Effect of perturbations on the stability of triangular points. In the restricted problem of three bodies with variable mass

The effect of small perturbations and in the coriolis and the centrifugal forces respectively on the stability of the triangular points in the restricted problem of three bodies with variable mass has been studied. It is found that the range of stability of triangular points increases or decreases depending upon whether the perturbation point (, ) lies in one or the other of the two parts in which the (, ) plane is divided by the line J₈–J₉=0 where J₈ and J₉ depend upon , the constant due to the variation in mass governed by Jeans' law.     

The local complex of high-velocity clouds (geometry and kinematics)

Many HVC - high velocityHi clouds - are added to the known combination of diffuse soft X-rays and radioloops. Among these HVC there are previously examined complexes A, C, Magellanic Stream, etc. Their common composition has a clear geometry and kinematics.Two powerful long HVC filaments form the bridges between Loop I and double Loop II + III. The Bridges join the polarX _max regions in C band. The bridges ends at Loop I side are bounded by the systems of shorter filaments withX _max spots in M₁ and larger energy bands. There are no HVC in the spots themselves. The opposite ends of bridges reach Loops II and III centres. The two structures have the features of rotational symmetry.The isolines X-ray count rates pass along HVC chains with the same _r -velocities. The frequent alternation of different _r on the same filament is better explained by the turbulent gas motion than by the differences of HVC distance.All of the above-mentioned, as well as the _r signs of dependence on the galactical longitude, are the result of HVC interaction with X-rays. The whole composition from HVC-loops-X-rays is a component of the local system (Gould Belt).     

Взаимооействие Излучения Рентгеновскооо Истооника с АтмосФерой Нормальной Звезды в Тесных Двойных Системах

, . : , . , . . ( ) . . . HZ Her=Her X1, . . , . , ., hv 15–30 . , . Sco X1 .     

A study of the contrast of sunspots from photometric images

The thermal contrast , and the umbra-penumbraA _u/A _p, were calculated for 63 sunspots of various sizes and morphologies. Contrary to the assumptions of the PSI model, andA _u/A _p were found to be quite variable. The values of ranged from 0.1807 to 0.4266;A _u/A _p ranged from 0.0089 to 0.4899. The values of andA _u/A _p correlated well (r = 0.6018;p<0.005) and the regression for andA _u/A _p was obtained: = (0.220 ± 0.016) + (0.340 ± O.06)A _u/A _p. The values of andA _u/A _p were then compared with complexity ratings, magnetic field strength, time, and . The quantities andA _u/A _p were found to be independent of the complexity, magnetic field strength, and time factors. The correlation between andA _u/A _p lead to the proposed division of into an umbral thermal contrast _u, and a penumbral thermal contrast _p. These values were calculated from the photometric data: _u = 0.57 ± 0.01 and _p = 0.26 ± 0.006.     

Time-dependent Green's functions of the cosmic ray equation of transport

Two spherically symmetric time-dependent Green's functions of the equation of transport for cosmic rays in the interplanetary region are derived by transform techniques. The solar wind velocity is assumed radial and of constant speedV. In the first model the radial diffusion coefficient =₀ r (₀ constant), and in the second solution =₀= constant. The solutions are for monoenergetic, impulsive release of particles from a fixed heliocentric radius. Integration of the solutions over timet, fromt=0 tot=, gives the steady-state Green's functions obtained previously.     

Комптоновское рассеяние в источниках с синхротронной реабсорбцией

, ( ). n =3–5, T _e =4T _b (1 + ), - ( ) ,T _b - . , . , . W _H , ,n =3, =1. n =3–5(E), (E) , , = 1 – (), |()| < 1, |(E)| < 1. 3 273.     

