Dynamical evolution of Saturn's F ring dust particles

Saturn's F ring has been the subject of study due to its peculiar structure and the proximity to two satellites, named Prometheus (interior) and Pandora (exterior to the ring), which cause perturbations to the ring particles. Early results from Voyager data have proposed that the ring is populated with centimetre- and micrometre-sized particles. The Cassini spacecraft also detected a less dense part in the ring with width of 700 km. Small particles suffer the effects of solar radiation. Burns et al. showed that due to effects of one component of the solar radiation, the Poynting–Robertson drag, a ring particle will decay in the direction of the planet in a time much shorter than the age of the Solar system. In this work, we have analysed a sample of dust particles (1, 3, 5 and 10 μm) under the effects of solar radiation, the Poynting–Robertson drag and the radiation pressure components and the gravitational effects of the satellites Prometheus and Pandora. In this case, the high increase of the eccentricity of the particles leads almost all of them to collide with the outer edge of the A ring. The inclusion of the oblateness of Saturn in this system significantly changes the outcome, since the large variation of the eccentricity is reduced by the oblateness effect. As a result, there is an increase in the lifetime of the particle in the envelope region. Our results show that even the small dust particles, which are very sensitive to the effects of solar radiation, have an orbital evolution similar to larger particles located in the F ring. The fate of all particles is a collision with Prometheus or Pandora in less than 30 years. On the other hand, collisions of these particles with moonlets/clumps present in the F ring could change this scenario.     

Evidence for material between Saturn's A and F rings from the Voyager 2 photopolarimeter experiment

The region in the Saturn system between the F ring and the outer edge of the A ring is an area that appears, in images from the imaging experiment, to be virtually devoid of material except for three small satellites. Near the orbit of 1980S28, Atlas—the innermost satellite—the Voyager Photopolarimeter Stellar Occultation data show a discontinuity in count rate which marks a boundary between the tenuous materials near the outer edge of the A ring and the orbit of Atlas. The data pertaining to this region have been examined with the aid of statistics and models generated from other similar ring structures. It is concluded that the discontinuity is real, implying the existence of tenuous material of normal optical depth of 0.01 to 0.006 in this region.     

Appearance of Saturn’s F ring azimuthal channels for the anti-alignment configuration between the ring and Prometheus

In this article we explore the aspect of the F ring with respect to the anti-alignment configuration between the ring and Prometheus. We focus our attention on the shape of the F ring’s azimuthal channels which were first reported by Porco et al. (Porco, C.C., Baker, E., Barbara, J., Beurle, K., Brahic, A., Burns, J.A., Charnoz, S., Cooper, N., Dawson, D.D., Del Genio, A.D., Denk, T., Dones, L., Dyudina, U., Evans, M.W., Giese, B., Grazier, K., Helfenstein, P., Ingersoll, A.P., Jacobson, R.A., Johnson, T.V., McEwen, A., Murray, C.D., Neukum, G., Owen, W.M., Perry, J., Roatsch, T., Spitale, J., Squyres, S., Thomas, P., Tiscareno, M., Turtle, E., Vasavada, A.R., Veverka, J., Wagner, R., West, R. [2005] Science, 307, 1226-1236) and numerically explored by Murray et al. (Murray, C.D., Chavez, C., Beurle, K., Cooper, N., Evans, M.W., Burns, J.A., Porco, C.C. [2005] Nature 437, 1326-1329) who found excellent agreement between Cassini’s ISS reprojected images and their numerical model via a direct comparison. We find that for anti-alignment the channels are wider and go deeper inside the ring material. From our numerical model we find a new feature, an island in the middle of the channel. This island is made up of the particles that have been perturbed the most by Prometheus and only appears when this satellite is close to apoapsis. In addition, plots of the anti-alignment configuration for different orbital stages of Prometheus are obtained and discussed here.     

