The influence of line-tying on coronal perturbations in a gravitationally stratified equilibrium

We study the influence of gravitational stratification of the solar atmosphere on the stability of coronal magnetic structures. In particular we question whether the (presumably stabilizing) influence of the anchoring of the magnetic field lines in the solar photosphere (line-tying) can be adequately modelled by either rigid wall or flow-through boundary conditions on the coronal perturbations, as is commonly done. Using the ideal MHD model without gravitational effects,inertial line-tying alone cannot lead to afull stabilization, as marginal stability cannot be crossed by including only the rapid density increase at the photospheric interface.We demonstrate, using the (localized) ballooning ordering, that when gravity and the corresponding intrinsically stable stratification of the photosphere is included, the points of marginal stability are no longer independent of the density. The sharp increase in density and associated decrease in pressure scale height at the solar surface leads to a stabilizing effect, which may result in a full transition from unstable to stable modes. Gravitational effects imply that rigid wall conditions represent photospheric field line anchoring better than flow-through conditions for determining the stability or modes of oscillation of a coronal equilibrium. Applying rigid wall conditions gives good approximations for frequencies that are much larger than photospheric time scales when the plasma is stable, and growth rates when the plasma is unstable. At the same time we show however that near marginal stability, even when gravity is included, rigid wall conditions are still violated.     

Phase relation between the poloidal and toroidal solar-cycle general magnetic fields and location of the origin of the surface magnetic fields

The phase relation of the poloidal and toroidal components of the solar-cycle general magnetic fields, which propagate along isorotation surfaces as dynamo waves, is investigated to infer the structure of the differential rotation and the direction of the regeneration action of the dynamo processes responsible for the solar cycle. It is shown that, from the phase relation alone, (i) the sign of the radial gradient of the differential rotation (/r) can be determined in the case that the radial gradient dominates the differential rotation, and (ii) the direction of the regeneration action can be determined in the case that the latitudinal gradient (/) dominates the differential rotation. Examining the observed poloidal and toroidal fields, it is concluded that (i) the / should dominate the differential rotation, and (ii) the determined sign of the regeneration factor (positive [negative] in the northern [southern] hemisphere) describing the direction of the regeneration action requires that the surface magnetic fields should originate from the upper part of the convection zone according to the model of the solar cycle driven by the dynamo action of the global convection.     

The virial-based solution for the velocity of gaseous sphere gravitational contraction

It is found that the relationship between the potential energy and the moment of the inertia independent of the radial mass distribution obtained earlier for the sphere also holds in the case of the ellipsoidal mass distribution for the ellipsoid of rotation.The possibility of application of the energy virial relations for solution of the evolutionary problems of the gravitating gaseous sphere, with the help of the relationship found earlier, is demonstrated. The physical conditions on the gaseous sphere boundary are introduced. The existence of two branches of evolution, the proton one and the electron one, is established. The problem of the gravitational contraction velocity during sphere evolution is solved. The relationship between the boundary temperature and the gaseous sphere radius as well as between the luminosity and the body mass is obtained. Some limiting relations for the final stage of the gaseous sphere evolution are found.

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Non-thermal effects associated with steep temperature gradients in the transition zone

We examine some of the possible consequences associated with the steep temperature gradients believed to exist in the transition zone. It is shown that the heat flux in the transition zone may be weakly electrostatically unstable and that the thermal electric field associated with the same step temperature gradients will lead to the generation of copious numbers of non-thermal electrons boiling off into the corona.     

Convective instability of thin flux tubes

The stability of magnetic flux tubes embedded vertically in a convection zone is investigated. For thin tubes, the dominant instability is of the convective type, i.e. it is driven by buoyancy forces associated with displacements along the tube. The stability is determined by = 8P/B ²; if _c the tube is convectively stable, otherwise it is unstable, where the critical value _c depends on the stratification of the convection zone. For a solar convection zone model, _c = 1.83, corresponding to a magnetic field strength of 1350 G at the surface of the Sun. It is concluded that the flux tubes making up the small scale field of the Sun are probably hydrodynamically stable.In tubes with > _c, the instability is expected to transform the tube either into a state of vanishing surface field strength (in the case of an upward flow), or one with a field strength higher than the original value (if the instability sets in as a downward flow). Following Parker, we suggest that this effect is related to the concentrated nature of the observed solar fields.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

О лагранжевых и зйлеровых решеиях обощенной задачи трех тел

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This paper is a continuation and a generalization of one published earlier (Duboshin, 1969): it discusses the problem whether there exist the Lagrangian and the Eulerian solutions of the generalized three-body (material points) problem. Every point in this generalized problem acts on another, one with a force (attractive or repulsive) directed along the straight line passing through these points, and in an arbitrary manner depending on time, mutual distance and its derivatives, the first and the second. Here, generally speaking, the third axiom of dynamics (law of action and reaction) is not presupposed as fulfilled, that is, it is supposed that every two material points interact in a different way.This most general assumption being made, we establish the conditions which must dictate the laws of the interactions, so that the three points can always remain at the apexes of the equilateral triangle (Langrangian solution), or remain always on a straight line (Eulerian solution).The author believes that such general treatment of the three-body problem can be useful for theoretical studies in celestial mechanics and also for practical applications in the study of isolated stellar systems.

