Mapping the shape of the accretion disk of Hercules X‐1

Hercules X‐1 is an x‐ray binary with a 1.7 day orbit and which exhibits a regular 35‐day intensity cycle, which comes in two types: 0.2 orbital phase turn‐on and 0.7 phase turn‐on. The cycle is well measured by the RXTE/ASM and is caused by a sequence of occultations by the inner and outer edges of the accretion disk. In addition to the 35‐day x‐ray cycle, the accretion disk shadows the companion star HZ Her to give the regular and well known optical modulation, and gives a modulation of the EUV emission from the system. The x‐ray modulation is most precisely measured and best for determination of the disk shape. Here disk and emission region models are used to derived the disk shape from the 0.2 turn‐on cycles and compared to a previous derivation based on 0.7 turn‐on cycles. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The specific features of the evolution of the viscous protoplanetary circumsolar disk

The problem of angular-momentum and mass transport in the disk is discussed and the disk viscosity is estimated. The evolution of the gas-dust protoplanetary disk at the stage of its formation inside the protostellar (protosolar) accretion envelope is considered. The conditions for the radial growth of the disk are estimated. For the subsequent period, when the central star (young Sun) is in the T Tauri phase, the temporal variations of the radius, mass, and the surface density of the disk, as well as the total mass flux from the disk onto the star (Sun), i.e., the mass accretion rate, are evaluated. The constraints on the initial value of the angular momentum of the protoplanetary circumsolar disk (that is, on the angular momentum of the protosolar cloud) are discussed with due regard for cosmochemical data.Translated from Astronomicheskii Vestnik, Vol. 38, No. 6, 2004, pp. 559–576.Original Russian Text Copyright © 2004 by Makalkin.     

Anisotropic illumination of a circumbinary disk in the presence of a low-mass companion

The model of a young star with a protoplanetary disk and a low-mass companion (q ≤ 0.1) moving in a circular orbit inclined to the disk plane is considered. Hydrodynamic models of such a system have been calculated by the SPH method. The perturbations in the disk caused by the orbital motion of the companion are shown to lead to a strong dependence of the disk illumination conditions on azimuth (because of extinction variations between the star and the disk surface) and, as a result, to the appearance of a large-scale asymmetry in the disk images. Calculations show that the dependence of the disk illumination on azimuth is stronger in the central part of the disk than on the periphery. The bright and dark (shadow) regions are located asymmetrically relative to the line of nodes. The sizes of these regions and their positions on the disk depend on model parameters and orbital phase. During the orbital motion, the bright and dark regions do not follow the companion but execute small-amplitude oscillations relative to some direction. The model properties described above open up new possibilities for detecting low-mass companions in the vicinity of young stars. Stars with protoplanetary disks seen face-on or at low inclinations i are best suited for this purpose.     

A mathematical model of the initial stage in the formation of a disk galaxy

The collapse of a homogeneous, initially spheroidal halo under self gravitation, has been considered. It is found that a weak magnetic field (as is plausible to belong to such a cloud) has little influence on the collapse, except probably sufficiently close to the centre where the gas density, and consequently the magnetic field, becomes rather high. The equatorial collapse is centrifugally balanced at a certain stage, while collapse in the perpendicular direction continues. A thick stellar disk is formed within a time-scale <3×10⁹ yr. Brisk star formation takes place while the collapse of the gaseous disk is still in progress. This gives rise to the halo stars with low metal content and high Z-motion. A bulge is formed at the centre simultaneously. This is the first phase of formation of a disk galaxy. The thin disk is formed at a later stage as the remaining primordial gas and the gas released by the evolution of stars in the thick disk gradually settles on to it.The presented model is rather a crude one. Many aspects have not been considered, and many details have not been worked out. It is hoped that a more detailed and comprehensive model will be arrived at in the future.Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September–6 October, 1984.     

Wavelength dependence of the polarization of radiation from an accretion disk: Testing accretion disk models

We show that a fundamental choice between various models of an accretion disk around a black hole can be made based on the spectral wavelength distribution of the polarization. This conclusion is based on the possibility of comparing the observed spectral distribution of the polarization with its theoretical values obtained in various accretion disk models. The expected power-law wavelength (frequency) dependences of the polarization for various accretion disk models known in the literature are presented in the table.     

