Excitation of Orbital Inclinations of Asteroids during Depletion of a Protoplanetary Disk: Dependence on the Disk Configuration

The pumping up of orbital inclinations of asteroids caused by sweeping secular resonances associated with depletion of a protoplanetary disk is discussed, focusing on the dependence on the disk inclinations and surface density distribution. The asteroids have large mean inclinations that cannot be explained by present planetary perturbations alone. It has been suggested that the sweeping secular resonances caused by disk depletion are responsible for these high inclinations. Nagasawa et al. (2000, Astron. J.119, 1480-1497) showed that the inclinations of asteroids are pumped up if the disk is depleted in an inside-out manner on a time scale longer than 3×10⁵ years. Their assumed disk midplane is not on the invariant plane. However, it should be affected by the inclination of the disk plane. Here we investigate the dependence on the disk inclinations. We assume a disk depletion model in which the disk inside the jovian orbit has been removed and the residual outer disk is uniformly depleted. We calculate the locations of the secular resonances and the excitation magnitude of the inclinations with analytical methods. We found that the inclinations are pumped up to the observational level for a depletion time scale longer than 10⁶ years in the case of the disk plane that coincides with the invariant plane. The required time scale is longest (3×10⁶ years) if the disk plane coincides with the jovian orbital plane. However, it is still within the observationally inferred depletion time scale. We also studied dependence on a disk surface density gradient and found that the results do not change significantly as long as the inner disk depletion is faster than the outer disk one.     

The effect of projection on the observed gas velocity fields in barred galaxies

The problem of determining the pattern of gas motions in the central regions of disk spiral galaxies is considered. Two fundamentally different cases—noncircular motions in the triaxial bar potential and motions in circular orbits but with orientation parameters different from those of the main disk—are shown to have similar observational manifestations in the line-of-sight velocity field of the gas. A reliable criterion is needed for the observational data to be properly interpreted. To find such a criterion, we analyze two-dimensional nonlinear hydrodynamic models of gas motions in barred disk galaxies. The gas line-of-sight velocity and surface brightness distributions in the plane of the sky are constructed for various inclinations of the galactic plane to the line of sight and bar orientation angles. We show that using models of circular motions for inclinations i>60° to analyze the velocity field can lead to the erroneous conclusions of a “tilted (polar) disk” at the galaxy center. However, it is possible to distinguish bars from tilted disks by comparing the mutual orientations of the photometric and dynamical axes. As an example, we consider the velocity field of the ionized gas in the galaxy NGC 972.     

Potential of a gaussian ring. A new approach

A fundamentally new approach to an elliptic Gaussian ring has been developed. It has been ascertained that it can be produced from a uniform plane elliptic disk by mass balayage into an elementary homothetic layer with the center of homothety at an ellipse focus. An advantage of new interpretation is in the fact that the spatial potential of a Gaussian ring is expressed in terms of the potential of a uniform elliptic disk, well-known in the finite form, and its derivatives. A general formula for the potential of a two-dimensional homothetic layer has been derived with this purpose. As a result, the potential of a Gaussian ring is represent-able in a simple analytical form in terms of standard complete elliptic integrals in both elliptic and Cartesian coordinates. The mass asymmetry along the ring is considered explicitly. The potential formulas are verified numerically and have no singular points at ellipse foci. Particular cases are considered; the 3D potential surface and system of equipotentials are constructed. Knowledge of the potential extends the range of application of a Gaussian ring in the problem of calculation of secular perturbations in celestial mechanics.     

On spiral structure formation in a galaxy with a bar-like nucleus

A new approach to the problem of the formation of galaxy spiral structures having a rotating bar-like nucleus is offered. The process of disk formation due to matter accretion onto the disk is considered in terms of the solution of the key problem on the motion of the matter element in the equatorial plane of the galaxy in the corotation resonance region. It is shown that in the vicinity of unstable libration points high-density regions are formed, which elongate with time following the separatrix shape and forming thereby spiral arms.     

