On the evolution of obstars from the main sequence to the Helium exhaustion phase

The evolution of a 20M star of extreme Population I (X=0.602,Z=0.044) from the main sequence through the He-exhaustion has been calculated with particular attention to the treatment of the semiconvective zones. Two different relations as convective instability criteria have been adopted _{R a} +(/(4–3)) (d ln /d lnP) or _{R a} ). The He-burning phase is substantially different in the two cases. In the first evolutionary picture the star begins the He-burning phase as red supergiant, while in the second one as blue supergiant. The two evolutions are compared with the observational blue to red supergiants ration _B/n _R in connection with the problem of the existence of the neutrino processes and taking into account the possible presence of a high percentage of binary systems among supergiants.We draw the conclusion that the massive star evolution seems to be still completely uncertain and also not able to give a decisive test for or against the neutrino emission.     

Emden-chandrasekhar axisymmetric,rigidly rotating polytropes

An approximate analytical method of solving the polytropic equilibrium equations, first developed by Seidov and Kuzakhmedov (1978), has been extended and generalized to equilibrium configurations of axisymmetric systems in rigid rotation, with polytropic index,n =n _p + _n , nearn _p =0, 1, and 5. Though the details of the method depend on the value ofn _p , acceptable results are obtained for | _n | 0.5 to describe slowly rotating configurations in the range 0n1.5, 4.5n5. In the limit of rotational equilibrium configurations, when the distorsion may be large enough, a satisfactory approximation holds only in the range 0n, 1n1.5, 4.5n5.     

Correlations between statistical population indices and spectral characteristics of carbon stars

The coefficients of correlation between spectroscopic data published by Yamashita (1967) and others for carbon stars and the statistical population indices calculated for these stars at the Toru Observatory are calculated (Table II). The intensity estimates of Cai 4227 Å, Nai D lines, the C¹³/C¹² ratio, then=n(Li/Ca) index, as well as CN and probably C₂ bands are higher in population I carbon stars. The CH(G) band and probably hydrogen (H, H, H) lines as well as Baii 4554 and 4934 Å lines are stronger in population II carbon stars. The photoelectric colour indices, corrected for interstellar reddening do not show significant population effects. They can be used as spectral type equivalents. For a population criterion the CH/CN intensity ratio is proposed.     

Spectrophotometry of comet Hartley-Good (1985l)

We present spectrophotometric studies of comet Hartley-Good (1985l) in the spectral region 3200–7000 Å. The emission features of molecules CN, CH, C₂, and C₃ are observed. The variation of the emission strength of different species has been studied as a function of heliocentric distance. The abundances (N) and production rates (Q) of the molecules are also estimated.     

Implications of a strongly peaked polar magnetic field

Using the flux-transport equation in the absence of sources, we study the relation between a highly peaked polar magnetic field and the poleward meridional flow that concentrates it. If the maximum flow speed _m greatly exceeds the effective diffusion speed /R, then the field has a quasi-equilibrium configuration in which the poleward convection of flux via meridional flow approximately balances the equatorward spreading via supergranular diffusion. In this case, the flow speed () and the magnetic field B() are related by the steady-state approximation () (/R)B()/B() over a wide range of colatitudes from the poles to midlatitudes. In particular, a general flow profile of the form sin ^p cos ^q which peaks near the equator (q p) will correspond to a cos ⁿ magnetic field at high latitudes only if p = 1 and _m = n /R. Recent measurements of n 8 and 600 km² s^–1 would then give _m 7 m s^–1.     

