Instabilities in a nonstationary model of self-gravitating disks. III. The phenomenon of lopsidedness and a comparison of perturbation modes

This is an examination of the gravitational instability of the major large-scale perturbation modes for a fixed value of the azimuthal wave number m = 1 in nonlinearly nonstationary disk models with isotropic and anisotropic velocity diagrams for the purpose of explaining the displacement of the nucleus away from the geometric center (lopsidedness) in spiral galaxies. Nonstationary analogs of the dispersion relations for these perturbation modes are obtained. Critical diagrams of the initial virial ratio are constructed from the rotation parameters for the models in each case. A comparative analysis is made of the instability growth rates for the major horizontal perturbation modes in terms of two models, and it is found that, on the average, the instability growth rate for the m = 1 mode with a radial wave number N = 3 almost always has a clear advantage relative to the other modes. An analysis of these results shows that if the initial total kinetic energy in an isotropic model is no more than 12.4% of the initial potential energy, then, regardless of the value of the rotation parameter Ω, an instability of the radial motions always occurs and causes the nucleus to shift away from the geometrical center. This instability is aperiodic when Ω = 0 and is oscillatory when Ω ≠ 0 . For the anisotropic model, this kind of structure involving the nucleus develops when the initial total kinetic energy in the model is no more than 30.6% of the initial potential energy.     

Instabilities in a nonstationary model of self-gravitating disks. II. Warp modes of vertical oscillations

Gravitational instabilities with respect to warp modes of vertical oscillations are examined for nonlinearly nonequilibrium disk models with isotropic and anisotropic velocity diagrams. Nonstationary analogs of the dispersion relations for vertical oscillations in these models are derived in a general form. A detailed study is made of the major large scale oscillatory modes, which correspond primarily to the most common type of warp in the form of an integral sign, as well as to dome-shaped, U-shaped, and precessional warps. Critical diagrams showing the initial virial relation as a function of the rotation parameter for the nonstationary model are constructed for each of these vertical oscillation modes. A comparative analysis is made of the growth rates of the instabilities for these modes in order to determine the dependence of the characteristic times for their appearance on the basic physical parameters of the two models.     

Linear stability of a self-gravitating ring

Stability of a self-gravitating ring about a central body is considered. The purpose is to derive a bound on the mass of the ring in order that the system will be linearly stable. Our bound will, in some cases, be the best possible bound. The bound is also expanded as an asymptotic series. Comparisons of our result are made with respect to previous analyses performed by Tisserand, Pendse and Willerding.     

Nonaxisymmetric instabilities in self-gravitating disks. II. Linear and quasi-linear analyses

We studied global nonaxisymmetric hydrodynamic instabilities in an extensive collection of hot, self-gravitating polytropic disk systems, systems that covered a wide expanse of the parameter space relevant to protostellar and protoplanetary systems. We examined equilibrium disk models varying three parameters: the ratio of the inner to outer equatorial radii, the ratio of star mass to disk mass, and the rotation law exponent q. We took the polytropic index n=1.5 and examined the exponents q=1.5 and 2, and the transitional one q=1.75. For each of these sets of parameters, we examined models with inner to outer radius ratios from 0.1 to 0.75, and star mass to disk mass ratios from 0 to 10³. We numerically calculated the growth rates and oscillation frequencies of low-order nonaxisymmetric disk modes, modes with azimuthal dependence ∝e ^im? . Low-m modes are found to dominate with the character and strength of instability strongly dependent on disk self-gravity. Representatives of each mode type are examined in detail, and torques and mass transport rates are calculated.     

A simplified model for a nonlinear tidal effect on accretion disks in CVs

This paper investigates the tidal effect on accretion disk in CVs and sets up a simplified model in which the secondary's gravitation is substituted by a mean tidal torque. We find that a linear tidal torque will not be able to maintain an equilibrium disk. By using the result of the radius of the equilibrium disk approximately equals to the tidal radius, which was obtained by using the two dimensional numerical simulation invoking nonlinear tidal effect, we give the modified tidal dissipation function for our simplified model which could be used to interpret the outburst of the dwarf nova with tidal effect. The paper also shows that the radius of an equilibrium disk with a torus is slightly small than the Lubow-Shu radius, and the tidal effect may also cause the cycle of quiescence-superoutburst in addition to the cycle of quiescence-outbursts-superoutburst.     

