On topological stability in the general three-body problem

The confining curves in the general three-body problem are studied; the role of the integralc ² h (angular momentum squared times energy) as bifurcation parameter is established in a very simple way by using symmetries and changes of scale. It is well known (Birkhoff, 1927) that the bifurcations of the level manifolds of the classical integrals occur at the Euler-Lagrange relative equilibrium configurations. For small values of the mass ratio ε=m ₃/m ₂ both the positions of the collinear equilibrium points and thec ² h integral are expanded in power series of ε. In this way the relationship is found between the confining curves resulting from thec ² h integral in the general problem, and the zero velocity curves given by the Jacobi integral in the corresponding restricted problem. For small values of ε the singular confining curves in the general and in the restricted problem are very similar, but they do not correspond to each other: the offset of the two bifurcation values is, in the usual, system of units of the restricted problem, about one half of the eccentricity squared of the orbits of the two larger bodies. This allows the definition of an approximate stability criterion, that applies to the systems with small ε, and quantifies the qualitatively well known destabilizing effect of the eccentricity of the binary on the third body. Because of this destabilizing effect the third body cannot be bounded by any topological criterion based on the classical integrals unless its mass is larger than a minimum value. As an example, the three-body systems formed by the Sun, Jupiter and one of the small planets Mercury, Mars, Pluto or anyone of the asteroids are found to be ‘unstable’, i.e. there is no way of proving, with the classical integrals, that they cannot cross the orbit of Jupiter. This can be reliably checked with the approximate stability criterion, that given for the most important three-body subsystems of the Solar System essentially the same information on ‘stability’ as the full computation of thec ² h integral and of the bifurcation values.     

On the topological trigger of large eruptive solar flares

The possibility of studying the topological properties of the magnetic fields in solar active regions is considered in terms of simple models. Analysis of the field topology shows that the topological trigger effect should be taken into account when large eruptive flares are modeled.     

On radiative pumping of interstellar methanol masers

From the observed data of 17 Class-II methanol masers and their asociated HII regions and infrared sources and using the maser photon emission rate and the brightness temperature as two constraints on the pump, we conclude that infrared sources with a brightness temperature of about 100 K and a photon rate of about 10⁵³s⁻¹, associated with compact HII regions are the most probable pumping source     

On the flowers-ruderman instability mechanism

In the context of neutron star stability, Flowers and Ruderman (1977) pointed out that, if magnetic flux tubes passed from a magnetostatic equilibrium into the surrounding vacuum and back, the equilibrium might be unstable to displacements that lowered the external magnetic field energy without correspondingly increasing the combined internal and magnetic field energy within the conductor. They also discussed how the growth rate of such instabilities might be reduced if, as in the neutron star, the fluid is bounded by a solid finitely conducting mantle. These ideas are illustrated here by means of simple examples.     

On the mechanism of formation of loop prominences

A mechanism is suggested for the formation of loop-type prominences in solar-active regions following flare events. The mechanism is based on the already existing idea of compression of a coronal plasma element resulting in enhanced radiation and consequent cooling of the element. A model is suggested for such a compression based on the concept of a contracting, force-free filamentary structure. If the current in a filament increases with time, then there is a radial contraction of the filament. Since the coronal plasma is frozen into the magnetic field lines of the filament, a contraction of the filament causes a compression of the filamentary plasma. This model of compression is shown to be in approximate qualitative and quantitative agreement with observations.     

On the explosion mechanism of SNe type Ia

In this article we discuss the first simulations of two- and three-dimensional Type Ia supernovae with an improved hydrodynamics code. After describing the various enhancements, the obtained results are compared to those of earlier code versions, observational data and the findings of other researchers in this field.     

On the excitation mechanism in roAp stars

We investigate a model for the excitation of high-order oscillations in roAp stars. In this model we assume that the strong concentration of magnetic field about the magnetic poles is enough to suppress convection. Thus the model considered is composed of two polar regions, in which convection is presumed to be suppressed totally, and an equatorial region, where the convection is unaffected. This model is generated by building pairs of locally spherically symmetrical equilibria to represent the polar and equatorial regions of the star, which are patched together below the base of the convection zone. Gravitational settling of heavy elements is taken into account by choosing appropriate chemical composition profiles for both the polar and equatorial regions. Our results indicate that the composite model is unstable against axisymmetric non-radial high-order modes of pulsation that are aligned with the magnetic poles. The oscillations are excited by the κ mechanism acting principally in the hydrogen ionization zones of the polar regions. The effect of the lateral inhomogeneity on the second frequency differences is also investigated; we find that the perturbation to them by the inhomogeneity is of the same order as the second differences themselves, thereby hindering potential attempts to use such differences to identify the degrees of the modes in a straightforward way.     

