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NASA NTRS1983

Recent work on bipolar nebulae

The results of recent studies of bipolar nebulae (BPN) using nebular-polarization mapping, spectropolarimetry, near-IR spectroscopy, far-IR photometry, and radio-maser and continuum observations are surveyed. The characteristics of several BPN of different evolutionary types are discussed and illustrated with spectra, model drawings, and maps. As shown in a Hertzsprung-Russell diagram of 19 BPN, this morphological class includes pre-main-sequence stars, red giants in transition to ordinary planetary nebulae, pre-white-dwarfs, a dust-shrouded carbon star, and a visual binary with a type-O primary. VLA 6-cm observations of the latter object, MWC 349, reveal a morphology similar to the optical structure of the Red Rectangle illuminated by HD 44179: it is suggested that equatorial dusty tori may occur commonly at different phases of stellar evolution, and hence that BPN may be relatively abundant, although short-lived, phenomena.

Cohen, M.↗

NASA NTRS1983

Load deflection characteristics of inflated structures

A single, closed form relationship to relate load to the deformed dimensions of the horizontal torus was developed. Wall elasticity was included in the analysis, and special care was taken to predict the final footprint area of the loaded structure. The test fixture utilized is shown. The tori used for the bulk of the testing were rubber inner tubes for a 32 and 160 pneumatic tire. The inner tube being tested was plumbed, to a mercury-filled manometer, which had a 50 inch measurement capacity, by use of a special adapter. The adapter fit over the valve stem and allowed air to be added from a shop-air source and to be bled through the standard valve mechanism. In this fashion, tests requiring the maintenance of a constant indication of air pressure could be run with little difficulty.

Baumgarten, J. R.↗

NASA NTRS1984

The Solid Model Geometry Generator (SMGG)

The Solid Model Geometry Generator (SMGG) system provides the capacity to model complex solid objects through the composition of primitive parts. The parts are specified through input of dimension and orientation parameters. The parts may later be edited, the model may be displayed (through a variety of display options), and the resulting geometry formatted for subsequent analysis. The SMGG system was originally constructed for use in the preliminary stages of space station and other spacecraft design. Because the system models a design through the use of basic shapes common to many solid objects and provides limited capabilities for producing irregularly shaped parts, it can be used for a variety of applications. Currently, seven primitive parts may be specified and produced through SMGG. These include boxes, spheres, cones, paraboloids, tori, and translationally or rotationally swept parts. Each part may be specified by the user through input of basic part dimensions and a local orientation. For example, a box is specified by its length, width, height and orientation in space (rotation, translation, and scaling).

Jones, K. H.↗

NASA NTRS1983

Corotation anisotropies in Saturn's magnetosphere

Ion data from the Voyager 1 and 2 low-energy charged particle (LECP) experiment are fit to a second-order harmonic expansion to determine anisotropies within the Saturnian magnetosphere. Anisotropies from the low-energy channels (28-130 keV) are often consistent with those expected from corotation (generally with a small radial component on the dayside) but are at times distinctly different from corotation. On the dayside, near the noon meridian, first-order anisotropies often depart significantly from the corotation direction. On the nightside, amplitudes are consistent with full corotation but begin to drop below corotation values at a dipole L of approximately 27 Saturn radii (corresponding to a velocity of approximately 265 km/s). Second-order anisotropies are significant, even dominant at times, on the dayside where a relatively broad range of pitch angles is sampled by the instrument. In all cases there is a departure of approximately 180 deg from the first-order anisotropies expected due to corotation beginning outside the Rhea L shell and continuing through at least the orbit of Dione. This is the region where the cold and hot plasma tori have been observed. The anisotropies expected from rigid corotation of the observed flux distributions are computed, and it is concluded that parts of the Saturnian magnetosphere are not rigidly corotating. Calculations based on the combined effects of corotation plus solar wind generated convective electric fields appear to provide insights into the anisotropies along the dawn meridian. However, on the dayside near noon, turbulence and/or time variations seem necessary to explain the departure from simple convection models.

