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NASA NTRS1993

Studies of extra-solar OORT clouds and the Kuiper disk

This is the second report for NAGW-3023, Studies of Extra-Solar Oort Clouds and the Kuiper Disk. We are conducting research designed to enhance our understanding of the evolution and detectability of comet clouds and disks. This area holds promise for also improving our understanding of outer solar system formation, the bombardment history of the planets, the transport of volatiles and organics from the outer solar system to the inner planets, and the ultimate fate of comet clouds around the Sun and other stars. According to 'standard' theory, both the Kuiper Disk and Oort Cloud are (at least in part) natural products of the planetary accumulation stage of solar system formation. One expects such assemblages to be a common attribute of other solar systems. Therefore, searches for comet disks and clouds orbiting other stars offer a new method for infering the presence of planetary systems. Our three-year effort consists of two major efforts: (1) observational work to predict and search for the signatures of Oort Clouds and comet disks around other stars; and (2) modelling studies of the formation and evolution of the Kuiper Disk (KD) and similar assemblages that may reside around other stars, including Beta Pic. These efforts are referred to as Task 1 and 2, respectively.

Stern, S. Alan↗
NASA NTRS1993

Physical properties and evolutionary time scales of disks around solar-type and intermediate mass stars

Recent observations of circumstellar disks and their evolutionary timescales are reviewed. It is concluded that disks appear to be a natural outcome of the star-formation process. The disks surrounding young stars initially are massive, with optically thick structures comprised of gas and micron-sized grains. Disk masses are found to range from 0.01 to 0.2 solar masses for solar-type PMS stars, and from 0.01 to 6 solar masses for young, intermediate mass stars. Massive, optically thick accretion disks have accretion rates between 10 exp -8 and 10 exp -6 solar masses/yr for solar type PMS stars and between 10 exp -6 and 10 exp -4 solar masses/yr for intermediate stars. The results suggest that a significant fraction of the mass comprising the star may have passed through a circumstellar accretion disk.

Strom, Stephen E.↗
NASA NTRS1947

Determination of elastic stresses in gas-turbine disks

A method is presented for the calculation of elastic stresses in symmetrical disks typical of those of a high-temperature gas turbine. The method is essentially a finite-difference solution of the equilibrium and compatibility equations for elastic stresses in a symmetrical disk. Account can be taken of point-to-point variations in disk thickness, in temperature, in elastic modulus, in coefficient of thermal expansion, in material density, and in Poisson's ratio. No numerical integration or trial-and-error procedures are involved and the computations can be performed in rapid and routine fashion by nontechnical computers with little engineering supervision. Checks on problems for which exact mathematical solutions are known indicate that the method yields results of high accuracy. Illustrative examples are presented to show the manner of treating solid disks, disks with central holes, and disks constructed either of a single material or two or more welded materials. The effect of shrink fitting is taken into account by a very simple device.

Manson, S S↗
NASA NTRS1994

Studies of extra-solar Oort Clouds and the Kuiper Disk

The March 1994 Semi-Annual report for Studies of Extra-Solar Oort Clouds and the Kuiper Disk is presented. We are conducting research designed to enhance our understanding of the evolution and detectability of comet clouds and disks. This area holds promise for also improving our understanding of outer solar system formation, the bombardment history of the planets, the transport of volatiles and organics from the outer solar system to the inner planets, and to the ultimate fate of comet clouds around the Sun and other stars. According to 'standard' theory, both the Kuiper Disk and Oort Cloud are (at least in part) natural products of the planetary accumulation stage of solar system formation. One expects such assemblages to be a common attribute of other solar systems. Therefore, searches for comet disks and clouds orbiting other stars offer a new method for inferring the presence of planetary systems. Our three-year effort consists of two major efforts: observational work to predict and search for the signatures of Oort Clouds and comet disks around other stars; and modeling studies of the formation and evolution of the Kuiper Disk (KD) and similar assemblages that may reside around other stars, including beta Pic.

Stern, S. Alan↗
NASA NTRS1994

Nonlinear calculations of the time evolution of black hole accretion disks

Based on previous works on black hole accretion disks, I continue to explore the disk dynamics using the finite difference method to solve the highly nonlinear problem of time-dependent alpha disk equations. Here a radially zoned model is used to develop a computational scheme in order to accommodate functional dependence of the viscosity parameter alpha on the disk scale height and/or surface density. This work is based on the author's previous work on the steady disk structure and the linear analysis of disk dynamics to try to apply to x-ray emissions from black candidates (i.e., multiple-state spectra, instabilities, QPO's, etc.).

