Negative Angular Momentum Research Articles

Negative Energy And Angular Momentum Modes Of Thin Accretion Disks

This work derives the linearized equations of motion, the Lagrangian density, the Hamiltonian density, and the canonical angular momentum density for general perturbations [∝ exp (imφ) with m = 0, ± 1, ...] of a geometrically thin self-gravitating, homentropic fluid disk including the pressure. The theory is applied to “eccentric,” m = ± 1 perturbations of a geometrically thin Keplerian disk. We find m = 1 modes at low frequencies relative to the Keplerian frequency. Further, it is shown that these modes can have negative energy and negative angular momentum. The radial propagation of these low-frequency m = 1 modes can transport angular momentum away from the inner region of a disk and thus increase the rate of mass accretion. Depending on the radial boundary conditions there can be discrete low-frequency, negative-energy, m = 1 modes.

The Angular Momentum Distribution of Gas and Dark Matter in Galactic Halos

(Abridged) We report results of a series of non radiative N-body/SPH simulations in a LCDM cosmology. We find that the spin of the baryonic component is on average larger than that of the dark matter (DM) component and we find this effect to be more pronounced at lower redshifts. A significant fraction f of gas has negative angular momentum and this fraction is found to increase with redshift. We describe a toy model in which the tangential velocities of particles are smeared by Gaussian random motions. This model is successful in explaining some of the angular momentum properties. We compare and contrast various techniques to determine the angular momentum distributions (AMDs). We show that broadening of velocity dispersions is unsuitable for making comparisons between gas and DM. We smooth the angular momentum of the particles over a fixed number of neighbors. We find that an analytical function based on gamma distribution can be used to describe a wide variety of profiles, with just one parameter \alpha. The distribution of the shape parameter $\alpha$ for both gas and DM follows roughly a log-normal distribution. The mean and standard deviation of log(\alpha) for gas is -0.04 and 0.11 respectively. About 90-95% of halos have \alpha =1.09 \pm 0.2. \alpha_Gas is also biased towards slightly higher values compared to \alpha_DM.

Spectral stability of the Coulomb–Dirac Hamiltonian with anomalous magnetic moment

We show that the point spectrum of the standard Coulomb–Dirac operator H 0 is the limit of the point spectrum of the Dirac operator with anomalous magnetic moment H a as the anomaly parameter tends to 0. For negative angular momentum quantum number κ, this holds for all Coulomb coupling constants c for which H 0 has a distinguished self-adjoint realisation. For positive κ, however, there are some exceptional values for c, and in general an index shift between the eigenvalues of H 0 and the limits of eigenvalues of H a appears, accompanied with additional oscillations of the eigenfunctions of H a very close to the origin.

Axial Angular Momentum: Vertical Fluxes and Response to Torques

Abstract The horizontally averaged global angular momentum μ at a certain height reacts only to the vertical divergence of the angular momentum flux at least above the crest height of the earth's orography. The flux is tied to the torques at the surface. Data are used to evaluate the flux and the response of μ to the torques. It is shown that the accuracy of the data is sufficient for an investigation of this interaction. It is found that the horizontally averaged angular momentum in the upper troposphere and lower stratosphere tends to be negative before an event of positive friction torque. Downward transports of negative angular momentum from these layers allow the angular momentum to further decrease near the ground, even shortly before the event although the friction torque is positive at that time. The impact of the mountains during this process is demonstrated. The ensuing positive response to the friction torque is felt throughout the troposphere. The final decay of this reaction involves downward...

Magnetized orbits around a Kerr black hole

We study the motion of magnetized particles near a rotating black hole. The main result is that the spacetime curvature and electromagnetic field conspire to allow for the existence, inside the ergosphere, of stable circular orbits occupied by particles with negative total energy and angular momentum. Since these particles would never populate stable orbits were they not magnetized, a large binding energy is required to let them exist. A simple model of a magnetized belt in the ergosphere of a massive black hole with a strong magnetic field, shows that it can store a binding energy as high as 1054 erg, an amount comparable with the energy detected in gamma ray bursts. Besides the above astrophysical considerations, this paper contains a formal deduction, from an appropriate Hamiltonian, of the equations of motion of a neutral and magnetized fluid made of spinless dust particles interacting with a magnetic field. This analysis does not appear to have been done before.