On the mechanism of X-ray emission from radio pulsars

We discuss the correlations between the luminosities of radio pulsars in various frequency ranges and the magnetic fields on the light cylinder. These correlations suggest that the observed emission is generated in outer layers of the pulsar magnetospheres by the synchrotron mechanism. To calculate the distribution functions of the relativistic particles in the generation region, we use a model of quasilinear interactions between the waves excited by cyclotron instability and particles of the primary beam and the secondary electron—positron plasma. We derive a formula for calculating the X-ray luminosity L _x of radio pulsars. A strong correlation was found between L _x and the parameter \(\dot P_{ - 15} /P^{3.5}\), where P is the neutron-star rotation period, in close agreement with this formula. The latter makes it possible to predict the detection of X-ray emission from more than a hundred (114) known radio pulsars. We show that the Lorentz factors of the secondary particles are small (γ _p = 1.5–8.5), implying that the magnetic field near the neutron-star surface in these objects is multipolar. It follows from our model that almost all of the millisecond pulsars must emit X-ray synchrotron radiation. This conclusion differs from predictions of other models and can be used to test the theory under consideration. The list of potential X-ray radiators presented here can be used to search for X-ray sources with existing instruments.     

On a probable mechanism of superrotation of the atmosphere of venus

It is shown in the paper that the mechanism of superrotation of the atmosphere of Venus consists of several interrelated processes, including the transport of angular momentum from the solid planet to the atmosphere at a wind flow over the planet’s surface relief, the upward transport of momentum by threedimensional turbulent vortices, the inverse energy cascade in a large-scale quasi-two-dimensional flow, and the horizontal transfer of angular momentum in the Hadley cell. These processes make different contributions to the superrotation at different altitudes.     

On the problem of the formation of quasar emission lines by the Cherenkov mechanism

In a series of papers of You, Cheng, et al. (cf., for example, [2–4]) the Cherenkov mechanism of radiation was proposed as the explanation of the wide emission lines in the spectra of quasars. This mechanism acts because the refractive index of the plasma in a certain frequency range near a spectral line can exceed one. It has been found that the role of Cherenkov radiation becomes significant for an optically thick medium when the density of the packet of relativistic electrons ñ_e is 10⁴–10⁶ cm^–3. However, the question of the formation of a spectral line as the result of ordinary (recombination and collision) processes under the same physical conditions has not been considered, and hence no comparison has been made between the intensities of lines formed by different mechanisms. Moreover, a large number of effects that may have significant influence on the profile of a line (multiple scattering in the medium, redistribution of radiation over frequencies within a line, redistribution of energy between a line and the continuous spectrum) have remained unexamined by these authors.The present work aims at sharpening some of the formulas used in [2–4] and filling up some of these gaps. We pose the classical problem of formation of a spectral line taking account of the action of the Cherenkov radiation mechanism and give an exact solution of it. The computations are carried out for the line L. It is shown that under the values presently accepted for the electron temperature for an average quasar (T_e 1.5 · 10⁴ K) the influence of the Cherenkov mechanism becomes noticeable only for implausibly high densities of relativistic electrons (10¹¹ cm^–3, The geometric model proposed in [4] for quasar radiation in a line encounters insuperable difficulties involving the energy of the quasar and the sizes of the radiating regions.Translated fromAstrofizika, Vol. 37, No. 3, 1994.     

On a possible mechanism of solar faculae heating

A new mechanism of solar faculae heating is suggested. Interaction of the convective motion with the magnetic field results in decrease of its scale down to values providing for an ohmic dissipation and leading to heating at the photospheric level. Photospheric magnetic fields, faculae and granulation are considered as a combined problem. The heating mechanism causes the observed correlation of faculae brightness with the velocity field. Some points of observation are proposed for examining the action of the suggested mechanism. The effective decreasing of the magnetic field scale may be responsible for the origin of the fine structure. The model does not contradict generally accepted ideas on the active region development.     