Carbary, J. F.↗

NASA NTRS1984

The Jovian nebula - A post-Voyager perspective

Voyager 1 carried a diverse collection of magnetospheric probes through the inner Jovian magnetosphere in March 1979. The ensuing data analysis and theoretical investigation provided a comprehensive description of the Jovian nebula, a luminous torus populated with newly released heavy ions drawn from Io's surface. Recent refinements in earth-based imaging instrumentation are used to extend the Voyager in situ picture in temporal and spatial coverage. An analysis of S III and S II forbidden-line optical emissions observed during the Jovian apparitions of 1981 through 1983 reveals three distinct torus components. Regularities have been identified in the ion partitioning and ion densities in the hot outer and inner tori, sharply defined radial structure is found in the plasma near Io, and the relative permanence of the cool inner torus is inferred. An extended cloud of neutral material is required as a source of fresh ions in the nebula.

Trauger, J. T.↗

NASA NTRS1986

SMP: A solid modeling program version 2.0

The Solid Modeling Program (SMP) provides the capability to model complex solid objects through the composition of primitive geometric entities. In addition to the construction of solid models, SMP has extensive facilities for model editing, display, and analysis. The geometric model produced by the software system can be output in a format compatible with existing analysis programs such as PATRAN-G. The present version of the SMP software supports six primitives: boxes, cones, spheres, paraboloids, tori, and trusses. The details for creating each of the major primitive types is presented. The analysis capabilities of SMP, including interfaces to existing analysis programs, are discussed.

Randall, D. P.↗

NASA NTRS1986

Integrability and structural stability of solutions to the Ginzburg-Landau equation

The integrability of the Ginzburg-Landau equation is studied to investigate if the existence of chaotic solutions found numerically could have been predicted a priori. The equation is shown not to possess the Painleveproperty, except for a special case of the coefficients that corresponds to the integrable, nonlinear Schroedinger (NLS) equation. Regarding the Ginzburg-Landau equation as a dissipative perturbation of the NLS, numerical experiments show all but one of a family of two-tori solutions, possessed by the NLS under particular conditions, to disappear under real perturbations to the NLS coefficients of O(10 to the -6th).

Keefe, Laurence R.↗

NASA NTRS1986

Damped response of shells by a constrained viscoelastic layer

Vibration absorbers are introduced into an asymmetric configuration of thin cylinders and tori enclosing an acoustic medium. The absorbers consist of thin axial strips bonded to the cylinder with a thin viscoelastic layer. The constrained layer dissipates the energy of relative motions between strip and cylinder. The absorber is most effective on response modes with two or more circumferential waves. The use of transfer matrices is extended to the coupled cylinder-absorber system.

El-Raheb, M.↗

NASA NTRS1989

Building Mathematical Models Of Solid Objects

Solid Modeling Program (SMP) version 2.0 provides capability to model complex solid objects mathematically through aggregation of geometric primitives (parts). System provides designer with basic set of primitive parts and capability to define new primitives. Six primitives included in present version: boxes, cones, spheres, paraboloids, tori, and trusses. Written in VAX/VMS FORTRAN 77.

Randall, Donald P.↗

NASA NTRS1989

A torus bifurcation theorem with symmetry

Hopf bifurcation in the presence of symmetry, in situations where the normal form equations decouple into phase/amplitude equations is described. A theorem showing that in general such degeneracies are expected to lead to secondary torus bifurcations is proved. By applying this theorem to the case of degenerate Hopf bifurcation with triangular symmetry it is proved that in codimension two there exist regions of parameter space where two branches of asymptotically stable two-tori coexist but where no stable periodic solutions are present. Although a theory was not derived for degenerate Hopf bifurcations in the presence of symmetry, examples are presented that would have to be accounted for by any such general theory.

