Stability of the system of stars,gas and magnetic fields

Linear stability of a system of stars, gas and magnetic fields under the existence of a relative motion between the stars and the gas is investigated by the use of the magnetohydrodynamic and the polytropic equations for the gas and the collisionless Boltzmann equation for the stars together with the Poisson equation. The star system is supposed to have the anisotropic Schwarzschild distribution. The critical wavenumber is calculated and it is found that the system becomes universally unstable under some conditions.     

On the possibility of studying the dynamics of astrophysical disks in a two-dimensional formulation

A closed system of two-dimensional equations describing the dynamics of rotating, gravitating gas disks is derived. It is an integrodifferential system for barotropic disks and a differential system for polytropic disks. For both barotropic and polytropic disks, these equations differ both from the dynamical equations used in the literature for astrophysical disks and from the traditional equations of two-dimensional hydrodynamics. The sufficient conditions under which the dynamics of a disk can be described in a two-dimensional formulation are obtained. The first condition reflects the thin-disk approximation. The second condition imposes a limit on the characteristic times of processes studied in a two-dimensional formulation. In most cases this condition limits the characteristic frequency of a process to the disk's rotational frequency.Translated from Astrofizika, Vol. 39, No. 3, pp. 441–466, July–September, 1996.     

Three-dimensional numerical simulation of a nonstationary gravitating <Emphasis Type="Italic">N</Emphasis>-body system with gas

We developed a three-dimensional numerical model to investigate nonstationary processes in gravitating N-body systems with gas. We used efficient algorithms for solving the Vlasov and Poisson equations that included the evolutionary processes under consideration, which ensures rapid convergence at high accuracy. We give examples of the numerical solution of the problem on the growth of physical instability in the model of a flat rotating disk with a gaseous component and its three-dimensional dynamics under various initial conditions including a nonzero velocity dispersion along the rotation axis.     

Is Hale–Bopp A ‘Juvenile’ Comet – Study Of The Energy Balance To Explain The Vapor Flux Of Volatiles From The Surface

Sublimation of minor gases from ices inside of a porous comet nucleus strongly depends on the effective energy input. Our model meant to describe the gas flux inside and out of the porous nucleus has been used to study the influence of physical and structural parameters on the effective energy input. We solve the conservation equations for H₂O and CO as the most abundant minor component of higher volatility under appropriate boundary conditions. From the calculations we obtain the gas flux from volatile, icy components inside the porous nucleus, temperature profiles, changes in relative chemical abundances, and the gas flux into the coma for each of the volatiles. We will show results from our calculations for a model comet in the orbit of Hale-Bopp (C/1995 O1). In this paper we focus on the energy balance at the surface. We will also relate measurements of molecule fluxes to available energies and try to provide hints about the evolutionary status of the comet. This revised version was published online in July 2006 with corrections to the Cover Date.     

3D global simulations of galactic magnetic fields and gas flows

The evolution of three-dimensional (3D), dynamo excited galactic magnetic fields under the influence of a time-dependent gas flow in spiral arms is already well investigated. Our principal goal is to check how the dynamo-driven turbulent magnetic fields affect the gas flows. Numerical solutions of the full set of 3D MHD equations for dynamos in spiral galaxies are presented. Further we try to investigate the nonlinear evolution of magnetic instabilities in a global galactic model. The model includes differential rotation, eddy diffusivity and tensorial alpha-effect. In a first step the flow is driven by a prescribed gravitational potential. The vertical density stratification and the radial-azimutal spiral pattern are taken closely to observational data. We use a modified variant of the highly parallelized time-stepping ZeusMP code for the simulations of global galactic magnetic fields and gas flows. This revised version was published online in August 2006 with corrections to the Cover Date.     

Hydrodynamic study of condensation and sublimation of ice particles in cometary atmospheres

Condensation of ice particles in the vicinity of a cometary nucleus as pointed out by Yamamoto and Ashihara (1985, Astron. Astrophys. 152, L17–L20) is fully studied by solving the hydrodynamic equations for ice particles and H₂O gas. Formulation is presented for the hydrodynamics including condensation and sublimation of ice particles, and energy exchange between ice particles and the gas in a dustless comet. It is shown that sublimation of ice particles condensed leads to heating of the ambient gas, resulting in the higher gas temperature than those predicted by the models proposed so far. Compared with the previous calculation carried out under the conditions at the encounter of the spacecraft to Halley's Comet, the present results have revealed that the survival distance of ice particles against sublimation is longer, but that their size, which attains its maximum of 6.4 Å at 51 km from the center of the nucleus, is smaller, resulting in a larger fraction of uncondensed H₂O gas. Discussion is given on the physical conditions under which condensation of ice particles can take place in cometary comae.     

