Effect of various cross-section energy dependences in calculations of cosmological viscosity

The Einstein Field Equations for homogeneous cosmologies are considered within the viscosity approximation. It is shown that some power laws T ^m (whereT is the temperature) for the cross-section lead to collisionless behavior near the initial singularity in a big bang model. Under some circumstances one may have two viscous phases, as the cosmic fluid passes from collisionless to collisional to collisionless again, while the universe expands.Research was sponsored in part by the Aerospace Research Laboratories, Office of Aerospace Research, United States Air Force, Contract F33615-68-C-1675.     

Velocity dispersion profiles ofN-body simulations

The time evolution of the velocity dispersion as a function of radius, called v-profiles, of threeN-body simulations of Wielen are presented in units ofr/R _G (whereR _G is the gravitational or virial radius) and discussed as a function of mass sample. The evolution of the radial and tangential components of the velocity dispersion is discussed, and each v-profile is fitted to a simple power law in the halo (0.15r/R _G2.0). Several structural features appear at late time intervals: (a) an upturn in the radial component of v which occurs in a decreasing shell (closer to the core) in time, (b) the v-profile of the massive particles mimics that of the total sample, since equipartition of kinetic energy does not obtain, and (c) a local minimum atr0.3–0.5R _G appears in one model which coincides with the local minimum in the number density profiles and possibly with feature (a).The line-of-sight v-profile, called LS-profile, of each model as a function of time and mass sample are also presented and discussed. They contain the same structural features as the v-profiles. Projection factors at small radii are also discussed. The LS-profiles of the models can be compared with the observed velocity dispersion profiles of clusters of galaxies in Struble (1979a).     

Comparative Solar Seeing and Scintillation Studies at the Fuxian Lake Solar Station

Starting November 1999 we are carrying out simultaneous seeing observations with the Solar Differential Image Motion Monitor (S-DIMM) at the Fuxian Lake station of the Yunnan Observatory and a solar scintillometer of the type used in the recent site survey by one of us (Beckers et al., 1997). The purpose was to compare the two methods of assessing the daytime atmospheric seeing for a lake site. We report here the first results of this comparison. We find that the relation between the seeing as measured by the S-DIMM (the Fried parameter r ₀) and the scintillation in the solar irradiance (_I) differs greatly from the relation found by Seykora (1993) for NSO/Sac Peak. We conclude that the _I measurements give a good indication for the amount of near-Earth seeing but that they are a poor proxy for the total atmospheric seeing. We interpret the simultaneous (r ₀, _I) observations in terms of an atmospheric seeing model and find good quantitative agreement with a model in which a fraction () of the seeing originated near the Earth (ground or water) and the rest (1–) originates at higher layers. For lake sites is small all day and the seeing is determined primarily by the refractive index variations at higher atmospheric layers. For land sites is small in the early morning but rapidly increases as the day progresses, near-Earth seeing dominating there most of the time.     

Expanding and shearing magneto-viscous fluid cosmological model in general relativity

The object of this paper is to investigate the behavior of a magnetic field in a viscous fluid cosmological model. It has been assumed that the expansion () is proportional to the eigenvalue ₁ of the shear tensor _i ^j and the coefficient of shearing viscosity is proportional to the scalar of expansion. The paper also discusses the behavior of the model when the magnetic field tends to zero and comments on some other physical properties.     

Околозвездные оБлака по данным 2800 Mgii

2800 Mgii (. 1). (N ⁺/N ₁1000) , , (N ⁺/N ₁10). , . —, , . — . : ; 0.002 1 , 0.1 ; () 100 ^–3; ; ; , 10 ; 10^–4 1 . 2800 Mgii .     

Statistical analysis of multiple absorption spectra in QSO

A detailed statistical analysis was carried out for several quasars with multiple red-shifts systems. The most important results are (a) The statistical test of the reliability of az-system is very sensitive toz, the total number of absorption lines, the selected set of reference lines and the number of identified lines (b) The standard deviation from , the average number of randomz-systems per random spectra is larger than . Consequently, the reliability of any system depends predominately on and not on .     

