Two stages of dust delivery from satellites to planetary rings

Faint rings of micrometre-sized dust particles embrace many planets in the Solar system. As a rule, they are replenished by ejecta from embedded atmosphereless moons. On a number of occasions, the ejecta are generated by hypervelocity meteoroid impacts into the moons. Small ejecta fragments are then swiftly shifted into rings by an array of non-gravitational forces, e.g. radiation pressure or plasma drag. A significant fraction of ejecta mass, however, is contained in relatively big, multi-micrometre fragments which are subject to gravity only. Having escaped from the satellite, they stay close to its orbit and form a belt around planet. This belt is itself a source of ring dust through collisional disruption of its particles. Here the contributions of belts to the respective rings are estimated for selected satellites of Jupiter and Saturn. The belts under review could supply substantially more dust to rings than the direct ejecta from satellites and should be taken into account when estimating ring dust budgets. The belts are very difficult to observe, however, and some of them remain a theoretical proposition. We find an appealing evidence for the belts due to Amalthea and Thebe around Jupiter, and for the belt due to Enceladus around Saturn.     

Strands and braids in narrow planetary rings: a scattering system approach

We address the occurrence of narrow planetary rings and some of their structural properties, in particular when the rings are shepherded. We consider the problem as Hamiltonian scattering of a large number of non-interacting massless point particles in an effective potential. Using the existence of stable motion in scattering regions in this set up, we describe a mechanism in phase space for the occurrence of narrow rings and some consequences in their structure. We illustrate our approach with three examples. We find eccentric narrow rings displaying sharp edges, variable width and the appearance of distinct ring components (strands) which are spatially organized and entangled (braids). We discuss the relevance of our approach for narrow planetary rings.     

Size distribution of particles in planetary rings

Harris (Icarus24, 190–192) has suggested that the maximum size of particles in a planetary ring is controlled by collisional fragmentation rather than by tidal stress. While this conclusion is probably true, estimated radius limits must be revised upward from Harris' values of a few kilometers by at least an order of magnitude. Accretion of particles within Roche's limit is also possible. These considerations affect theories concerning the evolution of Saturn's rings, of the Moon, and of possible former satellites of Mercury and Venus. In the case of Saturn's rings, comparison of various theoretical scenarios with available observational evidence suggests that the rings formed from the breakup of larger particles rather than from original condensation as small particles. This process implies a distribution of particle sizes in Saturn's rings possibly ranging up to ～100 km but with most cross-section in cm-scale particles.     

Interaction of planetary nebulae with prenebulae debris

In the present poster we suggest that some of the structures observed in the envelopes of planetary nebulae are caused by the interaction of central star wind and radiation with preplanetary nebula debris: planets, moons, minor objects and ring and ring arcs.Recently considerable amount of planetary material has been reported to exist around solar type stars, this debris could be evaporated during the envelope ejection and alter the chemical abundance and produce some of the envelope inhomogeneities.If there are massive enough rings of material surrounding the progenitor and planets in their vicinity, arc rings could be formed. If the rings are viewed pole on when the envelope is detached from the central star, it will interact with the arc ring material and produce ansae and pedal and garden-hose-shape structures observed in some planetaries.Paper presented at the Conference onPlanetary Systems: Formation, Evolution, and Detection held 7–10 December, 1992 at CalTech, Pasadena, California, U.S.A.     

Collision mechanics and the structure of planetary ring edges

A numerical simulation of collisional evolution, originally developed to model planetary accretion processes, is applied to a hypothetical ring with parameters modeled after Saturn's rings in order to study changes in radial structure near ring edges. The tendency of rings to spread so as to conserve angular momentum while energy is dissipated in collisions is confirmed if random motion is in equilibrium. Even with no energy loss (coefficient of restitution in velocity ε = 1), spreading occurs becase random motion is increasing. With a moderately side-scattering collisional model, characteristic of collisions of nonrotating spheres (the slippery “billiard-ball” model), random motion increases for ε > 0.63, in agreement with analytical models. For isotropic scattering, which may be more realistic given particle rotation, damping dominates for ε up to 0.83. As long as random motion is damped, ring edges may contract rather than spread, producing concentrations of material just inside the ring edges reminiscent of results of earlier stimulation which did not precisely conserve angular momentum.     

