kinks' that scatter the particles. For simplicity, we assume that the field is self-similar, and take lambda(sub coh) to be a fixed fraction zeta of the local disk height H. Ion viscosity in the presence of magnetic fields is generally taken to be the cross-field viscosity, wherein the effective mean free path is the ion Larmor radius lambda(sub L), which is much less than the ion-ion Coulomb mean free path A(sub ii) in hot accretion disks. However, we arrive at a formulation for a 'hybrid' viscosity in which the tangled magnetic field acts as an intermediary in the transfer of momentum between different layers in the shear flow. The hybrid viscosity greatly exceeds the standard cross-field viscosity when (lambda/lambda(sub L)) much greater than (lambda(sub L)/lambda(sub ii)), where lambda = ((lambda(sub ii)(sup -1) + lambda(sub (coh)(sup -1))(sup -1) is the effective mean free path for the ions. This inequality is well satisfied in hot accretion disks, which suggests that the ions may play a much larger role in the momentum transfer process in the presence of magnetic fields than was previously thought. The effect of the hybrid viscosity on the structure of a steady-state, two-temperature, quasi-Keplerian accretion disk is analyzed. The hybrid viscosity is influenced by the degree to which the magnetic field is tangled (represented by zeta = lambda(sub coh)), and also by the relative accretion rate M/M(sub E), where M(sub E) = L(sub E)/c(sup 2) and L(sub E) is the Eddington luminosity. We find that ion viscosity in the presence of magnetic fields (hybrid viscosity) can dominate over conventional magnetic viscosity for fields that are tangled on sufficiently small scales.

Subramanian, Prasad↗

NASA NTRS2002

Hydrodynamic Models of Line-Driven Accretion Disk Winds III: Local Ionization Equilibrium

We present time-dependent numerical hydrodynamic models of line-driven accretion disk winds in cataclysmic variable systems and calculate wind mass-loss rates and terminal velocities. The models are 2.5-dimensional, include an energy balance condition with radiative heating and cooling processes, and includes local ionization equilibrium introducing time dependence and spatial dependence on the line radiation force parameters. The radiation field is assumed to originate in an optically thick accretion disk. Wind ion populations are calculated under the assumption that local ionization equilibrium is determined by photoionization and radiative recombination, similar to a photoionized nebula. We find a steady wind flowing from the accretion disk. Radiative heating tends to maintain the temperature in the higher density wind regions near the disk surface, rather than cooling adiabatically. For a disk luminosity L (sub disk) = solar luminosity, white dwarf mass M(sub wd) = 0.6 solar mass, and white dwarf radii R(sub wd) = 0.01 solar radius, we obtain a wind mass-loss rate of M(sub wind) = 4 x 10(exp -12) solar mass yr(exp -1) and a terminal velocity of approximately 3000 km per second. These results confirm the general velocity and density structures found in our earlier constant ionization equilibrium adiabatic CV wind models. Further we establish here 2.5D numerical models that can be extended to QSO/AGN winds where the local ionization equilibrium will play a crucial role in the overall dynamics.

Pereyra, Nicolas Antonio↗

NASA NTRS1991

Optical properties of grains in molecular clouds and accretion disks

A baseline model of the composition and abundances of grains and gases in molecular cloud cores and accretion disks around young stars is defined by employing: a wide range of astronomical data and theory; the composition of primitive bodies in the solar system; and solar elemental abundances. It is proposed that in the coldest portions of these objects the major grain species include amorphous olivine, amorphous orthopyroxene, volatile and refractory organics, water ice, troilite, and metallic iron. Using a combination of laboratory measurements of optical constants and asymptotic theory, values of the real and imaginary indices of refraction of these grain species over a wavelength range that runs from the vacuum UV to the radio domain are derived. Auxiliary information for these grain species, such as their vaporization temperatures bulk densities, and their fractional abundances by mass. The above information on grain properties in molecular cloud cores and accretion disks is used to estimate the Rosseland mean opacity of the grains in both environments and the IR and microwave opacity of grains in accretion disks.

Pollack, J. B.↗

NASA NTRS1979

The structure and appearance of winds from supercritical accretion disks. I - Numerical models

Equations for the structure and appearance of supercritical accretion disks and the radiation-driven winds which emanate from them are derived and solved by a steady-state hydrodynamic computer code with a relaxation technique used in stellar structure problems. The present model takes into account the mass of the accreting star, the total accretion rate, a generalization of the disk alpha parameter which accounts for heating by processes in addition to viscosity, and the ratio of the total luminosity to the Eddington luminosity. Solutions indicate that for accretion onto a hard-surfaced star, steady, optically thick winds result for even slightly supercritical accretion, and the object will appear as a supergiant star with a high mass loss rate and a nonblackbody spectrum. Winds from black hole accretion disks are expected to depend on the form of the accretion interior to the critical radius, possibly consisting of no ejection at all, a wind similar to that of a hard-surfaced star, or a column of material ejected from a hole in the accretion disk.