Scattering properties of a moonlet (satellite) embedded in a particle ring: Application to the rings of Saturn

The gravitational influence of moonlets or satellites on the radial structure of the rings of Saturn has been calculated numerically. A drastic change in the surface mass density is obtained even after a single scattering process of the ring particles on a moonlet (satellite). The final surface density shows a significant radial structure, which has been used to estimate the radius and the mass of moonlets or satellites embedded in rings of low optical depth (E ring, Cassini division, C ring).     

Irregular satellite capture during planetary resonance passage

The passage of Jupiter and Saturn through mutual 1:2 mean-motion resonance has recently been put forward as explanation for their relatively high eccentricities [Tsiganis, K., Gomes, R., Morbidelli, A., Levison, H.F., 2005. Nature 435, 459-461] and the origin of Jupiter's Trojans [Morbidelli, A., Levison, H.F., Tsiganis, K., Gomes, R., 2005. Nature 435, 462-465]. Additional constraints on this event based on other small-body populations would be highly desirable. Since some outer satellite orbits are known to be strongly affected by the near-resonance of Jupiter and Saturn (“the Great Inequality”; ?uk, M., Burns, J.A., 2004b. Astron. J. 128, 2518-2541), the irregular satellites are natural candidates for such a connection. In order to explore this scenario, we have integrated 9200 test particles around both Jupiter and Saturn while they went through a resonance-crossing event similar to that described by Tsiganis et al. [Tsiganis, K., Gomes, R., Morbidelli, A., Levison, H.F., 2005. Nature 435, 459-461]. The test particles were positioned on a grid in semimajor axes and inclinations, while their initial pericenters were put at just 0.01 AU from their parent planets. The goal of the experiment was to find out if short-lived bodies, spiraling into the planet due to gas drag (or alternatively on orbits crossing those of the regular satellites), could have their pericenters raised by the resonant perturbations. We found that about 3% of the particles had their pericenters raised above 0.03 AU (i.e. beyond Iapetus) at Saturn, but the same happened for only 0.1% of the particles at Jupiter. The distribution of surviving particles at Saturn has strong similarities to that of the known irregular satellites. If saturnian irregular satellites had their origin during the 1:2 resonance crossing, they present an excellent probe into the early Solar System's evolution. We also explore the applicability of this mechanism for Uranus, and find that only some of the uranian irregular satellites have orbits consistent with resonant pericenter lifting. In particular, the more distant and eccentric satellites like Sycorax could be stabilized by this process, while closer-in moons with lower eccentricity orbits like Caliban probably did not evolve by this process alone.     

The 1966 observations of the coorbiting satellites of Saturn S10 and S11

Most of the positions of faint satellite images obtained during the 1966 Saturn ring plane crossing fit the period of the coorbital satellites 1980 S1 and 1980 S3. In 1966 the satellites were separated by 137° in orbital longitude. Until the mutual interaction of the satellites is understood and applied to derive the precise orbital motion, the 1966 and 1980 observations cannot be linked.     

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.     

On the gravitational fields of Pandora and Prometheus

Utilizing topographic models of Saturn's F-ring shepherd satellites Prometheus (S16 1980S27) and Pandora (S15 1980S26), derived by Stooke (1994), and supposing that their mass density is constant, we derived basic geometrical and dynamical characteristics of the moons. They include the volume and mass, the mean radii, the tensor of inertia, and Stokes coefficients of the harmonic expansions of external gravitational potential. The best fitting ellipsoid approximations of the topography were calculated. A simple method of determining the gravitational potential on the surface of an irregular satellite is presented. Examples of equipotential surfaces of the satellites are shown     