On the metallicity gradient in the Galactic disk

The problem of the chemical composition gradient in the Galactic disk is studied based on a sample of metallicity estimates of open star clusters, using Gaia DR2-improved distance estimates. A clearly non-monotonic variation was observed in the average metallicity of clusters with increasing Galactocentric distance. One can clearly see the metallicity jump of 0.22 in [Fe/H] at a Galactocentric distance of about9.5 kpc, which appears to be linked to the outer boundary of the thinnest and youngest component of the Galactic disk. The absence of a significant metallicity gradient in the internal(R 9 kpc) and external(R 10 kpc) regions of the disk demonstrates the absence of noticeable metal enrichment at times of the order of the ages corresponding to those of the disk regions under consideration. Observational data show that the disk experiences noticeable metal enrichment only during the starburst epochs. No significant dependence was identified between the average metallicity and the age of the clusters.     

The relative orientation of the accretion disk and host galaxy disk in Seyferts

We present the results of the study of the orientation of the accretion disk relative to the host galaxy disk in Seyfert galaxies. We used a sample selected by a mostly isotropic property, the flux at 60 μm, with radio and optical data homogeneously observed and analyzed, to avoid selection effects. We found that the observed i and δ values, galaxy inclination and difference between the position angle of the jet and the galaxy major axis, respectively, are consistent with a random β-distribution, the angle between the jet and the galaxy plane axis. We also found that the previously suggested Zone of Avoidance disappears and was probably due to a selection effect. We suggest several explanations for the misalignment of the accretion disk relative to the galaxy disk.     

Saturn: UBV photoelectric pinhole scans of the disk

UBV pinhole scans of the Saturn disk have been made with a photoelectric area-scanning photometer. Limb profiles, spaced parallel to the equator, were obtained over the entire southern hemisphere of the planet. Saturn was found to exhibit strong limb brightening in the ultraviolet, moderate limb brightening at blue wavelengths, and strong limb darkening in the visual region of the spectrum. Latitudinal variations in the disk profiles were found. In general, the degree of limb brightening decreases towards the polar region. Pronounced asymmetry is apparent in the disk profiles in each color. The sunward limb is significantly brighter than the opposite limb. This asymmetry depends on phase angle; approaching zero at opposition, it reaches a maximum near quadrature. Our observations are interpreted using an elementary radiative transfer model. The Saturn atmosphere is approximated by a finite homogeneous layer of isotropically scattering particles overlying a Lambert scattering haze or cloud layer. The reflectivity of the haze or clouds is a strongly dependent function of wavelength. Our best-fitting model consists of a clear H₂ layer of column density ～31 km-am above the haze or clouds; the maximum permitted H₂ column density is ～46 km-am. The H₂ column density above the equatorial region appears to be less than at temperate latitudes. The phase-dependent asymmetry in the disk profiles is a natural consequence of the scattering geometry. Our results are consistent with current knowledge of the Saturn atmosphere.     

Formation of astrophysical jets by a contracting magnetic accretion disk

In the present paper, we discuss an MHD model for the formation of astrophysical jets, in which the directed flows are ejected along the rotation axis of an accretion disk formed from a cloud having a large scale magnetic field parallel to the angular momentum axis of the disk. The acceleration of jets is due to thej×B force in the relaxing magnetic twist which is produced by the rotation of the disk. The characteristic features of the jets, predicted by our mechanism and hopefully to be proven by observations, are the helical velocity and the hollow cylindrical shape of the jet, with a diameter of roughly the size of the region from which the acceretion disk collected its mass. Justification for the assumption of the perpendicular orientation of the disk, or the parallelism of the jets, to the external magnetic field may be provided by the fact that the component of rotation whose axis is perpendicular to the field may have been damped in the earlier phase of the cloud contraction.Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 Septemper–6 October, 1984.     

Multi-color coronographic imaging of the beta pictoris disk

In this paper we present multicolor images of the Beta Pictoris disk, obtained with a new Coronograph, built at STScI, for ESO's New Technology Telescope. These B, V, and R observations probe the Beta Pictoris circumstellar disk in to a distance of 35 AU (2) from the central star. We derive surface brightness profiles for the disk and discuss the results in the context of two-component disk models (e.g. Backmanet al. 1992), which are based on fits to available optical and infrared data for Beta Pictoris's disk. These models generally imply that the disk is composed of 1) an outer disk extending from 100–1000 AU, with a midplane particle density decreasing as n(r) r^–3, 2) a transition region extending from 10–100 AU with lower density and either smaller grains or a less steep spatial gradient than the outer component, 3) an innermost clear zone with even lower density.     

