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At least 253 records · Page 14

Sudden loss of mass from a binary gravitating system

Mitalas's (1980) study is generalized to treat sudden mass loss from a binary syste in an originally elliptical orbit. The orbits are characterized by angular momentum and energy, and it is shown that none of the changes in the relative orbit depends on which object it is that loses part of its mass. It is pointed out that, in principle, each could lose a different fraction. Time averages are introduced so that the orbital changes, which depend on where in orbit the mass loss takes place, can be suitably averaged over a statistical ensemble of initial systems. Even though many results that appear to be new are presented, it is noted that the main thrust is to choose and manipulate variables yielding the greatest economy of description and the greatest power of computation. Graphs are included showing the fraction of systems that on the average will be disrupted, the mean orbital changes for the survivors, and the extreme limits for the change in eccentricity.

Noerdlinger, P. D.↗

Spacecraft attitude control momentum requirements analysis

The relationship between attitude and angular momentum control requirements is derived for a fixed attitude, Earth orbiting spacecraft with large area articulating appendages. Environmental effects such as gravity gradient, solar radiation pressure, and aerodynamic forces arising from a dynamic, rotating atmosphere are examined. It is shown that, in general, each environmental effect contributes to both cyclic and secular momentum requirements both within and perpendicular to the orbit plane. The gyroscopic contribution to the angular momentum control requirements resulting from a rotating, Earth oriented spacecraft is also discussed. Special conditions are described where one or more components of the angular momentum can be made to vanish, or become purely cyclical. Computer generated plots for a candidate space station configuration are presented to supplement the analytically derived results.

Robertson, Brent P.↗

Orbital, Rotational and Climatic Interactions: Energy Dissipation and Angular Momentum Exchange in the Earth-Moon System

A numerical ocean tide model has been developed and tested using highly accurate TOPEX/Poseidon (T/P) tidal solutions. The hydrodynamic model is based on time stepping a finite difference approximation to the non-linear shallow water equations. Two novel features of our implementation are a rigorous treatment of self attraction and loading (SAL), and a physically based parameterization for internal tide (IT) radiation drag. The model was run for a range of grid resolutions, and with variations in model parameters and bathymetry. For a rational treatment of SAL and IT drag, the model run at high resolution (1/12 degree) fits the T/P solutions to within 5 cm RMS in the open ocean. Both the rigorous SAL treatment and the IT drag parameterization are required to obtain solutions of this quality. The sensitivity of the solution to perturbations in bathymetry suggest that the fit to T/P is probably now limited by errors in this critical input. Since the model is not constrained by any data, we can test the effect of dropping sea-level to match estimated bathymetry from the last glacial maximum (LGM). Our results suggest that the 100 m drop in sea-level in the LGM would have significantly increased tidal amplitudes in the North Atlantic, and increased overall tidal dissipation by about 40%. However, details in tidal solutions for the past 20 ka are sensitive to the assumed stratification. IT drag accounts for a significant fraction of dissipation, especially in the LGM when large areas of present day shallow sea were exposed, and this parameter is poorly constrained at present.

Egbert, Gary D.↗

Unsolved problems in planetary ring dynamics

Voyager photographic data are used for microscopic and macroscopic analyses of the dynamics of the Saturn rings. Attention is given to particle collisions, local velocity dispersion, the particle size distribution, mechanisms governing the ring structure and interactive effects with Saturn satellite orbits. The mechanical properties and collision dynamics of the particles are discussed, along with models for perturbed and unperturbed disks. The forces involved and true scale of particle erosion are considered, as are instabilities in the rings, satellite torques, resonances, and the time scale for the evolution of the satellite orbits. Finally, the possibility that angular momentum exchanges are occurring between individual rings and satellite orbits is examined.