Angular Momentum Distribution of Hot Gas and Implications for Disk Galaxy Formation

We study the angular momentum profiles both for dark matter and for gas within virialized halos using a statistical sample of halos drawn from cosmological hydrodynamics simulations. Three simulations have been analyzed: one is the nonradiative simulation and the other two have radiative cooling. We find that the gas component, on average, has a larger spin and contains a smaller fraction of mass with negative angular momentum than its dark matter counterpart in the nonradiative model. As to the cooling models, the gas component shares approximately the same spin parameter as its dark matter counterpart, but the hot gas has a higher spin and is more aligned in angular momentum than dark matter, while the opposite holds for the cold gas. After the mass of negative angular momentum is excluded, the angular momentum profile of the hot gas component approximately follows the universal function originally proposed by Bullock et al. for dark matter, though the shape parameter μ is much larger for hot gas and is comfortably in the range required by observations of disk galaxies. Since disk formation is related to the distribution of hot gas that will cool, our study may explain the fact that the disk component of observed galaxies contains a smaller fraction of low angular momentum material than dark matter in halos.

Spiral Bending Waves Launched at a Vertical Secular Resonance

The excitation of spiral bending waves at a secular vertical resonance in a particle disk is examined. These waves are one-armed spirals of very long wavelength that are launched at sites where a secondary's nodal regression rate matches that of the disk. Nodal bending waves usually propagate radially outward as leading waves from a secular resonance exterior to the perturber, and inward as trailing waves from a secular resonance that lies interior. Their pattern speed is negative, so the spiral pattern rotates in a retrograde sense. The waves carry negative angular momentum but very little energy, and their excitation can damp the inclination of the secondary. Here we apply this theory to the case of two mutually precessing planets orbiting in a particle disk and compare their damping rate with the more familiar inclination excitation due to mean motion vertical resonances. We suggest that under certain circumstances, nodal wave damping may be an important element in maintaining planetary and/or embryo orbits in a nearly coplanar state.

The angular momentum distribution within haloes in different dark matter models

We study the angular momentum profile of dark matter haloes for a statistical sample drawn from a set of high-resolution cosmological simulations of 256(3) particles. Two typical cold dark matter (CDM) models have been analysed, and the haloes are selected to have at least 3 x 10(4) particles in order to measure the angular momentumprofile reliably. In contrast with the recent claims of Bullock et al., we find that the degree of misalignment of angular momentum within a halo is very high. Approximately 50 per cent of haloes have more than 10 per cent of the halo mass in the mass of negative angular momentum j. After the mass of negative j is excluded, the cumulative mass function M(

The Angular Momentum of Gas in Protogalaxies. I. Implications for the Formation of Disk Galaxies

We use numerical simulations of structure formation in a cold dark matter cosmology to compare the angular momentum distributions of dark matter and nonradiative gas in a large sample of halos. We show that the two components have identical spin parameter distributions and that their angular momentum distributions within individual halos are very similar, all in excellent agreement with standard assumptions. Despite these similarities, however, we find that the angular momentum vectors of the gas and dark matter are poorly aligned, with a median misalignment angle of � 30 � , which might have important implications for spin correlation statistics used in weak lensing studies. We present distributions for the component of the angular momentum that is aligned with the total angular momentum of each halo and find that for between 5% and 50% of the mass, this component is negative. This disagrees with the generally adopted ‘‘ universal ’’ angular momentum distribution, for which the mass fraction with negative specific angular momentum is zero. We discuss the implications of our results for the formation of disk galaxies. Since galactic disks generally do not contain counterrotating stars or gas, disk formation cannot occur under detailed conservation of specific angular momentum. We suggest that the material with negative specific angular momentum combines with positive angular momentum material to build a bulge component, and we show that in such a scenario the remaining material can form a disk with a density distribution that is very close to exponential. Subject headings: dark matter — galaxies: formation — galaxies: halos — galaxies: structure — methods: n-body simulations