Formation of planetary systems by successive contractions of the solar nebula

The theory discussed in the present paper is a solar nebula-type theory which assumes the initial existence of a big disk-shaped gas cloud in rotational motion around the Sun. At the outer edge of the gas cloud there is a steady loss of angular momentum, which is mainly caused by the diffusion induced by turbulence and shock waves. This leads to the formation of a doughnutshaped gas ring at the edge of the cloud, outside of which there is plasma in a state of partial corotation. The gas ring is then slowly shifted towards the Sun, whereby the grains of solid matter within the gas cloud are also transported and collected within the gas torus. During the contraction process the following two situations arise: First, due to the small amount of friction, the angular momentum of the inner part of the ring rapidly exceeds that of the outer part. Second, the angle between the orbits of the inner and outer part of the gas ring increases gradually. When, during contraction, a certain distance is covered, the gas ring turns over, i.e. there is a sudden interchange of the inner and outer parts of the gas ring, where two adjacent rings of solid matter (jet streams) are formed. Immediately after the turn-over process the speed of contraction is at first drastically reduced, but then the gas ring is shifted once more towards the Sun. This process is then repeated periodically. The planets originate from the outer rings of solid matter, which contain much more matter than their adjacent inner rings. The inclination between the inner and outer rings is roughly 5°. In particular, Mercury, the Moon, Titan as well as Triton result from the innermost rings of matter. Having gone through the formation process, most of the planets acquire a rotating gas disk out of which the regular satellites are also created by the same periodic contraction process (hetegonic principle). This theory is the first that can explain all noteworthy facts about our planetary system and the satellite systems in a qualitative yet conclusive way.     

A deep search for Martian dust rings and inner moons using the Hubble Space Telescope

It has long been suspected that Mars might be encircled by two faint rings, one originating from each of its moons Phobos and Deimos. Meteoroid impacts into these moons should release clouds of dust that quickly spread out to become rings; similar dust rings have been associated with several small inner moons of the gas giants. On May 28, 2001 Mars’ hypothetical ring plane appeared edge-on to Earth within weeks of its opposition, providing the best Earth-based opportunity to detect these rings in several decades. Using the Wide Field/Planetary Camera 2 (WFPC2) on the Hubble Space Telescope, we obtained a set of deep exposures off the east and west limbs of Mars to search for these hypothetical rings. No rings were detected. This result limits normal optical depths to ∼3×10⁻⁸ for the Phobos ring and ∼10⁻⁷ for the Deimos ring. These limits fall at the low end of prior dynamical predictions and a factor of 1000 below previous observational limits. However, our limit for the Deimos ring is more tentative because of large uncertainties about this ring's expected shape, size and orientation. Our data set is also sensitive to small, previously undetected inner moons. No moons were detected down to a radius limit of 75–125 m. Longitudinal coverage of the region near and between Phobos and Deimos is 40–80% complete. We conclude by describing a promising opportunity for further Martian ring viewing in December 2007.     

Limits on the Orbits of Possible Eccentric and Inclined Moons of Extrasolar Planets Orbiting Single Stars

