The development of large-scale instability in stellar accretion disks and its influence on the redistribution of angular momentum

The paper continues our studies of large-scale instability arising during shearmotions in stellar accretion disks due to the development of small perturbations. The evolution of a local perturbation introduced into the outer part of a stationary accretion disk is modeled mathematically. The possible formation of large-scale structures that propagate throughout the disk, leading to an appreciable redistribution of angular momentum, is demonstrated.     

Magneto-rotational instability in the accreting envelope of a protostar and the formation of the large-scale magnetic field

We investigate the role of the magnetic field in the collapse of a gas-dust cloud into a massive gravitating object. Observations of one such object (G31.41) indicate that the magnetic field has an hourglass shape oriented along the rotation axis of the matter, due to the freezing-in of the magnetic-field lines in the accreting matter. It is believed that accretion in stellar disks is associated with the transport of angular momentum from the center to the periphery, which could be initiated by large-scale vortex structures arising in the presence of unstable rotational flows of matter. The numerical simulations have established that the equilibrium configuration of a gas-dust disk rotating in a spherically symmetrical gravitational potential is subject to the development of strong instability in the presence of a weak magnetic field. It is shown that the development of instability leads to a transport of angular momentum to the disk periphery by large-scale vortex structures, together with the accretion of matter onto the gravitating object. The magnetic-field lines near the equator take on a chaotic character, but an hourglass configuration is observed near the rotation axis, in agreement with observations.     

The development of large-scale instability in Keplerian stellar accretion disks

Our previous studies of large-scale vortical flows arising in shear flows of stellar accretion disks with Keplerian azimuthal velocity distributions as a result of the development of small perturbations are continued. The development of large-scale instability in an accretion disk is investigated via mathematical modeling. One result obtained is the change of the disk flow structure due to the formation of large vortices. In the limiting case, sufficiently long evolution leads to the formation of several asymmetric spiral structures of the flow of disk matter. The presence of large-scale structures leads to angular-momentum redistribution in the disk.     

Over-reflection instability and the developed turbulence in accretion disks in close binaries

The results of studies of the over-reflection mechanism for the development of hydrodynamical instability in the accretion disks of close binary stars are presented. The driving of this instability is shown to result in the generation of regular, large-scale, spiral-vortex structures and the development of turbulence in the disk. The derived estimates of the coefficient of turbulent viscosity are in good agreement with the observations, and are able to explain the high rate of angular-momentum transfer and the measured accretion rate. The developed theoretical model is used with the observational data to derive a power-law spectrum for the developed turbulence.     

Formation of planetary systems and brown dwarfs around single stars

The conditions for the formation of planets and brown dwarfs around single main-sequence stars are considered in two scenarios. The formation of planets and brown dwarfs requires that the initial specific angular momentum of a solar-mass protostar be (0.32)×10¹⁸ cm²/s. The accreted matter of the protostar envelope forms a compact gas ring (disk) around the young star. If the viscosity of the matter in this ring (disk) is small, increasing its mass above a certain limit results in gravitational instability and the formation of a brown dwarf. If the viscosity of the gas is sufficiently large, the bulk of the protostar envelope material will be accreted by the young star, and the gas disk will grow considerably to the size of a protoplanetary dust disk due to the conservation of angular momentum. The formation of dust in the cool part of the extended disk and its subsequent collisional coalescence ultimately results in the formation of solar-type planetary systems.     

Influence of luminosity bursts on properties of protostellar disks

A (2+ 1)-dimensional numerical model for the formation and evolution of young stellar objects with sub-solar masses is presented. The numerical hydrodynamicall code describing the formation and evolution of a pølar disk in a two-dimensional approximation is supplemented by one-dimensional code for the evolution of the star and an algorithm for establishing the vertical structure of the disk. This code is used to investigate the influence of luminosity bursts with intensities similar to those observed in FU Orionis objects (FUors) on the properties and thermal balance of pølar disks. A model with gravitational instability and fragmentation of the disk, with subsequent migration of the fragments onto the protostar, is used as a basic model for FUors. Typical FUor bursts (L ～ 100 L ^⊙) can appreciably influence the thermal balance of their disks and parent envelopes, leading to an increase in the disk temperature by more than a factor of two. On the other hand, massive fragments in the disk are only weakly perturbed by such bursts, partially due to screening by the disk and partially due to their high temperature brought about by adiabatic heating. Apart from massive fragments, the characteristic thermal time scales are appreciably shorter than the dynamical time scales throughout the radial extent of the disk and envelope; this enables the use of a stationary radiative-transfer equation when determining the vertical structure of the disk.     