Borderies, N.↗

Elementary derivation of the perturbation equations of celestial mechanics

The equations of celestial mechanics that govern the temporal rates of change of orbital elements are completely derived using elementary dynamics and proceeding only from Newton's equation and its solution. Two orbital equations and the four most meaningful orbital elements - semimajor axis, eccentricity, inclination, and longitude of pericenter - are written in terms of the orbital energy (E) and angular momentum (H) per unit mass. The six resulting equations are differentiated with respect to time to see the effect on the orbital elements of small changes in E and H. The usual perturbation equations in terms of disturbing-force components are then derived by computing the manner in which perturbing forces change E and H. The results are applied in a qualitative discussion of the orbital evolution of particles in nonspherical gravitational fields, through atmospheres, and under the action of tides.

Burns, J. A.↗

Nucleon localization function in rotating nuclei

An electron localization function was originally introduced to visualize in positional space bond structures in molecules. It became a useful tool to describe electron configurations in atoms, molecules, and solids. In nuclear physics, a nucleon localization function (NLF) has been used to characterize cluster structures in light nuclei, formation of fragments in fission, and pasta phases appearing in the inner crust of neutron stars. In the case of a deformed rotating nucleus, several NLFs can be introduced, depending on the definition of the spin-quantization axis, direction of the total angular momentum, and self-consistent symmetries of the system. Contributions to the NLF from the current density, spin-current tensor density, and density gradient terms are negligible in the nuclear interior. The oscillating pattern of the simplified NLF can be explained in terms of a constructive interference between kinetic-energy and particle densities. The characteristic nodal pattern seen in the NLF in the direction of major axis of a rotating nucleus comes from single-particle orbits carrying large aligned angular momentum. The variation of the NLF along the minor axis of the nucleus can be traced back to deformation-aligned orbits.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

$\gamma$-Unstable Bohr Hamiltonian with sextic potential for odd-A nuclei

We report in this paper, odd-A nuclei in the vibrational to γ-soft transitional region are studied in the collective model, in which the odd-A system is described by the Bohr Hamiltonian with the quasi exactly solvable sextic β-part potential for the even-even core coupled with a single nucleon in a j = 3/2 orbit via the β-independent five-dimensional spin-orbit interaction and the total angular momentum degeneracy breaking term. To test the validity of the coupling scheme, we use the model to reproduce experimentally available level energies and B(E2) values of 187,189,191,193,195 Ir. It is clearly shown from both the level energies and the known B(E2) values for 191,193I r fitted that the model with the β-independent five-dimensional spin-orbit interaction and the total angular momentum degeneracy breaking term seems adequate to describe the low-lying level pattern and the structure of these odd-A nuclei.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Eccentric gravitational instabilities in nearly Keplerian disks

The growth of global gravitational instabilities in young stellar objects (YSOs) with associated circumstellar disks is studied. The possibility that the accretion ultimately owes its origin to the growth of spiral gravitational instabilities is explored. The results indicate that YSO disks will be unstable to the growth of eccentric distortions which have growth rates comparable to the orbital frequency at the outer edge of the disk. Thus, the distortions grow on nearly a dynamical time scale. Perturbations with m = 1 force the star to move from the center of mass and thereby transfer angular momentum to the stellar orbit. Depending on whether or not an axisymmetric stability parameter Q barrier exists near the corotation radius of the disturbance, this coupling may lead to mass accretion or to the formation of a binary companion from the disk, or both.

Adams, Fred C.↗

The effect of galaxy triaxiality on globular clusters

Evidence of triaxiality and central mass concentration in the Galaxy and in M31 and M87 is examined. It is proposed that globular clusters on box orbits in the inner parts of these systems pass close enough to the center to be destroyed by tidal shocks. Remaining clusters will preferentially populate tube orbits with relatively high angular momentum. The process is used to explain the cluster distribution in M87 reported by Lauer and Kormendy (1986). Models are presented for cluster destruction by massive black holes in M87's dark halo. Consideration is given to techniques for testing the suggestion that clusters form only on box orbits.