Limits are placed on the range of orbits and masses of possible moons orbiting extrasolar planets which orbit single central stars. The Roche limiting radius determines how close the moon can approach the planet before tidal disruption occurs; while the Hill stability of the star–planet–moon system determines stable orbits of the moon around the planet. Here the full three-body Hill stability is derived for a system with the binary composed of the planet and moon moving on an inclined, elliptical orbit relative the central star. The approximation derived here in Eq. (17) assumes the binary mass is very small compared with the mass of the star and has not previously been applied to this problem and gives the criterion against disruption and component exchange in a closed form. This criterion was applied to transiting extrasolar planetary systems discovered since the last estimation of the critical separations (Donnison in Mon Not R Astron Soc 406:1918, 2010a) for a variety of planet/moon ratios including binary planets, with the moon moving on a circular orbit. The effects of eccentricity and inclination of the binary on the stability of the orbit of a moon is discussed and applied to the transiting extrasolar planets, assuming the same planet/moon ratios but with the moon moving with a variety of eccentricities and inclinations. For the non-zero values of the eccentricity of the moon, the critical separation distance decreased as the eccentricity increased in value. Similarly the critical separation decreased as the inclination increased. In both cases the changes though very small were significant.     

On the rotation of a moonlet embedded in planetary rings

We examine the rotation of a small moonlet embedded in planetary rings caused by impacts of ring particles, using analytic calculation and numerical orbital integration for the three-body problem. Taking into account the Rayleigh distribution of particles' orbital eccentricities and inclinations, we evaluate both systematic and random components of rotation, where the former arises from an average of a large number of small impacts and the latter is contribution from large impacts. Calculations for parameter values corresponding to inner parts of Saturn's rings show that a moonlet would spin slowly in the prograde direction if most impactors are small particles whose velocity dispersion is comparable to or smaller than the moonlet's escape velocity. However, we also find that the effect of the random component can be significant, if the velocity dispersion of particles is larger and/or impacts of large particles comparable to the moonlet's size are common: in this case, both prograde and retrograde rotations can be expected. In the case of a small moonlet embedded in planetary rings of equal-sized particles, we find that the systematic component dominates the moonlet rotation when m/M?0.1 (m and M are the mass of a particle and a moonlet, respectively), while the random component is dominant when m/M?0.3. We derive the condition for the random component to dominate moonlet rotation on the basis of our results of three-body orbital integration, and confirm agreement with N-body simulation.     

Escape from planetary neighbourhoods

In this paper we use recently developed phase-space transport theory coupled with a so-called classical spectral theorem to develop a dynamically exact and computationally efficient procedure for studying escape from a planetary neighbourhood. The 'planetary neighbourhood' is a bounded region of phase space where entrance and escape are only possible by entering or exiting narrow 'bottlenecks' created by the influence of a saddle point. The method therefore immediately applies to, for example, the circular restricted three-body problem and Hill's lunar problem (which we use to illustrate the results), but it also applies to more complex, and higher-dimensional, systems possessing the relevant phase-space structure. It is shown how one can efficiently compute the mean passage time through the planetary neighbourhood, the phase-space flux in, and out, of the planetary neighbourhood, the phase-space volume of initial conditions corresponding to trajectories that escape from the planetary neighbourhood, and the fraction of initial conditions in the planetary neighbourhood corresponding to bound trajectories. These quantities are computed for Hill's problem. We study the dependence of the proportions of these quantities on energy and dimensionality (two-dimensional planar and three-dimensional spatial Hill's problem). The methods and quantities presented are of central interest for many celestial and stellar dynamical applications such as, for example, the capture and escape of moons near giant planets, the formation of binaries in the Kuiper belt and the escape of stars from star clusters orbiting about a galaxy.     

The low-excitation structures of planetary nebulae

The low excitation properties of the planetary nebula (PN) NGC 6720 are known to be unusual, and to imply large ring/core emission ratios. We point out that such characteristics are by no means confined to this source alone, and that high ratios may occur in a large fraction of elliptical and circular PNe. Such trends may arise because of the presence of thin low-excitation emission sheets 'wrapped' within and around the primary outflows. The widths of such shells are required to be exceedingly small, and may (for certain cases) be of order ≪10⁻² pc. Such a mechanism appears capable of explaining most of the observed emission properties, and may arise through shock interaction between differing envelopes. Alternative explanations in terms of bipolar or cylindrical outflows are shown to be implausible.     

