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NASA NTRS1990

Vertical structure of accretion disks - A simplified analytical model

A simplified model of the vertical structure of accretion disks is derived. Analytical expressions for the temperature and density structure, which represent a generalization of the gray model long known in the theory of classical stellar atmospheres, are presented. The formalism naturally explains similarities and differences between the structure of a disk and a stellar atmosphere. In particular, the influence of viscous dissipation and external irradiation of the disk by the central star, as well as of the finite optical thickness of the disk, may be easily accounted for and explained by the present model.

Hubeny, I.↗

NASA NTRS1991

Luminosity limit for alpha-viscosity accretion disks

The existence of a luminosity limit for alpha-viscosity physically thin accretion disks around black holes is established, using a new formulation of the radiation equation bridging optically thick and thin regimes. For alpha close to unity, this limit can be lower than the Eddington limit. Physically, this limit is due to the combined effects of gas and radiation pressure which become too large to satisfy vertical hydrostatic balance at intermediate optical depths for sufficiently high luminosities. This effect was overlooked in previous treatments using only the optically thin or thick limits of the radiative equation.

Liang, Edison P.↗

NASA NTRS1991

Diskoseismology: Probing accretion disks. I - Trapped adiabatic oscillations

The normal modes of acoustic oscillations within thin accretion disks which are terminated by an innermost stable orbit around a slowly rotating black hole or weakly magnetized compact neutron star are analyzed. The dominant relativistic effects which allow modes to be trapped within the inner region of the disk are approximated via a modified Newtonian potential. A general formalism is developed for investigating the adiabatic oscillations of arbitrary unperturbed disk models. The generic behavior is explored by way of an expansion of the Lagrangian displacement about the plane of symmetry and by assuming separable solutions with the same radial wavelength for the horizontal and vertical perturbations. The lowest eigenfrequencies and eigenfunctions of a particular set of radial and quadrupole modes which have minimum motion normal for the plane are obtained. These modes correspond to the standard dispersion relation of disk theory.

Nowak, Michael A.↗

NASA NTRS1993

Radiation from magnetized accretion disks in active galactic nuclei

We present a model of AGN based on accretion disks around 10 exp 8 solar mass black holes, which incorporates a strong magnetic field in the disk, with loops above the disk in which B is about 100 G. The magnetic energy in the loops dissipates, accelerating electrons to relativistic energies. The electrons emit synchrotron and inverse-Compton radiation, much of which is reflected or scattered by gas in the disk. We calculate the emitted spectrum from infrared to gamma rays. Of the total emission, 23 percent goes into a nu exp -1 power law and 77 percent into thermal radiation at 24,000 K (due to the disk, which is heated by nonthermal radiation and energetic ions). The model accounts quantitatively for the X-ray and gamma-ray backgrounds, and it accounts qualitatively for certain features observed in individual AGNs: a far-infrared cutoff, a minimum at a few microns, the ultraviolet bump, the Compton reflection bump at about 30 keV, and a gamma-ray tail.

Field, G. B.↗

NASA NTRS1994

On the effects of tidal interaction on thin accretion disks: An analytic study

We calculate tidal effects on two-dimensional thin accretion disks in binary systems. We apply a perturbation expansion to obtain an analytic solution of the tidally induced waves. We obtain spiral waves that are stronger at the inner parts of the disks, in addition to a local disturbance which scales like the strength of the local tidal force. Our results agree with recent calculations of the linear response of the disk to tidal interaction.

Dgani, R.↗

NASA NTRS2001

Early dust evolution in protosellar accretion disks

We investigate dust dynamics and evolution during the formation of a protostellar accretion disk around intermediate-mass stars via two-dimensional numerical simulations.