Ostriker, J. P.↗

Ring torque on Janus and the melting of Enceladus

The absence of craters noted on Voyager 2 images of Encedalus indicates geologically recent resurfacing, probably due to internal melting; heating mechanism calculations, however, yield heating rates too small to cause melting. If Janus, whose orbital mean motion is currently decreasing as Janus' orbit evolves outward due to resonant torques from Saturn's rings, were ever to become locked into a stable 2:1 orbital commensurability with Encedalus, the resulting angular momentum transfer could have sufficiently enhanced the eccentricity of Encedalus' orbit for the ensuing tidal heating to have melted Encedalus' interior. However, the predicted rapid time scale for ring evolution due to resonant torques from Saturn's inner moons remains a major problem.

Lissauer, J. J.↗

Disk-satellite interactions

The rate at which angular momentum and energy are transferred between a disk and a satellite which orbit a central mass is calculated. It is shown that the angular momentum and energy transfer at Lindblad resonances tends to increase the satellite's orbit to lowest order in eccentricity, whereas the transfer at corotation resonances tends to decrease it. The results are applied to the interaction between Jupiter and the protoplanetary disk. The angular momentum transfer is shown to be so rapid that substantial changes in both the structure of the disk and the orbit of Jupiter must have taken place on a time scale of a few thousand years.

Goldreich, P.↗

Simulations of Interacting Binary Systems—Pathways to Radio-bright Gamma-Ray Burst Progenitors

Although the association of gamma-ray bursts (GRBs) with massive stellar death is on firm footing, the nature of the progenitor system and the key ingredients required for a massive star to produce a GRB remain open questions. Here, we investigate the evolution of a 15–25M ⊙ massive star with a 10–15M ⊙ black hole (BH) using Modules for Experiments in Stellar Astrophysics. We quantify companion-influenced angular-momentum evolution over a stellar lifetime for orbital periods where tides are significant, varying stellar and BH masses, initial stellar spin, and accretion and dynamo prescriptions while tracking mass loss and angular momentum. The final spin is set by tidal torques versus stellar winds. For binaries that initially avoid Roche-lobe overflow, tides can spin up the star, but a late-stage expansion can drive tidal stripping; associated mass and angular-momentum loss can suppress spin-up. We find that massive-star BH binaries at comparable mass ratios may be potential GRB progenitors for short orbital periods (∼20–5 × 10 2 days) and long orbital periods (∼2 × 10 3 –4 × 10 3 days), where our suite of lifetime simulations reveals a favored parameter space with negligible mass loss and enough spin angular momentum to power a GRB jet. For initially nonrotating stars, this provides a lower limit on the final spin above a threshold estimate consistent with forming a postcollapse BH mass of 5–10M ⊙ with a spin parameter ≥ 0.5. For initially rapidly rotating stars, tidal interactions may sustain high spin when mass loss is negligible because the binary is not tidally synchronized.

Hernandez, Angel [Univ. of Colorado, Boulder, CO (↗

Orbit-modulated transport and sources in time-dependent plasmas

The orbit-modulation framework for steady-state ion-orbit boundary fluxes is reformulated to apply to time-dependent plasmas. The new formulation can quantify the extent to which orbit fluxes are affected by the time dependence of the distribution function, and may be applied both to time-dependent physical scenarios and to computationally expensive simulations that are unable to reach a true steady state. As the system tends to a time-independent state, the orbit-loss fluxes approach their steady-state values, which are determined entirely by upstream transport (turbulent and collisional) and upstream sources and sinks. This result holds for the fluxes of any moments that are expressible in terms of the invariants that determine the orbits, including parallel toroidal angular momentum.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Dust and the intrinsic spectral index of quasar variations: hints of finite stress at the innermost stable circular orbit