On the mechanism of catastrophic destruction of minor planets by high-velocity impact

For the study of the collisional breakup of minor planets, semiquantitative interpretations of the catastrophic destruction of cubic rock targets by high-velocity impact reported by A. Fujiwara, G. Kamimoto, and A. Tsukamoto (1977, Icarus31, 277–288) are attempted. The conditions for transition and core-type destruction are derived from consideration of the side surface spallation, or central spallation, and the back surface spallation caused by the rarefaction pulses. In the derivation, the strengths of the original P-pulse at the crater rim and the bottom are given by application of the failure criterion. As the condition for complete destruction, an empirical rule is proposed. It is found that the critical sizes for these destructions vary as E^0.40 and the previously reported $\text{E}\text{M}\text{-}\text{scaling}$ is only an approximate rule (E, impact energy; M, target mass). The possibilities of extending of these results to larger bodies of any other shape are discussed.     

On the possible mechanism of formation of emission rim in hydrogen filaments

Hα filtergrams of the chromosphere show an emission rim in many hydrogen filaments. We suppose that formation of this rim is due to photospheric radiation reflected by the filament in the direction of the chromosphere. The calculations show that: (1) the maximum contrast of the rim relative to the undisturbed chromosphere amounts to 1.4; (2) the larger the optical thickness of the filament and the closer to the solar limb it is situated, the brighter and wider is the rim; (3) the rim was not observed in filaments whose heights exceeds 10000km above the chromosphere. These results are in close agreement with observations.     

On the convective mechanism for formation of the plasma sheet in the magnetospheric tail

Calculation of stationary distributions of the most important plasma parameters (particle energy, density, field-aligned and transversal pressure) is performed for a model magnetotail plasma sheet which is formed by convecting plasma mantle particles injected into the closed geomagnetic field line tubes. Computations have been done for two convection models: (i) a model of completely adiabatic particle motion with conservation of the first two invariants and (ii) a model with a strong pitch-angle diffusion which maintains isotropy. It is found that in both cases the heating and compression of the plasma are somewhat more effective than is necessary to account for the observed gradients of magnetic field in the magnetospheric tail. A leakage of accelerated particles through the dawn and dusk edges of the plasma sheet is proposed as a possible mechanism for maintenance of stationary convection in the magnetotail. The question of the dependence of the stationary magnetotail parameters on the solar wind state is discussed briefly.     

Optical pumping and the D-line ratio of Comet 1962-III

Spectral observations of Comet 1962-III made prior to perihelion passage revealed a sodium D-line ratio of 2.5. Due to the inadequacy of normal atomic processes in explaining this ratio, an optical pumping process is considered. It is found that such a mechanism can produce the observed D-line ratio if the sodium atoms within the coma were under the influence of a magnetic field and if they were excited by circularly polarized radiation from the sun.This research was supported in part by NASA Grant NGR 44-005-022.     

Diamagnetic pumping near the base of a stellar convection zone

The property of inhomogeneous turbulence in conducting fluids to expel large‐scale magnetic fields in the direction of decreasing turbulence intensity is shown as important for the magnetic field dynamics near the base of a stellar convection zone. The downward diamagnetic pumping confines a fossil internal magnetic field in the radiative core so that the field geometry is appropriate for formation of the solar tachocline. For the stars of solar age, the diamagnetic confinement is efficient only if the ratio of turbulent magnetic diffusivity η_T of the convection zone to the (microscopic or turbulent) diffusivity η_in of the radiative interior is η_T/η_in ≥ 10⁵. Confinement in younger stars requires larger η_T/η_in. The observation of persistent magnetic structures on young solar‐type stars can thus provide evidence for the nonexistence of tachoclines in stellar interiors and on the level of turbulence in radiative cores. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the hydrodynamic mechanism of the generation of the global poloidal flux on the Sun

The mechanism of the generation of the poloidal flux on the Sun caused by the differential rotation of the star is considered. Ranges have been found in which the poloidal flux is generated.     

On the quality of resonant absorption as a coronal loop heating mechanism

The qualityQ of a resonance is defined as the ratio of the total energy contained in the system to the dissipation per driving cycle. Hence, a good quality resonance is one with little losses, i.e., little dissipation per driving cycle. However, for heating coronal plasmas by means of resonant absorption of waves, bad quality resonances are required. Here, the quality of the MHD resonances that occur when an inhomogeneous coronal loop is excited by incident waves is investigated for typical coronal loop parameter values in the frame work of linear, resistive MHD. It is shown that the resonances in coronal loops have bad quality and, hence, yield a lot of Ohmic heating per driving cycle compared to the total energy stored in the loop. As a consequence, the time scales of the heating process are relatively short and resonant absorption turns out to be a viable candidate for the heating of the magnetic loops observed in the solar corona.