Solar nubula hydrodynamicscoagulation clouds↗

NASA NTRS2003

Probing the Inflow/Outflow and Accretion Disk of Cygnus X-1 in the High State with the Chandra High Energy Transmission Grating

Cygnus X-1 was observed in the high state at the conjunction orbital phase (0) with Chandra High Energy Transmission Grating (HETG). Strong and asymmetric absorption lines of highly ionized species were detected, such as Fe xxv, Fe xxiv, Fe xxiii, Si xiv, S xvi, Ne x, etc. In the high state the profile of the absorption lines is composed of an extended red wing and a less extended blue wing. The red wings of higher ionized species are more extended than those of lower ionized species. The detection of these lines provides a way to probe the properties of the flow around the companion and the black hole in Cyg X-1 during the high state. A broad emission feature around 6.5 keV was significantly detected from the spectra of both the Chandra/HETG and the RXTE/Proportional Counter Array. This feature appears to be symmetric and can be fitted with a Gaussian function rather than the Laor disk line model of the fluorescent Fe K(alpha) line from an accretion disk. The implications of these results on the structure of the accretion flow of Cyg X-1 in the high state are discussed.

Feng, Y. X.↗

NASA NTRS1994

The vertical structure and stability of accretion disks surrounding black holes and neutron stars

The structure and stability of the inner regions of accretion disks surrounding neutron stars and black holes have been investigated. Within the framework of the alpha viscosity prescription for optically thick disks, we assume the viscous stress scales with gas pressure only, and the alpha parameter, which is less than or equal to unity, is formulated as alpha(sub 0)(h/r)(exp n), where h is the local scale height and n and alpha(sub 0) are constants. We neglect advective energy transport associated with radial motions and construct the vertical structure of the disks by assuming a Keplerian rotation law and local hydrostatic and thermal equilibrium. The vertical structures have been calculated with and without convective energy transport, and it has been demonstrated that convection is important especially for mass accretion rates, M-dot, greater than about 0.1 times the Eddington value, M-dot(sub Edd). Although the efficiency of convection is not high, convection significantly modifies the vertical structure of the disk (as compared with a purely radiative model) and leads to lower temperatures at a given M-dot. The results show that the disk can be locally unstable and that for n greater than or = 0.75, an S-shaped relation can exist between M-dot and the column density, sigma, at a given radius. While the lower stable branch (derivative of M-dot/derivative of sigma greater than 0) and middle unstable branch (derivative of M-dot/derivative of sigma less than 0) represent structures for which the gas and radiation pressure dominate respectively, the stable upper branch (derivative of M-dot/derivative of sigma greater than 0) is a consequence of the saturation of alpha. This saturation of alpha can occur for large alpha(sub 0) and at M-dot less than or = M-dot(sub Edd). The instability is found to occur at higher mass accretion rates for neutron stars than for black holes. In particular, the disk is locally unstable for M-dot greater than or = 0.5 M-dot(sub Edd) for neutron stars and for M-dot greater than or = M-dot(sub Edd) for black holes for a viscosity prescription characterized by n = 1 and alpha(sub 0) = 10.

Milsom, J. A.↗

NASA NTRS1994

Nonthermal accretion disk models around neutron stars

We consider the structure and emission spectra of nonthermal accretion disks around both strongly and weakly magnetized neutron stars. Such disks may be dissipating their gravitational binding energy and transferring their angular momentum via semicontinuous magnetic reconnections. We consider specifically the structure of the disk-stellar magnetospheric boundary where magnetic pressure balances the disk pressure. We consider energy dissipation via reconnection of the stellar field and small-scale disk turbulent fields of opposite polarity. Constraints on the disk emission spectrum are discussed.

Tavani, M.↗

NASA NTRS1982

Convective accretion disks and the onset of dwarf nova outbursts

Vertically integrated, steady state convective models of accretion disks have been constructed to explore the mechanism of instability in dwarf novae. The models and observations of dwarf novae suggest a picture in which transferred matter piles up in an optically thin torus. The torus eventually becomes optically thick, and the resulting convective structure is thermally unstable. Matter then flows inward, and the sudden conversion of gravitational potential energy to radiation is identified as the dwarf nova outburst. At sufficiently high mass accretion rates, the inflow is continuous.

