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).     

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.     

Search for and limits on plume activity on Mimas, Tethys, and Dione with the Cassini Visual Infrared Mapping Spectrometer (VIMS)

Cassini Visual Infrared Mapping Spectrometer (VIMS) observations of Mimas, Tethys, and Dione obtained during the nominal and extended missions at large solar phase angles were analyzed to search for plume activity. No forward scattered peaks in the solar phase curves of these satellites were detected. The upper limit on water vapor production for Mimas and Tethys is one order of magnitude less than the production for Enceladus. For Dione, the upper limit is two orders of magnitude less, suggesting this world is as inert as Rhea (Pitman, K.M., Buratti, B.J., Mosher, J.A., Bauer, J.M., Momary, T., Brown, R.H., Nicholson, P.D., Hedman, M.M. [2008]. Astrophys. J. Lett. 680, L65-L68). Although the plumes are best seen at ∼2.0 μm, Imaging Science Subsystem (ISS) Narrow Angle Camera images obtained at the same time as the VIMS data were also inspected for these features. None of the Cassini ISS images shows evidence for plumes. The absence of evidence for any Enceladus-like plumes on the medium-sized saturnian satellites cannot absolutely rule out current geologic activity. The activity may below our threshold of detection, or it may be occurring but not captured on the handful of observations at large solar phase angles obtained for each moon. Many VIMS and ISS images of Enceladus at large solar phase angles, for example, do not contain plumes, as the active “tiger stripes” in the south pole region are pointed away from the spacecraft at these times. The 7-year Cassini Solstice Mission is scheduled to gather additional measurements at large solar phase angles that are capable of revealing activity on the saturnian moons.     

The structure and time variability of the ring atmosphere and ionosphere

The saturnian system is subject to constant bombardment by interplanetary meteoroids and irradiation by solar UV photons. Both effects release neutral molecules from the icy ring particles either in the form of impact water vapor or gas emission in the form of H₂O, O₂ and H₂. The observations of the Cassini spacecraft during its orbit insertion have shown the existence of molecular and atomic oxygen ions. Subsequent modeling efforts have led to the picture that an exospheric population of neutral oxygen molecules is probably maintained in the vicinity of the rings via photolytic-decomposition of ice and surface reactions. At the same time, ionized products O⁺ and ions move along the magnetic field lines and, depending on the optical local thickness rings, can thread through the ring plane or impact a ring particle, the ion principal sink. In addition, collisional interactions between the ions and neutrals will change the scale height of the ions and produce a scattered component of O₂ molecules and O atoms which can be injected into Saturn’s upper atmosphere or the inner magnetosphere. The ring atmosphere, therefore, serves as a source of ions throughout Saturn’s magnetosphere. If photolysis of ice is the dominant source of O₂, then the complex structure of the ring atmosphere/ionosphere and the injection rate of neutral O₂ will be subject to modulation by the seasonal variation of Saturn along its orbit. In this work, we show how the physical properties of the ring oxygen atmosphere, the scattered component, and the magnetospheric ion source rate vary as the ring system goes through the cycle of solar insolation. In particular, it is shown that the magnetopheric ions should be nearly depleted at Saturn’s equinox if O₂ is produced mainly by photolysis of the ring material.     

Observation of saturnian stream particles in the interplanetary space

In January 2004 the dust instrument on the Cassini spacecraft detected the first high-velocity grain expelled from Saturn - a so-called stream particle. Prior to Cassini’s arrival at Saturn in July 2004 the instrument registered 801 faint impacts, whose impact signals showed the characteristic features of a high-velocity impact by a tiny grain. The impact rates as well as the directionality of the stream particles clearly correlate with the sector structure of the interplanetary magnetic field (IMF). The Cosmic Dust Analyser (CDA) registered stream particles dominantly during periods when the IMF direction was tangential to the solar wind flow and in the prograde direction. This finding provides clear evidence for a continuous outflow of tiny dust grains with similar properties from the saturnian system. Within the compressed part of co-rotating interaction regions (CIRs) of the IMF, characterized by enhanced magnetic field strength and compressed solar wind plasma, CDA observed impact bursts of faster stream particles. We find that the bursts result from the stream particles being sped up inside the compressed CIR regions. Our analysis of the stream-particle dynamics inside rarefaction regions of the IMF implies that saturnian stream particles have sizes between 2 and 9 nm and exit the saturnian systems closely aligned with the planet’s ring plane with speeds in excess of 70 km s⁻¹.     

Carbon dioxide on the satellites of Saturn: Results from the Cassini VIMS investigation and revisions to the VIMS wavelength scale