The pressure of an equilibrium interstellar medium in galactic disks

Based on an axisymmetric galactic disk model, we estimate the equilibrium gas pressure P/k in the disk plane as a function of the galactocentric distance R for several galaxies (MW, M33, M51, M81, M100, M101, M106, and the SMC). For this purpose, we solve a self-consistent system of equations by taking into account the gas self-gravity and the presence of a dark pseudo-isothermal halo. We assume that the turbulent velocity dispersions of the atomic and molecular gases are fixed and that the velocity dispersion of the old stellar disk corresponds to its marginal stability (except for the Galaxy and the SMC). We also consider a model with a constant disk thickness. Of the listed galaxies, the SMC and M51 have the highest pressure at a given relative radius R/R ₂₅, while M81 and the Galaxy has the lowest pressure. The pressure dependence of the relative molecular gas fraction confirms the existence of a positive correlation between these quantities, but it is not so distinct as that obtained previously when the pressure was estimated very roughly. This dependence breaks down for the inner regions of M81 and M106, probably because the gas pressure has been underestimated in the bulge region. We discuss the possible effects of factors other than the pressure affecting the relative content of the molecular gas in the galaxies under consideration.     

Equations of radiation gas dynamics in tetrad form for astrophysical applications

This paper deals with the representation of relativistic equations of gas dynamics with due regard to the general relativity theory effects in the form accepted and widely applied in the special relativity theory. With this purpose, a strict formal definition of a non-inertial co-moving reference frame without rotation is carried out on the basis of a tetrad formalism by use of the Fermi—Walker rules of transport of 4-frame. The equations of physical kinetics, relativistic collapse, Einstein's equations, equations of relatiivistic radiation gas dynamics for ideal and dissipative gases, Taub's equations for a shock wave, which allow for radiation and electron-positron pairs, are obtained in this reference frame. On the basis of the local Lorentz transformation and the Ricci rotation coefficients, these equations are written in the laboratory reference frame, in order to illustrate the fact that the general relativity effects can be simply taken into account in the equations having a form accepted in the special relativity theory.     

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.     

Influence of fast interstellar gas flow on the dynamics of dust grains

The orbital evolution of a dust particle under the action of a fast interstellar gas flow is investigated. The secular time derivatives of Keplerian orbital elements and the radial, transversal, and normal components of the gas flow velocity vector at the pericentre of the particle’s orbit are derived. The secular time derivatives of the semi-major axis, eccentricity, and of the radial, transversal, and normal components of the gas flow velocity vector at the pericentre of the particle’s orbit constitute a system of equations that determines the evolution of the particle’s orbit in space with respect to the gas flow velocity vector. This system of differential equations can be easily solved analytically. From the solution of the system we found the evolution of the Keplerian orbital elements in the special case when the orbital elements are determined with respect to a plane perpendicular to the gas flow velocity vector. Transformation of the Keplerian orbital elements determined for this special case into orbital elements determined with respect to an arbitrary oriented plane is presented. The orbital elements of the dust particle change periodically with a constant oscillation period or remain constant. Planar, perpendicular and stationary solutions are discussed. The applicability of this solution in the Solar System is also investigated. We consider icy particles with radii from 1 to 10 μm. The presented solution is valid for these particles in orbits with semi-major axes from 200 to 3000 AU and eccentricities smaller than 0.8, approximately. The oscillation periods for these orbits range from 10⁵ to 2 × 10⁶ years, approximately.     

Critical accretion flow of gas onto compact stars

The critical accretion flow of gas onto compact stars with mass of 0.6M is investigated by numerical integrations of the time-dependent hydrodynamic equations in the sphericallysymmetric and optically thick case. For the compact stars surrounded by such a dense cloud of gas, the radiation pressure force decelerates the infall gas significantly and free fall regime of the gas is not at all attained. This results in incident low velocities at the standing shock front close to the stellar surface, low temperatures of the gas around the compact stars, and no X-ray in white dwarfs but soft X-rays in neutron stars, respectively. Some applications of the results to the X-ray sources are discussed.     

