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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Infrared spectra of obscuring dust tori around active galactic nuclei. I - Calculational method and basic trends

Using a new 2D radiative transfer algorithm, we have calculated the thermally reradiated infrared spectra of the compact dust tori which are thought to surround many AGN. These tori radiate anisotropically. Face-on tori may be from one-half to a few orders of magnitude brighter than edge-on tori throughout the infrared. Their spectra at nearly all viewing angles are basically 'bumps' which are about 50 percent wider than blackbodies and peak in the mid-infrared at a wavelength determined mainly by the flux of nuclear radiation on the inner edge of the torus. The infrared color temperatures are hotter for face-on tori than edge-on tori by about 100 K. The 10 micron silicate feature often associated with dust can appear in absorption, emission, or not at all. There is a rough tendency for absorption features to be more prominent for edge-on tori than for face-on tori.

Pier, Edward A.↗
DOE OSTI2018

Prym Differentials on Variable Tori

We consider multiplicative functions and Prym differentials on variable tori. We prove counterparts of the theorem on the total sum of residues for Prym differentials of any integer order on tori. As a consequence, reciprocity laws are proved. We construct elementary Prym differentials of all kinds with any integer order which holomorphically depend on the moduli of tori and characters. We derive an analogue of the Appell decomposition formula for functions with characters. We also study vector bundles of Prym differentials of any integer order over the product of Teichmueller spaces for a torus and a group of characters.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2021

Investigations of Relations Between Jupiter-Europa and Jupiter-Ganymede Resonant Tori in the Planar Bicircular Restricted 4-Body Problem

Most unstable periodic orbits of the planar circular restricted 3-body problem (PCRTBP) persist as invariant tori when a periodic forcing is added to the equations of motion. Among the persisting orbits are unstable resonant periodic or- bits. In this study, we first compute invariant tori in the planar concentric cir- cular restricted 4-body problem corresponding to exterior Jupiter-Europa and in- terior Jupiter-Ganymede PCRTBP resonant periodic orbits. Motivated by the 2:1 Laplace resonance between the orbits of Europa and Ganymede around Jupiter, we then use the computed tori to characterize relations between m:n Jupiter-Ganymede and m:2n Jupiter-Europa PCRTBP resonant orbits.

de la Llave, Rafael↗
NASA NTRS1982

Approximate constants of motion for classically chaotic vibrational dynamics - Vague tori, semiclassical quantization, and classical intramolecular energy flow

Substantial short time regularity, even in the chaotic regions of phase space, is found for what is seen as a large class of systems. This regularity manifests itself through the behavior of approximate constants of motion calculated by Pade summation of the Birkhoff-Gustavson normal form expansion; it is attributed to remnants of destroyed invariant tori in phase space. The remnant torus-like manifold structures are used to justify Einstein-Brillouin-Keller semiclassical quantization procedures for obtaining quantum energy levels, even in the absence of complete tori. They also provide a theoretical basis for the calculation of rate constants for intramolecular mode-mode energy transfer. These results are illustrated by means of a thorough analysis of the Henon-Heiles oscillator problem. Possible generality of the analysis is demonstrated by brief consideration of classical dynamics for the Barbanis Hamiltonian, Zeeman effect in hydrogen and recent results of Wolf and Hase (1980) for the H-C-C fragment.

Shirts, R. B.↗
NASA NTRS1986

Satellite tori at Saturn

The inner satellites of Saturn are icy bodies imbedded in a plasma environment in which they are continuously bombarded by energetic ions, corotating plasma, and solar radiation. Laboratory sputtering experiments indicate that this should result in the injection of substantial amounts of neutral H, H2, OH, H2O, and O2 into the magnetosphere. The atomic processes affecting these neutrals and the neutrals and ions formed from them are modeled, and the steady state neutral and ion densities expected in the plasma tori of Enceladus, Dione-Tethys, and Rhea are calculated. Comparison with observations shows that recombination can limit the Enceladus and Dione-Tethys tori to the observed densities, but that transport rates of at least 4 x 10 to the -8th Saturn radii squared/s are required to limit torus densities at Rhea to the observed values.