Modulation of circumstellar extinction in a young binary system with a low-mass companion in a noncoplanar orbit

We consider a model of cyclic brightness variations in a young star with a low-mass (q = M ₂/M ₁ ≤ 0.1) companion that accretes matter from the remnants of a protostellar cloud (circumbinary disk). We assume that the orbit of the companion is circular and that its plane does not coincide with the disk plane. We have computed grids of hydrodynamic models for such a binary by the SPH method based on which we have investigated the circumstellar extinction variations produced by the streams of matter and density waves excited in the circumbinary disk by the orbital motion of the companion. We show that, depending on the inclination and orientation of the binary’s line of nodes relative to the observer, the brightness of the primary component can undergo various (in shape and depth) oscillations with a period equal to the orbital one. In contrast to the models with coplanar circular orbits, the accretion rate onto the components of a binary with a noncoplanar orbit depends on the orbital phase. The results of our computations can be used to study the cyclic activity of UX Ori stars and young eclipsing binaries with anomalously long eclipses.     

Influence of Star Formation on Large Scale Structures of Galactic Magnetic Fields

In order to study magnetic field generation in galaxies with active processes such as intensive star formation, supernovae explosions, etc, a model is needed to differentiate between the properties of interstellar medium in different parts of the galactic disk. In this paper we consider galactic dynamo equations with stochastic coefficients where the parameters responsible for dissipation randomly depend on time and spatial coordinates and are distributed around two values corresponding to aweakly heated neutral component and a hot ionized component. Ionized gas is assumed to be concentrated in small regions evenly distributed over the galactic disk plane. The ratio of the total area of such regions to the entire disk plane corresponds to the mean surface star-formation density in the given region of the galactic disk. Unlike in our previous papers, we take into account the dissipation in the disk plane. We have obtained numerical estimates of the exponential growth rate for different numbers of areas containing ionized gas. We show that the influence of the fluctuations on the magnetic field behavior has a threshold nature; intensive star formation leads to the destruction of large scale magnetic field structures.     

Kuiper Belt structure as a reflection of the migration process of a planet

One of the main particular features of the structure of the Kuiper Belt is that it contains clusters of objects of small orbital eccentricity and inclination (“cold population”). In order to solve the problem of the origin of the objects, we considered the process of the gravitational interaction of a comparatively small-mass planet with a planetesimal disk. We found that one particular property of the process is that the planet changes its direction of migration. The interaction with the planet results in the transportation of a considerable portion of planetesimals from the inner zone out to the Kuiper Belt. After such a transition of the objects, the planet returns to the inner regions of the planetesimal disk. Numerical simulations show that the reversible migration of a planet of a mass similar to that of the Earth can explain the main properties of the Kuiper Belt’s cold population orbit distribution.     

A new mechanism of ring formation in barred galaxies

In this paper we establish the possibility of a new mechanism for the formation of ring-like structures in barred galaxies. We study the stability of periodic orbits with respect to perturbations perpendicular (vertical stability) or tangent (plane stability) to the plane of motion and we find that matter can be trapped in the case of a relatively strong and fast bar, in a narrow annular region around the bar. The periodic orbits inside the annulus are totally stable—i.e., both vertically and plane. The region outside the annulus is depleted of matter by the action of vertical or plane instability. The resulting ring-like structure has the geometrical characteristics of the true inner rings observed in barred galaxies. In this way the formation of inner rings seems to be a result of combined action ofvertical and plane instability. A similar study of stability in the outer parts of the Galaxy, where outer rings are observed, shows that the above mechanism is absent there.     

Bounded motion in a generalized two-body problem

In this paper we prove the existence of ring-type bounded motion in an isolated system consisting of a massive point particle and a homogeneous cube. We study the case of planar motion where the particle moves in a symmetry plane of the cube and we use a rotating frame of reference with its center at the mass center of the cube and its axes coinciding with the symmetry axes of the cube. We prove that, for negative values of the total energy and properly chosen values of the total angular momentum, the relative distance of the bodies has an upper and a lower bound-i.e., the regions of possible motion lie inside an annulus around the cube (motion inside a ring or an island).     

Galactic scale gas flows in colliding galaxies: 3-Dimensional,N-body/hydrodynamics experiments

We present some results from three dimensional computer simulations of collisions between models of equal mass galaxies, one of which is a rotating, disk galaxy containing both gas and stars and the other is an elliptical containing stars only. We use fully self consistent models in which the halo mass is 2.5 times that of the disk. In the experiments we have varied the impact parameter between zero (head on) and 0.9R (whereR is the radius of the disk), for impacts perpendicular to the disk plane. The calculations were performed on a Cray 2 computer using a combined N-body/SPH program. The results show the development of complicated flows and shock structures in the direction perpendicular to the plane of the disk and the propagation outwards of a density wave in both the stars and the gas. The collisional nature of the gas results in a sharper ring than obtained for the star particles, and the development of high volume densities and shocks.     

