On the damping of the bending waves in Saturn’s ring

We study numerically the motion of a single particle in the bending wave of finite thickness in Saturn’s ring. We include the forcing due to the planet, a moon, the coriolis force and the self gravity of the ring. In particular, we compute the variation of the velocity arising due to the variation of the amplitude and the phase of the epicyclic motion across the local vertical height of the ring. We suggest that the dissipation of energy due to the collision of ring particles in this shear layer damps out the bending wave of Saturn’s ring at the 5:3 vertical resonance of Mimas within a distance of 150 km from the site of its launching as is observed in Voyager data.     

Constraints on the C ring parameters of Saturn at the Titan −1:0 resonance

A one-armed spiral bending wave in Saturn's rings excited by Titan's −1:0 inner vertical resonance is one of the most prominent oscillatory features observed by Voyager 1 . We study detailed dynamics of the particles inside the ring, and show that one of the main causes of the complete dissipation of the bending wave within a distance of ∼85 km from the resonance site could be as a result of the presence of a strong shear caused by radial velocity variation along the vertical direction. Assuming this to be the only source, Voyager data would suggest that if the surface density of matter is around 0.45 g cm⁻² and the amplitude of the bending wave is around 1200 m, then the upper limit of total vertical thickness of the C ring near this resonance is around 40 m.     

The magnitude and color of the Saturn system

Brightness measurements made during 1963-1965 and 1991-2009 are used in constructing models of the brightness of the Saturn system in the Johnson B, V, R and I system. The models cover nearly the full range of phase angles and ring opening angles visible from the Earth and are believed to be accurate to 0.03-0.05 magnitudes. A U-filter model is also selected which covers ring opening angles of between 4° and 14°. The model is the first such one that treats the light from the rings as a function of the saturnicentric latitude from the Earth and Sun in a way that is consistent with observations and theoretical considerations. Six conclusions of this work are: (1) the Saturn system brightens as the solar phase angle decreases, (2) the Saturn system has an opposition surge, (3) the opposition surge increases as the ring opening angle increases, (4) the solar phase angle coefficient increases as the ring opening angle increases, (5) the B-V, V-R and R-I color indexes change by up to 0.2 magnitudes as Saturn orbits the Sun and (6) the V-filter model in this report is a better fit to the 1963-2009 data than the one proposed by Harris (Harris, D.L. [1961]. In: Kuiper, G.P., Middlehurst, B.M. (Eds), Planets and Satellites. Univ. of Chicago, Chicago, IL, pp. 272-342].     

The E ring in the vicinity of Enceladus: I. Spatial distribution and properties of the ring particles

Saturn's diffuse E ring is the largest ring of the Solar System and extends from about (Saturn radius RS=60,330 km) to at least encompassing the icy moons Mimas, Enceladus, Tethys, Dione, and Rhea. After Cassini's insertion into her saturnian orbit in July 2004, the spacecraft performed a number of equatorial as well as steep traversals through the E ring inside the orbit of the icy moon Dione. Here, we report about dust impact data we obtained during 2 shallow and 6 steep crossings of the orbit of the dominant ring source—the ice moon Enceladus. Based on impact data of grains exceeding 0.9 μm we conclude that Enceladus feeds a torus populated by grains of at least this size along its orbit. The vertical ring structure at agrees well with a Gaussian with a full-width-half-maximum (FWHM) of ∼4200 km. We show that the FWHM at is due to three-body interactions of dust grains ejected by Enceladus' recently discovered ice volcanoes with the moon during their first orbit. We find that particles with initial speeds between 225 and 235 m s⁻¹ relative to the moon's surface dominate the vertical distribution of dust. Particles with initial velocities exceeding the moon's escape speed of 207 m s⁻¹ but slower than 225 m s⁻¹ re-collide with Enceladus and do not contribute to the ring particle population. We find the peak number density to range between 16×¹⁰⁻² m⁻³ and 21×¹⁰⁻² m⁻³ for grains larger 0.9 μm, and 2.1×¹⁰⁻² m⁻³ and 7.6×¹⁰⁻² m⁻³ for grains larger than 1.6 μm. Our data imply that the densest point is displaced outwards by at least with respect of the Enceladus orbit. This finding provides direct evidence for plume particles dragged outwards by the ambient plasma. The differential size distribution for grains >0.9 μm is described best by a power law with slopes between 4 and 5. We also obtained dust data during ring plane crossings in the vicinity of the orbits of Mimas and Tethys. The vertical distribution of grains >0.8 μm at Mimas orbit is also well described by Gaussian with a FWHM of ∼5400 km and displaced southwards by ∼1200 km with respect to the geometrical equator. The vertical distribution of ring particles in the vicinity of Tethys, however, does not match a Gaussian. We use the FWHM values obtained from the vertical crossings to establish a 2-dimensional model for the ring particle distribution which matches our observations during vertical and equatorial traversals through the E ring.     