Richardson, J. D.↗
NASA NTRS1987

Types of planetary tori

While satellite tori are morphologically similar, they divide into dynamically distinct groups whose global balances of ions and neutrals are presently modeled in order to determine how a torus behaves as a consequence of whether it generates itself and whether it disperses or recombines in place. Six possible types of behavior result; attention is given to the equilibrium and stability of each type. The behavior of a perturbation is characterized by a trajectory in the two-dimensional space formed by the ion density and neutral density perturbations. The equilibrium is stable if a perturbation follows its trajectory toward the origin, but is unstable if the motion is away from it. An attempt is made to classify the Jupiter and Saturn tori in this light.

Huang, T. S.↗
NASA NTRS1992

Radiation-pressure-supported obscuring tori around active galactic nuclei

Radiation pressure acting on dust grains can support the vertical thickness of the obscuring tori believed to exist in active galactic nuclei. Using the results of 2D radiation transfer calculations, we evaluate the radiation force acting on these tori. We find that on the inner edge of the torus the radiation force is about 350 l(E) times the gravitational force of the nucleus, where l(E) is the Eddington ratio. Beyond a few torus heights from the inner edge, the radiation force is negligible with respect to gravity. However, between these two extremes lies a region of considerable size where the ratio of radiation force to gravity is nearly constant and can be of order unity for l(E) about 0.1. If the distribution of material within the torus is sufficiently lumpy, there is a significant time-varying component to the radiation force. This drives the random motions of the constituent clouds, thickening the torus at lower values of l(E).

Pier, Edward A.↗
NASA NTRS1993

The nature of the hydrogen tori of Titan and Triton

The nature of the hydrogen tori of Titan and Triton is examined. Critical time scales of the two tori are discussed. For the Titan torus, where atom-atom collisions are not important, the time scale for solar radiation pressure to act on the system is shown to be comparable to the hydrogen lifetime due to ionization and charge exchange losses by solar, magnetospheric, and solar wind processes. The solar radiation pressure then provides a mechanism which destroys the initial azimuthal symmetry of the hydrogen atom orbits about the planet and causes atom orbits to move inward and to collide with the planet on its dusk side. For Triton, the atom-atom collision time scale dominates all other time scales in the system. The evolution of the torus is then an inherently nonlinear problem that depends upon the collisional redistribution of atom-orbit velocities in the presence of a planetary gravitational force field. This nonlinear process introduces an expansion mechanism into the torus problem which dramatically alters its structure.

Smyth, William H.↗
NASA NTRS1994

Neutron tori around Kerr black holes

Models of stationary, axisymmetric, non-self-gravitating tori around stellar mass Kerr black holes are calculated. Such objects may form as a result of a merger between two neutron stars, a neutron star and a stellar mass black hole, or a 'failed supernova' collapse of a single rapidly rotating star. We explore a large range of parameters: the black hole mass and angular momentum, the torus mass, angular momentum and entropy. Physical conditions within the tori are similar to those in young and hot neutron stars, but their topology is different, and the range of masses and energies is much larger.

Witt, H. J.↗
NASA NTRS2020

Rapid and Accurate Computation of Invariant Tori, Manifolds, and Connections Near Mean Motion Resonances in the Periodically Perturbed Planar Circular Restricted 3-Body Problem Models

When the planar circular restricted 3-body problem (RTBP) is periodically perturbed, most unstable resonant periodic orbits become invariant tori. In this study, we 1) develop a quasi-Newton method which simultaneously solves for the tori and their center, stable, and unstable directions; 2) implement continuation by both perturbation as well as rotation numbers; 3) compute Fourier-Taylor parameterizations of the stable and unstable manifolds; 4) globalize these manifolds; 5) compute homoclinic and heteroclinic connections. Our methodology improves on efficiency and accuracy compared to prior studies, and applies to a variety of periodic perturbations. We demonstrate the tools on the planar elliptic RTBP.

