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.     

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.     

The configuration of a thin,rotating self-similar disk in general relativity

Einstein's equations for a rotating pressure-free space-time are reduced to a system of four first-order non-linear ordinary differential equations in one self-similar dimensionless variable. Numerical results are given for the vacuum solution. A compatible thin disk can be specified by a surface density and an angular velocity . Self-similarity as a statement of the absence of scales implies that and can be written as=c ²/4Gr, =c/r, and demands that and be pure numbers.     

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.     

Pulsar dispersion measures and the mean and mean-squared interstellar electron density

Theoretical distributions of pulsar dispersion measures (times sinb ^II) are computed for various assumed pulsar spatial distributions above (and below) the galactic plane, assuming a distribution for the ionized gas. The statistics on the twelve high-latitude pulsars lead to the conclusion that the pulsar distribution inz is at least as broad as the distribution of the ionized gas. The value derived for the local mean interstellar electron density in the galactic plane is 0.12 cm^–3 and is interpreted to be due to a uniform ionized intercloud medium.Interstellar absorption of radio waves at low frequencies and cosmic X-rays at low energies are considered with regard to irregularities in the distribution of ionized gas. It is shown that if the obervations are made with a wide angle receiver the effective absorption optical deph is –²/2 where is the mean value and is the dispersion in . This relation assumes is much larger than . Analysis of recent low-frequency radio measurements from a satellite-borne receiver, however, leads to the conclusion that effects of irregulatirities are large.     

Cycle latitude effects for sunspot groups

Digitized Mount Wilson sunspot data from 1917 to 1985 are analyzed to examine meridional motion and rotation properties as a function of latitude and distance () from the average latitude of activity (₀) in each hemisphere. Latitude dependence similar to previous results is found, but only for spot groups whose areas are decreasing from one day to the next. A previous study of active region magnetic fields, using this technique of motions as a function of the average latitude of activity, had shown meridional motions on average toward ₀. In this analysis of spot data some evidence is seen for motion away from ₀, with some slight evidence for faster rotation equatorward of ₀ and slower motion poleward of ₀, similar to the torsional oscillation phenomenon. For reasons that are not clear, both of these effects are significantly more pronounced for sunspot groups whose areas are decreasing.Operated by the Association of Universities for Research in Astronomy, Inc., under Cooperative Agreement with the National Science Foundation.     

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 .     

A Survey for Hα emitting galaxies AT z ≃ 2.2

The deepest survey for H emitting galaxies at z 2.2has recently been made in narrow-band ( 1%) filters around2.1m using SOFI at the ESO NTT telescope. An effective area of 100 sq. arcmin and a comoving volume of 9000 Mpc³ (forH₀ = 50, q₀ = 0.5) has been covered to a volume weighted 3 line flux limit of 5 × 10^-17 erg s^-1cm^-2. Our survey covered the WFPC2 and STIS fields in the HubbleDeep Field South and an anonymous field about 30 deg. away. Thefaintest limit reached was 3 × 10^-17 erg s^-1 cm^-2 onthe WFPC2 field. In total, 10 convincing candidates with deduced starformation rates in the range 9 - 50 M/yr and an equal number ofmarginal ones have been identified for confirmation and follow-upspectroscopy with ISAAC at the VLT. Based on a very preliminaryanalysis we compare our results with those of earlier surveys andbriefly discuss some possible implications for the form of theevolution out to z 2 and the effects of clustering.     

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.     

The peculiarities of diffusion of the galactic cosmic rays at low energies

I give an interpretation of a result of Simpsonet al. (1988) on the variation with kinetic energyT _i of the mean pathlengthX _m (T _i ) of the galactic cosmic rays (CGRs) in the range 0.1T _i 10.0 GeV nucl^–1. I argue that the data onX _m (T _i ) may be interpreted in terms of a model of GCR diffusion on the one-dimensional Alfvén-wave turbulence, having a cutoff in the spectrum at frequencies _h , where _h is the proton gyrofrequency. The cutoff results in changing of the character of variation of the GCR diffusion coefficientD(T _i )T ^a in the rangeT _i 1 GeV nucl^–1 towards some more complicated variation at 0.1T _i 1.0 GeV nucl^–1 due to the peculiarities of the pitch-angle scattering at 90⁰.     

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.     

Unified Hamiltonian stability theory

We show that the spectral stability of Hamiltonian equilibria and periodic orbits may be analyzed by the same method. This is accomplished via the Cayley transform, =(+1)/(–1), which maps the unit circle onto the imaginary -axis. The advantages and disadvantages of the new method over previous techniques are elucidated.     

Rosat X-ray light curves of early-type stars

We have investigated ROSAT X-ray data of OB stars to search for evidence of time variability in the X-ray emission from early-type stars. As an example for such studies we present a detailed variability analysis for our two program stars Ori and Ori which have been multiply observed with ROSAT. The long-term analysis of both stars now covers a time range of 2.5 years and includes six pointed PSPC observations, an additional pointed HRI observation of Ori and the ROSAT all-sky survey data of both stars. Over a long time range the X-ray light curves of Ori and Ori show no evidence for variability. In the case of Ori we detected a moderate increase in X-ray count rate during a period of 2 days which can be explained as a strong shock propagating in the wind of an O-type star.     