Vangils, S. A.↗

NASA NTRS1990

Thermal plasma in outer planet magnetospheres

The plasma environments of the outer planets are a study in contrasts. The magnetosphere of Jupiter is dominated by the prodigious plasma output of Io, with losses due to diffusion driven by mass loading. At Saturn, the small icy satellites are the major sources of plasma for the inner magnetosphere. The low mass loading rates there imply that the densities of the plasma tori are limited by dissociative recombination, rather than diffusive transport. At Uranus, the icy satellites are negligible plasma sources compared to the input from the extended neutral hydrogen cloud and the ionosphere. Convection driven by the solar wind penetrates deep into the inner magnetosphere because of the unique orientation of the rotation axis of Uranus. The expected magnetosphere of Neptune is similar to that of Saturn and Jupiter, with Triton, the ring arcs, and the planet as possible plasma sources. The Voyager 2 encounter with Neptune holds out the hope of a passage through a nonterrestrial auroral region, a unique event in planetary exploration.

Belcher, J. W.↗

NASA NTRS1989

The physical state of the obscuring torus in Seyfert galaxies

Calculations are presented describing the ionization, chemical, and thermal state of molecular material in the obscuring tori close to the nuclei of many Seyfert galaxies. These are unusual molecular clouds: their electron fractions are about .001 and their temperatures are about 1000 K. Cooling is accomplished primarily by radiation of NIR H2 lines and FIR CO lines. High-J (C-12)(O-16) rotational lines should eventually be detectable from the nearer Seyfert galaxies. Medium-J lines due to (C-13)(O-16) and (C-12)(O-18) as well as (C-12)(O-16) should also be strong. Because ordinary molecular clouds are weak in these lines, the nuclear CO emissions can be distinguished from CO emission farther out in the host galaxy's disk.

Krolik, Julian H.↗

NASA NTRS1991

Fractal dimension in nonhyperbolic chaotic scattering

In chaotic scattering there is a Cantor set of input-variable values of zero Lebesgue measure (i.e., zero total length) on which the scattering function is singular. For cases where the dynamics leading to chaotic scattering is nonhyperbolic (e.g., there are Kolmogorov-Arnol'd-Moser tori), the nature of this singular set is fundamentally different from that in the hyperbolic case. In particular, for the nonhyperbolic case, although the singular set has zero total length, strong evidence is presented to show that its fractal dimension is 1.

Lau, Yun-Tung↗

NASA NTRS1992

Hard X-ray tests of the unified model for an ultraviolet-detected sample of Seyfert 2 galaxies

An ultraviolet-detected sample of Seyfert 2 galaxies shows heavy photoelectric absorption in the hard X-ray band. The presence of UV emission combined with hard X-ray absorption argues strongly for a special geometry which must have the general properties of the Antonucci and Miller unified model. The observations of this sample are consistent with the picture in which the hard X-ray photons are viewed directly through the obscuring matter (molecular torus?) and the optical, UV, and soft X-ray continuum are seen in scattered light. The large range in X-ray column densities implies that there must be a large variation in intrinsic thicknesses of molecular tori, an assumption not found in the simplest of unified models. Furthermore, constraints based on the cosmic X-ray background suggest that some of the underlying assumptions of the unified model are wrong.

Mulchaey, John S.↗

NASA NTRS1992

Non-Hamiltonian perturbations of integrable systems and resonance trapping

This paper studies general, non-Hamiltonian perturbations of integrable systems with two degrees of freedom and derives conditions for temporary and permanent resonance trapping. The analysis involves a noncanonical transformation of variables near the resonant manifold and averaging with respect to the fast phase to investigate oscillatory behavior on the intermediate timescale. The resulting reduced system is Hamiltonian to leading order and permits, after averaging on the intermediate, or libration, timescale, a canonical transformation to action-angle variables in the oscillation zone. The final system so obtained reveals the possible existence of two- and three-dimensional invariant tori in the vicinity of the resonant manifold. An explicit divergence condition for general perturbations to be dissipative on the slow timescale follows from the analysis. An application of this approach to the problem of resonant trapping and escape is outlined for the restricted problem of three bodies subject to dissipative perturbations with a radial symmetry.

