The chaotic dynamics of Prometheus and Pandora
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Prometheus Pandora Voyager satellites Prometheus-P↗
Engineering topics
Goldreich, P.
Publications and source records attributed to Goldreich, P..
Toward a theory of interstellar turbulence. 2: Strong alfvenic turbulence
We continue to investigate the possibility that interstellar turbulence is caused by nonlinear interactions among shear Alfven waves. Here, we restrict attention to the symmetric case where the oppositely directed waves carry equal energy fluxes. This precludes application to the solar wind in which the outward flux significantly exceeds the ingoing one. All our detailed calculations are carried out for an incompressible magnetized fluid. In incompressible magnetohydrodynamics (MHD), nonlinear interactions only occur between oppositely direct waves. We present a theory for the strong turbulence of shear Alfven waves. It has the following main characteristics. (1) The inertial-stage energy spectrum exhibits a critical balance between linear wave periods and nonlinear turnover timescales. (2) The 'eddies' are elongated in the direction of the field on small spatial scales; the parallel and perpendicular components of the wave vector, k(sub z) and k(perpendicular) are related by k(sub z) approximately equals k(sub perpendicular to)(exp 2/3) L(exp -1/3), where L is the outer scale of the turbulence. (3) The 'one-dimensional' energy spectrum is proportional to k(sub perpendicular)(exp -5/3)-an anisotropic Kolmogorov energy spectrum. Shear Alfvenic turbulence mixes specific entropy as a passive contaminant. This gives rise to an electron density power spectrum whose form mimics the energy spectrum of the turbulence. Radio wave scattering by these electron density fluctuations produces anisotropic scatter-broadened images. Damping by ion-neutral collisions restricts Alfvenic turbulence to highly ionized regions of the interstellar medium.
Goldreich, P.↗
Toward a theory of interstellar turbulence. 1: Weak Alfvenic turbulence
We study weak Alfvenic turbulence of an incompressible, magnetized fluid in some detail, with a view to developing a firm theoretical basis for the dynamics of small-scale turbulence in the interstellar medium. We prove that resonant 3-wave interactions are absent. We also show that the Iroshnikov-Kraichnan theory of incompressible, magnetohydrodynamic turbulence -- which is widely accepted -- describes weak 3-wave turbulence; consequently, it is incorrect. Physical arguments, as well as detailed calculations of the coupling coefficients are used to demonstrate that these interactions are empty. We then examine resonant 4-wave interactions, and show that the resonance relations forbid energy transport to small spatial scales along the direction of the mean magnetic field, for both the shear Alfven wave and the pseudo Alfven wave. The three-dimensional inertial-range energy spectrum of 4-wave shear Alfven turbulence guessed from physical arguments reads E(k(sub z), k(sub perpendicular)) approximately V(sub A)v(sub L)L(exp -1/3)k(sub perpendicular)(exp -10/3), where V(sub A) is the Alfven speed, and v(sub L) is the velocity difference across the outer scale L. Given this spectrum, the velocity difference across lambda(sub perpendicular) approximately k(sub perpendicular exp -1) is v(sub lambda (sub perpendicular)) is approximately v(sub L)(lambda(sub perpendicular)/L)(exp 2/3). We derive a kinetic equation, and prove that this energy spectrum is a stationary solution and that it implies a positive flux of energy in k-space, along directions perpendicular to the mean magnetic field. Using this energy spectrum, we deduce that 4-wave interactions strengthen as the energy cascades to small, perpendicular spatial scales; beyond an upper bound in perpendicular wavenumber, k(sub perpendicular)L is approximately (V(sub A)/v(sub L))(exp 3/2), weak turbulence theory ceases to be valid. Energy excitation amplitudes must be very small for the 4-wave inertial-range to be substantial. When the excitation is strong, the width of the 4-wave inertial-range shrinks to zero. This seems likely to be the case in the interstellar medium.
Sridhar, S.↗
Neutron starquake models for gamma-ray bursts
The component parts of gamma-ray burst models based on neutron starquakes are assessed. The requirements for, and the properties of, neutron starquakes are reviewed. The coupling of seismic waves to Alfven waves is evaluated and the behavior of Alfven waves in the magnetosphere is investigated. An attempt is made to identify the principal sources of free energy in the interiors of old neutron stars.
Blaes, O.↗
Neptune's story
It is conjectured that Triton was captured from a heliocentric orbit as the result of a collision with what was then one of Neptune's regular satellites. The immediate post-capture orbit was highly eccentric. Dissipation due to tides raised by Neptune in Triton caused Triton's orbit to evolve to its present state in less than one billion years. For much of this time Triton was almost entirely molten. While its orbit was evolving, Triton cannibalized most of the regular satellites of Neptune and also perturbed Nereid, thus accounting for that satellite's highly eccentric and inclined orbit. The only regular satellites of Neptune that survived were those that formed well within 5 Neptune radii, and they move on inclined orbits as the result of chaotic perturbations forced by Triton.