Periodic instabilities in protostellar disks with azimuthal magnetic fields

The stability of magnetohydrodynamic oscillations in a protostellar disk with a toroidal magnetic field is analyzed. It is shown that, apart from the aperiodic magnetorotational instability, two other types of periodic instabilities of non-axisymmetric perturbations can exist. The simultaneous presence of azimuthal and vertical components of the wave vector are necessary for these to exist. One instability is due to the inductive winding-up of the azimuthal magnetic field of the wave, and the other arises when the field amplitude is increased by a comoving Hall wave, transferring magnetic field into a region of enhanced field intensity. The bandwidths of the unstable wave numbers are analyzed as a function of the Hall current, the β parameter of a plasma, and the angle between the direction of wave propagation and the plane of the disk. Regions in the accretion disks typical of T Tauri stars are indentified where these instabilities could be most active.     

Hall instability in protostellar disks

Non-axial perturbations of a protostellar disk possessing vertical and azimuthal magnetic-field components are studied in the framework of Hall magnetohydrodynamics. The convective transport of the magnetic field by the Hall current leads to instability of fluctuations within a limited interval of wave numbers. The fundamental possibility of the existence of Hall instability in a medium that does not contain an inhomogeneous density distribution, which has not been discussed earlier, is demonstrated. The dependence of the instability increment on both the plasma parameter ?? and the degree of ionization of the protostellar material are analyzed. Possible consequences for weakly ionized astrophysical disks are discussed.     

Effect of the initial density and angular-velocity profiles of pre-stellar cores on the properties of young stellar objects

The physical properties of young stellar objects are studied as functions of the initial spatial distributions of the gas surface density Σ and angular velocity Ω in pre-stellar cores using numerical hydrodynamic simulations. Two limiting cases are considered: spatially homogeneous cores with Σ = const and Ω = const and centrally concentrated cores with radius-dependent densities Σ ∝ r ⁻¹ and Ω ∝ r ⁻¹. The degree of gravitational instability and protostellar disk fragmentation is mostly determined by the initial core mass and the ratio of the rotational to the gravitational energy, and depends only weakly on the initial spatial configuration of pre-stellar cores, except for the earliest stages of evolution, when models with spatially homogeneous cores can be more gravitationally unstable. The accretion of disk matter onto a protostar also depends weakly on the initial distributions of Σ and Ω, with matter from the collapsing core falling onto the disk at a rate that is slightly higher in models with spatially homogeneous cores. An appreciable dependence of the disk mass, disk radius, and the disk-to-protostar mass ratio on the initial density and angular velocity profiles of the parent core is found only for class 0 young objects; this relationship is not systematic in the later I and II stages of stellar evolution. The mass of the central protostar depends weakly on the initial core configuration in all three evolutionary stages.     

Excitation of Turbulence in Protoplanetary Disks around Binary Stars

Accretion disks around young binary stars are subject to strong forces exerted by the system components. Gas–dynamical interactions excite strong non-linear perturbations in the disk, which can give rise to turbulence. This study considers a mechanism for the excitation of turbulence based on the instability of non-linear waves in a rotating flow. It is shown that the spectrum of non-linear perturbations excited in the inner part of the disk leads to turbularization of the flow. Estimates of the Shakura–Syunyaev index, α ～ 0.01?0.05, are obtained for use in numerical models of accretion disks.     

Disk boundaries in spiral galaxies

We explore the hypothesis that the outer boundaries (“cutoffs”) of the stellar disks observed in many galaxies are determined by the condition of local gravitational (Jeans) stability for the gaseous protodisks at large galactocentric distances. The ratio of the surface density of the disk Σ_disk to the critical value for Jeans instability Σ_crit is computed for a number of galaxies, assuming that the gas velocity dispersion in the forming disk corresponded to its current thickness and that the disk itself is in a quasi-equilibrium state. The mean estimated stellar velocity dispersion in the vicinity of the cutoff (12 km/s) is close to the typical velocity dispersions of gaseous clouds in disk galaxies. At greater distances, such velocity dispersions should ensure gravitational stability of the disk both at the present epoch and in the past. The cutoff radius of the disk R _cut is correlated with other disk parameters, and the ratio Σ_disk/Σ_crit at R _cut is close to unity in most cases. We conclude that the available observational data agree well with the hypothesis that stellar disk cutoffs are due to a rapid decrease in the star-formation rate beyond R _cut, where the gaseous disk has always been stable.     