Determination of the total amount of hydrogen atoms in a quiescent prominence

A brief quantitative review of the determination of the chemical composition of the Sun and stars is given. The method of estimation of the total amount of hydrogen atoms in a prominence is considered.The values of relative abundances of some infrequent elements in the solar atmosphere are refined using metal emission lines in the spectrum of a quiescent prominence. The most probable values of relative abundances for itrium _Y1×10^–9, zirconium _Zr2×10^–9, and scandium _Sc3.8×10^–9 are derived.     

Mean free paths and diffusion coefficients for energetic protons at small heliodistances calculated using Helios 1 and 2 data

Pitch angle scattering of energetic particles (100 MeV) in the interplanetary medium are studied using Helios 1 and 2 magnetometer and plasma data during 1976 near the minimum of solar activity. An IMF configuration was used in the computer experiments which allowed the pitch angle diffusion coefficient, D and hence the parallel mean free path, to be determined. The radial mean free path was found to vary as _r r ^-0.9 between 0.4 and 1 AU, but between 0.3 and 0.4 AU it decreases significantly. To reconcile our value of _r at 1 AU, lying between 0.01 and 0.02 AU, with the average prompt solar proton event profile, an increasing value of _r at lower radial distances would be required.     

Statistical survey of planetary nebulae: Distances,masses, and distribution in the galaxy

On the basis of empirical (D)-dependency at the frequency of 5 GHz constructed using 15 planetary nebulae with the independently measured distances (10^–171×10^–20 W m^–2 Hz^–1 ster^–1), we evaluated distances of 335 objects. Independent evidence of the correctness of the accepted scale are given. Then(D)-dependency is constructed and it is shown that atD<0.08 pc the mean electron density is higher than the one determined by the Seaton method. We showed that the filling factor diminishes with the increase of the PN diameter (1 atD0.08 pc and 0.2 atD0.4 pc). the ionized mass of 33 PNs is determined. With the diameter increase the ionized mass grows and atD0.4 pc reaches the valueM0.07M . We used the new distance scale when investigating the space distribution of PNs. The mean scale height =130±15 pc and the mean gradient of the change of surface densitym=0.37, which allowed us to estimate the total number of nebulae in the GalaxyN4×10⁴. We divided the PNs according to their velocities (withV _LSR>35 km s^–1 andV _LSR<35 km s^–1) and permitted us to confirm that the PN belong to different sub-systems of the Galaxy. The estimated local formation rate of PNs [=(4.6±2.2)×10^–12 pc^–3 yr^–1] is a little higher than the one of the white dwarfs. That can be explained by a large number of PNs having binary cores, which used in our sample. The statistical estimation of PN expansion velocity showed thatV _ex increases from 5–7 km s^–1 (atD0.03 pc) to 40–50 km s^–1 (atD0.8 pc).     

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.     

Rigorous estimates for the series expansions of Hamiltonian perturbation theory

In the present paper we prove a theorem giving rigorous estimates in the problem of bringing to normal form a nearly integrable Hamiltonian system, using methods of classical perturbation theory, i.e. series expansions in the small parameter . For any order of normalization, we give a lower bound _* ^r for the convergence radius of the normalized Hamiltonian, and a greater bound for the remainder, i.e. the non normalized part of the Hamiltonian. As an application, we consider the case of weakly coupled harmonic oscillators with highly nonresonant frequencies and show how, by optimizing, for fixed , the orderr of normalization, one gets for the remainder a greater bound of the formAe ^–(*₁/) ^a , with positive constantsA,a and ₁ ^* exponential estimate of Nekhoroshev's type.     

The helium content of the peculiar Oosterhoff type I globular cluster ω Centauri

An investigation of the observational properties for RR Lyrae variables in the galactic globular cluster Centauri is reported. The results show that Centauri belongs to the Oosterhoff Group I, notwithstanding the large, Oo II-like value of the average of the periods of ab-type RR Lyrae. The helium content is derived for this cluster from the analysis of the variables in the (A-logT _e) plane. It is shown that the helium abundance is very close to the value Y=0.30, about 0.05 larger than the value derived for the normal Oo I globular cluster M3.     

