Stability of the triangular libration points of the circular restricted problem in the presence of resonances

The stability of triangular libration points, when the bigger primary is a source of radiation and the smaller primary is an oblate spheroid. has been investigated in the resonance cases ₁ = 2₂ and ₁ = 3₂. The motion is unstable for all the values of parameters q and A when ₁ = 2₂ and the motion is unstable and stable depending upon the values of the parameters q and A when ₁ = 3₂. Here q is the radiation parameter and A is the oblateness parameter.     

Effects of metal abundances on the evolutionary period changes of classical Cepheids

Some peculiarities in the behaviour of a model self-gravitating system described by hydrodynamical equations and isothermal equation of state connected with the presence of thermodynamical fluctuations in real systems were investigated in numerical experiment. The values of density and velocity , , respectively, were computed by numerical code perturbed on each time-step and in each computational cell by random values , for modeling such fluctuations. Perturbed values _i = _i + _i ,v _i = _i + v _i were used to initiate the next step of computations. This procedure is equivalent to an introduction into original hydrodynamical equations of Langevin sources which are random functions. It is shown that these small fluctuations (= v =0,² =v ² = 10^–8) grow many times in marginally-stable state.     

Existence of the continuations in theN-body problem

The method of obtaining the estimates of the maximalt-interval ( _–, ₊) on which the solution of theN-body problem exists and which is such that some fixed mutual distance (e. g. ₁₂) exceeds some fixed non-negative lower bound, for allt contained in ( _–, ₊), is considered. For given masses and initial data, the increasing sequences of the numbers _k , each of which provides the estimate ₊ > _k , are constructed. It appears that if ₊ = +, then .     

Spectrophotometric observations and evolutionary status of ten Be stars

The continuum energy distribution data of ten Be stars — namely, HR 1761, HR 1786, HR 1820, Ori, Ori, OT Gem, Lyr, HR 7983, Cyg, and 59 Cyg — have been presented in the wavelength range 3200–8000 Å. The observed energy distribution curve shows near infrared excess for majority of Be stars and a double Balmer jump for HR 8047 and HR 8146. Empirical effective temperatures of these stars have been estimated by comparing the observed continuum energy distributions with that of computed theoretical models given by Kurucz (1979).On the basis of an HR diagram with evolutionary tracks for different solar masses the masses of these Be stars have been estimated. Position of these studied stars on the HR diagram suggests that these Be stars may be in the stage of core contraction after exhausting hydrogen at the centre and have undergone hydrogen exhaustion in the thick shell.     

The 4∶1 resonance

We study the resonance ₁₂ = 41 and some near-resonance cases. The main peculiarity of this resonance is that for ₁₂ < 4 the characteristic of the central periodic orbits is broken into two and each part is joined with a resonant characteristic. This behaviour is described theoretically by means of the third integral. It seems that there are infinite families of simple periodic orbits near the escape region. Finally, a comparison is made with the cases near the ₁₂ = 21 resonance.     

Asymptotic properties of disk dynamo

The asymptotic properties of a turbulent disk dynamo at large dimensionless numbersR andR characterizing the helicity and the differential rotation are analysed. Three types of generations in the dependence of the relations betweenR andR are found: ²-dynamo and two types of -dynamo. For each of these types the rates of growth are obtained and the forms of solution are pointed out. Boundaries of the disk dynamo approximation are given.     

Compton scattering of relativistic electrons in compact X-ray sources

The problem of single Compton scattering is considered and the resulting spectrum, angular distribution and polarization of scattered photons in a general case are obtained. The inverse Compton scattering (ICS) for arbitrary energies of electronsE and photons ₀ is investigated in detail. In the case of isotropically-distributed initial photons and relativistic electrons, a strong rise of the scattered spectrum near the upper edge takes place, starting from the values of the characteristic parameterb4E ₀10 (in units of mc²=1). The energy-loss rate of relativistic electrons due to ICS is calculated. It is shown that the relativistic electrons of the energiesE100 MeV, when scattering on the X-rays with ₀~10KeV, transmit the dominant part of their energy to the photons which fall after scattering into the energy range of the electrons (100 MeV).The radiation spectrum of ICS, as well as the energy-losses of relativistic electrons distributed by power-lawE ^–, are calculated. The radiation spectrum reveals the power-law behaviour with the different indices in two limits: the dependence ^–(1)/2 at ₀1 gradually changes to ^–(+1) ln (₀) law for ₀1.     