Open clusters and the galactic disk

It is textbook knowledge that open clusters are conspicuous members of the thin disk of our Galaxy, but their role as contributors to the stellar population of the disk was regarded as minor. Starting from a homogenous stellar sky survey, the ASCC‐2.5, we revisited the population of open clusters in the solar neighbourhood from scratch. In the course of this enterprise we detected 130 formerly unknown open clusters, constructed volume‐ and magnitude‐limited samples of clusters, re‐determined distances, motions, sizes, ages, luminosities and masses of 650 open clusters. We derived the present‐day luminosity and mass functions of open clusters (not the stellar mass function in open clusters), the cluster initial mass function CIMF and the formation rate of open clusters. We find that open clusters contributed around 40 percent to the stellar content of the disk during the history of our Galaxy. Hence, open clusters are important building blocks of the Galactic disk (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Gravitational instability in the dust layer of a protoplanetary disk: Interaction of solid particles with turbulent gas in the layer

Gravitational instability of the dust layer formed after the aggregates of dust particles settle toward the midplane of a protoplanetary disk under turbulence is considered. A linearized system of hydrodynamic equations for perturbations of dust (monodisperse) and gas phases in the incompressible gas approximation is solved. Turbulent diffusion and the velocity dispersion of solid particles and the perturbation of gas azimuthal velocity in the layer upon the transfer of angular momentum from the dust phase due to gas drag are taken into account. Such an interaction of the particles and the gas establishes upper and lower bounds on the perturbation wavelength that renders the instability possible. The dispersion equation for the layer in the case when the ratio of surface densities of the dust phase and the gas in the layer is well above unity is obtained and solved. An approximate gravitational instability criterion, which takes the size-dependent stopping time of a particle (aggregate) in the gas into account, is derived. The following parameters of the layer instability are calculated: the wavelength range of its subsistence and the dependence of the perturbation growth rate on the perturbation wavelength in the circumsolar disk at a radial distance of 1 and 10 AU. It is demonstrated that at a distance of 1 AU, the gas–dust disk should be enriched with solids by a factor of 5–10 relative to the initial abundance as well as the particle aggregates should grow to the sizes higher than about 0.3 m in order for the instability to emerge in the layer in the available turbulence models. Such high disk enrichment and aggregate growth is not needed at a distance of 10 AU. The conditions under which this gravitational instability in the layer may be examined with no allowance made for the transfer of angular momentum from the gas in the layer to the gas in a protoplanetary disk outside the layer are discussed.     

On disk accretion

A simple but sufficiently accurate method for calculating an accretion disk structure is developed. The detailed analysis of the accretion disk is fulfilled by using this method. The effect of turbulent heat transfer on the disk structure is taken into account along with the effect of radiative transfer. The turbulent heat transfer is shown to play an important role, and may be even predominant in the inner disk region. The dependence of temperatureT and density on thez-coordinate is found. Simple analytic expressions are proposed for the run of the density in all the disk zones. It is shown that the inner disk region is convectively stable. The main parameters of all the zones are derived. The geometry of regular motions is studied; the regular hydrodynamical flows are found to appear directed both toward and outside the central object. A detailed comparison is made with the results of other authors.     

On the disk wind mass loss rates in QSOs

We derive here a relatively simple expression for the total wind mass loss rates in QSOs within the accretion disk wind scenario. We show that the simple expression derived here for QSO disk wind mass loss rate is in a very good agreement with the more “exact” values obtained through significantly more complex and detailed numerically intensive 2.5D time-dependent simulations. Additionally we show that for typical QSO parameters, the disk itself will be emitting mostly in the UV/optical spectrum, in turn implying that the X-ray emission from QSOs likely is produced through some physical mechanism acting at radii smaller than the inner disk radius (for a standard accretion disk, half of the initially gravitational potential energy of the accreting disk mass is emitted directly by the disk, while the other half “falls” closer towards the black hole than the inner disk radius). We also show that for typical QSO parameters, the disk itself is dominated by continuum radiation pressure (rather than thermal pressure), resulting in a “flat disk” (except for the innermost disk regions).     

Physics of the primitive solar accretion disk

The theory of viscous accretion disks developed by Lynden-Bell and Pringle has been applied to the evolution of the primitive solar nebula. The additional physical input needed to determine the structure of the disk is described. A series of calculations was carried out using a steady flow approximation to explore the effects on the disk properties of variations in such parameters as the angular momentum and accretion rate of the infalling material from a collapsing interstellar cloud fragment. The more detailed evolutionary calculations involved five cases with various combinations of parameters. It was concluded that the late stages of evolution of the disks would be dominated by the effects of mass loss from the expansion of a hot disk corona into space, and the effects of this were included in the evolutionary calculations. A new theory of comet formation is formulated upon these results. The most important result is the conclusion, which appears to be inescapable, that the primitive solar accretion disk was repeatedly unstable against axisymmetric perturbations, in which rings would form and collapse upon themselves, with the subsequent formation of giant gaseous protoplanets.     