Ghil, M.↗

NASA NTRS1992

Multispectral observations of the Jovian aurora

The upper atmospheres of the Earth and the outer planets form a screen on which precipitating charged particles, like the electron beam in a television, trace fleeting, but revealing patterns of visible, ultraviolet, infrared, and x ray emissions that offer valuable clues to processes occurring within the planetary magnetospheres. At Earth, years of in situ measurements, as well as ground based observations, have yielded a picture (still fuzzy) where the interaction of the solar wind with the magnetosphere of the Earth provides a complex path for the storage and release of energy during magnetic substorms; the ultimate manifestation of terrestrial auroral processes. More recent global imaging of substorm events from high above the Earth (greater than 3.5 R(sub e)) by Dynamics Explorer have made a unique contribution towards understanding the global and temporal evolution of such auroral events by providing a morphological perspective and by providing the crucial observational link that allows the separation of spatial and temporal variations inherent in the interpretation of in situ data. A similar role was played by the Hubble Space Telescope (HST) during the recent encounter of Ulysses with Jupiter in helping to define a new paradigm in Jovian auroral physics. The old paradigm portrayed Jupiter's magnetosphere as totally dominated by internal processes (i.e. Io related tori, heavy ions, etc.) where energetic heavy ion precipitation in the inner magnetosphere was solely responsible for the observed auroral phenomena. Ulysses and HST portray a more Earth-like paradigm where electron acceleration in the outer magnetosphere near the boundary with the solar wind plays a distinct role in the formation of auroral hot spots, yet energetic heavy ions also enter into the picture (similar to the role of the energetic ions from the terrestrial ring current during magnetic substorms). These heavy ions as a result of excitation during their transit through the atmosphere produce the x ray emissions observed in Roentgensatellit (ROSAT) x ray energy spectra.

Source record↗

NASA NTRS1994

Force-free fields in thin coronal loops

We solve the force-free equation J x B = 0 for fields which are toroidally symmetric. The technique utilizes an expansion about a cylindrical field and is therefore valid or tori with a large aspect ratio such as long, thin, coronal loops. The calculation is performed in spatial toroidal coordinates, rather than in the flux coordinates used by previous authors; this allows direct calculation of the loci of flux surfaces and of surfaces of constant magnetic pressure. Our solutions differ significantly from toroidal fields in laboratories, which are in general not force-free. They are characterized by field lines whose projections in the poloidal planes are circles with centers displaced by varying distances from the axis of the torus. In general, flux surfaces do not correspond to surfaces of constant magnetic pressure. We have examined solutions corresponding to simple analytic zero-order cylindrical fields. For moderate twists in the zero-order (cylindrical) field, the magnetic pressure is larger on the inner toroidal radius. However, this effect diminishes with twist angle and in fact, for extreme initial twists, the magnetic pressure can be larger on the outer radius. We compare our results with previous work utilizing flux coordinates.

Emslie, A. Gordon↗

NASA NTRS1994

Radiative excitation of molecules near powerful compact radio sources

In a recent paper, Barvainis & Antonucci searched for and failed to detect CO J = 1 goes to 0 absorption from the obscuring torus in the nearby powerful radio galaxy Cygnus A. We show that a plausible explanation for the lack of absorption (assuming that the ionization parameter within the torus is low enough for the gas to be molecular) is that radiative excitation of the CO molecules by the nonthermal radio continuum increases the excitation temperature of the lower rotational levels substantially, reducing the optical depths. The excitation temperature may approach the brightness temperature of the radio source at high enough flux-to-density ratios. Heating of the gas by the nonthermal excitation may also be important. We discuss the region of parameter space in which this excitation mechanism will be important and the implications for observations of obscuring tori.

Maloney, Philip R.↗