de la Llave, Rafael↗
DOE OSTI2024

The soaring kite: a tale of two punctured tori

We consider the 5-mass kite family of self-energy Feynman integrals and present a systematic approach for constructing an ε-form basis, along with its differential equation pulled back onto the moduli space of two tori. Each torus is associated with one of the two distinct elliptic curves this family depends on. We demonstrate how the locations of relevant punctures, which are required to parametrize the full image of the kinematic space onto this moduli space, can be extracted from integrals over maximal cuts. A boundary value is provided such that the differential equation is systematically solved in terms of iterated integrals over g-kernels and modular forms. Then, the numerical evaluation of the master integrals is discussed, and important challenges in that regard are emphasized. In an appendix, we introduce new relations between g-kernels.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

3d-3d correspondence for mapping tori

One of the main challenges in 3d-3d correspondence is that no existent approach offers a complete description of 3d N = 2 SCFT T [ M 3 ] — or, rather, a “collection of SCFTs” as we refer to it in the paper — for all types of 3-manifolds that include, for example, a 3-torus, Brieskorn spheres, and hyperbolic surgeries on knots. The goal of this paper is to overcome this challenge by a more systematic study of 3d-3d correspondence that, first of all, does not rely heavily on any geometric structure on M 3 and, secondly, is not limited to a particular supersymmetric partition function of T [ M 3 ]. In particular, we propose to describe such “collection of SCFTs” in terms of 3d N = 2 gauge theories with “non-linear matter” fields valued in complex group manifolds. As a result, we are able to recover familiar 3-manifold invariants, such as Turaev torsion and WRT invariants, from twisted indices and half-indices of T [ M 3 ], and propose new tools to compute more recent q -series invariants Z * ( M 3 ) in the case of manifolds with b 1 > 0. Although we use genus-1 mapping tori as our “case study,” many results and techniques readily apply to more general 3-manifolds, as we illustrate throughout the paper.

Topological Field Theories↗
DOE OSTI2022

Forces that control self-organization of chemically-propelled Janus tori

Control of the individual and collective behavior of self-propelled synthetic micro-objects has immediate application for nanotechnology, robotics, and precision medicine. Despite significant progress in the synthesis and characterization of self-propelled Janus (two-faced) particles, predictive understanding of their behavior remains challenging, especially if the particles have anisotropic forms. Here, by using molecular simulation, we describe the interactions of chemically-propelled microtori near a wall. The results show that a torus hovers at a certain distance from the wall due to a combination of gravity and hydrodynamic flows generated by the chemical activity. Moreover, electrostatic dipolar interactions between the torus and the wall result in a spontaneous tilt and horizontal translation, in a qualitative agreement with experiment. Simulations of the dynamics of two and four tori near a wall provide evidence for the formation of stable self-propelled bound states. Our results illustrate that self-organization at the microscale occurs due to a combination of multiple factors, including hydrodynamic, chemical, electrostatic and steric interactions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Diagnosing the Kinematics of the Tori in Active Galactic Nuclei with the Velocity-resolved Reverberation Mapping of the Narrow Iron K α Line

The properties of the dusty tori in active galactic nuclei (AGNs) have been investigated in detail, mainly focusing on the geometry and components; however, the kinematics of the torus are still not clear. The narrow iron K α line at 6.4 keV is thought to be produced by the X-ray reflection from the torus. Thus, the velocity-resolved reverberation mapping of it is able to constrain the kinematics of the torus. Such effort is limited by the spectral resolution of current charged coupled device (CCD) detectors and should be possible with the microcalorimeter on the next generation X-ray satellite. In this paper, we first construct the response functions of the torus under a uniform inflow, a Keplerian rotation, and a uniform outflow. Then the energy-dependent light curve of the narrow iron K α line is simulated according to the performance of the X-ray Integral Field Unit in Athena. Finally, the energy-dependent cross-correlation function is calculated to reveal the kinematic signal. According to our results, 100 observations with 5 ks exposure of each are sufficient to distinguish the above three velocity fields. Although the real geometry and velocity field of the torus could be more complex than we assumed, the present result proves the feasibility of the velocity-resolved reverberation mapping of the narrow iron K α line. The combination of the dynamics of the torus with those of the broad-line region and the host galaxy is instructive for the understanding of the feeding and feedback process of AGNs.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1986