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     

Supersymetric Taub model,the micro-superspace sector

Since there are reasons for expecting supersymmetry in an underlying quantum theory of gravity, one is led to study quantum and classical cosmology with supergravity. In particular, classical solutions corresponding to these models could also be used to generate the quantization of supersymmetric minisuperspaces. In generating these solutions, the solution to the Rarita-Schwinger field in the cosmological background is also obtained. In this paper the supercosmological equations of Einstein-Rarita-Schwinger are solved for the micro-superspace sector of the Taub model, under the assumption =₁₁*₂₂ and . The solution for the parameters of the metric and are proportional to each other in each order, the zeroth-order and also the second-order terms. The zeroth-order terms correspond to the solution in general relativity and are logarithmic in time, the ₁₂ terms have an hyperbolic time-dependence. The Rarita-Schwinger field has the form cos((2/D ³)ln |t–t ₀|) and oscillates an infinite number of times astt ₀. This oscillating behaviour of the solution for is not only present when spinor fields are treated in a curved background, but also some cosmological wave functions behave in this manner. This solution is at the same time the supercosmological solution for the microsuperspace sector of the Taub model and also the Rarita-Schwinger field in this background.This work was supported in part by CONACYT grant P228CCOX891723, and DGICSA SEP grant C90-03-0347.     

Bidimensional spectroscopy of network bright points

We develop an automatic, computer controlled procedure to select and to analyze the Network Bright Points (NBPs) on solar images. These have been obtained at the Sac Peak Vacuum Tower Telescope by means of the Universal Birefringent Filter and Zeiss H filters, tuned, respectively, along the profiles of the H, Mg-b1, Na-D2, and H lines.A structure is identified as an NBP if at the wavelength H- 1.5 A its maximum intensity is greater than I + 3 and its area is greater than 1.5 arc sec² at I + 1.5, where I is the mean value and the standard deviation of the intensity distribution on the image. Each detected NBP is then searched and confirmed in all the remaining 31 images at different wavelengths.For each NBP several parameters are measured (position, area, mean and maximum contrast, Dopplergram velocity, compactness, and so on) and some identification constraints are applied.The statistical analysis of the various parameter distributions, for NBPs present within an active region and its surroundings, shows that two types of NBPs can be identified according to the value of their mean contrast C _min the H- 1.5 Å image (C _m 0.1 type I, C _m> 0.1 type II). The type I NBPs (all occurring on the boundaries of the supergranular network) appear to be much more frequent (180/26) than the type II ones.The size A of type I NBPs is less than 1.0 arc sec for H/H wings but of the order of 1.2 arc sec for Na-D2 and Mg-bl. The mean contrast C _m is around the value of 10% along the Na-D2 and Mg-bl profiles and of 20% along the H/H wings.The C _m - A scatter diagrams show, for the photospheric radiation (h < 100 km), a narrow range of variability for C _min correspondence with a wide range for A. For radiation orginated at higher levels (h > 200 km), the C _m- A scatter diagrams seem to indicate, even if with a large variance, that the highest C _m's tend to correspond to the highest A values.The mean Doppler shift is close to zero for Na-D2 and Mg-bl lines but negative (downward motion) for H and H lines.The type II NBPs tends to be preferentially located in the neighbourhood of small, compact sunspots and their detectability is almost constant through all the 4 studied line profiles. No conclusions can be derived on the mean size, contrast and Doppler shift values because their distributions are too dispersed. The only positive information is that its C _m- A scatter diagram, in H and H wings, indicates a wide range of variability for C _m in correspondence with very narrow range of variability for A.     

Observed oddities in the lines H,K, b and Hβ

We compare microphotometer intensity traces perpendicular to dispersion in simultaneous spectrograms of good spatial resolution traced at various 's in each of the lines. Cross correlations between the different traces show the following: (a) For each _K there is a corresponding _{b 1}at which the coefficient of correlation, r, is a maximum, usually > 0.8. (b) No such high correlations are found between H and H. (c) Comparison of traces in the continuum and at all observed 's in K, H, b₁, b₂ show a range of 's in each line over which r is very significantly negative, while H shows no such peculiarity.     