Several of the icy satellites of Saturn show the spectroscopic signature of the asymmetric stretching mode of C-O in carbon dioxide (CO₂) at or near the nominal solid-phase laboratory wavelength of 4.2675 μm (2343.3 cm⁻¹), discovered with the Visible-Infrared Mapping Spectrometer (VIMS) on the Cassini spacecraft. We report here on an analysis of the variation in wavelength and width of the CO₂ absorption band in the spectra of Phoebe, Iapetus, Hyperion, and Dione. Comparisons are made to laboratory spectra of pure CO₂, CO₂ clathrates, ternary mixtures of CO₂ with other volatiles, implanted and adsorbed CO₂ in non-volatile materials, and ab initio theoretical calculations of CO₂ * nH₂O. At the wavelength resolution of VIMS, the CO₂ on Phoebe is indistinguishable from pure CO₂ ice (each molecule’s nearby neighbors are also CO₂) or type II clathrate of CO₂ in H₂O. In contrast, the CO₂ band on Iapetus, Hyperion, and Dione is shifted to shorter wavelengths (typically ∼4.255 μm (∼2350.2 cm⁻¹)) and broadened. These wavelengths are characteristic of complexes of CO₂ with different near-neighbor molecules that are encountered in other volatile mixtures such as with H₂O and CH₃OH, and non-volatile host materials like silicates, some clays, and zeolites. We suggest that Phoebe’s CO₂ is native to the body as part of the initial inventory of condensates and now exposed on the surface, while CO₂ on the other three satellites results at least in part from particle or UV irradiation of native H₂O plus a source of C, implantation or accretion from external sources, or redistribution of native CO₂ from the interior.The analysis presented here depends on an accurate VIMS wavelength scale. In preparation for this work, the baseline wavelength calibration for the Cassini VIMS was found to be distorted around 4.3 μm, apparently as a consequence of telluric CO₂ gas absorption in the pre-launch calibration. The effect can be reproduced by convolving a sequence of model detector response profiles with a deep atmospheric CO₂ absorption profile, producing distorted detector profile shapes and shifted central positions. In a laboratory blackbody spectrum used for radiance calibration, close examination of the CO₂ absorption profile shows a similar deviation from that expected from a model. These modeled effects appear to be sufficient to explain the distortion in the existing wavelength calibration now in use. A modification to the wavelength calibration for 13 adjacent bands is provided. The affected channels span about 0.2 μm centered on 4.28 μm. The maximum wavelength change is about 10 nm toward longer wavelength. This adjustment has implications for interpretation of some of the spectral features observed in the affected wavelength interval, such as from CO₂, as discussed in this paper.     

Origin of a partially differentiated Titan

Accretional temperature profiles for Saturn’s large moon Titan are used to determine the conditions needed for accretion to avoid global melting as a function of the timing, duration, and nebular conditions of Titan’s accretion. We find that Titan can accrete undifferentiated in a “gas-starved” disk even with modest quantities of ammonia mixed in with its ices. Simulations of impact-induced core formation are used to show that Titan can remain only partially differentiated after an outer Solar System late heavy bombardment capable of melting its outer layers, permitting some of its rock to consolidate into a core.     

On the origin of south polar folds on Enceladus

Recent high-resolution Cassini images of the south polar terrain of Enceladus reveal regions of short-wavelength deformation, inferred to be compressional folds between the Baghdad and Damascus tiger stripes (Spencer, J.R., Barr, A.C., Esposito, L.W., Helfenstein, P., Ingersoll, A.P., Jaumann, R., McKay, C.P., Nimmo, F., Waite, J.H. [2009a]. Enceladus: An active cryovolcanic satellite. In: Saturn after Cassini-Huygens. Springer, New York, pp. 683-722). Here, we use Fourier analysis of the bright/dark variations to show that the folds have a dominant wavelength of 1.1 ± 0.4 km. We use the simple model of lava flow folding from Fink (Fink, J. [1980]. Geology 8, 250-254) to show that the folds could form in an ice shell with an upper high-viscosity boundary layer of thickness <400 m, with a driving stress of 40-80 kPa, and strain rate between 10⁻¹⁴ s⁻¹ and 10⁻¹² s⁻¹. Such deformation rates imply resurfacing of the SPT in 0.05-5 Myr, consistent with its estimated surface age. Measurements of fold topography and more sophisticated numerical modeling can narrow down the conditions of fold formation and provide valuable constraints on the thermal structure of the ice shell on Enceladus.     

Exchange of ejecta between Telesto and Calypso: Tadpoles, horseshoes, and passing orbits

We have numerically integrated the orbits of ejecta from Telesto and Calypso, the two small Trojan companions of Saturn’s major satellite Tethys. Ejecta were launched with speeds comparable to or exceeding their parent’s escape velocity, consistent with impacts into regolith surfaces. We find that the fates of ejecta fall into several distinct categories, depending on both the speed and direction of launch.The slowest ejecta follow suborbital trajectories and re-impact their source moon in less than one day. Slightly faster debris barely escape their parent’s Hill sphere and are confined to tadpole orbits, librating about Tethys’ triangular Lagrange points L₄ (leading, near Telesto) or L₅ (trailing, near Calypso) with nearly the same orbital semi-major axis as Tethys, Telesto, and Calypso. These ejecta too eventually re-impact their source moon, but with a median lifetime of a few dozen years. Those which re-impact within the first 10 years or so have lifetimes near integer multiples of 348.6 days (half the tadpole period).Still faster debris with azimuthal velocity components ?10 m/s enter horseshoe orbits which enclose both L₄ and L₅ as well as L₃, but which avoid Tethys and its Hill sphere. These ejecta impact either Telesto or Calypso at comparable rates, with median lifetimes of several thousand years. However, they cannot reach Tethys itself; only the fastest ejecta, with azimuthal velocities ?40 m/s, achieve “passing orbits” which are able to encounter Tethys. Tethys accretes most of these ejecta within several years, but some 1% of them are scattered either inward to hit Enceladus or outward to strike Dione, over timescales on the order of a few hundred years.