Accretion of Saturn’s mid-sized moons during the viscous spreading of young massive rings: Solving the paradox of silicate-poor rings versus silicate-rich moons

The origin of Saturn’s inner mid-sized moons (Mimas, Enceladus, Tethys, Dione and Rhea) and Saturn’s rings is debated. Charnoz et al. [Charnoz, S., Salmon J., Crida A., 2010. Nature 465, 752–754] introduced the idea that the smallest inner moons could form from the spreading of the rings’ edge while Salmon et al. [Salmon, J., Charnoz, S., Crida, A., Brahic, A., 2010. Icarus 209, 771–785] showed that the rings could have been initially massive, and so was the ring’s progenitor itself. One may wonder if the mid-sized moons may have formed also from the debris of a massive ring progenitor, as also suggested by Canup [Canup, R., 2010. Nature 468, 943–946]. However, the process driving mid-sized moon accretion from the icy debris disks has not been investigated in details. In particular, Canup’s (2010) model does not seem able to explain the varying silicate contents of the mid-sized moons (from 6% to 57% in mass). Here, we explore the formation of large objects from a massive ice-rich ring (a few times Rhea’s mass) and describe the fundamental properties and implications of this new process. Using a hybrid computer model, we show that accretion within massive icy rings can form all mid-sized moons from Mimas to Rhea. However in order to explain their current locations, intense dissipation within Saturn (with Q_p < 2000) is required. Our results are consistent with a satellite origin tied to the rings formation at least 2.5 Gy ago, both compatible with either a formation concurrent to Saturn or during the Late Heavy Bombardment. Tidal heating related to high-eccentricity post-accretional episodes may induce early geological activity. If some massive irregular chunks of silicates were initially present within the rings, they would be present today inside the satellites’ cores which would have accreted icy shells while being tidally expelled from the rings (via a heterogeneous accretion process). These moons may be either mostly icy, or, if they contain a significant amount of rock, already differentiated from the ice without the need for radiogenic heating. The resulting inner mid-sized moons may be significantly younger than the Solar System and a ∼1 Gyr formation delay is possible between Mimas and Rhea. The rings resulting from this process would evolve to a state compatible with current mass estimates of Saturn’s rings, and nearly devoid of silicates, apart from isolated silicate chunks coated with ice, interpreted as today Saturn’s rings’ propellers and ring-moons (like Pan or Daphnis).     

Saturn's sweeper moons predicted

The recent observation of the absorption of radiation belts in the vicinity of Saturn's bright rings and historical observations of the ring system make the following related results apparent:

- The gaps in the rings are caused by the presence of at least 6 small, extremely dense and probably electrically charged ‘sweeper’ moons which effectively sweep the ring matter clean from the gaps. This is known due to the fading of the inner ring edges whereas the outer edges are well defined. Their orbital periods will differ from the expected Keplerian periods if the moons and Saturn do possess electric fields.

- Absorption of radiation belts near the rings (of Jupiter also) implies that the ring particles themselves are not absorbing the radiation but the small moons are. This is consistent with the observed radiation belt absorption near the outer Saturnian moons.

- If electric fields of the sweeper moons cause the ring edge fading as observed (and not simply gravitational), then Saturn itself must maintain an electric field in its vicinity by way of a sizeable proton wind to affect the uneven ring edge fading and will be surrounded by an H⁺ cloud at least to approximately the A-ring. this is consistent with the detection of an H⁺ cloud surrounding Saturn (Weiseret al., 1977, p. 755). The other possibility is that these moons are extremely dense and have very large internal magnetic fields.

- Because of their location, these moons must be captured and if very dense as believed, may be core remnants of a nova.