Protostar formation under two current carrying gas filaments collision

A model of protostar formation under two current carrying gas filaments collision is presented. The model implies MHD approach involving self-gravity and radiative cooling effects. We suppose that through the current carrying gas filament collision a magnetic field reconnection takes place. Using an appropriate self-consistent presentation for time and special dependences of physical quantities in MHD equations, we derive the full set of equations that describes time evolution of the physical quantities just after an occurrence of magnetic field reconnection. Numerical simulations reveal that the process consists of three main phases of evolution. The first is an appearance of preceding peaks in time profiles of density and temperature following by the next phase of depression of both temperature and density and the final fast condensation phase with either cooling or heating of matter depending on initial parameters of problem. Effects of initial conditions like as magnetic field strength, current strength, initial gravity energy, cooling time and a geometry of collision are investigated. Main conclusion is that protostar formation takes place within the time interval less than one free fall time and it is preceded by the appearance of dense and hot matter with lifetime much less than free fall time. The final temperature of the protostar depends on the physical conditions and mainly on the ratio between free fall time and cooling time in the colliding current carrying gas filaments.     

The nonlinear dispersion relation and solutions in the magnetosphere of a pulsar

Assuming some hydrogen atoms are distributed in the magnetosphere of a pulsar, the gas we are dealing with is a mixture of plasma and hydrogen atoms. Because the induced electrical field in the plasma surrounding the pulsar is very strong, due to the rotation of the pulsar associated with a strong magnetic field, the electric polarization of an atom will include the nonlinear term of the electric field. We obtain the nonlinear dispersion relation for the mixed gas from the Maxwell equations and derive the nonlinear Schrödinger equation, which has solitons as its solution under a certain condition. The curvature radiation of solitons moving along the magnetic field lines is a plausible way to explain the strong radio emission which comes from a pulsar, particularly some field lines existing near the light cylinder with radii of curvature smaller than the radius of the pulsar.     

A nonhydrostatic model of the global circulation of the atmosphere of venus

The mechanisms of the global circulation in the atmosphere of Venus have been studied with the use of numerical models. To calculate the heating/cooling of the atmosphere due to absorption/emission of electromagnetic radiation under initially weak and strong superrotation of the atmosphere, the complete system of gas dynamics equations in the relaxation approximation was considered. It has been shown that at sufficiently high rates of heating of the atmosphere by radiation on the day side and at sufficiently high rates of cooling on the night side, a thermal tide develops at altitudes of 40?C70 km, and its energy and impulse is transferred to the zonal superrotation of the atmosphere. Due to the interaction between the superrotation and the meridional transfer of the air mass through the polar region from the day side of the planet to the night side, near-polar vortices are formed at altitudes of 40?C70 km near the morning terminator.     

Propagation of weak discontinuities in a vibrationally-excited gas flow

Propagation of weak discontinuities headed by wavefronts of arbitrary shape in three dimensions are studied in vibrationally relaxing gas flow. The transport equations representing the rate of change of discontinuities in the normal derivatives of the flow variables are obtained, and it is found that the nonlinearity in the governing equations does not contribute anything to the vibrationally relaxing gas. An explicit criterion for the growth and decay of weak discontinuities along bi-characteristic curves in the characteristic manifold of the governing differential equations is given. A special case of interest is also discussed.     

Diffusion and heat flow equations for the mid-latitude topside ionosphere

For application to the mid-latitude topside ionosphere, we have derived diffusion and heat flow equations for a gas mixture composed of two major ions, electrons and a number of minor ions. These equations were derived by expanding the velocity distribution of each constituent about its 13 lower order velocity moments. As a consequence, each constituent was allowed to have its own temperature and drift velocity. The restriction to mid-latitudes results because we have assumed that the species temperature and drift velocity differences were small. In deriving the diffusion and thermal conduction equations, we have discovered some new transport effects. For the major ions, we have found that: (1) a temperature gradient in either gas causes thermal diffusion in both gases; (2) a temperature gradient in either gas causes heat to flow in both gases; and (3) a relative drift between the major ion gases induces a heat flow in both gases. Similar transport effects have also been found for the minor ions.     

