A study of asymptotic solutions in the vicinity of the collinear libration points of the restricted three-body problem

Some particular solutions of the restricted three-body problem which determine outgoing or incoming orbits near libration points are considered. The solutions are obtained in the form of absolutely convergent Liapounov series. It is proved that these asymptotic solutions are plane curves situated in the orbital plane of the primaries. Each family of asymptotic solutions for every collinear point consists of four solutions which are the separatrices of a saddle point. The angles of inclination of the separatrices are determined.

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B,V surface photometry of the UV continuum galaxy NGC 838

Surface photometry of the UV continuum galaxy NGC 838 has been carried out in theB, V system using photographic plates obtained with the 74 Kottamia telescope, Egypt. Isophotes, luminosity profiles, integrated photographic magnitudes, effective diameters and other photometric parameters are derived.The photoelectrically calibrated total apparent magnitudes areB _T =13.57 with maximum diameters 1.57×1.34 (at threshold _m =27.7 mag.//) andV _T =12.91 with maximum diameters 1.54×1.32 (at threshold _m =27.7 mag./). The integrated colour index(B–V) _T =0.66 and the effective surface brightness _e (B=19.0 mag./) and _e (V=19.7 mag./. The major axis is at position angle =85°±1°.The nucleus of NGC 838 is quite blue (integrated colour(B–V)=0.41 forr ^*<0.1) compared to normal galaxies while the colour becomes redder from the nucleus outwards. The UV excess, H emission and radio continuum emission previously observed from this galaxy by other investigators may be attributed to a recent burst of star formation in the nucleus of the galaxy of duration slightly greater than 2×10⁷ yr.     

Структура и эволюция Сверхмассивных вращающихся магнитных политроп

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The structure of rotating magnetic polytropes is considered in Roche approximation. Investigation of the influence of poloidal as well as toroidal magnetic fields on the conditions of the beginning of matter outflow due to rotational instability is carried out. The influence of the turbulent convection and twisting of magnetic force-lines on the time of smoothing of differential rotation is considered. The estimate of the magneto-turbulence energy generated by differential rotation is presented. Both maximum possible energy output and duration of the quasi-statical evolution phase up to the appearance of hydrodynamic instability due to the effects of general relativity are calculated for supermassive magnetic polytropes of index three with uniform or differential rotation. The radius-mass relation is obtained for supermassive differentially-rotating magnetic polytropes referring to the longest part of the quasi-statistical evolution stage; some consequences are pointed out, including the period-luminosity relation.The evolution of the considered models of supermassive rotating magnetic polytropes with different character of rotation and different geometry of a magnetic field is discussed.The results obtained are summarized in the last section.

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English translation will appear in the next issue ofAstrophys. Space Sci.

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Receipt delayed by postal strike in Great Britain     

Рассеяние света на анизотропных частицах

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Temperature variations in the solar photosphere

We reproduced the observed center-to-limb variations of 11 weak line profiles with the HSRA and the microturbulence distribution given by Lites (1973), introducing an anisotropic macroturbulence (vertical component of 1.5 km/sec and horizontal one of 2.3 km/sec).The variations of the profiles with the heliographic latitude cannot be explained with temperature variations (it comes out that T/T 10^–3), but we need instead a very small dependence on of the photospheric turbulence velocity field, the maximum of which, situated around - 40°–60°, is of about 3–4%, above the equatorial value. With the present measurements, however, we are not able to distinguish between variations of the micro- and macroturbulence components of the total velocity field.     

A Study of the Rotation of the Solar Corona

Synoptic photoelectric observations of the coronal Fexiv and Fex emission lines at 530.3 nm and 637.4 nm, respectively, are analyzed to study the rotational behavior of the solar corona as a function of latitude, height, time and temperature between 1976 (1983 for Fex) and 2001. An earlier similar analysis of the Fexiv data at 1.15 R over only one 11-year solar activity cycle (Sime, Fisher, and Altrock, 1989, Astrophys. J. 336, 454) found suggestions of solar-cycle variations in the differential (latitude-dependent) rotation. These results are tested over the longer epoch now available. In addition, the new Fexiv 1.15 R results are compared with those at 1.25 R and with results from the Fex line. I find that for long-term averages, both ions show a weakly-differential rotation period that may peak near 80° latitude and then decrease to the poles. However, this high-latitude peak may be due to sensing low-latitude streamers at higher latitudes. There is an indication that the Fexiv rotation period may increase with height between 40° and 70° latitude. There is also some indication that Fex may be rotating slower than Fexiv in the mid-latitude range. This could indicate that structures with lower temperatures rotate at a slower rate. As found in the earlier study, there is very good evidence for solar-cycle-related variation in the rotation of Fexiv. At latitudes up to about 60°, the rotation varies from essentially rigid (latitude-independent) near solar minimum to differential in the rising phase of the cycle at both 1.15 R and 1.25 R . At latitudes above 60°, the rotation at 1.15 R appears to be nearly rigid in the rising phase and strongly differential near solar minimum, almost exactly out of phase with the low-latitude variation.     