Cannizzo, J. K.↗

NASA NTRS1993

Effect of radiation forces on disk accretion by weakly magnetic neutron stars

Radiation forces are shown to be more important than general relativistic corrections to Newtonian gravitational forces in determining the motion of particles accreting onto a slowly rotating neutron star if the luminosity of the star is greater than about 1 percent of the Eddington critical luminosity (ECL). This is so even if the radius of the star is less than the radius of the innermost stable orbit. In particular, radiation drag causes matter accreting from a disk to lose angular momentum and spiral inward. At luminosities greater than about 0.2 ECL, a substantial fraction of the accreting matter can transfer most of its angular momentum and gravitational binding energy to the radiation field before reaching the stellar surface. These results have important implications for the X-ray spectra, time variability, and spin evolution of neutron stars with very weak magnetic fields and the prospects for detecting general relativistic effects near such stars.

Miller, M. C.↗

NASA NTRS1984

The nonaxisymmetric baroclinic instability in thin accretion disks

The instability of linear, nonaxisymmetric baroclinic waves in the radiative regions of a thin accretion disk is investigated with simplifying assumptions used in the representation of the structure of the basic state. As in stars with rotation laws deviating from rotation on cylinders, the departure from barotropy ('baroclinicity') resulting from such rotation feeds potential energy from the basic state into the kinetic energy of the baroclinic motions. The baroclinic instability is considered as a possible mechanism for driving turbulence in disks. Estimations of the Reynolds stress from baroclinic waves indicate that the degree of baroclinicity in stationary disk models is insufficient to account for the large viscosity inferred from observations of, e.g., cataclysmic variables.

Cabot, W.↗

NASA NTRS1992

Is the Oort A-value a universal growth rate limit for accretion disk shear instabilities?

A weak-field local MHD instability that is of importance to accretion disks is examined. The maximum growth rate of the instability is found to be not only independent of the magnetic field strength but independent of field geometry as well. In particular, all Keplerian disks are unstable in the presence of any weak poloidal field, with the ratio of the maximum growth rate to disk angular velocity given by 3/4. The maximum growth rate of any weak field configuration that is not purely toroidal is given by the local Oort A-value of the disk. The behavior is studied by using a form of the dynamical Hill equations. It is conjectured that the Oort A-value is an upper bound to the growth rate of any instability feeding upon the free energy of differential rotation.

Balbus, Steven A.↗

NASA NTRS1994

Theory of protostellar accretion disks

I will present an overview of the current paradigm for the theory of gaseous accretion disks around young stars. Protostellar disks form from the collapse of rotating molecular cloud cores. The disks evolve via outward angular momentum transport provided by several mechanisms: gravitational instabilities, thermal convective turbulence, and magnetic stresses. I will review the conditions under which these mechanisms are efficient and consistent with the observed disk evolutionary timescales of several million years. Time permitting, I will discuss outbursts in protostellar disks (FU Orionis variables), the effect of planet formation on disk structure, and the dispersal of remnant gas.

Ruden, S.↗

NASA NTRS2011

AGN Unification, X-Ray Absorbers and Accretion Disk MHD Winds

We present the 2D photoionization structure of the MHD winds of AGN accretion disks. We focus our attention on a specific subset of winds, those with poloidal currents that lead to density profiles n(r) \propto 1/r. We employ the code XSTAR to compute the local ionization balance, emissivities and opacity which are then used in the self-consistent transfer of radiation and ionization of a host of ionic species of a large number of elements over then entire poloidal plane. Particular attention is paid to the Absorption Measure Distribution (AMD), namely their hydrogen-equivalent column of these ions per logarithmic 7 interval, dN_H/dlog ? (? = L/n(r)r(sup 2) is the ionization parameter), which provides a measure of the winds' radial density profiles. For the given density profile, AMD is found to be independent of ?, in good agreement with analyses of Chandra and XMM data, suggesting the specific profile as a fundamental AGN property. Furthermore, the ratio of equatorial to polar column densities of these winds is \simeq 10(exp 4); as such, it is shown they serve as the "torus" necessary for AGN unification with phenomenology consistent with the observations. The same winds are also shown to reproduce the observed columns and velocities of C IV and Fe XXV of SAL QSOs once the proper ionizing spectra and inclination angles are employed.

