Normal forms for the epicyclic approximations of the perturbed Kepler problem

We compute the normal forms for the Hamiltonian leading to the epicyclic approximations of the (perturbed) Kepler problem in the plane. The Hamiltonian setting corresponds to the dynamics in the Hill synodic system where, by means of the tidal expansion of the potential, the equations of motion take the form of perturbed harmonic oscillators in a rotating frame. In the unperturbed, purely Keplerian case, the post-epicyclic solutions produced with the normal form coincide with those obtained from the expansion of the solution of the Kepler equation. In all cases where the perturbed problem can be cast in autonomous form, the solution is easily obtained as a perturbation series. The generalization to the spatial problem and/or the non-autonomous case is straightforward.     

Ultraviolet observations of Phoebe from the Cassini UVIS

Observations of Saturn's distant moon Phoebe were made at far-ultraviolet (FUV) (1100-1900 Å) and extreme-ultraviolet (EUV) (600-1100 Å) wavelengths by the Cassini Ultraviolet Imaging Spectrograph (UVIS) during the Cassini spacecraft flyby on June 11, 2004. These are the first UV spectra of Phoebe and the first detection of water ice on a Solar System surface using FUV wavelengths. The characteristics of water ice in the FUV are presented, and Hapke models are used to interpret the spectra in terms of composition and grain size; the use of both areal and intimate mixing models is explored. Non-ice species used in these models include carbon, ice tholin, Triton tholin, poly-HCN and kerogen. Satisfactory disk-integrated fits are obtained for intimate mixtures of ∼10% H₂O plus a non-ice species. Spatially resolved regions of higher (∼20%) and lower (∼5%) H₂O ice concentrations are also detected. Phoebe does not display any evidence of volatile activity. Upper limits on atomic oxygen and carbon are 5×¹⁰¹¹ and 2×¹⁰¹² atoms/cm², respectively, for solar photon scattering. The UVIS detection of water ice on Phoebe, and the ice amounts detected, are consistent with IR measurements and contribute to the evidence for a Phoebe origin in the outer Solar System rather than in the main asteroid belt.     

The albedo dichotomy of Iapetus measured at UV wavelengths

The dramatic hemispheric dichotomy in albedo displayed by Saturn's moon Iapetus has intrigued astronomers for centuries. Here we report on far-ultraviolet observations of Iapetus' bright and dark terrains from Cassini. We compare the reflectance spectra of Iapetus's dark terrain, Hyperion and Phoebe and find that both Phoebe and Hyperion are richer in water ice than Iapetus' dark terrain. Spectra of the lowest latitudes of the dark terrain display the diagnostic water ice absorption feature; water ice amounts increase within the dark material away from the apex (at 90° W longitude, the center of the dark leading hemisphere), consistent with thermal segregation of water ice. The water ice in the darkest, warmest low latitude regions is not expected to be stable and may be a sign of ongoing or recent emplacement of the dark material from an exogenic source.     

Thermal convection in ice-I shells of Titan and Enceladus

Cassini-Huygens observations have shown that Titan and Enceladus are geologically active icy satellites. Mitri and Showman [Mitri, G., Showman, A.P., 2005. Icarus 177, 447-460] and McKinnon [McKinnon, W.B., 2006. Icarus 183, 435-450] investigated the dynamics of an ice shell overlying a pure liquid-water ocean and showed that transitions from a conductive state to a convective state have major implications for the surface tectonics. We extend this analysis to the case of ice shells overlying ammonia-water oceans. We explore the thermal state of Titan and Enceladus ice-I shells, and also we investigate the consequences of the ice-I shell conductive-convective switch for the geology. We show that thermal convection can occur, under a range of conditions, in the ice-I shells of Titan and Enceladus. Because the Rayleigh number Ra scales with δ³/ηb, where δ is the thickness of the ice shell and ηb is the viscosity at the base of the ice-I shell, and because ammonia in the liquid layer (if any) strongly depresses the melting temperature of the water ice, Ra equals its critical value for two ice-I shell thicknesses: for relatively thin ice shell with warm, low-viscosity base (Onset I) and for thick ice shell with cold, high-viscosity base (Onset II). At Onset I, for a range of heat fluxes, two equilibrium states—corresponding to a thin, conductive shell and a thick, convective shell—exist for a given heat flux. Switches between these states can cause large, rapid changes in the ice-shell thickness. For Enceladus, we demonstrate that an Onset I transition can produce tectonic stress of ∼500 bars and fractures of several tens of km depth. At Onset II, in contrast, we demonstrate that zero equilibrium states exist for a range of heat fluxes. For a mean heat flux within this range, the satellite experiences oscillations in surface heat flux and satellite volume with periods of ∼50-800 Myr even when the interior heat production is constant or monotonically declining in time; these oscillations in the thermal state of the ice-I shell would cause repeated episodes of extensional and compressional tectonism.     