Photoionization of cool MHD disk winds

Recent ultraviolet observations point out that there is hot, dense plasma associated with the optical jet in some T Tauri stars. In this contribution, cool MHD disk wind physics is reviewed by means of a self-similar analytical model to analyze whether hot (Te ? 80,000 K) and dense (n_e ? 10⁹ cm^-3) plasma can be produced in disk winds. It is shown that these high densities can only be achieved at the base of the wind where the stellar X-rays radiation field is strong. The propagation of the X-rays radiation through the disk wind is analyzed: a cocoon of photoionized gas is generated around the star. However, it is difficult to foresee how temperatures as high as ～ 5 × 10⁴ can be reached unless a significant fraction of the X-rays radiation is produced by magnetic reconnection at the boundary between the stellar magnetosphere and the accretion disk.     

Structure of the satellitary accretion disk of Saturn

A detailed computation on the equilibrium structure of an accretion disk around Saturn from which the regular satellites presumably originated is reported. Such a disk is the predecessor of the self-dissipating disk that is formed when the mass infall stops (Cassen and Moosman, 1981, Icarus48, 353–376). When determining the disk structure local energy balance was assumed. Convention was taken into account by introducing local energy dissipation and, in an approximate manner, sonic convection. Changes in the disk structure were investigated by varying the free parameters, i.e., the external flux from both the protosun and the protoplanet, the abundance of dust and the strength of turbulence. It has been verified that the external energy flux does not play an important role in the evolution of the disk structure. Models characterized by either longer times (?3 10³ year) or a noticeable depletion of condensable elements (10^?2 times less than the solar value) have a total mass of the order of 0.34?0.1 times the mass of the regular satellites increased by the mass of the light elements. Low turbulence models (Reynolds critical number $\text{Re}{}^1\text{= 150}$) are characterized approximately by a total mass twice as large the mass of the regular satellites. All the studied models present a temperature distribution that allows the condensation of iron, silicate, and, in the outer regions, ice grains. All models but the one with 10^?2 of the solar value of condensable elements are characterized by a wide convective region that contains the formation zone of the regular satellites.     

Two-dimensional models of proto planetary disk chemistry

We have developed a two-dimensional model of a flared protoplanetary disk (PPD) incorporating a self-consistent treatment of gas and dust temperature, and a detailed treatment of the gas-phase chemistry as well as the freeze-out and desorption of material from dust grains. The results show that, in the inner 10 AU of the disk, the gas-phase abundances are dominated by material evaporated from dust grains. The surface layer of the disk shows many of the characteristics of photon-dominated regions. This revised version was published online in July 2006 with corrections to the Cover Date.     

Fundamentals of the mechanics of heterogeneous media in the circumsolar protoplanetary cloud: The effects of solid particles on disk turbulence

We formulate a complete system of equations of two-phase multicomponent mechanics including the relative motion of the phases, coagulation processes, phase transitions, chemical reactions, and radiation in terms of the problem of reconstructing the evolution of the protoplanetary gas-dust cloud that surrounded the proto-Sun at an early stage of its existence. These equations are intended for schematized formulations and numerical solutions of special model problems on mutually consistent modeling of the structure, dynamics, thermal regime, and chemical composition of the circumsolar disk at various stages of its evolution, in particular, the developed turbulent motions of a coagulating gas suspension that lead to the formation of a dust subdisk, its gravitational instability, and the subsequent formation and growth of planetesimals. To phenomenologically describe the turbulent flows of disk material, we perform a Favre probability-theoretical averaging of the stochastic equations of heterogeneous mechanics and derive defining relations for the turbulent flows of interphase diffusion and heat as well as for the “relative” and Reynolds stress tensors needed to close the equations of mean motion. Particular attention is given to studying the influence of the inertial effects of dust particles on the properties of turbulence in the disk, in particular, on the additional generation of turbulent energy by large particles near the equatorial plane of the proto-Sun. We develop a semiempirical method of modeling the coefficient of turbulent viscosity in a two-phase disk medium by taking into account the inverse effects of the transfer of a dispersed phase (or heat) on the growth of turbulence to model the vertically nonuniform thermohydrodynamic structure of the subdisk and its atmosphere. We analyze the possible “regime of limiting saturation” of the subdisk atmosphere by fine dust particles that is responsible for the intensification of various coagulation mechanisms in a turbulized medium. For steady motion when solid particles settle to the midplane of the disk under gravity, we analyze the parametric method of moments for solving the Smoluchowski integro-differential coagulation equation for the particle size distribution function. This method is based on the fact that the sought-for distribution function a priori belongs to a certain parametric class of distributions.