Predicted satellite plasma tori in the magnetosphere of Uranus

The paper formulates the rate equations for twelve species: water, hydroxyl, molecular and atomic oxygen, molecular and atomic hydrogen, and their respective first ions for conditions expected to hold in the magnetosphere of Uranus. These equations have been solved numerically for maximal and minimal source strengths of the five known satellites, and the expected neutral and plasma number densities in the tori predicted to be associated with them have been calculated. It is found that under most conditions, there should be a sensible plasma torus associated with each satellite whose orbit is enclosed within the assumed magnetosphere.

Eviatar, A.↗
NASA NTRS1988

Molecular tori in Seyfert galaxies - Feeding the monster and hiding it

The principal properties of the tori of gas which surround Seyfert nuclei are discussed. The internal state of the clouds and their size distribution function are examined, and it is shown that the Jeans mass scale results in clouds which are individually sufficiently opaque to block out the nucleus, and that the balance of processes which controls their size distribution function also forces the covering factor to be of the order of or greater than unity. Where the gravitational potential is dominated by stars, cloud-cloud collisions keep the molecular clouds close to the equatorial plane. Stirring by stellar processes is never strong enough to compete with collisional losses. The position of the inner edge of the torus is determined by a balance between the inward flow of clouds and the rate at which the nuclear continuum can evaporate them.

Krolik, Julian H.↗
NASA NTRS1991

Three-dimensional simulations of black hole tori

The global hydrodynamic nonaxisymmetric instabilities in thick constant angular momentum (l) accretion gas tori in orbit around a Schwarzschild black hole are investigated via 2D and 3D numerical simulations. A radially-wide torus is found to develop and m = 1 nonaxisymmetric density perturbation near the pressure maximum and a trailing spiral wave that extends through the outer part of the torus. This global wave transports angular momentum through the torus, causing the average angular momentum distribution to evolve slowly away from l = constant. The unstable mode drives an accretion flow from the torus into the black hole. The role of accretion is investigated by modeling a wide torus with an inner boundary at the cusp of the Schwarzschild effective potential. In such a torus, accretion is present throughout the evolution; only modest unstable mode growth is observed, and saturation occurs at low amplitude. Comparison simulations performed in the torus equatorial plane show qualitative similarities between the 2D and 3D system, although the 3D modes have a function dependence on height.

Hawley, John F.↗
NASA NTRS1994

X-ray bumps, iron K-alpha lines, and X-ray suppression by obscuring tori in Seyfert galaxies

We investigate the X-ray spectral properties of unobscured type 1 and obscured type 2 Seyferts as predicted by the unified Seyfert scheme. We consider the reprocessing of X-ray photons by photoelectric absorption, iron fluorescence, and Compton downscattering in the obscuring tori surrounding these active nuclei, and compute by Monte Carlo methods the reprocessed spectra as a function of the viewing angle. Depending on the optical depth and shape of the torus, and on the viewing angle, the X-ray flux can be suppressed by substantial factors when our line of sight is obscured. We show that an immediate consequence of the existence of an obscuring thick torus is the production in the spectra of type 1 Seyfert galaxies of a bump in the continuum above 10-20 keV and an Fe K-alpha line with significant equivalent width. In those type 2 Seyferts for which the hard X-ray spectrum has been substantially suppressed, the equivalent width of the Fe K-alpha line in the transmitted spectrum can be very large.

Krolik, Julian H.↗