     

An approach to the radial distribution of planetary orbits

The problem of determination of the radial distribution of the planetary orbits is approached under the assumption that the average present radial sizes of the orbits were already determined when the protoplanetary cloud flattened by initial angular momentum aggregated into a set of concentric rings from which the planetary material was ultimately collected. The object of this argument is to derive a consistent stationary distribution of orbits so that the problem of the non-stationary formation of the orbital rings is not here considered. Under the flattening assumption the 3D Poisson equation is replaced by the 2D Helmholtz equation (inhomogeneous) which is solved by use of an averaging theorem generalization of the well-known averaging theorem for the homogeneous Helmholtz equation. Augmenting the ring potentials obtained by specializing the mass distribution in the disk by a solar potential term and a rotational potential, differentiation leads to a generalization of the Kepler 3D law suitable for the many-body problem of a solar system with circular orbits. In this way a system of transcendental equations involving Bessel functions of the first and second kind are obtained which must be satisfied by the orbital radii. Naturally the restriction to circular orbits represents only an approximation to the orbital determination problem, but considering that no arguments have previously been available for the determination even of circular orbits it would seem to represent an advance.     

Negative diffusion in planetary rings with a nearby moon

This paper analyzes a process that has been observed in simulations of numerous systems where ring material is strongly perturbed by a nearby moon. If the ring particles can be imparted with a forced eccentricity on the order of 10⁻⁵ in a single pass by the moon, particle orbits are observed to move towards regions of higher density as a result of the organized collisions that occur in the dense peaks of the satellite wake. The width of the ring can decrease by as much as 90% if the forced eccentricity is greater than 3 × 10⁻⁵ and the unperturbed geometric optical depth is greater than 0.03. The fractional change in ring width is relatively insensitive to the particle size so long as the particle radius is much less than the product of the semimajor axis and the forced eccentricity. Including a power law particle size distribution with slope of −2.8 spanning a decade in particle radius reduces the fractional width change by about 10% compared to the uniform particle-size case. Adding gravitational interactions between ring particles only has a significant effect on ring confinement if the unperturbed geometric optical depth exceeds .03, but a 40% reduction in ring width is still achieved in a self-gravitating ring of geometric optical depth 0.3 if the forced eccentricity exceeds 3 × 10⁻⁵. This process does not require the material to be in resonance with the moon, nor does it have any minimum mass constraints because particle self-gravity is not required. The collisional damping of satellite wakes therefore provides a simple mechanism by which a single moon can reduce the radial extent of any ringlet that is close to it and has sufficient optical depth for collisions to be significant.     

The Hill stability of inclined bound triple star and planetary systems

The dynamical stability of a triple system composed of a binary or planetary system and a bound third body moving on a orbit inclined to the system is discussed in terms of Hill stability for the full three-body problem. The situation arises in the determination of stability of triple star systems against disruption and component exchange and the determination of stability of planetary systems against disruption, component exchange or capture. It is found that increasing the inclination of the third body decreases the Hill regions of stability. Increasing the eccentricity of the binary also produces similar effects. These type of changes make exchange or disruption of the component masses more likely. Increasing the eccentricity of the third body initially increases the stability of the system then decreases stability as the eccentricity reaches higher values.The Hill stability criterion is applied to extrasolar planetary systems to determine the critical distances at which planets of the same mass as the observed extrasolar planet moving on a circular orbit could remain on a stable orbit. It was found that these distances were sufficiently short suggesting that the presence of further as yet unobserved stable extrasolar planets in observed systems was very likely.     

Evolution of planetary ringmoon systems

The last few decades have seen an avalanche of observations of planetary ring systems, both from spacecraft and from Earth. Meanwhile, we have seen steady progress in our understanding of these systems as our intuition (and our computers) catch up with the myriad ways in which gravity, fluid and statistical mechanics, and electromagnetism can combine to shape the distribution of the submicron-to-several-meter size particles which comprise ring systems [1–5]. The now-complete reconnaissance of the gas giant planets by spacecraft has revealed that ring systems are invariably found in association with families of regular satellites, and there is an emerging perspective that they are not only physically but causally linked. There is also mounting evidence that many features or aspects of all planetary ring systems, if not the ring systems themselves, are considerably younger than the solar system.     