Astrometry and dynamics of Anthe (S/2007 S 4), a new satellite of Saturn

We describe the astrometry and dynamics of Anthe (S/2007 S 4), a new satellite of Saturn discovered in images obtained using the Imaging Science Subsystem (ISS) of the Cassini spacecraft. Included are details of 63 observations, of which 28 were obtained with Cassini's narrow-angle camera (NAC) and 35 using its wide-angle camera (WAC), covering an observation time-span of approximately 3 years. We estimate the diameter of Anthe to be ∼1.8 km. Orbit modeling based on a numerical integration of the full equations of motion fitted to the observations show that Anthe is in a first-order 11:10 mean motion resonance with Mimas. Two resonant arguments are librating: ?₁=11λ^′−10λ−? and ?₂=11λ^′−10λ−?^′−Ω^′+Ω, where λ, ? and Ω refer to the mean longitude, longitude of pericenter and longitude of ascending node of Mimas and Anthe, with the primed quantities corresponding to Anthe. These resonances cause periodic variations in the orbital elements. The semi-major axis varies by ±26 km over a 913-day period. Anthe is also close to a second-order eccentricity-type mean motion resonant relationship of the form 77:75 with Methone. Since Methone is also in a first-order resonance with Mimas [Spitale, J.N., Jacobson, R.A., Porco, C.C., Owen, W.M., 2006. Astron. J. 132, 692-710], an additional indirect perturbation exists between Methone and Anthe via Mimas. Neither effect is detectable in the orbit fitting and the short-term dynamical evolution of Anthe is dominated by the Mimas-Anthe resonances alone. The expected modulation effect from the Mimas-Tethys 4:2 inclination resonance is also insignificant over this time period. By including Cassini ISS observations of Mimas in the numerical integration fit, we estimate the GM of Mimas to be , consistent with Jacobson et al. [Jacobson, R.A., Spitale, J., Porco, C.C., Owen, W.M., 2006. Astron. J. 132, 711-713].     

The vertical structure of the F ring of Saturn from ring-plane crossings

We present a photometric model of the rings of Saturn which includes the main rings and an F ring, inclined to the main rings, with a Gaussian vertical profile of optical depth. This model reproduces the asymmetry in brightness between the east and west ansae of the rings of Saturn that was observed by the Hubble Space Telescope (HST) within a few hours after the Earth ring-plane crossing (RPX) of 10 August 1995. The model shows that during this observation the inclined F ring unevenly blocked the east and west ansae of the main rings. The brightness asymmetry produced by the model is highly sensitive to the vertical thickness and radial optical depth of the F ring. The F-ring model that best matches the observations has a vertical full width at half maximum of 13 ± 7 km and an equivalent depth of 10 ± 4 km. The model also reproduces the shape of the HST profiles of ring brightness vs. distance from Saturn, both before and after the time of ring-plane crossing. Smaller asymmetries observed before the RPX, when the Earth was on the dark side of the rings, cannot be explained by blocking of the main rings by the F ring or vice versa and are probably instead due to the intrinsic longitudinal variation exhibited by the F ring.     