Hoag’s object,remnant of a vanished bar?

The beautiful ringed Hoag’s object, named after its discoverer, is an interesting galaxy. Because of the roundness of its ring-like structure, it has been proposed to be a collisional ring galaxy; however, there is no obvious nearby culprit galaxy that could have collided with it. Considering an alternative, much gentler hypothesis, we study the development of the observed structure via a turning, bar perturbation in the disk potential. However, there is currently no obvious bar present, and rings produced by bars are typically oval. On the basis of much recent work improving our understanding of bar evolution, we assume the bar grows and then vanishes. In simulations of a disk of particles, under such a bar turning in the disk plane, we obtain a bulge core, empty void, and circular ring in the disk that mimic the observations of Hoag’s object. We conclude the inner edge of the ring is just beyond the outer Lindblad resonance (OLR) with the bar pattern speed. We estimate the amount of gas mass in the bulge core to be twice that of the ring. Our simulations indicate that the Hoag Object ring could survive at least 6 billion years after the bar vanishes.     

Instabilities in a nonstationary model of self-gravitating disks. I. Bar and ring perturbation modes

The instabilities of bar and ring mode perturbations against the background of a disk oscillating nonlinearly in its own plane are examined in a disk model which is a nonstationary generalization of the well known Bisnovatyi-Kogan-Zel'dovich model. Nonstationary analogs corresponding to a dispersion relation are found for these two oscillation modes. The results of the calculations are presented in the form of critical dependences of the initial virial ratio on the degree of rotation. A comparative analysis of the growth rates of the gravitational instability for these modes is also carried out. The bar mode instability occurs if the initial total kinetic energy of the disk is no more than 10.4% of the initial potential energy. The mechanism is associated with an instability in the radial motions which is aperiodic for small values of the rotation parameter Ω < 0.1, but is otherwise oscillatory. Calculations show that a ring structure can be formed as a result of an instability in the radial motions if the initial total energy of the model is no more than 5.2% of the initial potential energy, regardless of the value of Ω. __________ Translated from Astrofizika, Vol. 51, No. 3, pp. 487–499 (August 2008).     

Forced oscillations in a hydrodynamical accretion disk and QPOs

This is the second of a series of papers aimed to look for an explanation on the generation of high frequency quasi-periodic oscillations (QPOs) in accretion disks around neutron star, black hole, and white dwarf binaries. The model is inspired by the general idea of a resonance mechanism in the accretion disk oscillations as was already pointed out by Abramowicz and Klu’zniak (2001). In a first paper (P'etri, 2005a, paper I), we showed that a rotating misaligned magnetic field of a neutron star gives rise to some resonances close to the inner edge of the accretion disk. In this second paper, we suggest that this process does also exist for an asymmetry in the gravitational potential of the compact object. We prove that the same physics applies, at least in the linear stage of the response to the disturbance in the system. This kind of asymmetry is well suited for neutron stars or white dwarfs possessing an inhomogeneous interior allowing for a deviation from a perfectly spherically symmetric gravitational field. After a discussion on the magnitude of this deformation applied to neutron stars, we show by a linear analysis that the disk initially in a cylindrically symmetric stationary state is subject to {three kinds of resonances: a corotation resonance, a Lindblad resonance due to a driven force and a parametric resonance}. In a second part, we focus on the linear response of a thin accretion disk in the 2D limit. {Waves are launched at the aforementioned resonance positions and propagate in some permitted regions inside the disk, according to the dispersion relation obtained by a WKB analysis}. In a last part, these results are confirmed and extended via non linear hydrodynamical numerical simulations performed with a pseudo-spectral code solving Euler's equations in a 2D cylindrical coordinate frame. {We found that for a weak potential perturbation, the Lindblad resonance is the only effective mechanism producing a significant density fluctuation}. In a last step, we replaced the Newtonian potential by the so called logarithmically modified pseudo-Newtonian potential in order to take into account some general-relativistic effects like the innermost stable circular orbit (ISCO). The latter potential is better suited to describe the close vicinity of a neutron star or a black hole. However, from a qualitative point of view, the resonance conditions remain the same. The highest kHz QPOs are then interpreted as the orbital frequency of the disk at locations where the response to the resonances are maximal. It is also found that strong gravity is not required to excite the resonances.     