Excitation of turbulence in accretion disks of binary stars by non-linear perturbations

Accretion disks in binary systems can experience hydrodynamical influences at both their inner and outer edges. The former is typical for protoplanetary disks around young T Tauri stars, while the latter is typical for circumstellar disks in close binaries. This influence excites perturbations with various scales and amplitudes in the disk. The nonlinear evolution of perturbations with a finite, but small amplitude against the background of a sub-Keplerian flow is investigated. Nonlinear effects at the fronts of perturbation waves lead to the formation of discontinuities in the density and radial velocity; i.e., to formation of shocks. The tangential flow in the neighborhood of the shock becomes equivalent to a flow in a boundary layer. Due to an instability of the tangential flow, the disk becomes turbulent. The characteristics of the turbulence depend on the parameters of the perturbations, but the Shakura–Syunyaev α parameter does not exceed ~0.1.     

Observational Manifestations of the Precessional Wave in the Accretion Disk of a Cataclysmic Variable Star

Effects due to the interaction of the steam from the inner Lagrangian point with the accretion disk in a cataclysmic variable star are considered. The results of three-dimensional gas-dynamical numerical simulations confirm that the disk thickness in the vicinity of the interaction with the stream is minimum when the component-mass ratio is 0.6. As a consequence, some of the matter from the stream does not collide with the outer edge of the accretion disk, and continues its motion unperturbed toward the accretor. This part of the stream subsequent interacts (collides) with a thickening of the accretion disk due to the presence of a precessional wave in the disk, leading to the appearance of an additional zone of heating at the disk surface. This additional zone of enhanced luminosity (hot spot) is a direct observational manifestation of the precessional wave in the accretion disk.     

Turbulence in the Accretion Disks in Semi-Detached Binary Systems with Various Component-Mass Ratios

Results of three-dimensional gas-dynamical numerical simulations of the structure of matter flows in semi-detached binary systems with various component-mass ratios are considered. The main elements of the flows in the models studied are described. The characteristics of density waves inside the accretion disk for various component-mass ratios are considered. The influence of the precessional density wave on the development of instability in the accretion disks and the characteristics of developing turbulence are analyzed. Values of the Shakura–Syunyaev coefficient α for the simulated systems are calculated.     

Three-dimensional hydrodynamical modeling of the formation of the accretion disk in the SS 433 binary system

Three-dimensional hydrodynamical modeling of the formation of the accretion disk in the SS 433 binary system is carried out with various types of cooling and numerical grids. These computations show that a thick accretion disk with a height of 0.25–0.30 (in units of the component separation) is formed around the compact object, from a flow with a large radius (0.2–0.3 in the same units) that forms in the vicinity of the inner Lagrangian point. This disk has the form of a flattened torus. The number of orbits of a particle of gas in the disk is 100–150, testifying to a minimal influence of numerical viscosity in these computations. The computations also show that the stream flowing from L₁ is nearly conservative, and spirals in the disk are not formed due to the influence of the donor gravitation.     

Structure of the accretion disk in the cataclysmic variable UX UMa in the transition to its quiescent state

