The equilibrium,stability and evolution of a rotating magnetized gaseous disk

The exact solutions for the equilibrium of rotating gaseous disk with poloidal magnetic field are obtained. The stability of the disk with respect to uniform expansion and contraction is investigated by means of the variational principle. It is shown that if the equilibrium is determined by gravitational and magnetic forces only, the disk is in neutral equilibrium with respect to perturbations of the form r=r. The instability to short-waves perturbations is studied by the quasi-classical method. The analysis shows that if the magnetic field isH>2G, where is the surface density, then these perturbations are stabilized. The configurations of the electrical field induced by the rotation of magnetized disk are found. In conclusion, the questions of the evolution of the disk are discussed in connection with the quasar model when pulsar-like radiation is taken into account.     

Strictly nonlinear waves in an embedded rotating gaseous disk

Nonlinear waves of large amplitude in a gaseous disk, in which perturbations of the gravitational field can be neglected, are considered. Solutions are obtained in the form of a nonlinear, supersonic, periodic density wave, and rules are obtained for the propagation along the disk radius of a nonlinear impulse with a given profile. Translated from Astrofizika, Vol. 40, No. 2, pp. 291–302, April–June, 1997.     

On the mass and density of the stellar disk of M33

The disk surface density of the nearby spiral galaxy M33 is estimated assuming that it is marginally stable against gravitational perturbations. For this purpose we used the radial profile of line-of-sight velocity dispersion of the disk planetary nebulae obtained by Ciardullo et al. (2004). The surface density profile we obtained is characterized by the radial scalelength which is close to the photometrical one and is in a good agreement with the rotation curve of M33 and with the mass-to-light ratio which follows from the stellar population model. However at the galactocentric distance r > 7 kpc the dynamical overheating of the disk remains quite possible. The thickness of the stellar disk of M33 should increase outwards from the center. The dark halo to total mass ratio is estimated as a function of r. The effective oxygen yield obtained in the frame of instantaneous recycling approximation using the disk surface density and the observed gradient of O/H increases with radius. It may indicate that the role of accretion of metalpoor gas in the chemical evolution of interstellar medium decreases outwards.     

Optimal growth of small perturbations in thin gaseous disks

A thin gaseous disk with a nearly Keplerian rotation profile and free boundaries in the external gravitational field of a point gravitating object does not generate any growing perturbation eigenmodes. In spite of this, a significant transient growth of linear perturbations measured by the evolution of their total acoustic energy is possible in such a disk. This is shown within the framework of the simplest model of an inviscid polytropic thin disk with a finite radial extent in which small adiabatic perturbations that are a linear combination of neutral eigenmodes with a corotation radius beyond the outer flow boundary are considered.     

Effect of finite Larmor radius on the gravitational instability of a conducting plasma layer of finite thickness surrounded by a non-conducting matter

The gravitational instability of an incompressible, infinitely conducting plasma layer of finite thickness surrounded a non-conducting matter has been investigated taking into account the effect of the finite Larmor radius. The magnetic field is assumed to be directed parallel to the interfaces. Only the perturbations transverse to the magnetic field are considered, though both the symmetric and asymmetric nature of the perturbations are taken into account. Using the normal mode technique, dispersion relations are obtained.It is found that the finite larmor radius has, in general, a stabilizing influence on the configuration. Even when the system is thoroughly unstable, it has been shown that there exists a critical value of the wave-number, such that the motion is stabilized for wave-numbers of perturbations exceeding this critical value.     

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。     

Current‐driven instabilities in weakly ionized disks

Cool weakly ionized gaseous rotating disk form the basis for many models in astrophysics objects. Instabilities against perturbations in such disks play an important role in the theory of the formation of stars and planets. Traditionally, axisymmetric magnetohydrodynamic (MHD) and recently Hall‐MHD instabilities have been thoroughly studied as providers of an efficient mechanism for radial transfer of angular momentum, and of density radial stratification. In the current work, the Hall instability against axisymmetric perturbations in incompressible rotating fluid in external poloidal and toroidal magnetic field is considered. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Painlevé Analysis and Nonlinear Periodic Solutions for Isothermal Magnetostatic Atmospheres

The equations of magnetohydrodynamic equilibria for a plasma in a gravitational field are investigated analytically. For equilibria with one ignorable spatial coordinate, the equations reduce to a single nonlinear elliptic equation for the magnetic potential , known as the Grad–Shafranov equation. Specifying the arbitrary functions in the latter equation, one gets a nonlinear elliptic equation. Analytical solutions of the elliptic equation are obtained for the case of a nonlinear isothermal atmosphere in a uniform gravitational field. The solutions are obtained by using the Painlevé analysis, and are adequate for describing parallel filaments of diffuse, magnetized plasma suspended horizontally in equilibrium in a uniform gravitational field.     

Origin of the Cartwheel Galaxy: Disk Instability?

The linear theory and N-body simulations are used to present a new, alternative model of the galaxy A0035-324 (the “Cartwheel”), which is the most striking example of the relatively small class of ring galaxies. The model is based on the gravitational Jeans-type instability of both axisymmetric (radial) and nonaxisymmetric (spiral) small-amplitude gravity perturbations (e.g., those produced by spontaneous disturbances) of a dynamically cold subsystem (identified as the gaseous component) of an isolated disk galaxy. The simplified model of a galaxy is used in which stars (and a dark matter, if it exists at all) do not participate in the disk collective oscillations and just form a background charge. In the theory presented here, a case for both purely radial solutions and purely spiral solutions to the equations of motion of an infinitesimally thin gaseous disk is made, which is associated with both a radial density wave and a dominant spiral density wave which propagate outwards creating a rough ring and a number of spiral arms. Through three-dimensional numerical simulation of a collisionless set of many particles, I associate these gravitationally unstable axisymmetric waves and nonaxisymmetric waves with growing clumps of matter which take on the appearance of a ring and spokes of mass blobs.     