Negative Reynolds stress generation by accretion disc convection

The phenomenon of negative viscosity-alpha in convectively unstable Keplerian accretion discs is discussed. The convection is considered as a random flow with an axisymmetric mesoscale pattern. Its correlation tensor is computed with a time-averaging procedure using Kley's 2D hydrocode. There is a distinct anisotropy between the turbulence intensities in the radial and azimuthal directions, i.e. the radial velocity rms dominates the azimuthal one. As a consequence, an extra term in the expression for the turbulent transport of angular momentum appears which does not vanish for rigid rotation (‘Λ-effect’). It is negative (‘inwards transport’) and even seems to dominate the positive contribution of the eddy viscosity representing outwards transport of angular momentum. For a turbulence model close to that of the mixing-length theory, the rotational influence on the anisotropy of the turbulence intensities, , and the covariance 〈u′Ru′〉– representing the angular momentum transport – is computed and compared with the accretion disc simulations. Indeed, the negative angular momentum transport can be explained with the observed dominance of the radial turbulence intensity. If, on the other hand, in turbulence fields the azimuthal intensity would dominate or the turbulence is even isotropic, then we always find a positive transport of the angular momentum.

The near wake of a model horizontal-axis wind turbine at runaway

This paper completes a series which describes measurements within two chord lengths of the blades of a small horizontal-axis wind turbine over a wide range of operating conditions. Prior to the present experiment, the turbine was rebuilt to allow operation at its runaway point, where no power is produced. Runaway can be viewed as the upper limit on wind turbine performance at which thrust and wake expansion are maximised. The measurements, which approximate the mean and fluctuating velocity fields seen by an observer rotating with the blades, were obtained from a stationary X-probe hot-wire anemometer by the technique of phase-locked averaging. It is shown conclusively that there is negative (power-producing) angular momentum extracted from the wake, but a balancing positive angular momentum resides in the tip vortices. The mean velocity through the blades increases significantly with radius, in contrast to the near-constant velocity when the turbine is producing its maximum power. Comparisons with conventional blade calculations suggest that the circulation in the wake is related to the difference between the circumferential components of the lift and drag, rather than the magnitude of the lift as is often assumed. Within the range and accuracy of measurement, the pitch of the tip vortices is constant and proportional to the inverse of the tip speed ratio.

Circumnuclear Spiral Arms and Starburst Rings in Magnetized Barred Spiral Galaxies

The Seyfert galaxy NGC 1097 has a prominent bar and a luminous circumnuclear starburst ring. Magnetic fields as revealed by nonthermal radio continuum emissions correlate well with the optical barred spiral structure on large scales, have a gross enhancement overlapping with the optical/infrared ring, and show a trailing swirl around and within the ring. We propose a scenario of bar-excited long-trailing fast magnetohydrodynamic (MHD) density waves at the modified inner Lindblad resonance (mILR), physically identified with the outer rim of the ring. These sustained outgoing long waves are bounced back by the QM-barrier in the form of incoming short-trailing waves. The damping of these waves deposits a negative angular momentum into the magnetized circumnuclear gas disk. Thus, gas materials spiral inward, bring in frozen-in magnetic flux, and accumulate inside the mILR to create a circular zone of high density and magnetic flux vulnerable to massive star formation. Depending on the wave damping efficiency, this process may simultaneously sustain a net mass inflow across the ring and toward the nucleus. A wavelet analysis on a Hubble Space Telescope image of central NGC 1097 shows a distinct two-arm spiral structure extended down to the nucleus as a strong evidence for circumnuclear MHD density waves. We predict that magnetic field observations with improved sensitivity and resolution would eventually reveal a specific correspondence between circumnuclear optical and magnetic field spirals similar to those known to exist on large scales in nearby spiral galaxies, including NGC 1097.

