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NASA NTRS1984

Rotation and surface brightness in elliptical galaxies

Correlations between the mean surface brightness and level of rotational support are presented and discussed for the sample of elliptical galaxies presented by Davies et al. (1983). The importance of these distance-independent correlations lies in the ability to isolate the effects of projection, and hence to define an intrinsic, edge-on correlation. Thus the position of an elliptical galaxy in this plane contains information about its true shape. In addition, the slope of the 'edge-on' correlation can be compared cleanly with theoretical predictions. The correlation is interpreted as a manifestation of varying amounts of dissipation during the formation epoch of a galaxy, with higher surface brightness, rotating ellipticals having dissipated more binding energy.

Wyse, R. F. G.↗
NASA NTRS1985

Multigrid solutions to quasi-elliptic schemes

Quasi-elliptic schemes arise from central differencing or finite element discretization of elliptic systems with odd order derivatives on non-staggered grids. They are somewhat unstable and less accurate then corresponding staggered-grid schemes. When usual multigrid solvers are applied to them, the asymptotic algebraic convergence is necessarily slow. Nevertheless, it is shown by mode analyses and numerical experiments that the usual FMG algorithm is very efficient in solving quasi-elliptic equations to the level of truncation errors. Also, a new type of multigrid algorithm is presented, mode analyzed and tested, for which even the asymptotic algebraic convergence is fast. The essence of that algorithm is applicable to other kinds of problems, including highly indefinite ones.

Brandt, A.↗
NASA NTRS1986

Three-dimensional grids as solutions of elliptic systems

An elliptic grid generation scheme is described which produces a curvilinear, boundary-fitted grid for highly swept wings with sharp leading edges. The three-dimensional integration domain is segmented in successive crossflow sections wherein the physical coordinates are transformed to computational coordinates by solving an elliptic set of two quasi-linear differential equations. Grid points are clustered in the vicinity of the wing surface, especially in the neighborhood of the leading edges. The formulation of the source terms in the equations governing the transformation contains adjustable parameters which are determined from limiting forms of the elliptic equations along the boundaries. The source terms are assigned to each grid point by interpolation of these parameters into the interior domain. The formulation does not depend on the boundary shape or on the distribution of the grid points along the boundaries. For the first time, the discretized governing equations have been solved using a fast AF1 iteration scheme.

Hartwich, P.-M.↗
NASA NTRS1985

Multigrid solutions to quasi-elliptic schemes

Quasi-elliptic schemes arise from central differencing or finite element discretization of elliptic systems with odd order derivatives on non-staggered grids. They are somewhat unstable and less accurate than corresponding staggered-grid schemes. When usual multigrid solvers are applied to them, the asymptotic algebraic convergence is necessarily slow. Nevertheless, it is shown by mode analyses and numerical experiments that the usual FMG algorithm is very efficient in solving quasi-elliptic equations to the level of truncation errors. Also, a new type of multigrid algorithm is presented, mode analyzed and tested, for which even the asymptotic algebraic convergence is fast. The essence of that algorithm is applicable to other kinds of problems, including highly indefinite ones.

Brandt, A.↗
NASA NTRS1987

Jacobi-Bessel analysis of reflector antennas with elliptical apertures

Although many reflector antennas possess circular projected apertures, there are recent satellite and ground antenna applications for which it is desirable to employ reflectors with elliptical apertures. Here a modification of the Jacobi-Bessel expansion is presented for the diffraction analysis of reflectors with elliptical apertures. A comparative study is also performed between this modified Jacobi-Bessel algorithm and the one which uses the Jacobi-Bessel expansion over a circumscribing circular region. Numerical results are presented for offset reflectors with elliptical and circular apertures and the improved convergence properties of the modified algorithm are highlighted.