Compositional mapping of Saturn's satellite Dione with Cassini VIMS and implications of dark material in the Saturn system

Cassini VIMS has obtained spatially resolved imaging spectroscopy data on numerous satellites of Saturn. A very close fly-by of Dione provided key information for solving the riddle of the origin of the dark material in the Saturn system. The Dione VIMS data show a pattern of bombardment of fine, sub-0.5-μm diameter particles impacting the satellite from the trailing side direction. Multiple lines of evidence point to an external origin for the dark material on Dione, including the global spatial pattern of dark material, local patterns including crater and cliff walls shielding implantation on slopes facing away from the trailing side, exposing clean ice, and slopes facing the trailing direction which show higher abundances of dark material. Multiple spectral features of the dark material match those seen on Phoebe, Iapetus, Hyperion, Epimetheus and the F-ring, implying the material has a common composition throughout the Saturn system. However, the exact composition of the dark material remains a mystery, except that bound water and, tentatively, ammonia are detected, and there is evidence both for and against cyanide compounds. Exact identification of composition requires additional laboratory work. A blue scattering peak with a strong UV-visible absorption is observed in spectra of all satellites which contain dark material, and the cause is Rayleigh scattering, again pointing to a common origin. The Rayleigh scattering effect is confirmed with laboratory experiments using ice and 0.2-μm diameter carbon grains when the carbon abundance is less than about 2% by weight. Rayleigh scattering in solids is also confirmed in naturally occurring terrestrial rocks, and in previously published reflectance studies. The spatial pattern, Rayleigh scattering effect, and spectral properties argue that the dark material is only a thin coating on Dione's surface, and by extension is only a thin coating on Phoebe, Hyperion, and Iapetus, although the dark material abundance appears higher on Iapetus, and may be locally thick. As previously concluded for Phoebe, the dark material appears to be external to the Saturn system and may be cometary in origin. We also report a possible detection of material around Dione which may indicate Dione is active and contributes material to the E-ring, but this observation must be confirmed.     

The shape and dynamics of a heliotropic dusty ringlet in the Cassini Division

The so-called “Charming Ringlet” (R/2006 S3) is a low-optical-depth, dusty ringlet located in the Laplace gap in the Cassini Division, roughly 119,940 km from Saturn center. This ringlet is particularly interesting because its radial position varies systematically with longitude relative to the Sun in such a way that the ringlet’s geometric center appears to be displaced away from Saturn’s center in a direction roughly toward the Sun. In other words, the ringlet is always found at greater distances from the planet’s center at longitudes near the sub-solar longitude than it is at longitudes near Saturn’s shadow. This “heliotropic” behavior indicates that the dynamics of the particles in this ring are being influenced by solar radiation pressure. In order to investigate this phenomenon, which has been predicted theoretically but not observed this clearly, we analyze multiple image sequences of this ringlet obtained by the Cassini spacecraft in order to constrain its shape and orientation. These data can be fit reasonably well with a model in which both the eccentricity and the inclination of the ringlet have “forced” components (that maintain a fixed orientation relative to the Sun) as well as “free” components (that drift around the planet at steady rates determined by Saturn’s oblateness). The best-fit value for the eccentricity forced by the Sun is 0.000142 ± 0.000004, assuming this component of the eccentricity has its pericenter perfectly anti-aligned with the Sun. These data also place an upper limit on a forced inclination of 0.0007°. Assuming the forced inclination is zero and the forced eccentricity vector is aligned with the anti-solar direction, the best-fit values for the free components of the eccentricity and inclination are 0.000066 ± 0.000003 and 0.0014 ± 0.0001°, respectively. While the magnitude of the forced eccentricity is roughly consistent with theoretical expectations for radiation pressure acting on 10-to-100-μm-wide icy grains, the existence of significant free eccentricities and inclinations poses a significant challenge for models of low-optical-depth dusty rings.     

