Regular and Chaotic Solutions of the Sitnikov Problem near the 3/2 Commensurability

Regular solutions at the 3/2 commensurability are investigated forSitnikovs problem. Utilizing a rotating coordinate system and theaveraging method, approximate analytical equations are obtained for thePoincare sections by means of Jacobian elliptic functions and 3periodicsolutions are generated explicitly. It is revealed that the system exhibitsheteroclinic orbits to saddle points. It is also shown that chaotic regionemerging from the destroyed invariant tori, can easily be seen for certaineccentricities. The procedure of the current study provides reliable answersfor the long-time behavior of the system near resonances.     

A new octuple Earth-crossing meteoroid stream

It was shown that the orbit of Virginid meteors is an octuple Earth-crosser so that the stream can produce eight related meteor showers. Of these eight theoretical showers five are identified in the catalogues; one of these is the Cygnids.     

Comparison between a radiative wind model for be stars and high angular resolution data from the GI2T interferometer

I present theoretical line profiles and intensity maps from an axi-symmetric radiative wind model from a rapidly rotating Be star. The introduction of a viscosity parameter in the latitude-dependent hydrodynamic code enables us to consider the effects of the viscous force in the azimuthal component of momentum equations (Araújo et al. 1994). Both velocity field and density law derived from the hydrodynamic equations have been used for solving the statistical equilibrium equations. By adopting the Sobolev approximation, we could easily obtain a good estimate of both electronic density and hydrogen level populations throughout the envelope. The numerical calculation was performed for parameters characterisic of the Be star Cassiopeiae.     

Non-linear stability zones around triangular equilibria in the plane circular restricted three-body problem with oblateness

Non-linear stability zones of the triangular Lagrangian points are computed numerically in the case of oblate larger primary in the plane circular restricted three-body problem. It is found that oblateness has a noticeable effect and this is identified to be related to the resonant cases and the associated curves in the mass parameter versus oblateness coefficientA ₁ parameter space.     

Present Observational Status of the Intermediate Mass Stars: δ Sct Stars, γ Dor Stars and roAp Stars

The present observational status of the Sct stars, Dor stars and roAp stars is discussed. The Sct stars are the most intensively observed of the three groups, but it has become clear that there are severe problems in extracting asteroseismic information from them. Dozens of frequencies are observed, but hundreds of frequencies are predicted from the models; unique matches of observation and theory still elude us. The Sct stars are observationally complex – some recent `best case' campaigns are discussed. It is possible that substantial observational advances for Sct stars may need to await upcoming satellite missions. New Dor stars are beingdiscovered frequently, and new behaviour is being found for them. They constitutean observationally young field. Their pulsational frequency range is being expanded, their position in the HR diagram is becoming better known (but is yet to be fully constrained), and the possibility exists of hybrid Dor – Sct stars that have greatasteroseismic promise, although it is clear such stars are rare, if they do exist. It has been observationally challenging to extract more than a fewfrequencies for any Dor star so far. Exciting spectroscopic discoveries of new behaviour in roAp stars promise unprecedented information about the structure of the peculiar atmospheres ofthose stars – pulsation amplitude and phase in 3D, magnetic field structurein 3D, abundance stratification in 3D, realistic T- for the most peculiarstars – as well as entirely new information about the interaction of pulsation,rotation and magnetic fields. Recent theoretical work has led to new understandingof the previously inexplicable frequency spacing of HR 1217 with new Whole Earth Telescope observations supporting this theory. An `improved oblique pulsator model' has been developed in which the pulsationaxis is not the magnetic axis; this model has passed several observationaltests and new ones are being devised to examine it further.     

Cosmological molecular hydrogen and the distortion of the relict radiation spectrum

The distortions of the relict radiation spectrum in the region of the wavelength <120 are considered. These distortions are due to the emission of photons under the formation of molecular hydrogen in the expanding universe in the cosmological epoch 40z200. It is shown that the real intensity of the relict radiation in the region of the wavelength under consideration must significantly exceed Planck's intensity, with a radiation temperature amounting to 2.8 K.     