Goldreich, P.↗
Neutron starquakes and the nature of gamma-ray bursts
The possibility that gamma-ray bursts originate from quakes deep in the solid crust of a neutron star is investigated. Seismic waves are radiated if shear stress is relieved by brittle fracture. However they cannot propagate directly to the surface but are temporarily trapped below a reflecting layer. The shaking of the stellar surface couples the seismic waves to Alfven waves which propagate out into the magnetosphere. The crust-magnetosphere transmission coefficient strongly increases with wave frequency and magnetic field strength. Alfven wave luminosities sufficient to power galactic gamma-ray bursts are possible if magnetic fields greater than 100 billion G cover at least part of the stellar surface. As the Alfven waves propagate out into the low density magnetosphere, they become increasingly charge starved, thereby accelerating particles to relativistic energies.
Madau, P.↗
Lunar and planetary studies
This grant supports the core program in planetary astronomy at Caltech. The research includes observations in the IR, sub-mm, mm and cm wavelengths at national and Caltech observatories with a strong emphasis on integrating the observations with spacecraft data and with models of atmospheric structure, dynamics and chemistry. Muhleman's group made extensive observations of Saturn, Uranus and Neptune which are being interpreted in terms of deep atmospheric structures which are obvious in the 2 and 6 cm maps of Saturn and Uranus. The microwave measurements are one of the few sources of information below the 2 bar level. Goldreich is investigating the dynamics of narrow rings with postdoctoral fellow, Pierre-Yves Longaretti. Their work has focused on the role of collisional stresses on the precession of the rings, since the Voyager radio science results imply that the previous model based on the ring's self-gravity is not the entire story. In addition Borderies, Goldreich and Tremaine have completed an investigation of the dynamics of the Encke division in Saturn's A ring.
Muhleman, Duane O.↗
Research at Palomar Observatory in planetary astronomy
A wide range of observational studies are carried out to improve our understanding of the bodies of the outer solar system. Using the 200-inch Hale telescope, near-infrared observations are made of Uranus, Neptune, and the Pluto-Charon system. High time resolution occultation observations of the Uranus Ring system are used to study in detail the dynamics of this system. Occultation studies of Neptune are probing this intriguing ring-arc system. Occulation observations of the Pluto-Charon system probe the surface properties of these distant bodies. In addition, the plate material of the PSSII servey is being used to search for new comets and asteroids. Researchers observed one Neptune stellar occultation in July 1987 and completed the analysis of a series of seven separate Neptune occultation observations in conjunction with Nicholson et al., of Cornell. The analysis has shown that minimum of three ring arcs, at radii ranging from 54,000 km - 67,000 km are required to account for the high quality ring events. Current theoretical models can account for these data. Of two observations scheduled of Pluto-Charon mutual occulations scheduled for the 200-inch, the Charon eclipse event was successfully observed (the other was clouded out).
Soifer, B. T.↗
Research in planetary astronomy at Palomar Observatory
The goals of this program are three fold. The ring systems in the outer solar system were studied. New comets and asteroids in the solar system were surveyed. The volatile surface coverings of the primitive bodies in the outer solar system were studied via infrared spectroscopy.
Soifer, B. T.↗
Towards a theory for Neptune's arc rings
It is proposed that the incomplete rings of Neptune consist of a number of short arcs centered on the corotation resonances of a single satellite. The satellite must have a radius of the order of 100 km or more and move on an inclined orbit. Corotation resonances are located at potential maxima. Thus, mechanical energy dissipated by interparticle collisions must be continually replenished to prevent the arcs from spreading. It is shown that each corotation resonance is associated with a nearby Lindblad resonance, which excites the ring particles' orbital eccentricity, thus supplying the energy required to maintain the arc. The ultimate energy reservoir is the satellite's orbital energy. Therefore, interaction with the arcs damps the satellite's orbital inclination. The self-gravity of the arcs limits their contraction and enforces a relation between arc length and mass. The estimated arc masses are so small, of the order of 10 to the 16th g, that the satellite's orbital inclination suffers negligible decay over the age of the solar system. The inferred surface mass densities are comparable to those found in the major rings of Saturn and Uranus.