Energetic electron signatures of Saturn's smaller moons: Evidence of an arc of material at Methone

We present several energetic charged particle microsignatures of two Lagrange moons, Telesto and Helene, measured by the MIMI/LEMMS instrument. These small moons absorb charged particles but their effects are usually obscured by Tethys and Dione, the two larger saturnian satellites that occupy the same orbits. The scales and structures of these microsignatures are consistent with standard models for electron absorption from asteroid-sized moons in Saturn's radiation belts. In the context of these observations, we also examine the possibility that the 3 km Satellite Methone is responsible for two electron microsignatures detected by Cassini close to this moon's orbit. We infer that a previously undetected arc of material exists at Methone's orbit (R/2006 S5), we speculate how such a structure could form and what its physical characteristics and location could be. The origin of this arc could be linked to a possible presence of a faint ring produced by micrometeoroid impacts on Methone's surface, to E-ring dust clump formation at that distance or to temporary dust clouds produced by enceladian activity that spiral inwards under the effect of non-gravitational forces.     

The topography of Iapetus' leading side

We have used Cassini stereo images to study the topography of Iapetus' leading side. A terrain model derived at resolutions of 4-8 km reveals that Iapetus has substantial topography with heights in the range of −10 km to +13 km, much more than observed on the other middle-sized satellites of Saturn so far. Most of the topography is older than 4 Ga [Neukum, G., Wagner, R., Denk, T., Porco, C.C., 2005. Lunar Planet. Sci. XXXVI. Abstract 2034] which implies that Iapetus must have had a thick lithosphere early in its history to support this topography. Models of lithospheric deflection by topographic loads provide an estimate of the required elastic thickness in the range of 50-100 km. Iapetus' prominent equatorial ridge [Porco, C.C., and 34 colleagues, 2005. Science 307, 1237-1242] reaches widths of 70 km and heights of up to 13 km from their base within the modeled area. The morphology of the ridge suggests an endogenous origin rather than a formation by collisional accretion of a ring remnant [Ip, W.-H., 2006. Geophys. Res. Lett. 33, doi:10.1029/2005GL025386. L16203]. The transition from simple to complex central peak craters on Iapetus occurs at diameters of 11±3 km. The central peaks have pronounced conical shapes with flanking slopes of typically 11° and heights that can rise above the surrounding plains. Crater depths seem to be systematically lower on Iapetus than on similarly sized Rhea, which if true, may be related to more pronounced crater-wall slumping (which widens the craters) on Iapetus than on Rhea. There are seven large impact basins with complex morphologies including central peak massifs and terraced walls, the largest one reaches 800 km in diameter and has rim topography of up to 10 km. Generally, no rings are observed with the basins consistent with a thick lithosphere but still thin enough to allow for viscous relaxation of the basin floors, which is inferred from crater depth-to-diameter measurements. In particular, a 400-km basin shows up-domed floor topography which is suggestive of viscous relaxation. A model of complex crater formation with a viscoplastic (Bingham) rheology [Melosh, H.J., 1989. Impact Cratering. Oxford Univ. Press, New York] of the impact-shocked icy material provides an estimate of the effective cohesion/viscosity at . The local distribution of bright and dark material on the surface of Iapetus is largely controlled by topography and consistent with the dark material being a sublimation lag deposit originating from a bright icy substrate mixed with the dark components, but frost deposits are possible as well.     

Distribution of icy particles across Enceladus' surface as derived from Cassini-VIMS measurements

The surface of Enceladus consists almost completely of water ice. As the band depths of water ice absorptions are sensitive to the size of particles, absorptions can be used to map variations of icy particles across the surface. The Visual and Infrared Mapping Spectrometer (VIMS) observed Enceladus with a high spatial resolution during three Cassini flybys in 2005 (orbits EN 003, EN 004 and EN 011). Based on these data we measured the band depths of water ice absorptions at 1.04, 1.25, 1.5, and 2 μm. These band depths were compared to water ice models that represent theoretically calculated reflectance spectra for a range of particle diameters between 2 μm and 1 mm. The agreement between the experimental (VIMS) and model values supports the assumption that pure water ice characterizes the surface of Enceladus and therefore that variations in band depth correspond to variations in water ice particle diameters. Our measurements show that the particle diameter of water ice increases toward younger tectonically altered surface units with the largest particles exposed in relatively “fresh” surface material. The smallest particles were generally found in old densely cratered terrains. The largest particles (∼0.2 mm) are concentrated in the so called “tiger stripes” at the south pole. In general, the particle diameters are strongly correlated with geologic features and surface ages, indicating a stratigraphic evolution of the surface that is caused by cryovolcanic resurfacing and impact gardening.     