Moonlet Collisions and the Effects of Tidally Modified Accretion in Saturn's F Ring

We both test and offer an alternative to a meteoroid bombardment model (M. R. Showalter 1998, Science282, 1099-1102) and suggest that anomalous localized brightenings in the F ring observed by Voyager result from disruptive collisions involving poorly consolidated moonlets, or “rubble piles.” This model can also explain the transient events observed during ring plane crossing. We have developed an evolutionary model that considers both the competing effects of accretion and disruption at the location of the F ring. Our numerical model is a Markov process where probabilities of mass transfer between the states of the system form a “transition matrix.” Successive multiplications of this matrix by the state vector generate expectation values of the distribution after each time step as the system approaches quasi-equilibrium. Competing effects of accretion and disruption in the F ring are found to lead to a bimodal distribution of ring particle sizes. In fact, our simulation predicts the presence of a belt of kilometer-sized moonlets in the F ring. These moonlets may continually disrupt one another and re-accrete on short time scales. We also agree with J. N. Cuzzi and J. A. Burns (1988, Icarus74, 284-324), who suggest that the classical F ring itself may be the consequence of a relatively recent collision between two of the largest of these yet unseen objects. Cassini observations can confirm the existence of the moonlet belt by directly observing these objects or the waves they create in the rings.     

A new perspective on the irregular satellites of Saturn – II. Dynamical and physical origin

The origin of the irregular satellites of the giant planets has been long debated since their discovery. Their dynamical features argue against an in situ formation suggesting that they are captured bodies, yet there is no global consensus on the physical process at the basis of their capture. In this paper, we explore the collisional capture scenario, where the actual satellites originated from impacts occurred within Saturn's influence sphere. By modelling the inverse capture problem, we estimated the families of orbits of the possible parent bodies and the specific impulse needed for their capture. The orbits of these putative parent bodies are compared to those of the minor bodies of the outer Solar system to outline their possible region of formation. Finally, we tested the collisional capture hypothesis on Phoebe by taking advantage of the data supplied by Cassini on its major crater, Jason. Our results presented a realistic range of solutions matching the observational and dynamical data.     

The composition of Saturn's E ring

We present the first in situ direct measurement of the composition of particles in Saturn's rings. The Cassini cosmic dust analyser (CDA) measured the mass spectra of nearly 300 impacting dust particles during the 2004 October E ring crossing. An initial interpretation of the data shows that the particles are predominantly water ice, with minor contributions from possible combinations of silicates, carbon dioxide, ammonia, molecular nitrogen, hydrocarbons and perhaps carbon monoxide. This places constraints on both the composition of Enceladus, the main source of the E ring, as well as the grain formation mechanisms.     

Fates of satellite ejecta in the Saturn system

We use conventional numerical integrations to assess the fates of impact ejecta in the Saturn system. For specificity we consider impact ejecta launched from four giant craters on three satellites: Herschel on Mimas, Odysseus and Penelope on Tethys, and Tirawa on Rhea. Speeds, trajectories, and size of the ejecta are consistent with impact on a competent surface (“spalls”) and into unconsolidated regolith. We do not include near-field effects, jetting, or effects peculiar to highly oblique impact. Ejecta are launched at velocities comparable to or exceeding the satellite's escape speed. Most ejecta are swept up by the source moon on time-scales of a few to several decades, and produce craters no larger than 19 km in diameter, with typical craters in the range of a few km. As much as 17% of ejecta reach satellites other than the source moon. Our models generate cratering patterns consistent with a planetocentric origin of most small impact craters on the saturnian icy moons, but the predicted craters tend to be smaller than putative Population II craters. We conclude that ejecta from the known giant craters in the saturnian system do not fully account for Population II craters.     

Sources and losses of energetic protons in Saturn's magnetosphere

We present Cassini data revealing that protons between a few keV and about 100 keV energy are not stably trapped in Saturn's inner magnetosphere. Instead these ions are present only for relatively short times following injections. Injected protons are lost principally because the neutral gas cloud converts these particles to energetic neutral atoms via charge exchange. At higher energies, in the MeV to GeV range, protons are stably trapped between the orbits of the principal moons because the proton cross-section for charge exchange is very small at such energies. These protons likely result from cosmic ray albedo neutron decay (CRAND) and are lost principally to interactions with satellite surfaces and ring particles during magnetospheric radial diffusion. A main result of this work is to show that the dominant energetic proton loss and source processes are a function of proton energy. Surface sputtering by keV ions is revisited based on the reduced ion intensities observed. Relatively speaking, MeV ion and electron weathering is most important closer to Saturn, e.g. at Janus and Mimas, whereas keV ion weathering is most important farther out, at Dione and Rhea.     