Low energy γ-ray events in imaging Čerenkov telescope arrays

One of the major goals in VHE--ray astronomy is to open the energy range below 100 GeV with earthbound detectors. This paper demonstrates a new method for analyzing erenkov light of a shower in a erenkov telescope array. This method is successful for showers in this low energy regime where previous techniques (e.g. alpha analysis) are not applicable. A Monte Carlo simulation is applied to a system of 19 Whipple type [3, Cawley 1990] Imaging Atmospheric erenkov telescopes (IAT), each built as a 10 m diameter reflector and equipped with a 109 photomultiplier tube camera. The energy threshold for a single detector of this type is given [5, Kerrick et al. 1995] as 250 GeV. Analysis of simulated coincident events of the system for those events not having enough light to apply a standard imaging analysis [4, Hillas 1985], leads to a considerably lower threshold of 85 GeV. With a new analysis method of these events it is shown that it should be possible to distinguish between -ray induced and proton induced showers. The improvement of sensitivity (Q = figure of merit) of this analysis method is found to be Q=2.9.     

The thermal radiation spectra of supermassive stars and X-ray sources

In the external layers of supermassive stars and thermal sources of X-ray radiation electron scattering contributes more to the opacity than free-free process. Therefore, the thermal radiation spectrum of supermassive stars must greatly differ from Planckian. The approximate formulae obtained for the radiation spectra are applicable to any objects with a predominant role of electron scattering in the opacity and power dependence of plasma temperature and density on geometrical depth of the layers.In thermal radiation sources with power dependence of plasma temperature on depth of the layer the formation of power radiation spectraF(v)v ^– with >0 with >0 is possible. Such spectra can imitate the presence of non-thermal radiation mechanisms. This effect takes place also in the case of small optical depth on the Thomson scattering. Possibly, this effect is of interest for the theories of X-ray sources and X-ray solar flares.This case was considered also in the final version of the paper (Felten and Rees, 1972).     

Orbital Distribution Arbitrarily Close to the Homothetic Equilateral Triple Collision in the Free‐Fall Three‐Body Problem with Equal Masses

The existence of escape and nonescape orbits arbitrarily close to the homothetic equilateral triplecollision orbit is considered analytically in the threebody problem with zero initial velocities and equal masses. It is proved that escape orbits in the initial condition space are distributed around three kinds of isosceles orbits. It is also proved that nonescape orbits are distributed in between the escape orbits where different particles escape. In order to show this, it is proved that the homotheticequilateral orbit is isolated from other triplecollision orbits as far as the collision at the first triple encounter is concerned. Moreover, the escape criterion is formulated in the planarisosceles problem and translated into the words of regularizing variables. The result obtained by us explains the orbital structure numerically.     

Subarcsec 10μm imaging of bipolar flow sources

We have started a program of high-resolution (0.4/pixel) 10m imaging of bipolar outflow sources using the 10m camera CAMIRAS. We present recent results obtained at the Canada France Hawaii Telescope which reveal extended emission or IR companions in several luminous objects. The extended emission we detected probably arises from transiently heated very small grains, while the newly discovered companions could contribute significantly to the outflow activity and extended far-IR emission usually attributed to the main optical source.     

Obtaining the free frequencies of the non‐rigid Earth

In this paper, the mathematical algorithm elaborated by González, Getino and Farto (1998) is applied to four different nonrigid Earth models, in order to obtain the analytical expressions of the corresponding free frequencies. The solutions are studied, and the contributions of the different considered effects are evaluated. A numerical integration is also carried out, showing the validity of the obtained analytical solutions.     

A Method Solving Kepler’s Equation for Hyperbolic Case

We developed a method to solve Keplers equation for the hyperboliccase. The solution interval is separated into three regions; F 1, F 1, F 1. For the region F is large, we transformed the variablefrom F to exp F and applied the Newton method to the transformed equation.For the region F is small, we expanded the equation with respect to F andapplied the Newton method to the approximated equations. For the middleregion, we adopted a discretization of the Newton method and used the Taylorseries expansion for the evaluation of transcendental functions (Fukushima,1997). Numerical measurements showed that, in the case of Intel Pentiumprocessor, the new method is more than 3.7 times as fast as the combinationof a fourth order correction formula (Fukushima, 1997) and Roysstarting procedure (Roy, 1988) and others.     