Kazanas, Demos↗

NASA NTRS1994

Hot accretion disks with pairs: Effects of magnetic field and thermal cyclocsynchrotron radiation

We show the effects of thermal cyclosynchrotron radiation and magnetic viscosity on the structure of hot, two-temperature accretion disks. Magnetic field, B, is assumed to be randomly oriented and the ratio of magnetic pressure to either gas pressure, alpha = P(sub mag)/P(sub gas), or the sum of the gas and radiation pressures, alpha = (P(sub mag)/P(sub gas) + P(sub rad)), is fixed. We find those effects do not change the qualitative properties of the disks, i.e., there are still two critical accretion rates related to production of e(sup +/-) pairs, (M dot)((sup U)(sub cr)) and (M dot)((sup L)(sub cr)), that affect the number of local and global disk solutions, as recently found by Bjoernsson and Svensson for the case with B = 0. However, a critical value of the alpha-viscosity parameter above which those critical accretion rates disappear becomes smaller than alpha(sub cr) = 1 found in the case of B = 0, for P(sub mag) = alpha(P(sub gas) + P(sub rad)). If P(sub mag) = alpha P(sub gas), on the other hand, alpha(sub cr) is still about unity. Moreover, when Comptonized cyclosynchrotron radiation dominates Comptonized bremsstrahlung, radiation from the disk obeys a power law with the energy spectral index of approximately 0.5, in a qualitative agreement with X-ray observations of active galactic nuclei (AGNS) and Galactic black hole candidates. We also extend the hot disk solutions for P(sub mag) = alpha(P(sub gas) + P(sub rad)) to the effectively optically thick region, where they merge with the standard cold disk solutions. We find that the mapping method by Bjoernsson and Svensson gives a good approximation to the disk structure in the hot region and show where it breaks in the transition region. Finally, we find a region in the disk parameter space with no solutions due to the inability of Coulomb heating to supply enough energy to electrons.

Kusunose, Masaaki↗

NASA NTRS2002

Evolution of Pre-Main Sequence Accretion Disks

The aim of this project is to develop a comprehensive global picture of the physical conditions in, and evolutionary timescales of, pre-main sequence accretion disks. The results of this work will help constrain the initial conditions for planet formation. To this end we plan to: (1) Develop much larger samples of 3-10 Myr-old stars to provide better empirical constraints on protoplanetary disk evolution; (2) Study the dusty emission and accretion rates in these systems, with ages closer to the expected epoch of (giant) planet formation at 3-10 Myr; and (3) Develop detailed model disk structures consistent with observations to infer physical conditions in protoplanetary disks and to constrain possible grain growth as the first stage of planetesimal formation.

Hartmann, Lee W.↗

NASA NTRS1994

Nonlinear evolution of tidally distorted accretion disks: Two-dimensional simulations

According to a previously published linear analysis, the tidal distortion of accretion disks in binary star systems produces a local hydrodynamic instability to m = 1 internal waves, which may have arbitrarily small wavelengths in the absence of viscosity. The instability is three-dimensional and approximately incrompressible. To explore the nonlinear outcome of this instability, we develop a shearing-sheet approximation on scales comparable to the disk thickness. The large-scale azimuthal variation of the disk is represented by varying the local metric with time (local orbital phase). The hydrodynamic equations can then be posed two-dimensionally on local meridional planes. We solve these equations with a second-order gasdynamical code based on the Total-Variation-Diminishing scheme. Our simulations confirm the predicted linear growth rate. The modes saturate chaotically at velocities scaling as the product of the linear growth rate and the wavelength. If the wavelength is small compared with the disk thickness, the modes remain nearly incompressible even when nonlinear. The two-dimensional power spectrum of velocities after saturation is roughly isotropic and extends over a broad range of scales in an approximately power-law fashion. We measure the heating rate associated with the nonlinear dissipation of the modes. The dissipation implies a secular torque on the disk and a return of angular momentum to the secondary star via the tidal potential. The estimated torque is somewhat larger than the tidal torque produced by maximal disk viscosity (alpha approximately 1). At least in these two-dimensional simulations, however, there is no significant angular momentum flux within the disk.

Ryu, Dongsu↗