Rahmat-Samii, Yahya↗
NASA NTRS1987

The surface-brightness-effective-size relation for elliptical galaxies in the cores of clusters

Surface photometry of 372 elliptical galaxies has been performed using CCD images of the centers of 97 nearby rich Abell clusters. The strong correlation between surface brightness and effective size, originally found by Kormendy (1977), is clear in the data. Brightest cluster galaxies show much less scatter about the mean relation defined by these data than do lower-luminosity cluster ellipticals, and the slope of the relation is shallower for the brightest galaxies; these two results are tentative, however, because of uncertain selection and environmental effects. When combined with published central velocity dispersions, the photometry yields a relation for brightest cluster galaxies that is in good agreement with the mean relation for elliptical galaxies found by Djorgovski and Davis (1987). Use of the surface-brightness/scale-length relation to measure the lookback luminosity evolution of the stellar content in galaxies is promising.

Hoessel, J. G.↗
NASA NTRS1987

Mass distributions in elliptical galaxies at large radii

Recently, X-ray observations have shown that elliptical galaxies generally contain large quantities of hot gas. Central dominant cluster ellipticals have even more gas, which they have accreted from the surrounding clusters. The mass distributions in these galaxies can be derived from the condition of hydrostatic equilibrium. M87, the best studied central dominant galaxy, has a massive, dark halo with a total mass of about 4 x 10 to the 12th solar masses within a radius of 300 kpc. The total mass-to-light ratio within this radius is at least 150 solar mass/solar luminosity. The X-ray observations of normal ellipticals also strongly suggest that they have heavy halos, although the distribution of the mass is much less certain than in M87.

Sarazin, Craig L.↗
NASA NTRS1986

Accretion flows in elliptical galaxies

A steady-state infall model of gas in elliptical galaxies is developed to investigate the properties and structure of the X-ray-emitting gas observed in these systems. Models have been computed for galaxies with an external pressure (as might be important for ellipticals in clusters), and for varying supernova heating rates. All the models exhibit cooling flows, with mass accretion rates of 0.1 - 0.5 solar mass/yr. A correlation between the radio luminosity and the X-ray luminosity of elliptical galaxies is examined which, in the context of the infall models, may suggest that the radio emission arises from nuclear sources that are powered by the gas accretion flow. These radio sources may also be confined effectively by the X-ray emitting gas.

Vedder, Peter W.↗
NASA NTRS1988

The X-ray emission of normal elliptical galaxies - Steady state cooling flow models

Steady state, spherical, homogeneous cooling flow models are compared to the observed X-ray luminosities, spectra, and surface-brightness profiles of elliptical galaxies. Galaxies without heavy halos and SNe have temperatures which are too low and X-ray surface brightness profiles which are too rapidly decreasing with radius to fit the observations. Galaxies with heavy halos and SNe have luminosities which are too large except for the highest luminosity ellipticals. Galaxies without heavy halos but with SNe have temperatures which are probably too cool in the outer parts. Galaxies with heavy halos but without SNe, where the gas is heated by the motions of gas-losing stars and by infall and compression in a heavy halo potential, are favored. This suggests that elliptical galaxies have heavy halos of optically dark material.

Sarazin, Craig L.↗
NASA NTRS1989

Steady state cooling flow models with gas loss for normal elliptical galaxies

A grid of cooling flow models for the hot gas in normal elliptical galaxies is calculated, including the loss of gas due to inhomogeneous cooling. The loss process is modeled as a distributed sink for the gas with the rate of loss being proportional to the local cooling rate. The cooling flow models with gas loss have smaller sonic radii, smaller inflow rates in their central regions, lower densities, and higher temperatures than homogeneous models. The reduction in the amount of hot gas flowing into the center of the models brings the models into much better agreement with the observed X-ray surface brightness profiles of elliptical galaxies. However, there is a large dispersion in the observed X-ray luminosities of ellipticals, and this cannot be explained by variations in the efficiency of gas loss. The gas-loss models have X-ray surface brightness profiles which are much less centrally peaked than the no-gas-loss models.