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     

О форме электронной шапки вращающейся нейтронной звезды с сильным магнитным полем

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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.     

Apparent radii and other parameters for 416 B5 V-F5 V stars of the catalogue of the geneva observatory

Apparent radius, visual brightness, effective temperature and absolute radius for 416 B5 v-F5 v stars of the catalogue of the Geneva Observatory (Rufener, 1976) have been determined.Twenty-eight stars, anomalous in log versus (m _v)₀ diagrams, have been singled out. A good correlation for seven stars, in common with the list of Hanbury Brownet al. (1974), has been found. Similar parameters determined for 279 B5 v-F5 v stars of two preceding papers (Fracassiniet al., 1973, 1975) have allowed us to determine the averaged diagrams logq _v/q, logR/R and logT _e versus (B-V)₀ for 695 B5 v-F5 v stars.Moreover, in the present paper a good correlation logq _v/q versus logR/R and careful relation M _v=–7.40logR/R +3.31 for B5 v-F5 v stars have been determined. Plain correlations between logR/R and blanketing parameterm ₂ for some spectral types seem to point out that there arereal differences in the absolute radii of stars of thesame spectral type, in agreement with recent researches on the HR diagram (Houck and Fesen, 1978).Systematic differences between double (spectroscopic and visual) and single stars are found. In particular, the averaged relation m ₂ versus logR/R shows that A2 v-F5 v double stars may have a higher metallicity indexm ₂ and smaller absolute radii than single stars. Finally, the diagram logv sini versus logR/R confirms some properties of binary systems found by other researchers (Huang, 1966; Plavec, 1970; Levato, 1974; Kitamura and Kondo, 1978).Thesis for the degree in Applied Physics.     

Optically thick accretion onto black holes

Spherically symmetric, steady-state, optically thick accretion onto a nonrotating black hole with the mass of is studied. The gas accreting onto the black hole is assumed to be a fully ionized hydrogen plasma withn ₀=10⁸ cm^–3 andT ₀=10⁴ K far from the black hole, and a new approximate expression for the Eddington factor is introduced. The luminosity is estimated to beL=1.875×10³³ erg s^–1, which primarily arises from the optical surface (1) ofT10⁴ K. The accretion flow is characterized by 1 and (v/c)10. In the optically thin region, the flow remains isothermal, and the increase of temperature occurs at 1. The radiative equilibrium is strictly realized at (v/c)10.     

Движение малых частиц в окрестностях протосолнца переменной светимости

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Study of the nonradial directional property of the rays of the streamer belt and chains in the solar corona

Based on analyzing corona images taken by the LASCO C1, C2, and C3 instruments, a study is made of the behavior of the streamer belt spanning one half of the 1996–2001 cycle of solar activity, from minimum to maximum activity, in the absence of coronal mass ejections. It is shown that: (1) The position of the streamer belt relative to the solar equator is generally characterized by two angles: _o and _E, where _o is the latitudinal position (near the solar surface) of the middle of the base of the helmet, the top of which gradually transforms to a ray of the streamer belt with a further distance from the Sun, and _E is the latitude of this ray for R>5–6 R from the Sun's center where the ray becomes radial. (2) Only rays lying at some of the selected latitudes _o retain their radial orientation (_oE) throughout their extent. Namely: _o0° (equator), _o±90° (north and south poles), and the angle _o lying in the range ±(65°–75°) in the N- and S-hemispheres. (3) A deviation of rays from their radial orientation in the direction normal to the surface of the streamer belt occurs: for latitudes _o<|65°–75°| toward the equator (>0°) reaching a maximum in the N and S hemispheres, respectively, when _OM40°, and _OM–42° for latitudes _o>|65°–75°| toward the pole (<0°). The regularities obtained here are a numerical test which can be used to assess of the validity of the theory for describing the behavior of the Sun's quasi-stationary corona over a cycle of solar activity.     

Пе⌕вичный адрон: Происхождение звезд галактик и астрономицеской вселенной

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To the problem of satellite's perturbed motion under the influence of solar radiation pressure

A possibility of developing the analytical theory of perturbed motion for a balloon-satellite influenced by solar radiation pressure force is analysed here on the basis of the limit case modification of the two fixed centers problem whose force-field is a superposition of the Newtonian central field and a homogeneous one. Such an approach enables us in the intermediate orbit already to take into account the effect of a constant force, all coordinates of a satellite being expressed as functions of some monotonically increasing variable by means of inversion of elliptic quadratures. The relations between canonical constants of the intermediate orbit and a quasikeplerian elements coinciding in the absence of solar radiation pressure with keplerian ones are derived. The numerical results and illustrating the perturbations in the radius-vector of the intermediate orbit of a balloon-satellite of the Echo-I type are given.