Goldreich, P.↗
Evolution of the Janus-Epimetheus coorbital resonance due to torques from Saturn's rings
The effects of the gravitational interactions between Saturn's rings and the coorbital satellites, Janus and Epimetheus, on the 1:1 horseshoe resonance between these moons is examined. It is shown that the 7:6 resonance of these moons, which presumably maintains the sharp outer edge of the A ring, leads to a rapid tightening of the coorbital lock. The results lead to the prediction that the orbital configuration might evolve from the current horseshoe-type lock to one of tadpole orbits around a single Lagrangian point in about 20 myr.
Lissauer, J. J.↗
A granular flow model for dense planetary rings
In the present study of the viscosity of a differentially rotating particle disk, in the limiting case where the particles are densely packed and their collective behavior resembles that of a liquid, the pressure tensor is derived from both the equations of hydrodynamics and a simple kinetic model of collisions due to Haff (1983). Density waves and narrow circular rings are unstable if the liquid approximation applies, and the consequent nonlinear perturbations may generate 'splashing' of the ring material in the vertical direction. These results are pertinent to the origin of the ellipticities of ringlets, the nonaxisymmetric features near the outer edge of the Saturn B ring, and unexplained residuals in kinematic models of the Saturn and Uranus rings.
Borderies, N.↗
The eccentric Saturnian ringlets at 1.29 R(s) and 1.45 R(s)
The shapes and kinematics of the Titan and Maxwell ringlets of Saturn's C ring are studied. The ringlets are narrow and eccentric, with mean widths of about 25 km for Titan and abut 64 km for Maxwell, and with eccentricities of order 10 to the -4th. They have sharp edges on a scale of about 1 km, normal optical depths of roughly 0.5-2.0, normal optical depth of the surrounding region, and positive linear width-radius relations. The Titan ringlet is the only feature whose dynamics appears to be completely determined by an external satellite; the kinematics of the Maxwell ringlet are determined solely by Saturn's nonspherical gravity field. The comparatively large measured optical depths and large inferred mass extinction coefficients for the ringlets suggest an environment and particle size distribution different from the remainder of the C ring and presumably caused by the mechanism responsible for ring confinement.
Porco, C.↗
Saturn's nonaxisymmetric ring edges at 1.95 R(s) and 2.27 R(s)
The outer edges of Saturn's A and B rings, at 2.27 R(s) and 1.95 R(s), have been examined using data acquired by four Voyager experiments. The shapes and kinematics of these features are influenced by their proximity to strong low-order Lindblad resonances. The data for the A-ring edge are consistent with a seven-lobed radial distortion of amplitude 6.7 + or - 1.5 km which rotates with the mass-weighted mean angular velocity of the coorbital satellite system. The B-ring edge has essentially a double-lobed figure of radial amplitude 74 + or - 9 km which rotates with the mean motion of Mimas, though there is an indication that it is not completely described with a simple Saturn-centered ellipse. An upper limit of 10 m has been placed on the vertical thickness in the unperturbed region of the B ring.
Porco, C.↗
Excitation of inclinations in ring-satellite systems
Resonant gravitational interactions between a ring and a satellite produce secular variations of their orbital inclinations. Interactions at vertical resonances, analogous to Lindblad resonances but involving inclinations instead of eccentricities, excite inclinations. There is no inclination analog of the corotation resonance. An equatorial ring changes the inclination of a nearby satellite in qualitatively the same way that a satellite in an equatorial orbit changes the inclination of a nearby ring. Viscous dissipation in a ring leads to an equilibrium value of its inclination. These results provide a basis for discussing the origins of the inclinations of planetary rings.
Borderies, N.↗
A simple derivation of capture probabilities for the J + 1 : J and J + 2 : J orbit-orbit resonance problems
Henrad's (1982) method, which is based on an extension of the theory of adiabatic invariants, is presently applied to a simplified analytic derivation of the capture probabilities for the j + 1 : j and j + 2 : j orbital resonances. The results originally obtained by Yoder (1979) are thereby recovered.
Borderies, N.↗
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.↗
Eccentric ringlet in the Maxwell gap at 1.45 Saturn radii Multi-instrument Voyager observations
The results of Voyager experiments to characterize the eccentric ringlet at 1.45 Saturn radius are discussed. The Voyager I carried out microwave occultation trials with a dual-frequency transmitter, while Voyager 2 observed the occultation of delta Scorpii using an UV spectrometer and a photopolarimeter. The ringlet was associated with a basically empty region next to an edge of the C ring which decreased to a few hundred meters thickness. The width of the ringlet in the gap was estimated to vary from 38-88 km, and it maintains an elliptical shape. It precesses within the 265 km gap it occupies, and has a double-peaked core 15 km wide. The bulk of the ringlet is particles of less than 1 cm radius.
Esposito, L. W.↗