ABSTRACT We present a study of 9 242 spectroscopically confirmed quasars with multiepoch ugriz photometry from the SDSS Southern Survey. By fitting a separable linear model to each quasar’s spectral variations, we decompose their five-band spectral energy distributions into variable (disc) and non-variable (host galaxy) components. In modelling the disc spectra, we include attenuation by dust on the line of sight through the host galaxy to its nucleus. We consider five commonly used attenuation laws, and find that the best description is by dust similar to that of the Small Magellanic Cloud, inferring a lack of carbonaceous grains from the relatively weak 2175-Å absorption feature. We go on to construct a composite spectrum for the quasar variations spanning 700–8000 Å. By varying the assumed power-law Lν ∝ να spectral slope, we find a best-fitting value α = 0.71 ± 0.02, excluding at high confidence the canonical Lν ∝ ν1/3 prediction for a steady-state accretion disc with a T ∝ r−3/4 temperature profile. The bluer spectral index of the observed quasar variations instead supports the model of Agol & Krolik, and Mummery & Balbus, in which a steeper temperature profile, T ∝ r−7/8, develops as a result of finite magnetically induced stress at the innermost stable circular orbit extracting energy and angular momentum from the black hole spin.

79 ASTRONOMY AND ASTROPHYSICS↗

Gluonic Structure from Instantons

The instanton vacuum provides an effective description of chiral symmetry breaking by local topological fluctuations of the gauge fields, as observed in lattice QCD simulations. The resulting effective dynamics at momenta below 1/$\bar{ρ}$ ≈ 0.6 GeV explains the basic features of light-quark correlation functions and is used extensively in studies of hadron structure. The instanton fields also make definite contributions to the gluonic structure of light hadrons, as expressed in the matrix elements of composite quark– gluon or gluon operators. The article reviews the gluonic structure of light hadrons (nucleon, pion) induced by instantons. This includes: (i) twist-2 parton distributions and momentum sum rule; (ii) twist-3 angular momentum and spin-orbit interactions; (iii) twist-3 and twist-4 quark–gluon correlations and power corrections; (iv) trace anomaly and hadron mass decomposition; (v) scalar gluon form factors and mechanical properties; (vi) axial anomaly and pseudoscalar gluon form factors. It also discusses possible further applications of the methods and recent developments including gauge field configurations beyond instantons.

Weiss, C. [Thomas Jefferson National Accelerator F↗

A global approach to kinematic path planning to robots with holonomic and nonholonomic constraints

Robots in applications may be subject to holonomic or nonholonomic constraints. Examples of holonomic constraints include a manipulator constrained through the contact with the environment, e.g., inserting a part, turning a crank, etc., and multiple manipulators constrained through a common payload. Examples of nonholonomic constraints include no-slip constraints on mobile robot wheels, local normal rotation constraints for soft finger and rolling contacts in grasping, and conservation of angular momentum of in-orbit space robots. The above examples all involve equality constraints; in applications, there are usually additional inequality constraints such as robot joint limits, self collision and environment collision avoidance constraints, steering angle constraints in mobile robots, etc. The problem of finding a kinematically feasible path that satisfies a given set of holonomic and nonholonomic constraints, of both equality and inequality types is addressed. The path planning problem is first posed as a finite time nonlinear control problem. This problem is subsequently transformed to a static root finding problem in an augmented space which can then be iteratively solved. The algorithm has shown promising results in planning feasible paths for redundant arms satisfying Cartesian path following and goal endpoint specifications, and mobile vehicles with multiple trailers. In contrast to local approaches, this algorithm is less prone to problems such as singularities and local minima.

Divelbiss, Adam↗

Determination of X-ray Pulsar Geometry with IXPE Polarimetry

Using observations of X-ray pulsar Hercules X-1 by the Imaging X-ray Polarimetry Explorer we report a highly significant (>17σ) detection of the polarization signal from an accreting neutron star. The observed degree of linear polarization of ~10% is far below theoretical expectations for this object, and stays low throughout the spin cycle of the pulsar. Both the degree and angle of polarization exhibit variability with the pulse phase, allowing us to measure the pulsar spin position angle 57(2) deg and the magnetic obliquity 12(4) deg, which is an essential step towards detailed modelling of the intrinsic emission of X-ray pulsars. Combining our results with the optical polarimetric data, we find that the spin axis of the neutron star and the angular momentum of the binary orbit are misaligned by at least ~20 deg, which is a strong argument in support of the models explaining the stability of the observed superorbital variability with the precession of the neutron star.

x-ray polarimetry↗