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Plasma acceleration by radiation in X-ray pulsars

Charged particle acceleration is considered by a radiation flux from a star or hot spot in X-ray pulsars. It is shown that for any distance from the star there exists the upper velocity limit up to which a particle can be accelerated by radiation. This critical velocity does not depend on the luminosity of the spot. Near the hot spot surface the critical velocityv0.65c. These results are applied to plasma acceleration inX-ray pulsars. The mechanism is advanced, of -ray generation in the course of plasma accretion, onto a neutron star. It is shown that in the presence of a large magnetic field and high luminosity of the spot the relativistic electron-position avalanche may appear. The optical depth of the electron-positron cloud achieves the value of order one. The X-ray quanta emitted by the spot are scattered by relativistic (2.6) electron-positron pairs and are transformed into -radiation. Hard quanta with energy 1 MeV leave the generation region in the narrow cone 0.25.     

Effects of Hall current on hydromagnetic free-convective flow through a porous medium

An analysis of the effects of Hall current on hydromagnetic free-convective flow through a porous medium bounded by a vertical plate is theoretically investigated when a strong magnetic field is imposed in a direction which is perpendicular to the free stream and makes an angle to the vertical direction. The influence of Hall currents on the flow is studied for various values of .Nomenclature c _p specific heat at constant pressure - e electrical charge - E Eckert number - E electrical field intensity - g acceleration due to gravity - G Grashof number - H ₀ applied magnetic field - H magnetic field intensity - (j _x , j _y , j _z ) components of current densityJ - J current density - K permeability of porous medium - M magnetic parameter - m Hall parameter - n _e electron number density - P Prandtl number - q velocity vector - (T, T _w , T ) temperature - t time - (u, v, w) components of the velocity vectorq - U ₀ uniform velocity - v ₀ suction velocity - (x, y, z) Cartesian coordinates Greek Symbols angle - coefficient of volume expansion - _e cyclotron frequency - frequency - dimensionless temperature - thermal conductivity - coefficient of viscosity - magnetic permeability - kinematic viscosity - mass density of fluid - _e charge density - electrical conductivity - _e electron collision time     

A maximal background spectrum of gravitational radiation

A maximal spectrum of gravitational radiation from sources outside our galaxy is calculated. The sources are galaxies, quasars and events that occur in the early history of the universe. The major contribution is from galaxies whose effect extends over the frequency region 10^–810⁺⁴Hz, peaking at 10^–110 Hz, with a spectral flux of 10 erg cm^–2, s^–1. The main processes of gravitational radiation in the galaxies are stellar collapse into a black hole and dying binary systems. In the region 10^–410⁴ Hz the background spectrum is well above the detection levels of currently proposed detectors. FromMinimal considerations of this spectrum it is determined that the density of gravitational radiation is 10^–39g cm^–3. This background spectrum is sensitive to galactic evolution and especially sensitive to the upper mass limits and mass distribution of stars in galactic models. Therefore, the spectrum could provide information about galactic evolution complementary to that obtained by electromagnetic investigations.     

О механззме оптического, рентгеновского и гамма-излучения пульсара в краБе

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Distribution of polarization and intensity of radiation across the stellar disk and numberical values of atmospheric characteristics governing this distribution

Computations of polarization and intensity of radiation from a unit stellar surface area are presented, as well as a study of the numerical characteristics of atmospheres — single-scattering albedo and the initial source function(), which define the polarization behaviour of atmospheres. The radiatively stable models of stellar atmospheres presented by Kuruczet al. (1974) and Kurucz (1979) have been used for calculations. Since the versus optical depth dependence is rather weak, it has been assumed that (=cost. With a fixed effective temperatureT _eff maximum values of are characteristic of stars featuring the lowest surface gravity accelerationg. Among stars with radiatively stable atmospheres, maximum values of (=5000 Å) 0.4–0.6 are exhibited by supergiants withT _eff=8000–20 000 K. The plot of () is characterized by discontinuities at the boundaries of spectral series for hydrogen and, sometimes, for helium. Maximum are attained in the Lyman region of =912–1200 Å, where can reach the value 0.7–0.9 for supergiants, this value being 0.3 for Main-Sequence stars. For stars withT _eff 35 000 K, high values of also are attained for <912 Å. Within the infrared region, is always small because of bremsstrahlung absorption.A rapid growth of the source functionB with < typical for ultraviolet range (within the Wien part of spectrum), together with high values of results in the strong polarization of emission from a unit stellar surface element, sometimes exceeding the values for the case of a pure electron scattering. For longer wavelengths, where the limb-darkening coefficient is smaller, the plane of polarization abruptly turns 90° in the central parts of the visible stellar disk.