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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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All sourcesNASA NTRSDOE OSTI
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 OSTI2014

Three-dimensional tori and Arnold tongues

This study analyzes an Arnold resonance web, which includes complicated quasi-periodic bifurcations, by conducting a Lyapunov analysis for a coupled delayed logistic map. The map can exhibit a two-dimensional invariant torus (IT), which corresponds to a three-dimensional torus in vector fields. Numerous one-dimensional invariant closed curves (ICCs), which correspond to two-dimensional tori in vector fields, exist in a very complicated but reasonable manner inside an IT-generating region. Periodic solutions emerge at the intersections of two different thin ICC-generating regions, which we call ICC-Arnold tongues, because all three independent-frequency components of the IT become rational at the intersections. Additionally, we observe a significant bifurcation structure where conventional Arnold tongues transit to ICC-Arnold tongues through a Neimark-Sacker bifurcation in the neighborhood of a quasi-periodic Hopf bifurcation (or a quasi-periodic Neimark-Sacker bifurcation) boundary.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Hyperbolic tori in Hamiltonian systems with slowly varying parameter

This paper looks at a Hamiltonian system which depends periodically on a parameter. For each value of the parameter the system is assumed to have a hyperbolic periodic solution. Using the methods in KAM-theory it is proved that if the Hamiltonian is perturbed so that the value of the parameter varies with constant small frequency, then the nonautonomous system will have hyperbolic 2-tori in the extended phase space. Bibliography: 12 titles.

97 MATHEMATICS AND COMPUTING↗
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 OSTI2016

Star formation black hole growth and dusty tori in the most luminous AGNS at Z = 2–3.5

We report Herschel/SPIRE observations of 100 very luminous, optically selected active galactic nuclei (AGNs) at z=2--3.5 with log L{sub 1350} (erg s{sup −1}) ≥ 46.5 , where L{sub 1350} is λL{sub λ} at 1350 Å. The distribution in L{sub 1350} is similar to the general distribution of Sloan Digital Sky Survey AGNs in this redshift and luminosity interval. We measured star-formation (SF) luminosity, L{sub SF}, and SF rate (SFR) in 34 detected sources by fitting combined SF and torus templates, where the torus emission is based on Wide Field Infrared Survey Explorer observations. We also obtained statistically significant stacks for the undetected sources in two luminosity groups. The sample properties are compared with those of very luminous AGNs at z>4.5. The main findings are: (1) The mean and the median SFRs of the detected sources are 1176{sub −339}{sup +476} and 1010{sub −503}{sup +706} M{sub ⊙} yr{sup −1}, respectively. The mean SFR of the undetected sources is 148 M{sub ⊙} yr{sup −1}. The ratio of SFR to the black hole accretion rate is ≈80 for the detected sources and less than 10 for the undetected sources. Unlike a sample of sources at z ≃ 4.8 that we studied recently, there is no difference in L{sub AGN} and only a very small difference in L{sub torus} between the detected and undetected sources. (2) The redshift distribution of L{sub SF} and L{sub AGN} for the most luminous, redshift 2–7 AGNs are different. Similar to previous studies, the highest L{sub AGN} are found at z ≈ 3. However, the L{sub SF} of such sources peaks at z ≈ 5. Assuming the objects in our sample are hosted by the most massive galaxies at those redshifts, we find that approximately 2/3 of the hosts are already below the main sequence of SF galaxies at z = 2−3.5. (3) The spectral energy distributions (SEDs) of dusty tori at high redshift are similar to the shapes found in low redshift, low luminosity AGNs. Herschel upper limits put strong constraints on the long wavelength shape of the SED, ruling out several earlier suggested torus templates as applicable for this sample. (4) We find no evidence for a luminosity dependence of the torus covering factor in sources with log L{sub AGN} (erg s{sup −1}) = 44−47.5. This conclusion is based on the recognition that the estimated L{sub AGN} in several earlier studies is highly uncertain and non-uniformally treated. The median covering factors over this range are 0.68 for isotropic dust emission and 0.4 for anisotropic emission.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Radiation-driven outflows from and radiative support in dusty tori of active galactic nuclei

Substantial evidence points to dusty, geometrically thick tori obscuring the central engines of active galactic nuclei (AGNs), but so far no mechanism satisfactorily explains why cool dust in the torus remains in a puffy geometry. Near-Eddington infrared (IR) and ultraviolet (UV) luminosities coupled with high dust opacities at these frequencies suggest that radiation pressure on dust can play a significant role in shaping the torus. To explore the possible effects of radiation pressure, we perform three-dimensional radiative hydrodynamics simulations of an initially smooth torus. Our code solves the hydrodynamics equations, the time-dependent multi–angle group IR radiative transfer (RT) equation, and the time-independent UV RT equation. We find a highly dynamic situation. IR radiation is anisotropic, leaving primarily through the central hole. The torus inner surface exhibits a break in axisymmetry under the influence of radiation and differential rotation; clumping follows. In addition, UV radiation pressure on dust launches a strong wind along the inner surface; when scaled to realistic AGN parameters, this outflow travels at ∼5000 (M/10{sup 7}M{sub ⊙}){sup 1/4} [L{sub UV}/(0.1L{sub E})]{sup 1/4} km s{sup −1} and carries ∼0.1 (M/10{sup 7}M{sub ⊙}){sup 3/4} [L{sub UV}/(0.1L{sub E})]{sup 3/4} M {sub ⊙} yr{sup −1}, where M, L{sub UV}, and L{sub E} are the mass, UV luminosity, and Eddington luminosity of the central object respectively.

79 ASTRONOMY AND ASTROPHYSICS↗
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.↗
NASA NTRS1997

Studies of the Gas Tori of Titan and Triton

A model for the spatial distribution of hydrogen in the Saturn system including a Titan source, an interior source for the rings and inner icy satellites, and a Saturn source has been applied to the best available Voyager 1 and 2 UVS Lyman-alpha observations presented by Shemansky and Hall. Although the model-data comparison is limited by the quality of the observational data, source rates for a Titan source of 3.3 - 4.8 x 10(exp 27) H atoms/s and, for the first time, source rates larger by about a factor of four for the interior source of 1.4 - 1.9 x 10(exp 27) H atoms/s were determined. Outside the immediate location of the planet, the Saturn source is only a minor contribution of hydrogen. A paper describing this research in more detail has been submitted to The Astrophysical Journal for publication and is included in the Appendix. Limited progress in the development of a model for the collisional gas tori of Triton is also discussed.

Smyth, William H.↗
NASA NTRS2021

Using GPUs and the Parameterization Method for Rapid Search and Refinement of Connections between Tori in Periodically Perturbed Planar Circular Restricted 3-Body Problems

When the planar circular restricted 3-body problem is periodically perturbed, most unstable periodic orbits become invariant tori. However, 2D Poincare ́ sections no longer work to find their manifolds’ intersections; new methods are needed. In this study, we first review a method of restricting the intersection search to only certain manifold subsets. We then implement this search using Julia and OpenCL, representing the manifolds as triangular meshes and gaining a 30x speedup using GPUs. We finally show how to use manifold parametrizations to refine the ap- proximate connections found in the mesh search. We demonstrate the tools on the planar elliptic RTBP.

de la Llave, Rafael↗