The Christiansen Effect in Saturn’s narrow dusty rings and the spectral identification of clumps in the F ring

Stellar occultations by Saturn’s rings observed with the Visual and Infrared Mapping Spectrometer (VIMS) onboard the Cassini spacecraft reveal that dusty features such as the F ring and the ringlets in the Encke and the Laplace Gaps have distinctive infrared transmission spectra. These spectra show a narrow optical depth minimum at wavelengths around 2.87 μm. This minimum is likely due to the Christiansen Effect, a reduction in the extinction of small particles when their (complex) refractive index is close to that of the surrounding medium. Simple Mie-scattering models demonstrate that the strength of this opacity dip is sensitive to the size distribution of particles between 1 and 100 μm across. Furthermore, the spatial resolution of the occultation data is sufficient to reveal variations in the transmission spectra within and among these rings. In both the Encke Gap ringlets and F ring, the opacity dip weakens with increasing local optical depth, which is consistent with the larger particles being concentrated near the cores of these rings. The Encke Gap ringlets also show systematically weaker opacity dips than the F ring and Laplace Gap ringlet, implying that the former has a smaller fraction of grains less than ∼30 μm across. However, the strength of the opacity dip varies most dramatically within the F ring; certain compact regions of enhanced optical depth lack an opacity dip and therefore appear to have a greatly reduced fraction of grains in the few-micron size range. Such spectrally-identifiable structures probably represent a subset of the compact optically-thick clumps observed by other Cassini instruments. These variations in the ring’s particle size distribution can provide new insights into the processes of grain aggregation, disruption and transport within dusty rings. For example, the unusual spectral properties of the F-ring clumps could perhaps be ascribed to small grains adhering onto the surface of larger particles in regions of anomalously low velocity dispersion.     

On corotation torques, horseshoe drag and the possibility of sustained stalled or outward protoplanetary migration

We study the torque on low-mass protoplanets on fixed circular orbits, embedded in a protoplanetary disc in the isothermal limit. We consider a wide range of surface density distributions including cases where the surface density increases smoothly outwards. We perform both linear disc response calculations and non-linear numerical simulations. We consider a large range of viscosities, including the inviscid limit, as well as a range of protoplanet mass ratios, with special emphasis on the co-orbital region and the corotation torque acting between disc and protoplanet.
For low-mass protoplanets and large viscosity, the corotation torque behaves as expected from linear theory. However, when the viscosity becomes small enough to enable horseshoe turns to occur, the linear corotation torque exists only temporarily after insertion of a planet into the disc, being replaced by the horseshoe drag first discussed by Ward. This happens after a time that is equal to the horseshoe libration period reduced by a factor amounting to about twice the disc aspect ratio. This torque scales with the radial gradient of specific vorticity, as does the linear torque, but we find it to be many times larger. If the viscosity is large enough for viscous diffusion across the co-orbital region to occur within a libration period, we find that the horseshoe drag may be sustained. If not, the corotation torque saturates leaving only the linear Lindblad torques. As the magnitude of the non-linear co-orbital torque (horseshoe drag) is always found to be larger than the linear torque, we find that the sign of the total torque may change even for mildly positive surface density gradients. In combination with a kinematic viscosity large enough to keep the torque from saturating, strong sustained deviations from linear theory and outward or stalled migration may occur in such cases.     