Scanner observations of the Be starsν Gem,κ Ori,β Mon andω CMa

The photoelectric spectrophotometric scans of the Be stars Gem, Ori, Mon and CMa have been analyzed to find out few stellar parameters. The absolute energy distributions of these stars in the wavelength range 350–750 nm have been given. Their effective temperatures and gravities have been estimated from comparisons with non-LTE model atmospheres. The stars Gem and Mon have been found to have Balmer discontinuities in emission. The excess emission in the region 620–750 nm has been observed for Mon and CMa. The evolutionary aspects of these stars are discussed and their masses have been estimated.     

О колебаниях хвоста магнитосферы в приБлижении квазигидро динамики

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Influence du champ magnétique terrestre sur le mouvement d'un satellite autour de son centre de gravité

Résumé On étudie l'effet du champ magnétique terrestre sur le mouvement d'un satellite autour de son centre de gravité. Le satellite possède une symétrie dynamique et un moment magnétique propre dirigé suivant l'un des axes principaux d'inertie; le champ magnétique terrestre est assimilé au champ d'un dipôle dont les pôles coïncident avec les pôles terrestres. On néglige les perturbations de la trajectoire du satellite qui est supposée circulaire. La position du satellite par rapport à son centre de gravité est repérée dans un système d'axes lié au plan de l'orbite et le mouvement est décrit à l'aide des angles d'Euler , , . La symétrie sphérique et le choix du moment magnétique sur l'un des axes d'inertie permettent d'éliminer l'angle .La solution pour et peut se développer en séries de puissance d'un petit paramètre . Les séries convergent pour ||<1.Lorsque le moment magnétique est faible on la rotation du satellite rapide, est faible. Les développements sont calculés effectivement jusqu'à ².La comparaison des résultats avec l'intégration numérique du système d'équations différentielles est satisfaisante.

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The effect of the Earth's magnetic field on the motion of a satellite around its centre of mass is investigated. The satellite is assumed to be dynamically symmetric and to be magnetized in the same direction as that of a principal axis. The Earth's magnetic field is assumed to be a dipole field whose poles coincide with the rotation poles of the Earth. The satellite's orbit is circular and perturbations are neglected. The position of the satellite with respect to its centre of mass is given with respect to a coordinate system fixed in the orbital plane and the motion is described by Euler's angles , , . The spherical symmetry and the coincidence of the magnetic moment with a principal axis allow one to eliminate the angle .The solution for and , can be expanded in power series for small parameter .The series converge for <1. is small for a small magnetic moment or a high angular velocity of the rotating satellite. The terms of the expansion of the series are calculated up to ².The comparison of the results with those obtained by numerical integration of the differential equation is satisfactory.

     

The distribution law of stellarp-modes

We show that the overall densityg() of asymptotic acoustic frequencies of a star obeys a Weyl lawg() ^D–1, whereD is the dimensionality of the oscillating stellar configuration. For realistic stars with a finite non-zero surface sound speed,D is equal to the actual dimensionality of the star,D=3. For formal models with a vanishing sound velocity at the surface, heuristic arguments lead to a dimensionality parameterD=4.5. The empirical frequencies of Eddington's standard model are found to be consistent with the latter distribution, with reasonable agreement already occurring in the low-frequency range > _i 2× fundamental radial mode. We argue that real stars obey this 3.5-power law in some finite frequency interval _i << _f , _f being a very high frequency critically depending on the surface sound velocity, while the full asymptotic law, withD=3, holds for > _f .     

A Razin-Tsytovich effect for bremsstrahlung

It is shown that bremsstrahlung from electrons with Lorentz factor 1 is suppressed for >_p in a plasma with plasma frequency _p compared with emission in vacuo. For _p the ratio of the power emitted per unit frequency in the plasma to that in vacuo varies as ².This suppression effect is analogous to the suppression of synchrotron radiation in a plasma (Razin-Tsytovich effect). It is argued that such suppression is a characteristic property of emission by relativistic particles in a plasma.     