Luo, C.↗
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 NTRS1994

Thermal continua of AGN accretion disks

We have computed the thermal continuum energy distribution of thermal radiation from the atmospheres of supermassive accretion disks around supermassive black holes. Non-LTE radiative transfer is combined with a model of the vertical structure at each radius appropriate to the low effective gravities of these disks. Locally, the Lyman edge of H can be in emission or absorption. When the emission is summed over the disk with Doppler and gravitational redshifts taken into account, the observed continuum typically shows little sign of a discontinuity near the Lyman edge. For relatively cool disks, the Lyman edge is in absorption, but it appears as a slope change extending over several hundred angstroms, rather than an abrupt discontinuity. Disks around Kerr black holes can explain the observed range of soft X-ray luminosities of AGN, but disks around Schwarzschild holes are much too faint in soft X-rays.

Shields, G. 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 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

Non-LTE effects on the strength of the Lyman edge in quasar accretion disks

We have calculated UV/EUV (300 A which is less than or equal to lambda which is less than or equal to 1500 A) continuous energy distributions of accretion disks in the centers of active galactic nuclei (AGNs) for disk luminosities in the range 0.1 L(sub Edd) less than or equal to L(sub acc) less than 1.0 L(sub Edd) and central masses ranging from 10(exp 8) solar mass to 10(exp 9) solar mass. The vertical gas pressure structure of the disk and the disk height are obtained analytically; the temperature stratification and the resulting continuum radiation fields are calculated numerically. We have included non-Local Thermodynamic Equilibrium (LTE) effects of both the ionization equilibrium and the level populations of hydrogen and helium. We show that these non-LTE effects reduce the strength of the Lyman edge when comapred to the LTE case. In non-LTE we find that the edge can be weakly in emission or absorption for disks seen face-on, depending on the disk parameters.

Stoerzer, H.↗
NASA NTRS1994

Low-frequency modes and nonbarotropic effects in pseudo-Newtonian accretion disks

A recently developed formalism is used to reexamine the question of the existence of hydrodynamical modes that pulsate with very low frequencies in the inner regions of accretion disks. The formalism is valid in an exact sense for the adiabatic pulsations of rotating Newtonian fluids that are generally nonbarotropic (such as those with 'nonadiabatic temperature gradients,' for example), and hence its application in the present context represents an improvement over previous analyses that are more approximate. The formalism is applied to thin non-self-gravitating disks, with the gravitational potential of the central source modified in the usual way in order to simulate relativistic effects. In the barotropic limit, the analyses indicate that in many cases nearly Keplerian disks exhibit nonaxisymmetric modes of pulsation that are trapped in the inner disk regions, with pulsation periods much longer than the dynamical timescale. These results are similar to those of earlier calculations that assume disks pulsate without changing the temperature distribution. A method is developed for including lowest order nonbarotropic effects. Previous analyses have been incapable of accurately treating the nonbarotropic regime. The application of the present method to the low-frequency modes reveals that, due to unexpected cancellations among terms, the nonbarotropic correction to the pusation frequency omega is only of order tilde-omega(sub BV exp 2) omega, where tilde-omega(sub BV) is the appropriate dimensionless Brunt-Vaisala frequency. This correction is much smaller than the expected correction of order tilde-omega(sub BV) Omega, where Omega is the rotation angular velocity. The important conclusion drawn from this is that nonbarotropic corrections are generally small and hence that low-frequency modes persist into the nonbarotropic regime. For disk temperatures appropriate to X-ray emission, the adiabatic frequencies of trapped modes are of the same order as the frequencies associated with quasi-periodic oscillations (QPOs) of certain low-mass X-ray binaries and other X-ray sources. It is suggested that further consideration be given to the possiblity that modulation of emission processes by these modes can explain at least some of the QPO phenomena.

Ipser, James R.↗
NASA NTRS1994

Light echo detection of circumstellar disks around flaring stars

Light echoes can be used to detect and characterize disks around flaring stars. Such disks are thought to be a hallmark of planet formation but are very difficult to detect by ordinary means. Dwarf emission-line M stars experience flares with luminosities comparable to their quiescent photospheres on time scales of minutes, less than the light travel time across a disk many astronomical units in extent; they are thus ideal candidates for such a search. Bromley (1992) calculated that the detection of Jupiter-sized companions using light echoes requires photometric accuracies better than 1 part in 10(exp 6). However, a disk consisting of grains or small bodies will scatter a much larger fraction of the light than a planet of similar mass. I estimate the light echo amplitutdes from plausible geometries of circumstellar material and present simulation light curves. The light echo amplitudes are typically 1% of the flare and I conclude that such events will be detected best in cases where the flare is eclipsed by the star. An examination of the time scales associated with internal processes in a protoplanetary disks around dM stars indicates that any primordial disks may become undetectable in 10(exp 4) years and will have completely disappeared by 10(exp 8) years, the estimated age of dMe stars in the solar neighborhood. However, searches for light echoes might constrain the amount of material continuing to fall into these young stellar systems in the form of comet-like objects.