Dunes on Titan observed by Cassini Radar

Thousands of longitudinal dunes have recently been discovered by the Titan Radar Mapper on the surface of Titan. These are found mainly within ±30° of the equator in optically-, near-infrared-, and radar-dark regions, indicating a strong proportion of organics, and cover well over 5% of Titan's surface. Their longitudinal duneform, interactions with topography, and correlation with other aeolian forms indicate a single, dominant wind direction aligned with the dune axis plus lesser, off-axis or seasonally alternating winds. Global compilations of dune orientations reveal the mean wind direction is dominantly eastwards, with regional and local variations where winds are diverted around topographically high features, such as mountain blocks or broad landforms. Global winds may carry sediments from high latitude regions to equatorial regions, where relatively drier conditions prevail, and the particles are reworked into dunes, perhaps on timescales of thousands to tens of thousands of years. On Titan, adequate sediment supply, sufficient wind, and the absence of sediment carriage and trapping by fluids are the dominant factors in the presence of dunes.     

Geysers of Enceladus: Quantitative analysis of qualitative models

Aspects of two qualitative models of Enceladus’ dust plume—the so-called “Cold Faithful” [Porco, C.C., et al., 2006. Cassini observes the active south pole of Enceladus. Science 311, 1393-1401; Ingersoll, A.P., et al., 2006. Models of the Enceladus plumes. In: Bulletin of the American Astronomical Society, vol. 38, p. 508] and “Frigid Faithful” [Kieffer, S.W., et al., 2006. A clathrate reservoir hypothesis for Enceladus’ south polar plume. Science 314, 1764; Gioia, G., et al., 2007. Unified model of tectonics and heat transport in a Frigid Enceladus. Proc. Natl. Acad. Sci. 104, 13578-13591] models—are analyzed quantitatively. The former model assumes an explosive boiling of subsurface liquid water, when pressure exerted by the ice crust is suddenly released due to an opening crack. In the latter model the existence of a deep shell of clathrates below Enceladus’ south pole is conjectured; clathrates can decompose explosively when exposed to vacuum through a fracture in the outer icy shell. For the Cold Faithful model we estimate the maximal velocity of ice grains, originating from water splashing in explosive boiling. We find that for water near the triple point this velocity is far too small to explain the observed plume properties. For the Frigid Faithful model we consider the problem of momentum transfer from gas to ice particles. It arises since any change in the direction of the gas flow in the cracks of the shell requires re-acceleration of the entrained grains. While this effect may explain the observed speed difference of gas and grains if the gas evaporates from triple point temperature (273.15 K) [Schmidt, J., et al., 2008. Formation of Enceladus dust plume. Nature 451, 685], the low temperatures of the Frigid Faithful model imply a too dilute vapor to support the observed high particle fluxes in Enceladus’ plume.     

Numerical simulations of type III planetary migration – II. Inward migration of massive planets

We present a numerical study of rapid, so-called type III migration for Jupiter-sized planets embedded in a protoplanetary disc. We limit ourselves to the case of inward migration, and study in detail its evolution and physics, concentrating on the structure of the corotation and circumplanetary regions, and processes for stopping migration. We also consider the dependence of the migration behaviour on several key parameters. We perform this study using the results of global, two-dimensional hydrodynamical simulations with adaptive mesh refinement. The initial conditions are chosen to satisfy the condition for rapid inward migration. We find that type III migration can be divided into two regimes, fast and slow. The structure of the co-orbital region, mass accumulation rate and migration behaviour differ between these two regimes. All our simulations show a transition from the fast to the slow regime, ending type III migration well before reaching the star. The stopping radius is found to be larger for more massive planets and less massive discs. A sharp density drop is also found to be an efficient stopping mechanism. In the fast migration regime the migration rate and induced eccentricity are lower for less massive discs, but almost do not depend on planet mass. Eccentricity is damped on the migration time-scale.