The motion of a satellite in an axi-symmetric gravitational field

The equations for the variation of the osculating elements of a satellite moving in an axi-symmetric gravitational field are integrated to yield the complete first-order perturbations for the elements of the orbit. The expressions obtained include the effects produced by the second to eighth spherical harmonics. The orbital elements are presented in the most general form of summations by means of Hansen coefficients. Due to their general forms it is a simple matter to estimate the perturbations of any higher harmonic by simply increasing the index of summation. Finally, this paper gives the respective general expressions for the secular perturbations of the orbital elements. The formulae presented should be useful for the reductions of Earth-satellite observations and geopotential studies based on them.List of Symbols semi-major axis - C _jk ⁿ (, ) cosine functions of and - e eccentricity of the orbit - f acceleration vector of perturbing force - f sin²t - i inclination of the orbit - J _n coefficients in the potential expansion - M mean anomaly - n mean motion - p semi-latus rectum of the orbit - R, S, andW components of the perturbing acceleration - r radius-vector of satellite - r magnitude ofr - S _jk ⁿ (, ) sine functions of and - T time of perigee passage - u argument of latitude - U gravitational potential - true anomaly - V perturbing potential - G(M₊+m) (gravitational constant times the sum of the masses of Earth and satellite) - _n,k coefficients ofR component of disturbing acceleration (funtions off) - _n,k coefficients ofS andW components of disturbing acceleration (functions off) - mean anomaly at timet=0 - X ₀ ^n,m zero-order Hansen coefficients - argument of perigee - right ascension of the ascending node     

Concerning isothermal self-similar blast waves

We investigate the one-dimensional self-similar flow behind a blast wave from a plane explosion in a medium whose density varies with distance asx _– with the assumption that the flow is isothermal. If <0 a continuous solution passing through the origin and the shock does not exist. If 1/3>>0 one critical point exists. To be physically acceptable the flow must by-pass this critical point. It is shown that a continuous solution passing through both the origin and through the shock and by-passing the critical point does exist. If 1>>1/3 the first critical point does not exist but a second one appears. To be physically acceptable the flow must again by-pass this new critical point. We show that a continuous solution passing through both the origin and the shock and by-passing the new critical point exists in this case. If >1 no physically acceptable solution exists since the mass behind the shock is infinite.The dependence of the solutions on the parameter is analytic for >0 so that interpolation between neighboring values of is permitted.We investigate the stability of these isothermal blast waves to one-dimensional but non-self-similar perturbations. If 0<<5/7, the solutions are shown to be linearly unstable against short wavelength perturbations near the origin. If the solution crosses the shock with a normalized velocityu>2 the solution is linearly unstable against short wavelength perturbations near the shock for 1>>0. If the solution crosses the shock with normalized velocity 2>u>1 (and it must cross the shock withu>1), the solution is certainly unstable against short wavelength perturbations near the shock for >11/19 and, depending on the crossing velocity, can be unstable there for all .Thus for 1>>0, the solution is always unstable somewhere. Since there is no characteristic time scale in the system all instabilities grow as a power law of time rather than exponentially. The existence of these instabilities implies that initial deviations do not decay and the system does not tend to a self-similar form.     

Lower hybrid wave model for aurora

In the framework of non-linear fluid theory we use a lower hybrid (LH) wave of the form as a pump which interacts with the small fluctuations with the low-frequency vibrations _i or =0, where _i , is the hydrogen ion-cyclotron (HIC) gyrofrequency. The ponderomotive force generated by the beating of the high-frequency pump wave ₀ and the sideband LH waves (±₀) produces a non-linear coupling between the high- and low-frequency motions of electrons and ions. Under certain conditions the HIC waves and the zero-frequency waves both become parametrically unstable and start to grow. These excited waves then heat the ions by stochastic acceleration in the transverse direction, thus explaining the formation of ion comics along the auroral field lines. Electrons would be heated in the parallel direction directly by the pump field as well as by low-frequency waves. Thus a single mechanism can explain the existence of ion-cyclotron waves, zero-frequency waves, ion conics, and energetic electrons along the auroral field lines.     