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.     

Kelvin-Helmholtz instability of composite plasma in an oblique magnetic field with resistivity

Analytic structure of high-density steady isothermal spheres is discussed using the TOV equation of hydrostatic equilibrium which satisfies an equation of state of the kind:P = K _g , = _g c ².Approximate analytical solutions to the Tolman-Oppenheimer-Volkoff (TOV) equations of hydrostatic equilibrium in (, ), (,U) and (u, v) phase planes in concise and simple form useful for short computer programmes or on small calculator, have been given. In Figures 1, 2, and 3, respectively, we display the qualitative behaviours of the ratio of gas density _g to the central density _gc , _g / _gc ; pressureP to the _gc ,P/ _gc ; and the metric componente ^–, for three representative general relativistic (GR) isothermal configurations =0.1, 0.2, and 0.3. Figure 4 shows the solution curve (, ) for =0.1, 0.2, and 0.3 (=0 represents the classical (Newtonian) curve). Numerical values of physical quantitiesv (=4r ² P ^*(r)), in steps ofu (=M(r)/r)=0.03, and the mass functionU, in steps of =0.2 (dimensionless radial distance), are given, respectively, in Tables I and II. Other interesting features of the configurations, such as ratio of gravitational radius 2GM/c ² to the coordinate radiusR, mass distributionM(r)/M, pressure (or density) distributionP/P _c , binding energy (B.E.), etc., have also been incorporated in the text. It has further been shown that velocity of sound inside the configurations is always less than the velocity of light.Part of the work done at Azerbaijan State University, Baku, U.S.S.R., and Mosul University, Mosul, Iraq, 1985-1986     

The formation of a ring galaxy during a head-on collision between a disk and a spherical galaxy

The tidal force effects of a spherical galaxy passing head-on through a disk galaxy have been studied at various regions of the disk galaxy and for various orientations of the disk galaxy with respect to the direction of relative motion of the two galaxies. The density distribution of the disk galaxy is taken to be, (r)=_ce^–4r/R , where _c is the central density andR is the radius of the disk. The density distribution of the spherical galaxy is taken to be that of a oolytrope of indexn=4. It is found that as a result of the collision, through the central parts and the outer parts of the disk galaxy remain intact, the region in between these two regions disrupts. Thus a ring galaxy with a nucleus embedded in the ring-i.e., a ring galaxy of the RN-type, is formed.     

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 .     

On the Freundlich red shift

The Freundlich red shift of wavelengths in the solar spectrum is discussed. Born's approach on the photon-photon interaction is used in conjunction with Melvin's recalculation of Freundlich's universal constant in order to derive the cross-section for scattering in the solar atmosphere. The new cross-section appears to be = 1.58 × 10^–18 cm², which is about one thousand times Born's estimate for the effective cross-section. However, a modified value of the constant is in a good agreement with the one obtained by Ter Haar by scattering process methods, which leads to 10^–18 cm² for the photon-photon interaction cross-section of the solar atmosphere. A new expression for Freundlich's red shift formula is obtained. Some numerical examples are given and some interesting aspects of Freundlich's parameters are discussed.     

Search for a radio counterpart to GRB 940301 with westerbork

The COMPTEL instrument onboard theCompton Gamma-Ray Observatory imaged the bright gamma-ray burst GRB 940301 within 1.6 hours of the event, with a mean 1 error radius of 1.5°. The error region was subsequently refined by combining the COMPTEL location with the arc derived from differences in the event arrival time at the Ulysses and BATSE detectors. Westerbork observations of the COMPTEL error region began on March 4 1994 at 21 cm, however coverage of the refined position was not obtained until 32 days after the GRB occurrence, by which time the operating wavelength had changed to 92 cm. We have constrained the level of variability of sources within the triangulation arc-COMPTEL 2 error box region to be less than 40 mJy (5 upper limit) at 92 cm 41 days after the burst.     

Pulsars and interstellar medium: Multiple regression analysis of related parameters

An empirical relation which relates the 408 MHz galactic continuum background temperature (408GCBT) to dispersion measures, position and radio-luminosity of 325 pulsars is obtained by means of multple stepwise regression analysis. This relation showns that pulsars may be considered as galactic probes for the distribution of 408GCBT and interstellar electron density (IED) in interstellar medium (ISM).Peculiar pulsars (O-C±2.5) point out galactic regions where the observedT ₄₀₈ are higher (or lower) andn _e lower (or higher) than the averaged ones.Normal pulsars (–2.5T ₄₀₈ andn _e are in agreement, on, the average.Standard pulsars (O-C±0.05) show galactic regions where observed and computedT ₄₀₈ andn _e are in good agreement. Recent models of pulsar disk systems, suggested by Michel and Dessler (1981) could justify the conclusions drawn for peculiar pulsars having O-C>2.5.