Gaidos, Eric J.↗
NASA NTRS1995

Variability of accretion disks surrounding black holes: The role of inertial-acoustic mode instabilities

The global nonlinear time-dependent evolution of the inertial-acoustic mode instability in accretion disks surrounding black holes has been investigated. The viscous stress is assumed to be proportional to the gas pressure only, i.e., tau = alphap(sub g). It is found that an oscillatory nonsteady behavior exists in the inner regions of disks (r is less than 10r(sub g) where r(sub g) is the Schwarzschild radius) for sufficiently large alpha(greater than or approximately equal to 0.2) and for mass accretion rates less than about 0.3 times the Eddington value. The variations of the integrated bolometric luminosity from the disk, Delta L/L, are less than 3%. A power spectrum analysis of these variations reveals a power spectrum which can be fitted to a power-law function of the frequency Pis proportional to f(exp -gamma), with index gamma = 1.4-2.3 and a low-frequency feature at about 4 Hz in one case. In addition, a narrow peak centered at a frequency corresponding to the maximum epicyclic frequency of the disk at approximately 100-130 Hz and its first harmonic is also seen. The low-frequency modulations are remarkably similar to those observed in black hole candidate systems. The possible existence of a scattering corona in the inner region of the disk and/or other processes contributing to the power at high frequencies in the inner region of the accretion disk may make the detection of the high-frequency component difficult.

Chen, Xingming↗
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 NTRS1995

Studies of extra-solar Oort Clouds and the Kuiper Disk

This is the September 1995 Semi-Annual report for Studies of Extra-Solar Oort Clouds and the Kuiper Disk. We are conducting research designed to enhance our understanding of the evolution and detectability of comet clouds and disks. This area holds promise for also improving our understanding of outer solar system formation the bombardment history of the planets, the transport of volatiles and organics from the outer solar system to the inner planets, and to the ultimate fate of comet clouds around the Sun and other stars. According to 'standard' theory, both the Kuiper Disk and the Oort Cloud are (at least in part) natural products of the planetary accumulation stage of solar system formation. One expects such assemblages to be a common attribute of other solar systems. Therefore, searches for comet disks and clouds orbiting other stars offer a new method for inferring the presence of planetary systems. This project consists of two major efforts: (1) observational work to predict and search for the signatures of Oort Clouds and comet disks around other stars; and (2) modelling studies of the formation and evolution of the Kuiper Disk (KD) and similar assemblages that may reside around other stars, including beta Pic. These efforts are referred to as Task 1 and 2.

Stern, Alan↗
NASA NTRS1996

Dust Coagulation in Protoplanetary Accretion Disks

The time evolution of dust particles in circumstellar disk-like structures around protostars and young stellar objects is discussed. In particular, we consider the coagulation of grains due to collisional aggregation. The coagulation of the particles is calculated by solving numerically the non-linear Smoluchowski equation. The different physical processes leading to relative velocities between the grains are investigated. The relative velocities may be induced by Brownian motion, turbulence and drift motion. Starting from different regimes which can be identified during the grain growth we also discuss the evolution of dust opacities. These opacities are important for both the derivation of the circumstellar dust mass from submillimeter/millimeter continuum observations and the dynamical behavior of the disks. We present results of our numerical studies of the coagulation of dust grains in a turbulent protoplanetary accretion disk described by a time-dependent one-dimensional (radial) alpha-model. For several periods and disk radii, mass distributions of coagulated grains have been calculated. From these mass spectra, we determined the corresponding Rosseland mean dust opacities. The influence of grain opacity changes due to dust coagulation on the dynamical evolution of a protostellar disk is considered. Significant changes in the thermal structure of the protoplanetary nebula are observed. A 'gap' in the accretion disk forms at the very frontier of the coagulation, i.e., behind the sublimation boundary in the region between 1 and 5 AU.

Schmitt, W.↗
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 NTRS1997

Numerical Modeling of Tidal Effects in Polytropic Accretion Disks

A two-dimensional time-dependent hybrid Fourier-Chebyshev method of collocation is developed and used for the study of tidal effects in accretion disks, under the assumptions of a polytropic equation of state and a standard alpha viscosity prescription. Under the influence of the m = 1 azimuthal component of the tidal potential, viscous oscillations in the outer disk excite an m = 1 eccentric instability in the disk. While the m = 2 azimuthal component of the tidal potential excites a Papaloizou-Pringle instability in the inner disk (a saturated m = 2 azimuthal mode), with an elliptic pattern rotating at about a fraction (approx. = 1/3) of the local Keplerian velocity in the inner disk. The period of the elliptic mode corresponds well to the periods of the short-period oscillations observed in cataclysmic variables. In cold disks (r(Omega)/c(sub s) = M approx. = 40) we also find a critical value of the viscosity parameter (alpha approx. = 0.01), below which shock dissipation dominates and is balanced by the wave amplification due to the wave action conservation. In this case the double spiral shock propagates all the way to the inner boundary with a Mach number M(sub s) approx. = 1.3.

Godon, Patrick↗