Cassini imaging of Saturn's rings: II. A wavelet technique for analysis of density waves and other radial structure in the rings

We describe a powerful signal processing method, the continuous wavelet transform, and use it to analyze radial structure in Cassini ISS images of Saturn's rings. Wavelet analysis locally separates signal components in frequency space, causing many structures to become evident that are difficult to observe with the naked eye. Density waves, generated at resonances with saturnian satellites orbiting outside (or within) the rings, are particularly amenable to such analysis. We identify a number of previously unobserved weak waves, and demonstrate the wavelet transform's ability to isolate multiple waves superimposed on top of one another. We also present two wave-like structures that we are unable to conclusively identify. In a multi-step semi-automated process, we recover four parameters from clearly observed weak spiral density waves: the local ring surface density, the local ring viscosity, the precise resonance location (useful for pointing images, and potentially for refining saturnian astrometry), and the wave amplitude (potentially providing new constraints upon the masses of the perturbing moons). Our derived surface densities have less scatter than previous measurements that were derived from stronger non-linear waves, and suggest a gentle linear increase in surface density from the inner to the mid-A Ring. We show that ring viscosity consistently increases from the Cassini Division outward to the Encke Gap. Meaningful upper limits on ring thickness can be placed on the Cassini Division (3.0 m at r∼118,800 km, 4.5 m at r∼120,700 km) and the inner A Ring (10-15 m for r<127,000 km).     

Further evidence for the FU Orionis nature of PP 13S

We present optical and near-infrared images and spectroscopy together with submillimetre images of the candidate FU Orionis pre-main-sequence star PP 13S. A comparison of historical plates with our new images shows that PP 13S has dimmed and changed optical morphology significantly over the last half-century. In addition, its optical spectrum has undergone dramatic changes over a period of 18 yr from one dominated by strong continuum emission to one showing only ionized, shock-excited emission lines. The current association with several features indicative of both accretion and outflow suggests that, within the last few hundred years, PP 13S passed through an elevated emission state characteristic of the high-accretion events of known FU Orionis-type stars, and has since declined, over the last few decades, to a more quiescent state. The result of the outburst may well have been the formation of the shock-excited Herbig–Haro jet seen to extend from the obscured young star.
We additionally see significant morphological evolution of the source PP 13N . Its apparent association with a Herbig–Haro flow suggests that it also is actively accreting and driving a bipolar outflow.     

On the width and shape of the corotation region for low-mass planets

We study the coorbital flow for embedded, low-mass planets. We provide a simple semi-analytic model for the corotation region, which is subsequently compared to high-resolution numerical simulations. The model is used to derive an expression for the half-width of the horseshoe region, x _s, which in the limit of zero softening is given by   x _s/ r _p= 1.68( q / h )^1/2  , where q is the planet to central star mass ratio, h is the disc aspect ratio and   r _p  is the orbital radius. This is in very good agreement with the same quantity measured from simulations. This result is used to show that horseshoe drag is about an order of magnitude larger than the linear corotation torque in the zero-softening limit. Thus, the horseshoe drag, the sign of which depends on the gradient of specific vorticity, is important for estimates of the total torque acting on the planet. We further show that phenomena, such as the Lindblad wakes, with a radial separation from corotation of approximately a pressure scaleheight H can affect x _s, even though for low-mass planets   x _s≪ H   . The effect is to distort streamlines and reduce x _s through the action of a back pressure. This effect is reduced for smaller gravitational softening parameters and planets of higher mass, for which x _s becomes comparable to H .     

The gravitational influence of satellite Pan on the radial distribution of ring-particles in the region of the Encke-division in Saturn's a ring

Here we summarize the models and their similarities with respect to the gravitational influence of small satellites (moonlets) embedded in planetary rings, which have been developed by Petit and Hénon (1987a,b; 1988) and by Spahn (1987; Spahn et al. 1989; 1992). The results and their applicabilities are shown in the case of the Encke-gap Moon Pan located in the outer A-ring of Saturn's rings. To compare the model-profiles with the experimental ones (optical depth profile measured by Voyager-photopolarimeter), the structures embedded in the latter have been confirmed statistically using the wavelet analysis method. This analysis points to a size of Pan of about 13 km and an eccentricity of 10^–4 of its orbit.