Meier, D. L.↗

NASA NTRS1993

Spectrally resolved eclipse maps of the accretion disk in UX Ursae Majoris

An effort is made to observationally constrain accretion disks on the basis of light curves from the eclipsing cataclysmic variable UX Ursae Majoris, reconstructing the spectral energy distribution across the face of an accretion disk. The spectral resolution obtained suffices to reveal not only the radial dependence of absorption and emission line features within the disk, but also the spectral details of the bright spot that is formed where the accretion stream from the secondary star collides with the disk. The importance of such constraints for theoretical models is noted.

Rutten, Rene G. M.↗

NASA NTRS1983

Compton heated winds and coronae above accretion disks. I Dynamics

X rays emitted in the inner part of an accretion disk system can heat the surface of the disk farther out, producing a corona and possibly driving off a strong wind. The dynamics of Compton-heated coronae and winds are analyzed using an approximate two-dimensional technique to estimate the mass loss rate as a function of distance from the source of X rays. The findings have important dynamical implications for accretion disks in quasars, active galactic nuclei, X ray binaries, and cataclysmic variables. These include: mass loss from the disk possibly comparable with or exceeding the net accretion rate onto the central compact object, which may lead to unstable accretion; sufficient angular momentum loss in some cases to truncate the disk in a semidetached binary at a smaller radius than that predicted by tidal truncation theories; and combined static plus ram pressure in the wind adequate to confine line-emitting clouds in quasars and Seyfert galaxies.

Begelman, M. C.↗

NASA NTRS1992

Accretion disks in active galactic nuclei - Vertically averaged models

Simple models of accretion disks surrounding supermassive black holes in AGN are constructed. By considering several different opacity laws, it is shown that some conclusions arrived at by previous investigators are model-dependent. A simple technique for solving the full vertically averaged disk equations, taking into account both self-gravity and central object gravity and gas pressure and radiation pressure, is presented. The self-consistency of the standard non-self-gravitating, geometrically thin accretion disk models is discussed, and the findings of Lin and Shields (1986) that such models are valid only in a restricted parameter space are confirmed.

Cannizzo, John K.↗

NASA NTRS1987

Constraints on quasar accretion disks from the optical/ultraviolet/soft X-ray big bump

The simplest accretion-disk models have difficulties explaining the optical/UV/soft-X-ray 'big bump' in quasars. Here more realistic models are investigated, incorporating opacity and inclination effects while retaining an analytic form for ease of computation. It is found that opacity effects can explain the uniform 20,000-30,000 K 'maximum disk temperature' derived by previous workers. The observed spectral turndown would be the result of the onset of electron scattering and should not be identified with the hottest part of the disk. The frequency at which this spectral turndown occurs is only weakly dependent on the accretion-disk parameters. These opacity effects also allow high-frequency EUV and soft-X-ray extensions of the big bump without exceeding the Eddington limit strongly. For a wide range of disk parameters, the EUV spectra of quasar disks should have spectral slopes near -1.

Czerny, Bozena↗

NASA NTRS1993

A model of an X-ray-illuminated accretion disk and corona

The X-ray-illuminated surface of the accretion disk in a low-mass X-ray Binary (LMXRB) and the X-ray-heated corona above the disk produce optical, UV, and soft X-ray emission lines. This paper presents 1D models of the emission line spectra and the vertical temperature and density structures at different radii. The models include a detailed treatment of the important atomic processes and an escape probability treatment of radiative transfer. Soker and Raymond (1993) use the density structure predicted by these models for a 2D Monte Carlo simulation of the photon scattering in the accretion disk corona (ADC) to examine the effects of the ADC on the angular distribution of X-rays and the flux of X-rays incident on the outer disk. This paper concentrates on the emission line fluxes for various elemental abundances and disk parameters. The UV lines of the classic LMXRBs are consistent with the model predictions. Some CNO processing is necessary to account for the nitrogen and helium abundances in Sco X-1 and other LMXRBs. Comparison of the models with observed spectra also points to a soft X-ray component with luminosity comparable to the hard X-rays. The models predict a substantial luminosity in the group of highly ionized iron lines near 100 A.

Raymond, John C.↗