Stochastic wobble of accretion discs and jets from turbulent rocket torques

Models of accretion discs and their associated outflows often incorporate assumptions of axisymmetry and symmetry across the disc plane. However, for turbulent discs these symmetries only apply to averaged quantities and do not apply locally. The local asymmetries can induce local imbalances in outflow power across the disc mid-plane, which can in turn induce local tilting torques. Here we calculate the effect of the resulting stochastic torques on disc annuli that are a consequence of standard mean field accretion disc models. The torques induce a random walk of the vector perpendicular to the plane of each averaged annulus. This random walk is characterized by a radially dependent diffusion coefficient which we calculate for small angle tilt. We use the coefficient to calculate a radially dependent time-scale for annular tilt and associated jet wobble. The wobble time depends on the square of the wander angle so the age of a given system determines the maximum wobble angle. We apply this to examples of blazars, young stellar objects and binary engines of pre-planetary nebulae and microquasars. It is noteworthy that for an averaging time   t _w∼ 3 d  , we estimate a wobble angle for jets in SS 433 of  θ∼ 0.8°  , not inconsistent with observational data. In general the non-periodic nature of the stochastic wobble could distinguish it from faster periodic jet precession.     

The stellar-disk electric (short) circuit: observational predictions for a YSO jet flow

We discuss the star-disk electric circuit for a young stellar object (YSO) and calculate the expected torques on the star and the disk. We obtain the same disk magnetic field and star-disk torques as given by standard magnetohydrodynamic (MHD) analysis. We show how a short circuit in the star-disk electric circuit may produce a magnetically-driven jet flow from the inner edge of a disk surrounding a young star. An unsteady bipolar jet flow is produced that flows perpendicular to the disk plane. Jet speeds of order hundreds of kilometers per second are possible, while the outflow mass loss rate is proportional to the mass accretion rate and is a function of the disk inner radius relative to the disk co-rotation radius.     

Warped polar ring in the Arp 212 galaxy

The Fabry-Perot scanning interferometer mounted on the 6-m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences is used to study the distribution and kinematics of ionized gas in the peculiar galaxy Arp 212 (NGC 7625, IIIZw 102). Two kinematically distinct subsystems—the inner disk and outer emission filaments—are found within the optical radius of the galaxy. The first subsystem, at galactocentric distances r < 3.5 kpc, rotates in the plane of the stellar disk. The inner part of the ionized-gas disk (r<1.5–2 kpc) exactly coincides with the previously known disk consisting of molecular gas. The second subsystem of ionized gas is located at galactocentric distances 2–6 kpc. This subsystem rotates in a plane tilted by a significant angle to the stellar disk. The angle of orbital inclination in the outer disk increases with galactocentric distance and reaches 50° at r ≈ 6 kpc. The ionized fraction of the gaseous disk does not show up beyond this galactocentric distance, but we believe that the HI disk continues to warp and approaches the plane that is polar with respect to the inner disk of the galaxy. Hence Arp 212 can be classified as a galaxy with a polar ring (or a polar disk). The observed kinematics of the ionized and neutral gas can be explained assuming that the distribution of gravitational potential in the galaxy is not spherically symmetric. Most probably, the polar ring have formed via accretion of gas from the dwarf satellite galaxy UGC 12549.     

PGC 60020: a polar-ring galaxy

We present an analysis of new observations of a peculiar galaxy PGC60020, obtained with the 6-m BTA telescope of the SAO RAS with a multimode SCORPIO instrument. The observational data includes direct images in the B, V, R _c photometric bands and long-slit spectra in the red range (the H?? line spectral region). Based on the analysis of these data it was found that PGC60020 belongs to the type of classical polar-ring galaxies. Its main body is an S0 galaxy, around the major axis of which a disk of gas, dust and stars is rotating in the plane inclined at an angle of about 60° to the galactic plane. A loop-shaped structure stretches from the southern part of this disk (possibly, a tidal tail) towards the SDSS J 171745.58+404137.1 galaxy.     

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.