Nonlinear analysis of two contra-streaming electron beams-plasma system

The nonlinear theory of electromagnetic modes in the radio frequency range, excited from a system consisting of two contra-streaming electron beams, supports the experimental observation that out of is the most prominent mode.     

Density wave-star interaction in the theory of spiral galaxies

The dispersion relation has been derived for density waves propagating at an arbitrary angle. The analysis has shown the existence of a resonance which for a two-arm galaxy can be stable, neutral or unstable as }2$$ " align="middle" border="0"> , respectively.     

Epstein weight functions for non-radial oscillations of polytropes

Weight functions for the determination of the periods of linear adiabatic non-radial oscillations have been calculated in the same manner as Epstein's classic treatment of purely radial oscillations. Quadrupole (l=2) oscillations for thef and lower orderp andg-modes were considered. One group of static models were polytropes in the range 1.0n4.0 with ; thus included were configurations that were convectively stable, unstable and neutrally stable throughout. Another group consisted ofn=3.0 polytropes with convective shells or convective cores; ₁ was set at different values in each region in order to produce stability ( ) or instability ( ). The weight function provides a pictorial means for assessing the relative importance of each region of a given static model with respect to generating a given non-radial mode.     

Charged particle diffusion in the presence of Alfvén waves: The perpendicular particle flux

The diffusion of charged particles through a weak stochastic electro-magnetic field which is superimposed on a constant background magnetic field is considered. The stochastic electromagnetic fields are assumed to consist of unpolarized Alfvén waves propagating at arbitrary angles to the direction . When the Alfvén waves are propagating in directions other than and the particle gyro-radius,r _g, is sufficiently large (but may be smaller than the correlation length of the stochastic fields) it is shown that the particle flux perpendicular to the direction is , wherev is the particle speed andf the particle density. The expression forK differs from those calculated by previous authors. For small particle gyro-radii the flux S has a different functional form and is identical to that found by Urch (1977) to describe particle diffusion when the Alfvén waves only propagate in the direction .     

The light curved in the CM field

In this paper we introduce the CM field in Sections 2 and 3 based on the paper by Wang and Peng (1985), and calculate the light curved in the CM field in Section 4. The result shows thatP makes _CM larger than _C at , and smaller at . Under a special circumstance which source, CM lens, and observer are in the same line, if we get | ₀₌₀ , and | _=/2 , we can determine theP(M) andQ(M) of the CM lens,M is the mass of the CM lens.     

Non-singular de Sitter universe inR+R 2−2Λ gravity

For the theory described by the action and taking the FRW flat space metric we find an exact non-singular de Sitter model universe exp(t ²), with . It is also proved that the standard general relativity de Sitter cosmology , >0 is also a model of this higher derivative theory of gravity. If the metric is conformally flatS could describe a consistent quantum theory and its classical solutions would correspond to cosmological models in this theory.This work was supported in part by CONACYT grand P228CCOX891723, and DGICSA SEP grant C90-03-0347.     

3He enrichments by magnetosonic waves in current-driven instabilities

A theoretical model for³He enrichments in solar energetic particles is developed. First, current-driven, electrostatic instabilities that have frequencies ( is the cyclotron frequency of³He) are investigated for a plasma consisting of H,⁴He,³He, and electrons with the density of³He much lower than those of H and⁴He. It is found that in many cases the oblique ion-acoustic waves can have positive growth rates at frequencies and, at the same time, negative growth rates at and at _H. This can occur near the marginal state of the instability. The wave damping at these frequencies is caused by the cyclotron resonances of⁴He and H. The cyclotron damping at is negligible, however, because the abundance of³He is very small. The H cyclotron waves can be unstable at for a wide region of plasma parameters; the electron-to-ion temperature ratio must beT _e /T _H 1.5. To destabilize the₄He cyclotron waves with , high⁴He density and high electron temperature are both required. Then,³He enrichments are studied on the basis of the theory of nonlinear magnetosonic waves, which can promptly accelerate ions. The current-driven electrostatic waves with can enhance fluctuation velocities of³He. Thus, in the presence of these waves, magnetosonic waves can selectively accelerate³He particles to high energies. Finally, cyclotron resonances of heavy ions with the waves or are briefly discussed.     

On the structure and mass of the galactic halo

On the basis of a globular cluster study a crude estimate of the total mass of the galactic halo within 20 kpc from the centre is done. It gives a minimal halo mass of the order of , yielding possibilities for a mass as large as . The content of the interstellar matter in the halo is estimated too. It is found that the gas content is a few percents the minimal mass, the gas temperature is very high — about 1×10⁶ K, the magnetic field weak — about 0.25 nT. A weak nonthermal radio emission might be expected from such a halo.     

Der offene sternhaufen NGC 2362

The very young open star cluster NGC 2362 was investigated by the strip method on charts of two photographs taken with the 1-m Schmidt telescope of the European Southern Observatory. Up to the limiting magnitudeM _v ^* =5 _. ^m 8 the cluster contains 100 stars and can be described by the Gaussian density law (6). Further results are: Mass = 246 , central mass density ₀ = 43.1 = 246 pc^-3 , radiusR2.6 pc, mean velocity of the stars = 0.64 km s^–1.

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Mitteilungen Serie A.     

Steady wave model of spiral galaxies and its application in cosmogony

The model is based on the assumption that logarithmic spiral arms of most spiral galaxies are due to the totating density wave obeying the steady wave equation . It is shown that this equation accounts also for the so-called Titius-Bode's law in the solar system.     