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.     

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.     

Representation of the Earth's gravitational potential

The paper represents the Earth's gravitational potentialV, outside a sphere bounding the Earth, by means of its difference V from the author's spheroidal potential. The difference V is in turn represented as arising from a surface density on the sphere bounding the Earth. Because of the slow decrease with ordern of the normalized coefficients in the spherical harmonic expansion ofV, the density anomalies from which the higher coefficients arise must occur in regions close to the Earth's surface. The surface density is thus an idealization of the product of the density anomaly and the crustal thicknessb. Values of are computed from potential coefficients obtained from two sources, Rapp and the Smithsonian Astrophysical Observatory. The two sources give qualitative agreement for the values of and for its contour map. The numerical values obtained for are compatible with the idea that the responsible density anomalies are reasonably small, i.e., less than 0.05 g/cm³, and occur in the crust alone.This paper was prepared under the sponsorship of the Electronics Research Center of the National Aeronautics and Space Administration through NASA Grant NGR 22-009-311.     

On the relation between the amplitude of light and radial velocity variations of β Canis Majoris stars

The relation between the amplitude of light m and the amplitude of the radial velocity 2K for Canis Majoris stars is investigated. A linear relationship between m and 2K is found. However, the two stars BW Vul and Sco, which have the largest radial velocity variations, do not seem to share this relationship.     

Zonal comparison of modern selenodetic reference systems

An account is given of the results of a comparison of existing basic selenodetic systems in the equatorial zone of the Moon together with plan and altitude data, which have been provided by means of a specially worked out method, based on the use of the LAC charts of the Moon (scale 1:1000000), and which does not require the presence of common catalogued reference points. It is shown that systematic differences of the form () for different catalogues are, on the whole, relatively small and do not exceed 2. Systematic differences of the form () have a minimum in the region = ± 20° and significantly increase towards the edges of the visible disk, where they may attain a value of 6 between catalogues. Random errors in latitude have on the whole, a similar behaviour in different catalogues, being practically independent of longitude and not exceeding 3. Random errors in longitude significantly increase towards the limb regions in all the studied catalogues, and may reach values of 6 to 8. Author's estimates of the accuracy of absolute heights in selenodetic catalogues is not always sufficiently precise; in certain cases it was found that the accuracy was underestimated by a factor of one and a half. The data on relative heights in the LAC charts are expressed with a vertical step of 300 m, errors in these values are of the order of 250 m for each step in height. As a result of the comparison a set of better points has been obtained forming a catalogue which may be referred to as LPL. The selection was made on the basis of magnitude and character of both the systematic and random errors.     

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.

---

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.

     

Continental drift and rotation of the Earth

It is shown, based on certain simplifying assumptions, that an island the size of Greenland, drifting across the North Atlantic at 10 m/century produces a change in secular rotation T=0.01 s.Presented at the Symposium Star Catalogues, Positional Astronomy and Celestial Mechanics, held in honor of Paul Herget at the U.S. Naval Observatory, Washington, November 30, 1978.     

The cosmological model of Brans-Dicke theory

We use the generalized Brans-Dicke theory, in which the Pauli metric is identified to be the physical space-time metric, to study the Universe in different epochs. Exact analytical expressions for dilaton field , cosmological radiusR and density parameter are obtained fork=+1,0,–1 Universe in the radiation-dominated epoch. For matter dominated Epoch, exact analytical expressions for Hubble parameterH, cosmological radius, dilaton field, deceleration factorq, density parameter and the gravitational coupling of the ordinary matter are obtained for the flat Universe. Other important results are: (1) the density parameter is always less than unity for the flat Universe because the dilaton field plays a role as an effective dark matter, and (2) the new Brans-Dicke parameter must be larger than 31.75 in order to consistent with the observed data.     