A predator–prey model for moon-triggered clumping in Saturn’s rings

UVIS occultation data show clumping in Saturn’s F ring and at the B ring outer edge, indicating aggregation and disaggregation at these locations that are perturbed by Prometheus and by Mimas. The inferred timescales range from hours to months. Occultation profiles of the edge show wide variability, indicating perturbations by local mass aggregations. Structure near the B ring edge is seen in power spectral analysis at scales 200–2000 m. Similar structure is also seen at the strongest density waves, with significance increasing with resonance strength. For the B ring outer edge, the strongest structure is seen at longitudes 90° and 270° relative to Mimas. This indicates a direct relation between the moon and the ring clumping. We propose that the collective behavior of the ring particles resembles a predator–prey system: the mean aggregate size is the prey, which feeds the velocity dispersion; conversely, increasing dispersion breaks up the aggregates. Moons may trigger clumping by streamline crowding, which reduces the relative velocity, leading to more aggregation and more clumping. Disaggregation may follow from disruptive collisions or tidal shedding as the clumps stir the relative velocity. For realistic values of the parameters this yields a limit cycle behavior, as for the ecology of foxes and hares or the “boom-bust” economic cycle. Solving for the long-term behavior of this forced system gives a periodic response at the perturbing frequency, with a phase lag roughly consistent with the UVIS occultation measurements. We conclude that the agitation by the moons in the F ring and at the B ring outer edge drives aggregation and disaggregation in the forcing frame. This agitation of the ring material may also allow fortuitous formation of solid objects from the temporary clumps, via stochastic processes like compaction, adhesion, sintering or reorganization that drives the denser parts of the aggregate to the center or ejects the lighter elements. Any of these more persistent objects would then orbit at the Kepler rate. We would also expect the formation of clumps and some more permanent objects at the other perturbed regions in the rings… including satellite resonances, shepherded ring edges, and near embedded objects like Pan and Daphnis (where the aggregation/disaggregation cycles are forced similar to Prometheus forcing of the F ring).     

On the formation of the rings of saturn

It is shown in this paper that a satellite which revolves round a primary in a circular orbit in tied revolution and which spirals within Roche's limit must form by its disintegration a ring of ellipse-like cross-section which is more than 11 times larger than the original spherical diameter of the disintegrating body. The individual particles have elliptic orbits with small eccentricities and revolve in different planes at small inclinations to each other. By inelastic collisions of particles in differently inclined orbits the original considerable thickness of the ring is very greatly reduced.

Applied to the system of Saturn it is assumed that the Rings A and B are formed by disintegration of two different satellites. It can be shown that the satellite A had an original diameter of 1721 km and a density of 0.95 g/cm³, the satellite B a diameter of 2463 km and a density of 1.95.

Thus the hypothesis of G. P. Kuiper, that the rings of Saturn are composed of H²O-snow contaminated by silicate dust (as Jupiter III), seems to fit very well.     

On the rotational dynamics of Prometheus and Pandora

Possible rotation states of two satellites of Saturn, Prometheus (S16) and Pandora (S17), are studied by means of numerical experiments. The attitude stability of all possible modes of synchronous rotation and the motion close to these modes is analyzed by means of computation of the Lyapunov spectra of the motion. The stability analysis confirms that the rotation of Prometheus and Pandora might be chaotic, though the possibility of regular behaviour is not excluded. For the both satellites, the attitude instability zones form series of concentric belts enclosing the main synchronous resonance center in the phase space sections. A hypothesis is put forward that these belts might form “barriers” for capturing the satellites in synchronous rotation. The satellites in chaotic rotation can mimic ordinary regular synchronous behaviour: they preserve preferred orientation for long periods of time, the largest axis of satellite’s figure being directed approximately towards Saturn.     

Did Saturn's rings form during the Late Heavy Bombardment?