     

ОБ ионизации межзвездного магния

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On the stability of small quasiperiodic motions in the hamiltonian systems

Orbital stability of quasiperiodic motions in the many dimensional autonomic hamiltonian systems is considered. Studied motions are supposed to be not far from equilibrium, the number of their basic frequencies may be not equal to the number of degrees of freedom, and the procedure of their construction is supposed to be converged. The stability problem is solved in the strict nonlinear mode.Obtained results are used in the stability investigation of small plane motions near the lagrangian solutions of the three-dimensional circular restricted three-body problem. The values of parameters for which the plane motions are unstable have been found.

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Перенос резонансного излучения И случайные ълуждания Фотонов

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Transfer of resonance radiation in infinite medium is considered as a process of random walks of photons. Close relation is shown to exist between the problems of transfer of line radiation and the stable distributions of the probability theory. This relation is used as a basis of a new method for the investigation of the asymptotic properties of the radiation field far from the sources.

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Interaction between the interstellar medium and solar wind plasma

The interaction processes governing the penetration of the interstellar gas into the solar neighbourhood are re-examined — as well as photo-ionization and charge-exchange processes, proton elastic collisions and electron ionizations help reduce the nearby gas densities. The total destruction rate varies little during the solar cycle, by perhaps 10%. Particle heating, particularly via the elastic collisions, determines the gas characteristics in the gravitationally focussed tail—enhanced H-density is prevented, while the He-tail is effectively hotter than 10³ K.Termination of the solar wind is rediscussed in the light of both electron heating and the stronger gas/plasma interaction. The spiral interplanetary field is taken to break up and the subsonic plasma flow to be controlled by the pressure of slowly cooling electrons. The terminating collisionless shock is then, if it exists at all, very weak (M ₁<1.4), subcritical, and energetically unimportant. Cosmic rays are little affected by this sonic transition, but at least the electron component should be modulated by plasma turbulence throughout the ionizing flow.

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Взаимооействие Излучения Рентгеновскооо Истооника с АтмосФерой Нормальной Звезды в Тесных Двойных Системах

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Some fundamental elements of universe mechanics

An essential part in the mechanics under study is taking into consideration the effect of motions of the Universe objects upon that of an individual one surrounded by them including those infinitely far from it. Only macro-objects of the Universe are meant here.

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Zusammenfassung Ein wesentlicher Bestandteil der Mechanik unter unserer Betrachtung ist die Berechnung des Einflusses auf die Bewegung eines individuellen Objektes von Bewegungen der Universum Objekte die es umringen einschließlich jene Objekte, die unendlich entfernt sind. Nur Makroobjekte des Weltalles sind in der Absicht dabei.

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Hubble expansion in a euclidean framework

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Динамические равновесные плазменные конфигуации и физика магнитосферы

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Аккреция вещества с магнитным полем на коллапсирующую звезду. II. Самосогласованная стационарная картина

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On the stability of strongly non-homogeneous self-gravitating equilibria

The stability analysis of several stronglynon-homogeneous, self-gravitating, one-dimensionalunstable equilibrium systems is carried out with the help of numerical techniques. The evolution of the perturbed unstable equilibria is studied by following the motion of the boundary curves of water bag configurations defining the systems.It is found that initial perturbations drive the unstable equilibrium states out of equilibrium at rates depending on the typical scale length of the perturbations : the instability rates increase with .     

Planar orbits through second variations

The development and application of a predictor-corrector method for the computation of families of periodic motions as well as of singular periodic solutions from which branchings or change in the stability character occur, based on the use of second order variations is presented. Numerical results obtained by means of this method are also given. It is found that this algorithm consumes somewhat less computer time in determining orbits-members of a family of periodic orbits, while it represents a unique tool for the determination of branchings of various orders, as well as of the precise members of each family at which the orbits change from unstable to stable and viceversa.     

Движение малых частиц в окрестностях протосолнца переменной светимости

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Non-restricted double-averaged three body problem in Hill's case

A limiting case of the problem of three bodies (m ₀,m ₁,m ₂) is considered. The distance between the bodiesm ₀ andm ₁ is assumed to be much less than that between their barycenter and the bodym ₂ so that one may use Hill's approximation for the potential of interaction between the bodiesm ₁ andm ₂. In the absence of resonant relations the potential, double-averaged by the mean longitudes ofm ₁ andm ₂, describes the secular evolution of the orbits in the first approximation of the perturbation theory.As Harrington has shown, this problem is integrable. In the present paper a qualitative investigation of the evolution of the orbits and comparison with the analogous case in the restricted problem are carried out.The set of initial data is found, for which a collision between the bodiesm ₀ andm ₁ takes place.The region of the parameters of the problem is determined, for which plane retrograde motion is unstable.In a special example the results of approximate analysis are compared with those of numerical integration of the exact equations of the three body problem.

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Угловые Флуктуации Реликтового излучения, порождаемые космологической турбу лентностью

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