Sarazin, Craig L.↗
NASA NTRS1990

Collision probability at low altitudes resulting from elliptical orbits

The probability of collision between a spacecraft and another object is calculated for various altitude and orbit conditions, and factors affecting the probability are discussed. It is shown that a collision can only occur when the spacecraft is located at an altitude which is between the perigee and apogee altitudes of the object and that the probability per unit time is largest when the orbit of the object is nearly circular. However, at low altitudes, the atmospheric drag causes changes with time of the perigee and the apogee, such that circular orbits have a much shorter lifetime than many of the elliptical orbits. Thus, when the collision probability is integrated over the lifetime of the orbiting object, some elliptical orbits are found to have much higher total collision probability than circular orbits. Rocket bodies used to boost payloads from low earth orbit to geosynchronous orbit are an example of objects in these elliptical orbits.

Kessler, Donald J.↗
NASA NTRS1990

Instability of a supersonic shock free elliptic jet

This paper presents a comparison of the measured and the computed spatial stability properties of an aspect ratio 2 supersonic shock free elliptic jet. The shock free nature of the elliptic jet provides an ideal test of validity of modeling the large scale coherent structures in the initial mixing region of noncircular supersonic jets with linear hydrodynamic stability theory. Both aerodynamic and acoustic data were measured. The data are used to compute the mean velocity profiles and to provide a description of the spatial composition of pressure waves in the elliptic jet. A hybrid numerical scheme is applied to solve the Rayleigh problem governing the inviscid linear spatial stability of the jet. The measured mean velocity profiles are used to provide a qualitative model for the cross sectional geometry and the smooth velocity profiles used in the stability analysis. Computational results are presented for several modes of instability at two jet cross sections. The acoustic measurements show that a varicose instability is the jet's perferred mode of motion. The stability analysis predicts that the Strouhal number varies linearly as a function of axial distance in the jet's initial mixing region, which is in good qualitative agreement with previous measurements.

Baty, Roy S.↗
NASA NTRS1990

An experimental study of counter-rotating cores in elliptical galaxies

Recent observational studies (Franx and Illingworth 1987; Jedrzejewski and Schechter 1988; Bender 1988; Illingworth and Franx 1989) have shown that some elliptical galaxies have a small region near the center that rotates in the opposite direction from the outer parts of the galaxy. Often the rotation in the central part is much faster than that in the outer part. A few other galaxies show a small region near the center that rotates in the same direction as the rest of the galaxy, but much faster. Either way, the part near the center that shows a strange pattern of rotation (the 'core') has been interpreted as a distinct dynamical subsystem. Very briefly, the observational data seem to be that anomalies show up in rotation curves near the centers of some elliptical galaxies and that galaxies with these strange rotational properties do not show a photometric signature: there are no noticeable bumps in the brightness profile and no unusual shapes of isophotal contours that would suggest an excess of matter concentrated near the center. No strong color variations have been reported. The puzzle is to learn what we can about elliptical galaxies in general, and about galaxies with strange central regions in particular, from these observational facts. The authors' approach is experimental. They make a guess about the form of the dynamically distinct subsystem, and then build a galaxy model to test experimental consequences such as the amount of matter required to produce observable effects and the length of time over which these effects would remain observable. They sidestep questions about how the galaxy might have gotten to be that way in the first place. That gives them more freedom to explore a variety of suggestions about what kind of dynamical system might give rise to the observed rotational patterns.

Miller, R. H.↗
NASA NTRS1991

Anisotropic elliptic optical fibers

The exact characteristic equation for an anisotropic elliptic optical fiber is obtained for odd and even hybrid modes in terms of infinite determinants utilizing Mathieu and modified Mathieu functions. A simplified characteristic equation is obtained by applying the weakly guiding approximation such that the difference in the refractive indices of the core and the cladding is small. The simplified characteristic equation is used to compute the normalized guide wavelength for an elliptical fiber. When the anisotropic parameter is equal to unity, the results are compared with the previous research and they are in close agreement. For a fixed value normalized cross-section area or major axis, the normalized guide wavelength lambda/lambda(sub 0) for an anisotropic elliptic fiber is small for the larger value of anisotropy. This condition indicates that more energy is carried inside of the fiber. However, the geometry and anisotropy of the fiber have a smaller effect when the normalized cross-section area is very small or very large.