A role of cosmic rays in generation of radio and optical radiation by plasma mechanisms

The radiation of ultrarelativistic particles is examined in a quasi-uniform magnetic field superimposed by a wide spectrum of magnetic, electric, and electron density inhomogeneities created in a turbulent plasma. The radiation spectrum from a particle of a given energy is shown to acquire a high-frequency power-law tail with the same spectral index as the index of small-scale turbulence. For a power-law spectrum of ultrarelativistic electrons, dN()/d ~ ^–, with a cut-off at some energy _max, the radiation spectrum consists of a few power-law ranges; the radiation intensity may suffer jumps at frequencies which separate these ranges.In the high-frequency range the spectral index is determined by small-scale magnetic and electric fields. At intermediate frequencies the main contribution comes from the synchrotron radiation in a large-scale field; the radiation spectrum has an index =(–1)/2. The same index may be produced by large-scale Langmuir waves. At lower frequencies the radiation spectrum increases owing to the transition radiation caused by electron density fluctuations; in this case the spectral index is equal to +1–.The possibility of diagnostics of high-frequency cosmic plasma turbulence from radiation of high-energy particles is discussed. It is shown that the proposed theory may explain some features in the spectra of several cosmic objects.     

Nonlinearity of Nonradial Modes in Evolved Stars

We show that in evolved stars, even at relatively low surfaceamplitudes, nonradial modes become strongly nonlinear in thehydrogen shell source, where the Brunt-Väisälä frequency hasits absolute maximum. The measure of nonlinearity is the productof horizontal displacement times the radial wavenumber, . It becomes large already in evolved -Scuti stars.This nonlinearity presents a major problem for interpretations ofamplitude modulation in RR Lyrae stars in terms of nonradial modeexcitation.     

A Friedmann-Lemaître Universe Model with a Positive Cosmological Constant

The possibility of using a Friedmann-Lemaître model with a non-zero cosmological constant is investigated on the basis of analyses of the RATAN-600 and 87GB radio surveys and optical constraints. A zero deceleration parameter and critical matter density are features of the model. The model is in agreement with current observational data, including estimates of the age of the Universe, Hubble constant measurements, and the - z relation. A value for the cosmological constant is determined and its physical nature discussed.     

The Phase Space Structure Around L4 in the Restricted Three-Body Problem

The phase space structure around L ₄ in the restricted three-body problem is investigated. The connection between the long period family emanating from L ₄ and the very complex structure of the stability region is shown by using the method of Poincarés surface of section. The zero initial velocity stability region around L ₄ is determined by using a method based on the calculation of finite-time Lyapunov characteristic numbers. It is shown that the boundary of the stability region in the configuration space is formed by orbits suffering slow chaotic diffusion.     

Cosmological models with aG variable gravitational theory

A theory of gravitation with variableG is constructed as a modification of Brans-Dicke's theory. The theory is an attempt to include the effect both of matter and radiation on the inertia of a body, according to Mach's principle. Big Bang cosmological models are computed and the corresponding primordial chemical compositions are found.     

Spectropolarimetric Observations of the Unique White Dwarf GD 356 on the 6-m BTA

The results of spectropolarimetric observations of a unique magnetic white dwarf with emission lines, GD 356, on the 6-m BTA are presented. The star's magnetic field is estimated and it is shown not to rotate over times of 5 yr. Allowance for magnetic deformation of the star's surface, resulting an a nonuniform temperature distribution over its surface, showed that in the region of the magnetic poles the conditions may be satisfied for a radiative diskon in the form of a plasma jet, originating from the action of cyclotron radiation pressure. It is shown that the effect of nonuniformity of the surface temperature distribution of the white dwarf can produce the observed broad-band and resonance polarization of the stellar emission.     

Magnetic field measurements on four yellow supergiants. I

Multiyear high precision measurements of the longitudinal component of the magnetic field (B_e) of four supergiants are reported: Aqr (G0 Ib), Aqr (G2 Ib), Gem (G8 Ib), and Peg (K2 Ib). The best measurement accuracy, =0.8 G, was achieved for Peg. A Monte Carlo method was used to test the reliability of the derived measurement errors. The differences between the observational errors and the calculated Monte Carlo errors were 3.2%. For Aqr and Aqr no statistically significant value of the magnetic field was recorded when averaged over a night. For eGem the following overnight average values of the magnetic field were recorded on five nights: 11.1±2.7 G, 9.8±2.5 G, –10.5±3.0 G, 38.1±7.4 G, and 5.3±1.5 G. For Peg the magnetic field recorded over two nights was –5.3±0.9 G and – 2.7±0.8 G.Translated from Astrofizika, Vol. 48, No. 1, pp. 15–28 (February 2005).