Parameters of Dust Particles in the Martian Atmosphere

A critical analysis of the methods and results of estimating the optical thickness of the dust component in the Martian atmosphere ₀, the particle size r ₀, and the imaginary part of the refractive index n _ihas shown the following. (1) Observational data on the brightness distribution over the Martian disk as well as the phase dependences of diffusely reflected light and the azimuthal dependences of diffusely transmitted light are most appropriate to use only for verifying the reliability of the aerosol parameters determined by other methods. (2) If the morning and evening fogs in the atmosphere are disregarded, the Bouguer–Lambert–Beer method used to analyze the solar-brightness attenuation measured on the planetary surface yields overestimated extraatmospheric solar intensity I ₀and atmospheric optical depth ₀. At the Viking 1landing site, I ₀and ₀could be overestimated by a factor of 1.7 and by 0.35, respectively. (3) The aerosol size determined by analyzing measurements of the azimuthal dependences for the Martian sky brightness at low elevations of the Sun most likely corresponds to the fog particles. (4) If overestimated values of I ₀were used to standardize the observations of the solar radiation transmitted by the Martian atmosphere, then n _iwere also overestimated; using overestimated ₀also affected the reliability of the latter. (5) The problem of reliability of the available ₀and r ₀estimates for periods of high atmospheric transparency is yet to be solved. For the highest activity of the dust storm in 1971, it was found that 4.5 r ₀ 7.5 m for the lognormal particle size distribution with ²= 0.2 and the optical thickness of a dust cloud ₀ 15. (6) The spectral values of the apparent albedo of Mars measured in October 1971 at a phase angle of 42° in the spectral range 0.250 0.717 allowed the imaginary part of the refractive index to be estimated in terms of a model of a dust cloud composed of spherical particles with the lognormal size distribution with r ₀= 4.5 m and ²= 0.2.     

Rapidly rotating polytropes in the post-Newtonian approximation to general relativity

The study of uniformly polytropes with axial symmetry is extended to include all rotational terms of order ⁴, where is the angular velocity, consistently within the first post-Newtonian approximation to general relativity. The equilibrium structure is determined by treating the effects of rotation and post-Newtonian gravitation as independent perturbations on the classical polytropic structure. The perturbation effects are characterized by a rotation parameter = ²/2G _c and a relativity parameter, =p _c / _c C ² , wherep _c and _c are the central pressure and density respectively. The solution to the structural problem is obtained by following Chandrasekhar's series expansion technique and is complete to the post-Newtonian rotation terms of order ². The critical rotation parameterv _c , which characterizes the configuration with maximum uniform rotation, is accurately evaluated as a function of . Numerical values for all the structural parameters needed to determine the equilibrium configurations are presented for polytropes with indicesn=1, 1.5, 2, 2 5, 3, and 3.5.     

Plasmon neutrinos emission in a strong magnetic field

The decay of a longitudinal plasmon into two neutrinos is studied in the presence of a strong magnetic field. Contrary to the transverse case, for longitudinal plasmons the existence of a new mode, entirely dependent on the magnetic field, greatly enhances the energy loss at high densities. Denoting byQ _HandQ ₀the neutrino energy losses with and without magnetic field respectively, the situation is as follows: atH10¹¹ G andT10⁹K,Q ₀10⁵ Q _Hfor <10¹¹g cm^–3, WhileQ _H10¹⁰ Q ₀for >10¹¹g cm^–3. A second physically interesting feature is the anisotropic character of the energy loss which is highly peaked along the field lines, giving rise to a shorter cooling time in that direction than in any other.     

Effects of mass transfer on the unsteady free convection flow past an accelerated vertical porous plate with variable suction

An exact analysis of the effects of mass transfer on the flow of a viscous incompressible fluid past an uniformly accelerated vertical porous and non-porous plate has been presented on taking into account the free convection currents. The results are discussed with the effects of the Grashof number Gr, the modified Grashof number Sc, the Schmidt number Sc, and the suction parametera for Pr (the Prandtl number)=0.71 representating air at 20°C.Nomenclature a suction parameter - C species concentration - C species concentration at the free stream - g acceleration due gravity - Gc modified Grashof number (vg^*(C –C )/U ₀ ³ ) - Pr Prandtl number (C _p/K) - T temperature of the fluid near the plate - T dimensionless temperature near the plate ((T-T )/(T -T )) - U(t) dimensionless velocity of the plate (U/U ₀) - v normal velocity component - v ₀ suction/injection velocity - x, y coordinate along and normal to the plate - v kinematic viscosity (/gr) - C _p specific heat at constant pressure - C _w species concentration at the plate - C non-dimensional species concentration ((C-C )/(C _w -C )) - Gr Grashof number (g(T _w -T )/U ₀ ³ ) - D chemical molecular diffusivity - K thermal conductivity - Sc Schmidt number (/D) - T _w temperature of the plate - T free stream temperature - t time variable - t dimensionless time (tU ₀ ² /) - U ₀ reference velocity - u velocity of the fluid near the plate - u non-dimensional velocity (u/U ₀) - v dimensionless velocity (v/U ₀) - v ₀ non-dimensionalv ₀ (v ₀ /U₀)=–at^–1/2 - y dimensionless ordinate (yU ₀/) - density of the fluid - coefficient of viscosity     