Timelike geodesic motions within the general relativistic gravitational field of the rigidly rotating disk of dust

The general relativistic motion of a test particle near a rigidly rotating disk of dust is investigated. Circular orbits within the plane of the disk (centered on the rotation axis) are special cases of the geodesic motion. One finds that there is always a (stable or unstable) circular orbit for positive angular momentum and a given radius. However, for sufficiently relativistic disks there are regions within the plane of the disk in which a particle with negative angular momentum cannot follow a circular path. If the disk is still more strongly relativistic, then one finds circular orbits with negative energies of arbitrary magnitude. Within the theoretical construction of the Penrose effect, this property can be used to produce arbitrarily high amounts of energy. The study of Hamiltonian mechanics forms another topic of this article. It turns out that the stochastic behavior of the geodesics is related to the position of the region containing all the crossing points of the particle through the plane of the disk. If this region contains points lying inside the disk as well as points outside, the geodesic motion shows highly stochastic behavior. However, if the crossing region is completely inside or outside the disk, the motion proves to be nearly integrable. In these cases the corresponding Hamiltonian system is close to an integrable system of the so-called Liouville class.

The Response of Accretion Disks to Bending Waves: Angular Momentum Transport and Resonances

We investigate the linear tidal perturbation of a viscous Keplerian disk by a companion star orbiting in a plane inclined to the disk. We consider m = 1 perturbations with odd symmetry with respect to the z = 0 midplane. The response frequency may be either finite or vanishing. These long-wavelength perturbations produce a well-defined warp. Since the response of a viscous disk is not in phase with the perturbing potential, a tidal torque is exerted on the disk. When the perturber rotates outside the disk, this torque results in a decrease of the disk angular momentum and thus in an increase of its accretion rate. We show that this tidal torque is comparable to the horizontal viscous stress acting on the background flow when the perturbed velocities in the disk are on the order of the sound speed. If these velocities remain subsonic, the tidal torque can exceed the horizontal viscous stress only if the viscous parameter αv, which couples to the vertical shear, is larger than the parameter αh coupled to the horizontal shear. In protostellar disks, bending waves, which are predominantly excited in the outer regions, are found to propagate and transport a significant fraction of the negative angular momentum they carry deep into the disk inner parts. If the waves are reflected at the center, resonances occur when the frequency of the tidal waves is equal to that of some free normal global bending mode of the disk. If such resonances exist, tidal interactions may then be important even when the binary separation is large. Out of resonance, the torque associated with the secular perturbation, which is proportional to αv, is generally much larger than that associated with the finite-frequency perturbations. As long as the waves are damped before they reach the center, the torque associated with the finite-frequency perturbations does not depend on the viscosity, in agreement with theoretical expectation. These calculations are relevant to disks around young stars and maybe also to disks in X-ray binary systems.

Quantum perturbation theory for the level splitting in billiards

A perturbation theory is developed for the level splitting due to dynamical tunneling in two-dimensional billiards. Using a scattering-matrix approach, the splittings are expressed in terms of a matrix element connecting quasimodes localized in the subspace of positive and negative angular momentum, in analogy to the familiar degenerate double-well problem. The theory is shown to work well for billiards which are integrable, mixed, and strongly chaotic.

The poleward propagation of atmospheric angular momentum with a 30–60-day time scale