Stochastic and dynamic temperature changes in the interplanetary gas

Exact solutions have been found to the Fokker-Planck equations, incorporating stochastic velocity changes and modelling particles moving in an inverse square central force field under an inverse square collision frequency. The solutions for the velocity distribution contain a combination of collisional and dynamical (reversible) heating. At a general position, there are two populations each with three distinct temperatures, one normal to the orbital plane and the others closely parallel and perpendicular to the mean orbit. Collisional heating is strong and most readily detected in the secondary component of gas which reaches upstream directions along indirect orbits (attractive central force). For interplanetary helium gas reaching 1 a.u., the collisional heating ranges from effective transverse increase of 200 K and radial increase of 1500 K in the downstream wake, to several thousand K increase in radial temperature of the secondary component transverse to the initial gas stream. In interpreting 584 Å sky background radiation observations, the dynamical changes in the velocity spread have to be taken into account for helium gas that is initially hot, when Doppler shifts relative to the solar emission line are significant; the present solutions being the thermal approximations to the distribution function reveal the appropriate radial temperature as a function of space.     

Navier-Stokes and direct Monte-Carlo simulations of the circumnuclear gas coma: III. Spherical, inhomogeneous sources

We pursue our program of comparative simulations of the cometary gas coma by the two most advanced techniques available: (1) numerical solution of Navier-Stokes equations coupled to the Boltzman equation in the surface boundary layer, and (2) direct Monte-Carlo simulation. Here, we consider two different spherical but compositionally inhomogeneous nuclei, at three very different levels of gas production. The results show the same excellent agreement between the two methods in a domain adjacent to the surface as found precedingly, practically down to free-molecular conditions. A wealth of coma density patterns with non-intuitive structure is obtained. Some of these structures appear even under free-molecular effusion from the surface. The physical origin of all structures is discussed, and their evolution with changing gas production is studied. The computed comae are compared to those computed by various authors precedingly. Intercomparison of the present results demonstrates that differing inhomogeneity patterns may lead to similar structures in the gas coma. Comparison between these structures and those created by homogeneous, aspherical surfaces shows that it is not possible to guess from empirical rules which one of the two processes is responsible for the creation of a given structure. The implications for the interpretation of future high resolution images, or of future in situ mass spectrometric samplings of the near-nucleus gas coma are discussed.     

A relaxation method for the computation of model stellar atmospheres

A general Monte Carlo relaxation method has been formulated for the computation of physically self-consistent model stellar atmospheres. The local physical state is obtained by solving simultaneously the equations of statistical equilibrium for the atomic and ionic level populations, the kinetic energy balance equation for the electron gas to obtain the electron temperature, and the equation of radiative transfer. Anisotropic Thomson scattering is included in the equation of transfer and radiation pressure effects are included in the hydrostatic equation. The constraints of hydrostatic and radiative equilibrium are enforced. Local thermodynamic equilibrium (L.T.E.) is assumed as a boundary condition deep in the atmosphere. Elsewhere in the atmosphere L.T.E. is not assumed.The statistical equilibrium equations are solved with no assumptions made concerning detailed balance for the bound-bound radiative processes. The source function is formulated in microscopic detail. All atomic processes contributing to the absorption and emission of radiation are included. The kinetic energy balance equation for the electron gas is formulated in detail. All atomic processes by which kinetic energy is gained and lost by the electron gas are included.The method has been applied to the computation of a model atmosphere for a pure hydrogen early-type star. An idealized model of the hydrogen atom with five bound levels and the continuum was adopted. The results of the trial calculation are discussed with reference to stability, accuracy, and convergence of the solution.Contribution No. 385 from the Kitt Peak National Observatory.Operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

Toy Stars in two dimensions

Toy Stars are gas masses where the compressibility is treated without approximations but gravity is replaced by a force which, for any pair of masses, is along their line of centres and proportional to their separation. They provide an invaluable resource for testing the suitability of numerical codes for astrophysical gas dynamics. In this paper, we derive the equations for both small-amplitude oscillations and non-linear solutions for rotating and pulsating Toy Stars in two dimensions, and show that the solutions can be reduced to a small number of ordinary differential equations. We compare the accurate solutions of these equations with Smoothed Particle Hydrodynamics (SPH) simulations. The two-dimensional Toy Star solutions are found to provide an excellent benchmark for SPH algorithms, highlighting many of the strengths and also some weaknesses of the method.