Multiple expansion of the tidal potential

The Earth tidal deformation causes an additional gravitational potential. Its effect on the Moon orbital motion has been studied by several authors.In this contribution, we develop this additional potential without specifying the inertial frame chosen.For this purpose, we use the properties of the representation of rotation groups in 3 dimensions space. We finally obtain the interaction potential between the distorted Earth and the Moon which is a necessary preliminary to the study of the evolution of the Earth-Moon system.Nomenclature T.R.O Tide raising object - (, , ) Spherical coordinates of the T.R.O. - (J, _E ) Earth spin axis orientation. _E is the longitude of the ascending node of Earth's equator on thexy-plane - (a ,I ,e , , ,M ) Elliptics elements of the T.R.O     

Radiation from a strongly-magnetized plasma: The case of predominant scattering

On the basis of diffusion approach for normal modes, solutions of the radiative transfer problem are obtained and analysed for an optically thick tenuous plasma with a strong magnetic field. The case is considered when the scattering processes without change of photon frequency are dominant. The radiative transfer coefficients as well as spectra, angular dependences and polarization of the outgoing radiation are investigated in detail for a cold plasma,kT _emc ², |–s _B|kT _e/mc ² )^1/2|cos|, whereT _e is the electron plasma temperature, _B=eB/mc the electron cyclotron frequency,s=1,2,... the number of cyclotron harmonic and the angle between the magnetic field and wave vector. The effects of electronpositron vacuum polarization are taken into account and shown to be very significant. Simple analytic solutions are obtained for various limiting cases (small and large vacuum polarization; high, low and close to the cyclotron resonance radiation frequencies; different orientations of the magnetic field, etc). The results obtained are necessary for analysing X-ray and gamma-ray radiation from strongly magnetized neutron stars.     

On the spectrum of relativistic electrons accelerated in cosmic-ray sources

The data on the spectrum of the cosmic-ray electron component near the earth, on the radio-spectra of radio-galaxies, quasars and the Crab Nebula, as well as the data pertaining to the X-ray spectrum of the cosmic background, all agree that the sources of cosmic-ray electrons (such as supernovae and galactic nuclei) inject particles characterized by a power spectrumN(E)=KE ^–0, with 01.5–2.5. A mechanism is known in which the source emits a proton-nuclear component of cosmic rays with a spectrumN _n (E)=K _n E ^– _n, _n = + 2, =w cr/(w–w cr), wherew cr is the cosmic-ray energy density in the source, andw=w cr+w n+w _turb, the total energy density. We obtain =2.5 in agreement with observations on the natural assumption that =0.5. Within the framework of the same model with some additional assumptions, the electrons in the source, as well as those ejected by the source, are shown to have a power-spectrum characterized with _{0 n} = + 2. Thus the model discussed gives an adequate spectrum for both the proton-nuclear and the electron components of cosmic rays.     

Spectrophotometric observations of comet Hartley-Good (1985l)

Spectrophotometric observations of Cornet Hartley-Good (19851) during five nights in 1985 are presented in the wavelength range 3200–7000 ». The emission bands due to CN, CH, C₂, and C₃ molecules are observed. The abundances (N) and production rates (Q) of the molecules are derived.     

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.     

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.     

Scanner observations of comet P/Crommelin 18181

Spectral scans of the coma of comet P/Crommelin 1818. I have been obtained in the wavelength range 3200–6500 Å. Strong emission features of CN(3883 Å) and C₂ Swan bands (4695, 5165, and 5538 Å) have been identified. Some weak emission features of CH(3890 Å), C₃(4050 Å), CN(4200 »), and C₂ + CH(4358 ») were also detected. Sodium was found to be absent in this comet. An estimate of CN and C₂ abundances has been made and their production rate have been derived.     

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     

Circular Polarization of Starlight

Of the 7500 stars cited in the Catalog of starlight polarization, those which satisfy the condition P _obs % and A _V 0^m.5 are selected. It is presumed that the selected stars (n=216) have circularly polarized light.     

Simultaneous measurements of Ca+ K,Ca+ H,Hα, Hβ, and He D3 emission in prominences

Simultaneously measured line intensities of Ca⁺ K and H, H, H and He D₃ are presented and compared with recent model calculations by Heasley and Milkey (1978). The model calculations are compatible with the observations. There is indication that the observed branching of the relation E(Ca⁺ K and H) E(H) depends on the widths of the Ca⁺-lines.