The origin of Saturn's massive ring system is still unknown. Two popular scenarios—the tidal splitting of passing comets and the collisional destruction of a satellite—rely on a high cometary flux in the past. In the present paper we attempt to quantify the cometary flux during the Late Heavy Bombardment (LHB) to assess the likelihood of both scenarios. Our analysis relies on the so-called “Nice model” of the origin of the LHB [Tsiganis, K., Gomes, R., Morbidelli, A., Levison, H.F., 2005. Nature 435, 459-461; Morbidelli, A., Levison, H.H., Tsiganis, K., Gomes, R., 2005. Nature 435, 462-465; Gomes, R., Levison, H.F., Tsiganis, K., Morbidelli, A., 2005. Nature 435, 466-469] and on the size distribution of the primordial trans-neptunian planetesimals constrained in [Charnoz, S., Morbidelli, A., 2007. Icarus 188, 468-480]. We find that the cometary flux on Saturn during the LHB was so high that both scenarios for the formation of Saturn rings are viable in principle. However, a more detailed study shows that the comet tidal disruption scenario implies that all four giant planets should have comparable ring systems whereas the destroyed satellite scenario would work only for Saturn, and perhaps Jupiter. This is because in Saturn's system, the synchronous orbit is interior to the Roche Limit, which is a necessary condition for maintaining a satellite in the Roche Zone up to the time of the LHB. We also discuss the apparent elimination of silicates from the ring parent body implied by the purity of the ice in Saturn's rings. The LHB has also strong implications for the survival of the saturnian satellites: all satellites smaller than Mimas would have been destroyed during the LHB, whereas Enceladus would have had from 40% to 70% chance of survival depending on the disruption model. In conclusion, these results suggest that the LHB is the “sweet moment” for the formation of a massive ring system around Saturn.     

Chaotic motions of prometheus and pandora

Recent HST images of the saturnian satellites Prometheus and Pandora show that their longitudes deviate from predictions of ephemerides based on Voyager images. Currently Prometheus is lagging and Pandora leading these predictions by somewhat more than 20°. We show that these discrepancies are fully accounted for by gravitational interactions between the two satellites. These peak every 24.8 days at conjunctions and excite chaotic perturbations. The Lyapunov exponent for the Prometheus-Pandora system is of order 0.3 year⁻¹ for satellite masses based on a nominal density of 0.63 g cm⁻³. Interactions are strongest when the orbits come closest together. This happens at intervals of 6.2 years when their apses are antialigned. In this context, we note the sudden changes of opposite signs in the mean motions of Prometheus and Pandora at the end of 2000 occurred around the time their apsidal lines were antialigned.     

Saturn’s wayward shepherds: the peregrinations of Prometheus and Pandora

Saturn’s narrow F ring is flanked by two nearby small satellites, Prometheus and Pandora, discovered in Voyager images taken in 1980 and 1981 (Synnott et al., 1983, Icarus 53, 156-158). Observations with the Hubble Space Telescope (HST) during the ring plane crossings (RPX) of 1995 led to the unexpected finding that Prometheus was ∼19° behind its predicted orbital longitude, based on the Synnott et al. (1983) Voyager ephemeris (Bosh and Rivkin, 1996 Science 272, 518-521; Nicholson et al., 1996, Science 272, 509-515). Whereas Pandora was at its predicted location in August 1995, McGhee (2000, Ph.D. thesis, Cornell University) found from the May and November 1995 RPX data that Pandora also deviates from the Synnott et al. (1983) Voyager ephemeris. Using archival HST data from 1994, previously unexamined RPX images, and a large series of targeted WFPC2 observations between 1996 and 2002, we have determined highly accurate sky-plane positions for Prometheus, Pandora, and nine other satellites found in our images. We compare the Prometheus and Pandora measurements to the predictions of substantially revised and improved ephemerides for the two satellites based on an extensive analysis of a large set of Voyager images (Murray et al., 2000, Bull. Am. Astron. Soc. 32, 1090; Evans, 2001 Ph.D. thesis, Queen Mary College). From December 1994 to December 2000, Prometheus’ orbital longitude lag was changing by −0.71° year⁻¹ relative to the new Voyager ephemeris. In contrast, Pandora is ahead of the revised Voyager prediction. From 1994 to 2000, its longitude offset changed by +0.44° year⁻¹, showing in addition an ∼585 day oscillatory component with amplitude Δλ_CR0 = 0.65 ± 0.07° whose phase matches the expected perturbation due to the nearby 3:2 corotation resonance with Mimas, modulated by the 71-year libration in the longitude of Mimas due to its 4:2 resonance with Tethys. We determine orbital elements for freely precessing equatorial orbits from fits to the 1994-2000 HST observations, from which we conclude that Prometheus’ semimajor axis was 0.31 km larger, and Pandora’s was 0.20 km smaller, than during the Voyager epoch. Subsequent observations in 2001-2002 reveal a new twist in the meanderings of these satellites: Prometheus’ mean motion changed suddenly by an additional −0.77° year⁻¹, equivalent to a further increase in semimajor axis of 0.33 km, at the same time that Pandora’s mean motion changed by +0.92° year⁻¹, corresponding to a change of −0.42 km in its semimajor axis. There is an apparent anticorrelation of the motions of these two moons seen in the 2001-2002 observations, as well as over the 20-year interval since the Voyager epoch. This suggests a common origin for their wanderings, perhaps through direct exchange of energy between the satellites as the result of resonances, possibly involving the F ring.     