Our analysis of BV RI light curves for the cataclysmic variable UX UMa obtained in intermediate activity states, in the transition between the active and quiescent states of the system on March 12, 1997 and May 3, 2000, shows that the shapes of these light curves cannot be adequately described using the standard hot-spot model. A model with a “hot line” near the edge of the disk and a two-armed spiral structure on the disk surface reproduces much better out-of-eclipse variations in the light curves. The presence of an extended hot line can explain the anomalous shape of the I light curve on March 12, 1997. The decrease in the observed luminosity of the system between March 12, 1997 and May 3, 2000 could be due to a decrease in the disk luminosity by a factor of 2–2.5; the higher disk luminosity on the earlier date is associated with appreciable deviations of the radial temperature distribution of the disk material from that for the standard model. The phases and depths of dips in the out-of-eclipse sections of the UX UMa light curves are due primarily to the parameters of the complex shape of the accretion disk, which has a spiral structure located mainly near its outer edge. The contribution of the spiral arms in the V filter reaches 20–50% of the total disk radiation. The crest of the first spiral wave in our model maintains its approximate position in azimuth; this structure could represent a bulge in a halo at the outer edge of the disk near orbital phases φ ～ 0.7, in the direction of the continuation of the extended shock in the disk itself. The position of the crest of the second spiral arm changes with time. This structure may represent a one-armed spiral wave near the apastron of the weakly elliptical disk. Finally, the observations testify to the presence of another spiral arm that is les clearly manifest in terms of both its luminosity and its height above the unperturbed disk surface. Thus, in an intermediate activity state of UX UMa, the surface of the accretion disk is distorted by the action of a two-armed spiral structure in the outer regions of the disk, which is asymmetric in both its luminosity and dimensions, and a bulge at the disk edge in the region of its interaction with the inflow to the disk.     

A dipolar vortex model for the obscuring tori in active galactic nuclei

Motivated by currently available direct observations of occulting tori in Seyfert galaxies and ongoing discussions about tori as important structural components in Active Galactic Nuclei, we discuss the possibility that the “spinning up” of a torus by radiation or winds could transform it into a dipolar toroidal vortex. The vortex motion balances the torus’ self-gravitation, and can explain the existence of cool, thick tori inferred from observations. In turn, the toroidal vortex can be a source of matter to feed the accretion disk. The resulting instability could result in flares accompanied by the ejection of matter. Our numerical estimates of the model parameters for luminosities close to the Eddington limit are consistent with the observational data.     

A possible mechanism for the formation of tilted disks in intermediate polars

Using 3D gas dynamics, we numerically simulate accretion-disk formation in typical cataclysmic variable intermediate polars with dipolar magnetic fields (B _a = 10⁵?5 × 10⁵ G) and misaligned white-dwarf magnetic and rotation axes. Our simulations confirm that a significant misalignment of the axes results in a significant misalignment of the disk to the orbital plane. However, over time, this disk tilt disappears: early in the simulation, the initial particle positions in the rarefied tilted disk are governed solely by the magnetic field of the white dwarf. Due to the increasing disk mass and hence increasing disk gas pressure, the tilted disk eventually becomes decoupled from the magnetic field. The tidal action of the donor leads to a retrograde (i.e., nodal) precession of the tilted disk’s streamlines, and the disk becomes twisted. When the disk tilt is greater than 4°, the incoming gas stream no longer strikes the disk rim (i.e., bright shocked region). Matter is now transported over and under the disk rim to the inner regions of the disk. Over time, the increased mass of inner parts of the disk due to the action of the colinear gas stream returns the inner-disk regions to a colinear configuration. Meanwhile, the outer regions of the tilted, twisted disk become warped. Our simulations suggest that the lifetime of an intermediate polar’s tilted disk could be several tens to thousands of orbital periods.     

Kinematic properties of the Galactic thick disk from data from the RAVE DR4 catalog

The analysis of the kinematic properties of the Galactic thick disk based on data from modern catalogs of stellar radial velocities and proper motions is presented. A new aspect of new determination of the kinematic characteristics of the thick disk is that the selected objects define this disk’s properties near the plane of symmetry. The velocity dispersion of stars in the Galactic thick disk in the radial direction and the direction of the Galactic rotation have been determined. The stellar-velocity distribution in the direction of the rotation is asymmetric. The parameters of this asymmetry have been determined, and the lag of the rotational velocity of the thick disk relative to objects in the thin disk estimated. The value of this “asymmetric drift,” about 20 km/s, suggests larger spatial scales for the kinematic characteristics in the radial direction for the Galactic thick disk than for the thin disk.     

Mathematical modeling of the structure of an accretion disk in a stellar binary system

Numerical simulations of gas-dynamical processes taking place in the accretion disk of a stellar binary system are presented. The initial state of the disk is an equilibrium gaseous configuration. Mechanisms for the development of spiral waves and associated variations in the angular momentum of the gas are considered. The influence of the ratio of the binary-component masses and the initial disk configuration are investigated. It is concluded that the existence of a steady-state disk is impossible without a flow of gas from the donor star.