The relationship between r.m.s. doppler velocities and temperature in the solar transition region

An attempt is made in this paper to determine the coefficient a in a power-law relationship of the form V ~T between the r.m.s. velocity fluctuation, V for raster images with 3 resolution and the temperature, T of line formation using SMM solar data. For T between 8000 and 10⁵ K, the data suggest a best fit with 3/4 < 1. It is argued, however, that unresolved fine structure tends to reduce the observed value of V and that higher resolution data may yield different values for . Skylab data have shown that the non-thermal line broadening velocity, , is proportional to T ^1/2. Also, for all temperatures less than 10⁵ K, V . This latter result, however, is again dependent on spatial resolution and may not be true in observations made with sufficient spatial resolution. The magnitudes of both V and indicate that bulk motions play important roles in the structure of the solar atmosphere as well as in its energy and momentum balance. It is important, therefore, to identify the true nature of such motions with better accuracy than is possible with currently available data.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Remarks on the viscosity concept in the early universe

Some aspects of viscous cosmological models, mainly of Bianchi type-I, are studied, in particular with the purpose of trying to obtain a natural explanation of why the entropy per baryon in the universe, ~ 10⁹, is so large. Using the FRW metric it is first shown, in agreement with previous workers, that the expressions for the bulk viscosity as derived from kinetic theory in the plasma era is incapable of explaining the large value of. However it is possible to imagine the viscosity to be an impulse viscosity operative in one or several phase transitions in the early universe. This is the main idea elaborated on in the present paper. It is shown that in thek = 0 FRW space, an impulse bulk viscosity _infl ~ 10⁶⁰ g cm^–1 s^–1) acting at the phase transition at the end of the inflationary epoch corresponds to the correct entropy. If the space is anisotropic, it is natural to exploit the analogy with classical fluid dynamics to introduce the turbulent viscosity concept. This is finally discussed, in relation to an anisotropy introduced in the universe via the Kasner metric.     

A note on σ-stability in hydromagnetics

The concept of -stability is reviewed and applied to the case of aligned magnetoatmospheric flow. A sufficient condition for -stability is derived, and the upper bound arising from this condition is investigated as a function of .     

Seeing Conditions at Sutherland. Results of the 1992/93 seeing campaign

In order to decide whether the seeing conditions at SAAO/Sutherland justify the erection of a 3.5 m telescope and also to compare Sutherland with the Gamsberg/Namibia site, a seeing campaign covering 15 months has been carried out. For direct comparison with the results of the seeing campaign at Gamsberg twenty years before the same QUESTAR telescope was employed. The seeing is determined by the scattering of the star-trail exposed on a film in the focal plane of the telescope. The campaign commenced in February 1992. Up to May 1993, data for 204 nights, that is 47.3% of the total number of nights, were collected. Due to wind speeds above 30 km h^-1, 25 out of the 204 nights were not considered in the final reduction. The useful 179 nights are evenly distributed over the campaign period. The median seeing value for the whole period is = 0.52. There are differences during the year: the best season gives = 0.42, the worst = 0.67. Each night was divided into three intervals, although data for each of the three intervals were not always available. Generally, there is an improvement in the seeing during the course of a night. The results are compared to the seeing values of Gamsberg/Namibia and ESO/La Silla.     

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.     

The crossover and magneto-optical effects in sunspot spectra

Two peculiarities of the magnetic splitting of lines in sunspot spectra have been investigated. The first one consists of the fact that in a rather small region of the penumbra, near the umbrapenumbra boundary, the -component is absent in the spectra of one circular polarization while both -components are present. In the spectra of the opposite circular polarization, the -components are absent but the -component is present. By analogy with the magnetic stars, in whose spectra such an effect was observed by Babcock, this phenomenon was called by us the crossover effect in the sunspot spectra. Some properties of this effect in the different spectral lines were investigated. The nature of this effect is discussed.The second peculiarity consists of the anomalous splitting of the -component of Zeeman triplets which are of the same and opposite signs in comparison with splitting of the -components. The different possibilities of explanation are discussed.