Satellite formation,II

The satellite formation model of Harris and Kaula (Icarus24, 516–524, 1975) is extended to include evolution of planetary ring material and elliptic orbital motion. This model is more satisfactory than the previous one in that the formation of the moon begins at a later time in the growth of the earth, and that a significant fraction of the lunar material is processed through a circumterrestrial debris cloud where volatiles might have been lost. Thus the chemical differences between the earth and moon are more plausibly accounted for. Satellites of the outer planets probably formed in large numbers throughout the growth of those planets. Because of rapid inward evolution of the orbits of small satellites, the present satellite systems represent only satellites formed in the last few percent of the growths of their primaries. The rings of Saturn and Uranus are most plausibly explained as the debris of satellites disrupted within the Roche limit. Because such a ring would collapse onto the planet in the course of any significant further accretion by the planet, the rings must have formed very near or even after the conclusion of accretion.     

A numerical model of cohesion in planetary rings

We present a numerical method that incorporates particle sticking in simulations using the N-body code pkdgrav to study motions in a local rotating frame, such as a patch of a planetary ring. Particles stick to form non-deformable but breakable aggregates that obey the (Eulerian) equations of rigid-body motion. Applications include local simulations of planetary ring dynamics and planet formation, which typically feature hundreds of thousands or more colliding bodies. Bonding and breaking thresholds are tunable parameters that can approximately mimic, for example, van der Waals forces or interlocking of surface frost layers. The bonding and breaking model does not incorporate a rigorous treatment of internal fracture; rather the method serves as motivation for first-order investigation of how semi-rigid bonding affects the evolution of particle assemblies in high-density environments.We apply the method to Saturn’s A ring, for which laboratory experiments suggest that interpenetration of thin, frost-coated surface layers may lead to weak cohesive bonding. These experiments show that frost-coated icy bodies can bond at the low impact speeds characteristic of the rings. Our investigation is further motivated by recent simulations that suggest a very low coefficient of restitution is needed to explain the amplitude of the azimuthal brightness asymmetry in Saturn’s A ring, and the hypothesis that fine structure in Saturn’s B ring may in part be caused by large-scale cohesion.This work presents the full implementation of our model in pkdgrav, as well as results from initial tests with a limited set of parameters explored. We find a combination of parameters that yields aggregate size distribution and maximum radius values in agreement with Voyager data for ring particles in Saturn’s outer A ring. We also find that the bonding and breaking parameters define two strength regimes in which fragmentation is dominated either by collisions or other stresses, such as tides. We conclude our study with a discussion of future applications of and refinements to our model.     

Cratering rates in the outer Solar System

This paper is a compilation by table, graph, and equation of impact cratering rates from Jupiter to Pluto. We use several independent constraints on the number of ecliptic comets. Together they imply that the impact rate on Jupiter by 1.5-km-diameter comets is currently ?(d > 1.5 km) = 0.005−0.003+0.006 per annum. Other kinds of impactors are currently unimportant on most worlds at most sizes. The size-number distribution of impactors smaller than 20 km is inferred from size-number distributions of impact craters on Europa, Ganymede, and Triton; while the size-number distribution of impacting bodies larger than 50 km is equated to the size-number distribution of Kuiper Belt objects. The gap is bridged by interpolation. It is notable that small craters on Jupiter’s moons indicate a pronounced paucity of small impactors, while small craters on Triton imply a collisional population rich in small bodies. However it is unclear whether the craters on Triton are of heliocentric or planetocentric origin. We therefore consider two cases for Saturn and beyond: a Case A in which the size-number distribution is like that inferred at Jupiter, and a Case B in which small objects obey a more nearly collisional distribution. Known craters on saturnian and uranian satellites are consistent with either case, although surface ages are much younger in Case B, especially at Saturn and Uranus. At Neptune and especially at Saturn our cratering rates are much higher than rates estimated by Shoemaker and colleagues, presumably because Shoemaker’s estimates mostly predate discovery of the Kuiper Belt. We also estimate collisional disruption rates of moons and compare these to estimates in the literature.