Rotation curves and mass distributions in flat self-gravitating disks

We have developed a new approach that allows the surface-density distribution in flat finite-radius galactic disk models to be reconstructed from an arbitrary smooth angular-velocity distribution. Upper limits for the disk mass and radius are shown to exist for a wide class of rotation curves analytically extended to the unseen part of the disk.     

含粘滞和磁场的薄吸积盘不稳定性

本文采用微扰方法导出色散方程，并在四种情况下详细讨论了薄吸积盘的不稳定性。结果表明：在纯粘滞和纯磁场盘中都存在脉动不稳定性。而且在吸积盘内同时考虑粘滞和磁场时，存在两种不稳定性，一种是脉动不稳定性，另一种是单调不稳定性。同时数值计算还表明，脉动不稳定性更可能存在于盘的内区，而单调不稳定性则只在盘的外区，对短波扰动才有意义。这些结果为解释ＢＬＬａｃ天体、Ｓｅｙｆｅｒｔ星系及类星体等活动星系核的光变现象进一步提供了理论依据。     

Toward a more consistent evolution model for the local galactic disk

Infall models for the evolution of the local galactic disk were studied and confronted with a large number of observational constraints from the solar vicinity, inclusive of the white dwarf luminosity function. The models are characterized as follows: 1. The key-functions (SFR, IMF, gas infall rate) are not prescribed by simple laws, but are directly derived from observational constraints. 2. A scatter in the metallicity at fixed age is considered which partly reflects inhomogeous chemical evolution. 3. Special attention is drawn to the internal consistency of the models. 4. In addition to infall of low-metallicity gas, metal-enriched outflows are allowed. The “best” model is characterized by a disk age of ≈︁ 12 Gyr, a SFR which is decreasing over the first half and is nearly constant over the second half of the disk evolution, and by a similar temporal run of the gas infall rate. Moderate metal-enriched outflow can not be excluded.     

Dissipative-acoustic instability in accretion disks at a nonlinear stage

Nonstationary hydrodynamic models of a viscous accretion disk around a central compact object were constructed. Two different numerical methods (TVD and SPH) are used to study the dynamics of dissipatively unstable acoustic perturbations at the nonlinear stage in terms of the standard α-disk model. The standard disk accretion in the Shakura-Sunyaev model is unstable against acoustic waves for various parameters of the system. If the α parameter, which specifies the level of turbulent viscosity, exceeds α?0.03, then a complex nonstationary system of small-scale weak shock waves is formed. The growth rate of the perturbations is higher in the central disk region. For α?0.2, the relative shock amplitude can exceed 50% of the equilibrium disk parameters. The reflection of waves from the disk boundaries and their nonlinear interaction are important factors that can produce unsteady accretion. The luminosity of such a disk undergoes quasi-periodic oscillations at a level of several percent (?5%) of the equilibrium level.     

Some general relativistic effects on the dynamics of fluid disks rotating around a Schwarzschild black hole

In this paper we present various classes of solutions for perfect fluid disks rotating around Schwarzschild black holes. We study the profiles of pressure, density and specific angular momentum and the formation of cusp-like structures at the inner edge of the disks. Using the trial function method, we calculate the frequency of the global axi-symmetric oscillations. We compare the results with those of the corresponding Newtonian calculations to find the general relativistic effects.     

Dust ring formation due to sublimation of dust grains drifting radially inward by the Poynting-Robertson drag: An analytical model

Dust particles exposed to the stellar radiation and wind drift radially inward by the Poynting-Robertson (P-R) drag and pile up at the zone where they begin to sublime substantially. The reason they pile up or form a ring is that their inward drifts due to the P-R drag are suppressed by stellar radiation pressure when the ratio of radiation pressure to stellar gravity on them increases during their sublimation phases. We present analytic solutions to the orbital and mass evolution of such subliming dust particles, and find their drift velocities at the pileup zone are almost independent of their initial semimajor axes and masses. We derive analytically an enhancement factor of the number density of the particles at the outer edge of the sublimation zone from the solutions. We show that the formula of the enhancement factor reproduces well numerical simulations in the previous studies. The enhancement factor for spherical dust particles of silicate and carbon extends from 3 to more than 20 at stellar luminosities L_?=0.8-500L_⊙, where L_⊙ is solar luminosity. Although the enhancement factor for fluffy dust particles is smaller than that for spherical particles, sublimating particles inevitably form a dust ring as long as their masses decrease faster than their surface areas during sublimation. The formulation is applicable to dust ring formation for arbitrary shape and material of dust in dust-debris disks as well as in the Solar System.     