Kang, Soon Ahm↗
NASA NTRS1990

Instability of a supersonic shock-free elliptic jet

A comparison of the measured and the computed spatial stability properties of an aspect ratio 2, supersonic, shock free, elliptic jet is presented. The shock free nature of the elliptic jet furnishes a perfect test of the validity of modeling the large scale coherent structures in the initial mixing region of noncircular supersonic jets with the linear hydrodynamic stability theory. Aerodynamic and acoustic data are measured to compute the mean velocity profiles and to provide a description of the spatial composition of pressure waves in the elliptic jet. The measured mean velocity profiles are employed to provide a qualitative model for the cross sectional geometry and the smooth velocity profiles utilized in the stability analysis. It is shown that the measured frequency associated with peak amplitude noise radiation agrees with that frequency predicted to dominate the large scale structure near the end of the potential core.

Baty, Roy S.↗
NASA NTRS1991

The correlation function of galaxy ellipticities produced by gravitational lensing

The correlation of galaxy ellipticities produced by gravitational lensing is calculated as a function of the power spectrum of density fluctuations in the universe by generalizing an analytical method developed by Gunn (1967). The method is applied to a model where identical objects with spherically symmetric density profiles are randomly laid down in space, and to the cold dark matter model. The possibility of detecting this correlation is discussed. Although an ellipticity correlation can also be caused by an intrinsic alignment of the axes of galaxies belonging to a cluster or a supercluster, a method is suggested by which one type of correlation can be distinguished from another. The advantage of this ellipticity correlation is that it is one of the few astronomical observations that can directly probe large-scale mass fluctuations in the universe.

Miralda-Escude, Jordi↗
NASA NTRS1992

Elliptic jets, part 2. Dynamics of coherent structures: Pairing

The dynamics of the jet column mode of vortex pairing in the near field of an elliptic jet was investigated. Hot-wire measurements and flow visualization were used to examine the details of the pairing mechanism of nonplanar vortical elliptic structures and its effect on such turbulence measures as coherent velocities, incoherent turbulence intensities, incoherent and coherent Reynolds, stresses, turbulence production, and mass entrainment. It was found that pairing of elliptic vortices in the jet column does not occur uniformly around the entire perimeter, unlike in a circular jet. Merger occurs only in the initial major-axis plane. In the initial minor-axis plane, the trailing vortex rushes through the leading vortex without pairing and then breaks down violently, producing considerably greater entrainment and mixing than in circular or plane jets.

Husain, Hyder S.↗
NASA NTRS1991

Constraints on the origin of the ultraviolet upturn in elliptical galaxies from Hopkins Ultraviolet Telescope observations of NGC 1399

Results are presented of observations of the giant elliptical galaxy NGC 1399 in December 1990, which provide measurements of the spectral energy distribution of the elliptical galaxy and allow detection of absorption features in the sub-2000-A UV. The spectrum shows no emission features other than well-known geocoronal lines. Strong Lyman series absorption is evident at the galaxy redshift. Other absorption features attributable to the hot stellar population are detected, but there is no evidence of C IV 1548, 1551 absorption. Thse data are used to set constraints on the origin of the UV upturn in elliptical galaxies. The lack of detectable C IV absorption and the shape of the continuum spectrum exclude star formation with a standard IMF as the sole contributor to the 1550-A flux. The observed continuum flux decreases from 1050 A to the Lyman limit, indicating that the light is dominated by stars with temperatures less than 25,000 K. For star-formation models, this temperature puts the main-sequence turnoff near B0, implying either that star formation ended about 2 x 10 exp 7 yr ago, or that stars are currently forming with a truncated IMF.

Ferguson, Henry C.↗