E ring dust sources: Implications from Cassini's dust measurements

The Enceladus flybys of the Cassini spacecraft are changing our understanding of the origin and sustainment of Saturn's E ring. Surprisingly, beyond the widely accepted dust production caused by micrometeoroid impacts onto the atmosphereless satellites (the impactor-ejecta process), geophysical activities have been detected at the south pole of Enceladus, providing an additional, efficient dust source. The dust detector data obtained during the flyby E11 are used to identify the amount of dust produced in the impactor-ejecta process and to improve related modeling [Spahn, F., Schmidt, J., Albers, N., Hörning, M., Makuch, M., Seiß, M., Kempf, S., Srama, R., Dikarev, V.V., Helfert, S., Moragas-Klostermeyer, G., Krivov, A.V., Sremčević, M., Tuzzolino, A., Economou, T., Grün, E., 2006. Cassini dust measurements at Enceladus: implications for Saturn's E ring. Science, in press]. With this, we estimate the impact-generated dust contributions of the other E ring satellites and find significant differences in the dust ejection efficiency by two projectile families—the E ring particles (ERPs) and the interplanetary dust particles (IDPs). Together with the Enceladus south-pole source, the ERP impacts play a crucial role in the inner region, whereas the IDP impacts dominate the particle production in the outer E ring, possibly accounting for its large radial extent. Our results can be verified in future Cassini flybys of the E ring satellites. In this way poorly known parameters of the dust particle production in hypervelocity impacts can be constrained by comparison of the data and theory.     

The shapes and surface features of Prometheus and Pandora

Topographic models of Saturn's F-Ring shepherd satellites Prometheus and Pandora were derived from the shapes of limbs and terminators in Voyager images, modified locally to accommodate large craters and ridges. The models are presented here in tabular and graphic form, including the first published maps of the satellites. The shape of Prometheus is approximated by a triaxial ellipsoid with axes of 145, 85 and 60 km. The volume is estimated to be 3.9 ± 1.0 × 10⁵ km³, significantly smaller than previous estimates. A system of prominent ridges and valleys cross the north polar region. Prometheus appears to be less heavily cratered than the other small satellites near the edge of the rings, though this may be an artifact of the low resolution of available images. Pandora is approximated by a triaxial ellipsoid with axes of 114, 84 and 62 km. The volume is estimated to be 3.1 ± 1.0 × 10⁵ km³. Its surface appears to be very heavily cratered.     

Adaptive optics observations of small moons of saturn

We report near-infrared observations of Prometheus and Janus taken on 9 and 13 November 2000 (UT) with the Palomar Adaptive Optics System on the 5-m Hale telescope at Palomar Observatory. Dione, Rhea, and Tethys were used as guide “stars” for the adaptive optics system, and, though they were outside the isoplanatic patch of the region of interest, they allowed significant correction of the atmospheric turbulence.Prometheus, which is usually impossible to observe from the ground due to scattered light from the A ring, was imaged at superior conjunction with Saturn. At the time of the observations, the rings of Saturn were blocked by the southern limb of the planet while the moon passed just 0.35″ below the planet’s south pole. A K filter, in a methane absorption band, was used to suppress light from the disk of the planet, and template subtraction removed much of the scattered light from the A ring. Prometheus was found to be 21.9 ± 0.1° of mean longitude behind the position predicted by Voyager-era ephemerides, consistent with the orbital lag discovered during the 1995 ring-plane crossing.     