Effect of anisotropy and viscous dissipation on turbulence production

The paper is concerned with turbulent flow of incompressible, spatially homogeneous viscous fluid. A model for turbulence energy equation is obtained, ignoring the pressure redistribution term in dynamical equations for the Reynolds stresses. The mechanism of dissipation on turbulence production is discussed and shown that the turbulence kinetic energy decays upto a constant value as time becomes infinitely large, i.e., for isotropy, dissipation inhibits the production process and if > initially then dissipation causes reduction in anisotropy.     

Sound and thermal waves propagation in a hydrogen plasma heated by an external radiation field

The thermal equilibrium of a hydrogen plasma heated and ionized by an external radiation field, diluted by a factorW _* and defined by an effective temperatureT _*, is studied. In addition, the problem of propagation of acoustic and thermal waves in the above plasma model is also analysed. It is found that an external radiation field has stabilizing effects against wave amplification. From the dispersion relation obtained, the phase velocity for sound and thermal waves and their respective scale-length of damping (or anti-damping) is calculated as a function of the frequency for representative values of the plasma temperature and the external radiation fieldT _*.     

Static spherical configurations of cold matter in the Einstein-Cartan theory of gravitation

We investigate static, spherical configurations of cold catalized matter in the Einstein-Cartan theory of gravitation. Assuming that density of spin is proportional to the number density of baryonsn and using an equation of state of a degenerate, relativistic Fermi gas, we numerically integrated the relativistic equation of equilibrium. We have also studied the stability of those configurations. Configurations with central number densityn _c such that where is the effective pressure, are very similar to general relativistic configurations with the same central density. In the Einstein-Cartan theory there exists another disjoint family of equilibrium configurations for which but . Those configurations have very small masses 10^–6 g and raddi 10^–34 cm and are unstable.Supported in part by Research Grant MR-I-7.     

The spherically-symmetrical trajectories of spin particles in the Schwarzschild field

The motion of spin particles in the Schwarzschild field is examined in this paper. It is shown that Mathisson-Papapetrou equations under additional conditions , where is the Lie derivative of the Killing vector _j , permit only radial motion, motion in the equatorial plane and in the equilibrium points. All these types of motion are considered more in detail.     

Effect of central condensation on the modes of nonradial oscillations of stellar models

Modes of nonradial oscillations of six composite polytropic models have been investigated numerically to study the effect of central condensation parameter being the density at the centre and the mean density of a stellar model) on the modes of nonradial oscillations of stellar models.     

On the stability of ultrarelativistic stars

This paper present two new theorems on the theory of the stability of highly relativistic stars. Thefirst theorem states that a highly relativistic, spherical star is stable if and only if its adiabatic index (assumed to be constant in the interior regions) is greater than a certain critical value, _crit which depends in a specified way on the high-density equation of state. This critical value is analogous to the Newtonian value , but because of relativistic effects it is typically somewhat larger than . Thesecond theorem shows that at high central densities, the curves of —(binding energy) vs. radius, —E _B (R) for certain hot, isentropic sequences of stellar models must exhibit damped clockwise spirals. This spiraling reflects the onset of instability in one radial mode of pulsation after another as the central density increases along the sequence.     

The motion of the line of apsides of ζ phoenicis

An estimate of the period of the rotation of the line of apsides of the double-star system Phe is obtained by representing the density function as a product of a normal Gaussian distribution and an associated Legendre polynomial .The asymptotic behaviour of this function coincides with the results obtained by Zeldovichet al. (1981).The period of motion of the line of apsides of Phe (about 63 years) obtained in this way comes close to the period determined by an empirical formula for of Batten (1973).     

Fourier analysis of the light curves of eclipsing variable stars

The aim of the present paper is to find the eclipse perturbations, in the frequency-domain, of close eclipsing systems exhibiting partial eclipses.After a brief introduction, in Section 2 we shall deal with the evaluation of thea _n ^(l) integrals for partial eclipses and give them in terms ofa ₀ ⁰ ,a ₀ ⁰ (of the associated -functions) and integrals; while Section 3 gives the eclipse perturbations arising from the tidal and rotational distortion of the two components. The are given for uniformly bright discs (h=1) as well as for linear and quadratic limb-darkening (h=2 and 3, respectively).Finally, Section 4 gives a brief discussion of the results and the way in which they can be applied to practical cases.     

Asymptotic solutions for the Clairaut equation in the theory of rotating fluid masses

A procedure has been devised to construct a solution of the Clairaut equation in the form of an asymptotic expansion in terms of descending powers of , wherej denotes the order of spherical-harmonic distortion. It has been shown that asj and, therefore increases, the foregoing series approaches asymptotically a solution of our equation. The procedure is similar to the WKB-method of theoretical physics.     

Longitudinal distribution of X-bremsstrahlung on the solar disc

In this paper, the dependence of the intensity of solar bremsstrahlung in the spectral range from 1–60 keV on heliographic longitude is investigated. Considering a flare mechanism, which assumes that the electrons move in a preferred direction in the course of their acceleration (according to the model of Takakura and Kai (1966) the electrons move parallel to the solar surface), we come to the conclusion that the maximum of the bremsstrahlung intensity is shifted with increasing electron velocity towards the direction of motion of electron beams. In the case of the Takakura and Kai flare mechanism, the slow electrons ( ), i.e. with small energies of 1–10 keV, reach the maximum of the bremsstrahlung intensity round the CM; for higher velocities ( ), i.e. for higher energies of 10–60 keV, the direction of the maximum is shifted away from the CM towards the disc limb. These theoretical conclusions were proved by experimental research conducted by means of satellites.