Gravitational collapse and equilibrium conditions of a toroidal vortex with thermal pressure

We found the equilibrium conditions for a self-gravitating toroidal vortex by taking thermal pressure into account. These conditions are shown to significantly differ from those for a disk or a sphere. The evolution of a thin vortex turns it into a compact vortex that loses mechanical stability for low masses at a polytropic index γ<4/3 but retains stability for sufficiently high masses and densities determined by the velocity circulation in the vortex.     

Propagation and evolution of waves in a self-gravitating medium

The propagation and evolution of linear waves in a self-gravitating medium are discussed in a comparatively general way. In one special case, the well-known Jeans formula is recovered; in another, an important property of unstable waves in a self-gravitating medium is obtained, namely, the equiphase surfaces of the wave are “frozen” in the moving medium. When the motion of the basic state is one of shear flow (or differential rotation), this property implies that unstable waves would evolve into a quasi-stationary state. This shows that, for a self-gravitating medium, besides the usual non-linear effects, there is a special mechanism within the linear theory which prevents the infinite growth of unstable waves. Possible relation of this effect to the origin of celestial bodies is pointed out.     

On a simple model for self-regulating star formation in the galactic disk

Sternentstehung in Galaxien ist ein Prozeß mit Rückkopplung zum interstellaren Medium (ISM) und möglicherweise ein Teil eines selbstregu-lierenden Zyklus. DOPITA (1985) hat ein Modell vorgeschlagen, in dem Sternentstehung in Spiral- und irregulären Galaxien über den Druck im ISM selbstregulierend wirkt. In der vorliegenden Arbeit wird gezeigt, daß die verfügbaren Daten für die radialen Verteilungen von Gas, Gesamtmasse und Lymankontinuumphotonenfluß in der Scheibe unserer Galaxis dieses einfache Modell nicht stützen. Verschiedene mögliche Ursachen werden diskutiert.     

Structure and stability of rotating fluid disks around massive objects. I. Newtonian formulation

In this paper we have presented a very general class of solutions for rotating fluid disks around massive objects (neglecting the self gravitation of the disk) with density as a function of the radial coordinate only and pressure being nonzero. Having considered a number of cases with different density and velocity distributions, we have analysed the stability of such disks under both radial and axisymmetric perturbations. For a perfect gas disk with γ= 5/3 the disk is stable with frequency (MG/r³)^1/2 for purely radial pulsation with expanding and contracting boundary. In the case of axisymmetric perturbation the critical γ_c for neutral stability is found to be much less than 4/3 indicating that such disks are mostly stable under such perturbations. On leave of absence from Government College, Jagdalpur 494005.     

Eccentricity growth of planetesimals in a self-gravitating protoplanetary disc

We investigate the orbital evolution of planetesimals in a self-gravitating circumstellar disc in the size regime (∼1–5000 km) where the planetesimals behave approximately as test particles in the disc's non-axisymmetric potential. We find that the particles respond to the stochastic, regenerative spiral features in the disc by executing large random excursions (up to a factor of 2 in radius in ∼1000 yr), although typical random orbital velocities are of the order of one tenth of the Keplerian speed. The limited time frame and small number of planetesimals modelled do not permit us to discern any net direction of planetesimal migration. Our main conclusion is that the high eccentricities (∼0.1) induced by interaction with spiral features in the disc is likely to be highly unfavourable to the collisional growth of planetesimals in this size range while the disc is in the self-gravitating regime. Thus if , as recently argued by Rice et al., the production of planetesimals gets under way when the disc is in the self-gravitating regime (either at smaller planetesimal size scales, where gas drag is important, or via gravitational fragmentation of the solid component), the planetesimals thus produced would not be able to grow collisionally until the disc ceases to be self-gravitating. It is unclear, however, given the large amplitude excursions undergone by planetesimals in the self-gravitating disc, whether they would be retained in the disc throughout this period, or whether they would instead be lost to the central star.