Abstract The existence of the intraseasonal variation of relative atmospheric angular momentum and the poleward propagation of this physical quantity by the intraseasonal mode of atmospheric circulation have been amply demonstrated in previous studies. However, the temporal relationship between the intraseasonal variation and poleward propagation is not well understood and the possible mechanism causing the poleward propagation is unknown. Analyzing the 15-year (1979–1993) upper-air data of the National Meteorological Center (currently the National Centers for Environmental Prediction), we explored these two intriguing issues related to atmospheric angular momentum via case-study analyses. The major findings are as follows: 1. 1. The maximum (minimum) 30–60-day globally integrated atmospheric angular momentum occurs when the positive (negative) angular momentum anomalies of a 30–60-day cycle appear in the tropics-subtropics and those of the previous 30–60-day cycle propagate to the northern and southern midlatitudes. 2. 2. The eastward propagation of the 30–60-day global divergent circulation induces a 30–60-day flip-flop oscillation in the meridional circulation which in turn results in a similar alternation in the angular momentum tendency caused by the Coriolis torque. It was inferred from the zonal-mean angular momentum budget analysis that the 30–60-day variation of atmospheric angular momentum and its poleward propagation are results of the 30–60-day variation of the aforementioned momentum tendency.

Can FU Orionis Outbursts Regulate the Rotation Rates of T Tauri Stars?

We propose that FU Orionis outbursts may play an important role in maintaining the slow rotation of classical disk-accreting T Tauri stars. Current estimates for the frequency and duration of FU Orionis outbursts and the mass accretion rates of T Tauri and FU Orionis stars suggest that more mass may be accreted during the outbursts than during the T Tauri phases. If this is the case, then the outbursts should also dominate the accretion of angular momentum. During the outbursts, the accretion rate is so high that the magnetic field of the star should not disrupt the disk, and the disk will extend all the way in to the stellar surface. Standard thin disk models then predict that the star should accrete large amounts of angular momentum, which will produce a secular spinup of the star. We present boundary layer solutions for FU Orionis parameters which show that the angular momentum accretion rate drops below zero for stellar rotation rates which are always substantially below breakup, but depend on the mass accretion rate and on the adopted definition of the stellar radius. When the angular momentum accretion rate drops close to zero, the star will stop spinning up. Faster stellar rotation rates will produce negative angular momentum accretion which will spin the star down. Therefore, FU Orionis outbursts can keep the stellar rotation rate close to some equilibrium value for which the angular momentum accretion rate is small. We show that this equilibrium rotation rate may be similar to the observed rotation rates of T Tauri stars; thus we propose that FU Orionis outbursts may be responsible for the observed slow rotation of T Tauri stars. This mechanism is independent of whether the disk is disrupted by the stellar magnetic field during the T Tauri phase.

Mermin-Ho Texture and Its Transverse NMR Spectrum in a Rotating Cylinder

The Mermin-Ho texture of a superfluid 3 He A-phase confined in a rotating cylinder is studied. The case of a strong magnetic field applied along a cylinder axis is considered. The l and d textures are determined as a function of the angular velocity ω of the rotation. The lowest transverse NMR frequency of the spin wave mode is calculated from the obtained l and d configuration. In the rotating system, the energy term -ω L z lifts the degeneracy of the two types of Mermin-Ho textures which have positive and negative superflow angular momentum L z around the cylinder axis. These phenomena are expected to be identifiable by the NMR spectrum observation.

Splitting of electronic levels with positive and negative angular momenta in In0.53Ga0.47As/InP quantum dots by a magnetic field.

Splitting of electronic levels with positive and negative angular momenta in In0.53Ga0.47As/InP quantum dots by a magnetic field.

Single-Sided Shepherding

Narrow ringlets are observed to form at isolated Lindblad resonances in recent simulations (J. Hänninen and H. Salo, Icarus 108, 325-346 (1994) and 117, 435-438 (1995)). Our remarks are directed toward the interpretation of this phenomenon. Ringlet formation is a consequence of the negative angular momentum luminosity promoted by satellite perturbations of the streamlines of particle flow. Contraction halts once the surface density reaches a value such that the angular momentum luminosity vanishes. Our estimate for the formation time, tf ∼ (Mp/Ms)1/2Ω,-1, for low order resonances in optically thin rings is consistent with the results of the simulations. Ringlets drift across the width of resonance, W ∼ (Ms/Mp)1/2a, as a result of the unbalanced satellite torque. This occurs on the much longer timescale td ∼ (Mp/Ms)Ω-1 and cannot be observed in current simulations.