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.     

Similarity considerations and conservation laws for magneto-static atmospheres

The equations of magnetohydrostatic equilibria for a plasma in a gravitational field are investigated analytically. For equilibria with one ignorable spatial coordinate, the equations reduce to a single nonlinear elliptic equation for the magnetic potential A. Similarity solutions of the elliptic equation are obtained for the case of an isothermal atmosphere in a uniform gravitational field. The solutions are obtained from a consideration of the invariance group of the elliptic equation. The importance of symmetries of the elliptic equation also appears in the determination of conservation laws. It turns out that the elliptic equation can be written as a variational principle, and the symmetries of the variational functional lead (via Noether's theorem) to conservation laws for the equation. As an example of the application of the similarity solutions, we construct a model magnetostatic atmosphere in which the current density J is proportional to the cube of the magnetic potential, and falls off exponentially with distance vertical to the base, with an e-folding distance equal to the gravitational scale height. The solutions show the interplay between the gravitational force, the J × B force (B, magnetic field induction) and the gas pressure gradient.     

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).     

Analytical method for the effects of the asteroid belt on planetary orbits

Analytic expressions are derived for the perturbation of planetary orbits due to a thick constant density asteroid belt. The derivations include extensions and adaptations of Plakhov's analytic expressions for the perturbations in five of the orbital elements for closed orbits around Saturn's rings. The equations of Plakhov are modified to include the effect of ring thickness and additional equations are derived for the perturbations in the sixth orbital element, the mean anomaly. The gravitational potential and orbital perturbations are derived for the asteroid belt with and without thickness, and for a hoop approximation to the belt. The procedures are also applicable to Saturn's rings and the newly discovered rings of Uranus.The effects of the asteroid belt thickness on the gravitational potential coefficients and the orbital motions are demonstrated. Comparisons between the Mars orbital perturbations obtained using the analytic expressions and those obtained using numerical integration are discussed. The effects of the asteroid belt on the Earth based ranging to Mars are also demonstrated.     

Dynamical friction and formation of structures: Some cosmological and cosmogonical aspects

The influence of dynamical friction on peculiar velocities in a two-component medium is considered. One of the components is assumed to consist of heavy particles with small gravitational interactions and the other is assumed uniform and its particles of much less weight. Here the solutions for the stationary as well as for the cosmologically expanding medium are obtained. These solutions illustrate the possibility for clusters of galaxies to have super-low velocities. It is emphasized that the presence of two components leads to the formation of individual strings and general string structure in one of the component. A string-like structure of the Universe becomes inevitable in the case when an initial perturbations spectrum has a specific scale, and falls down abruptly for larger and smaller distances. Such a picture of the formation of large-scale structure of the Universe is similar to the formation of particle tracks in the Wilson chamber, where tracks are the observational clusters of galaxies, and ‘particles’ are invisible perturbations in the second (neutrino?) component.     

Gravitational collapse of polytropic, magnetized, filamentary clouds

For the case in which the gas of a magnetized filamentary cloud obeys a polytropic equation of state, gravitational collapse of the cloud is studied using a simplified model. We concentrate on the radial distribution and restrict ourselves to a purely toroidal magnetic field. If the axial motions and poloidal magnetic fields are sufficiently weak, we could reasonably expect our solutions to be a good approximation. We show that while the filament experiences gravitational condensation and the density at the centre increases, the toroidal flux-to-mass ratio remains constant. A series of spatial profiles of density, velocity and magnetic field for several values of the toroidal flux-to-mass ratio and the polytropic index, is obtained numerically and discussed.     

Rotating anisotropic two-fluid magnetocharged cosmological models in general relativity

Presenting some interesting new solutions, rotating models of anisotropic two-fluid universes coupled with a magnetic field are investigated and studied, where the anisotropic pressure is generated by the presence of two non-interacting perfect fluids which are in relative motion with respect to each other. Here special discussion is made of the physically interesting class of models in which one fluid is a comoving radiative perfect fluid which is taken to model the cosmic microwave background and the second a non-comoving perfect fluid which will model the observed material content of the universe. Besides studying their physical and dynamical properties the effects of rotation on these models are studied and the reactions of the magnetic and gravitational fields with respect to the rotational motion are discussed. Analysis on the rotational perturbations are also made, in the course of which the amount of anisotropy induced in pressure distribution by a small deviation from the Friedmann metric is also investigated. The models obtained here are found to be theoretically satisfactory and thereby substantiates the possibilities of existence of such astrophysical objects in this Universe and may be taken as good examples of real astrophysical situations.     

On the Hall Instability in Protostellar Disks

Astronomy Letters - Small perturbations of a protostellar disk with vertical and azimuthal magnetic field components are considered in terms of Hall magnetohydrodynamics. The dispersion equation...     

Theoretical profile of Saturn's rings

Steady-state solutions for the optical thickness of Saturn's rings are studied in terms of Hämeen-Anttila's (1983) theory of bimodal gravitating systems. The elastic properties of particles determine the behaviour of the rarefied mode (gaps), while the dense mode (ringlets) depends on the size and the internal density of the particles. In the outer parts of the rings the dense mode is unstable against the growth of gravitational perturbations. Inside the Roche distance this produces only very narrow ring-shaped configurations with helical orbits around them, and the system is not destroyed. The outer boundary of the rings corresponds to the distance beyond which the gravitational instability transforms the dense mode into strictly local condensations (moons). The inner boundary of the ring system is caused by the absence of dense mode near Saturn. The rarefied mode is stable in a larger region.