The proton-proton reaction and related reactions in an intense magnetic field

The reaction rates for the proton-proton reaction and the related electron capture reaction in a strongly magnetized relativistic electron gas of arbitrary degree of degeneracy are computed. The proton-proton reaction rates are unaffected by the presence of the magnetic field for field strengths up to the critical valueH _q =m ² c ³/e=4.414×10¹³G. For fields greater thanH _q , the proton-proton reaction rates are enhanced linearly with (=H/H _q ).The PeP reaction is investigated in detail for a wide range of temperatures, densities and magnetic field strengths that are of interest. The main results are as follows: In the non-degenerate regime the reaction rates are significantly reduced for high temperatures (T ₉5) and low fields (1). For instance, _pep(H)=0.04 _pep(O) at =10^–3,T ₉=10. For relatively high fields (>1) and low temperatures (T ₉2), the reaction rates are enhanced approximately linearly with . In the complete degenerate regime the reaction rates are reduced up to one-third of the field-free value for moderate densities (₆/_e10). At high densities (₆/_e10) the reaction rates are unaffected by the magnetic field.     

Search for the matter clumps in scalesZ ~ 1

The diagramV - log(1 +z _e ) as function of (, ) is considered for the quasars. HereV is the apparent visual magnitude,z _e is the emission line redshift, and are the equatorial coordinates. Two opposite extreme spots NE and SE are observed on the sky, where the inclination of the straight line fitting the dependenceV - log(1 +z _e ) is maximum and minimum. The coordinates of the centres of these extreme spots are ( _NE, _NE) = (282°, +42°) and ( _SE, _SE) = (70°, -38°) with errors 5°. A hypothesis of the Superattractor (SA) is proposed to explain such an effect. Two independent tests of this hypothesis are realized. First, the dependence or the frequency a of the absorbers in QSO spectra on (, ) is investigated. A region of the larger a is found. The coordinates of its centre are (, ) = (82°, - 10°) with error 5°. Second, the cases ofz _a >z _e are plotted in the Mercatorial projection (, ). The most of the casesz -z _e > 0.02 are concentrated within the circle with radiusR = 34° and centre (, ) = (50°, - 15°). The both anomalous regions overlap the Southern extreme spot around SE. The SA direction is (, ) = (67°, -21°) with errors about 12°. The redshift of SA isz _SA = 1.7 ± 0.3 that corresponds to the distancer _SA = (3100 ± 300)h ^–1 Mpc for the Hubble constantH ₀ = 75h kms^–1 Mpc^–1. The SA mass isM _SA ~ 10¹⁸-10²⁰ M . The orientation of the normal to the quasiperiodical large-scale sheet structure on the sky occurs near SA.     

Cyclotron waves in the solar wind

Cyclotron waves in the solar wind near 1 AU with frequencies well below the electron cyclotron frequency and wavelengths much larger than the electron cyclotron radius but less than the proton cyclotron radius are considered. The cyclotron radii are defined from parallel thermal velocity of electron component and proton component with respect to the interplanetary magnetic field. No LH cyclotron waves are found to propagate for _p < 0, where _p 1 –T _p/T _p is the temperature anisotropy of the proton component with respect to the interplanetary magnetic field. The damping or growth of RH cyclotron waves is found to depend on the frequency range and the temperature anisotropy of the proton component. The RH cyclotron waves are damped in the frequency range _r | _p | _p for _p < 0, where _p is the proton cyclotron frequency. RH cyclotron instabilities occur in the frequency range | _p | _p > _r > | _p | _p /(1– _r ) for _p < 0. The marginal state is at _r =| _p | _p .Abstract presented at theInternational Symposium on Solar-Terrestrial, São Paulo, Brazil, 17–22 June, 1974