Electrostatic Wave Instability and Plasma Radiation from Coronal Loops

Polarization properties of solar and stellar radio emission require, in some cases, emission below the third or fourth coronal electron gyro level, < 3,_c; 4, _c. In the context of plasma radiation, the source parameters should be such that the intermediate magnetic field condition 1 < _p ² / _c ² < 3 is satisfied. Supposing this condition, we investigate the generation of electrostatic waves in a warm background plasma with a high-energy component of magnetically trapped electrons. We invoke the conversion of upper-hybrid waves and Bernstein waves into electromagnetic radiation as being responsible for intense radio emission from a coronal magnetic loop. Moreover, odd-half harmonic emissions in the solar radio spectrum as well as the o-mode polarization at the second harmonic of the plasma frequency are natural consequence of this proposed model.     

A nonlinear tensor field and the second metric tensor

In our preceding paper {see [L. Sh. Grigorian and S. Gottlöber, Astrofizika (in press)]} we investigated a self-gravitating system consisting of a scalar field and a linear tensor field _ik= _ki with minimal coupling and with allowance for the action of vacuum polarization effects. In the present paper we investigate the case of a nonlinear tensor field _ik. The action S ⁽⁾ of the field _ik is determined by the difference R_ik — _ik, where R_ik is the space-time Ricci tensor and Rik is the analogous quantity constructed using the metric _ik=g_ik+_ik induced by _ik ( is a free parameter). Here S ⁽⁾ coincides with the previously known expression for the action of a linear field _ik. Equations of motion are derived for _ik in curved space-time. The energy-momentum metric tensor, determining the contribution of _ik to the gravitational field equations, is calculated.Translated from Astrofizika, Vol. 39, No. 1, pp. 135–144, January-March, 1996.     

Stokes parameters for thomson scattering in a cold magnetized plasma

The effect of a strong magnetic field on neutron stars or white dwarfs is calculated for Thomson scattering in a fully ionized collisionless plasma. The Stokes parameters for the scattered radiation are computed explicitly in terms of the state of polarization of the incident wave, the electron-cyclotron frequency, the plasma frequency, the angle of incidence, and the angle of scattering. The effects of the plasma are very insensitive to specific values of ( = ₂ ^p /²,_p denotes the electron plasma frequency) so long as 1, whereas the criterion for the magnetic field to substantially affect the Stokes parameters is that the photon frequency be less than the electron-cyclotron frequency. The effects of classical radiation damping and natural line broadening are briefly mentioned.     

Interpretation of distinct type IVmA- and IVμ-bursts on the basis of micro-instabilities and of resonant nonlinear interaction of waves

The generation of space charge waves by micro instabilities of the Harris type and their conversion into electromagnetic waves is discussed in the framework of the dispersion curves of the extraordinary wave mode in the warm plasma. Acceleration of electrons as also nonlinear interactions of waves are taken into account. A survey of the parameter regions of the Harris instabilities is given. Distinct values _p / _c and _p / _c result, enabling the instability as well as the conversion. The moving type IVmA bursts, and on the other side the impulsive cm-bursts and the first phase of type IV bursts are correlated to different values _p / _c and corresponding heights in the corona. The space charge waves can produce hydromagnetic waves by parametric excitation, too (type II bursts). The proposed mechanism is discussed with respect to the energy balance and to the magnetic configurations derived from observations with the Culgoora radioheliograph.     

On the origin of type III fundamental

A two-component scheme for the generation of type III fundamental radiation is proposed. The first component of the fundamental arises at a plasma level _{L t} because of the Rayleigh scattering of the plasma waves into electromagnetic radiation. The other component arises at _{L t} /2 because of the decay of the first component into plasma waves and the subsequent rescattering of the plasma waves into electromagnetic radiation _t 2( _t /2). By its properties (location, directivity, polarization) the second component is essentially the same as the second harmonic radiation produced by a stream of fast electrons at _L ( _t /2). This scheme is used to solve the main problems (localization and directivity of the source, polarization of type III fundamental) of the harmonic theory of type III solar bursts.