Thermal observations of Saturn's main rings by Cassini CIRS: Phase, emission and solar elevation dependence

Two and a half years after Saturn orbit insertion (SOI) the Cassini composite infrared spectrometer (CIRS) has acquired an extensive set of thermal measurements (including physical temperature and filling factor) of Saturn's main rings for a number of different viewing geometries, most of which are not available from Earth. Thermal mapping of both the lit and unlit faces of the rings is being performed within a multidimensional observation space that includes solar phase angle, spacecraft elevation and solar elevation. Comprehensive thermal mapping is a key requirement for detailed modeling of ring thermal properties.To first order, the largest temperature changes on the lit face of the rings are driven by variations in phase angle while differences in temperature with changing spacecraft elevation are a secondary effect. Ring temperatures decrease with increasing phase angle suggesting a population of slowly rotating ring particles [Spilker, L.J., Pilorz, S.H., Wallis, B.D., Pearl, J.C., Cuzzi, J.N., Brooks, S.M., Altobelli, N., Edgington, S.G., Showalter, M., Michael Flasar, F., Ferrari, C., Leyrat, C. 2006. Cassini thermal observations of Saturn's main rings: implications for particle rotation and vertical mixing. Planet. Space Sci. 54, 1167-1176, doi: 10.1016/j.pss.2006.05.033]. Both lit A and B rings show that temperature decreases with decreasing rings solar elevation while temperature changes in the C ring and Cassini Division are more muted. Variations in the geometrical filling factor, β, are primarily driven by changes in spacecraft elevation. For the optically thinnest region of the C ring, β variations are found to be nearly exclusively determined by spacecraft elevation. Both a multilayer and a monolayer model provide an excellent fit to the data in this region. In both cases, a ring infrared emissivity >0.9 is required, together with a random and homogeneous distribution of the particles. The interparticle shadowing function required for the monolayer model is very well constrained by our data and matches experimental measurements performed by Froidevaux [1981a. Saturn's rings: infrared brightness variation with solar elevation. Icarus 46, 4-17].     

Orbits and masses of Saturn's coorbital and F-ring shepherding satellites

We have obtained numerically integrated orbits for Saturn's coorbital satellites, Janus and Epimetheus, together with Saturn's F-ring shepherding satellites, Prometheus and Pandora. The orbits are fit to astrometric observations acquired with the Hubble Space Telescope and from Earth-based observatories and to imaging data acquired from the Voyager spacecraft. The observations cover the 38 year period from the 1966 Saturn ring plane crossing to the spring of 2004. In the process of determining the orbits we have found masses for all four satellites. The densities derived from the masses for Janus, Epimetheus, Prometheus, and Pandora in units of g cm⁻³ are , , , and , respectively.     

Dynamical evolution of the Prometheus–Pandora system

The system of Saturn's inner satellites is saturated with many resonances. Its structure should be strongly affected by tidal forces driving the satellites through several orbit–orbit resonances. The evolution of these satellites is investigated using analytic and numerical methods. We show that the pair of satellites Prometheus and Pandora has a particularly short lifetime (<20 Myr) if the orbits of the satellites converge without capture into a resonance. The capture of Pandora into a resonance with Prometheus increases the lifetime of the couple by a few tens of Myr. However, resonances of the system are not well separated, and capture results in a chaotic motion. Secondary resonances also disrupt the resonant configurations. In all cases, the converging orbits of these two satellites result in a close encounter. The implications for the origin of Saturn's rings are discussed.