Cassini Ring Seismology as a Probe of Saturn's Interior I: Rigid Rotation

Seismology of the gas giants holds the potential to resolve long-standing questions about their internal structure and rotation state. We construct a family of Saturn interior models constrained by the gravity field and compute their adiabatic mode eigenfrequencies and corresponding Lindblad and vertical resonances in Saturn's C ring, where more than twenty waves with pattern speeds faster than the ring mean motion have been detected and characterized using high-resolution Cassini Visual and Infrared Mapping Spectrometer (VIMS) stellar occultation data. We present identifications of the fundamental modes of Saturn that appear to be the origin of these observed ring waves, and use their observed pattern speeds and azimuthal wavenumbers to estimate the bulk rotation period of Saturn's interior to be $10{\rm h}\, 33{\rm m}\, 38{\rm s}^{+1{\rm m}\, 52{\rm s}}_{-1{\rm m}\, 19{\rm s}}$ (median and 5%/95% quantiles), significantly faster than Voyager and Cassini measurements of periods in Saturn's kilometric radiation, the traditional proxy for Saturn's bulk rotation period. The global fit does not exhibit any clear systematics indicating strong differential rotation in Saturn's outer envelope.Comment: 19 pages, 6 figures, 3 tables, accepted to ApJ; a bug fix improves the fit, predicts faster bulk spin periods (Figure 4) and virtually eliminates evidence for strong radial differential rotation (Figure 5

Saturn’s Probable Interior: An Exploration of Saturn’s Potential Interior Density Structures

The gravity field of a giant planet is typically our best window into its interior structure and composition. Through comparison of a model planet's calculated gravitational potential with the observed potential, inferences can be made about interior quantities, including possible composition and the existence of a core. Necessarily, a host of assumptions go into such calculations, making every inference about a giant planet's structure strongly model dependent. In this work, we present a more general picture by setting Saturn's gravity field, as measured during the Cassini Grand Finale, as a likelihood function driving a Markov Chain Monte Carlo exploration of the possible interior density profiles. The result is a posterior distribution of the interior structure that is not tied to assumed composition, thermal state, or material equations of state. Constraints on interior structure derived in this Bayesian framework are necessarily less informative, but are also less biased and more general. These empirical and probabilistic constraints on the density structure are our main data product, which we archive for continued analysis. We find that the outer half of Saturn's radius is relatively well constrained, and we interpret our findings as suggesting a significant metal enrichment, in line with atmospheric abundances from remote sensing. As expected, the inner half of Saturn's radius is less well constrained by gravity, but we generally find solutions that include a significant density enhancement, which can be interpreted as a core, although this core is often lower in density and larger in radial extent than typically found by standard models. This is consistent with a dilute core and/or composition gradients

Saturn’s Probable Interior: An Exploration of Saturn’s Potential Interior Density Structures

The gravity field of a giant planet is typically our best window into its interior structure and composition. Through comparison of a model planet's calculated gravitational potential with the observed potential, inferences can be made about interior quantities, including possible composition and the existence of a core. Necessarily, a host of assumptions go into such calculations, making every inference about a giant planet's structure strongly model dependent. In this work, we present a more general picture by setting Saturn's gravity field, as measured during the Cassini Grand Finale, as a likelihood function driving a Markov Chain Monte Carlo exploration of the possible interior density profiles. The result is a posterior distribution of the interior structure that is not tied to assumed composition, thermal state, or material equations of state. Constraints on interior structure derived in this Bayesian framework are necessarily less informative, but are also less biased and more general. These empirical and probabilistic constraints on the density structure are our main data product, which we archive for continued analysis. We find that the outer half of Saturn's radius is relatively well constrained, and we interpret our findings as suggesting a significant metal enrichment, in line with atmospheric abundances from remote sensing. As expected, the inner half of Saturn's radius is less well constrained by gravity, but we generally find solutions that include a significant density enhancement, which can be interpreted as a core, although this core is often lower in density and larger in radial extent than typically found by standard models. This is consistent with a dilute core and/or composition gradients

Numerical modeling of the disruption of Comet D/1993 F2 Shoemaker-Levy 9 representing the progenitor by a gravitationally bound assemblage of randomly shaped polyhedra

We advance the modeling of rubble-pile solid bodies by re-examining the tidal breakup of comet Shoemaker-Levy 9, an event that occurred during a 1.33 Jupiter radii encounter with that planet in July 1992. Tidal disruption of the comet nucleus led to a chain of sub-nuclei about 100-1000 m in diameter; these went on to collide with the planet two years later (Chodas & Yeomans 1996). They were intensively studied prior to and during the collisions, making SL9 the best natural benchmark for physical models of small body disruption. For the first time in the study of this event, we use numerical codes treating rubble-piles as collections of polyhedra (Korycansky & Asphaug 2009). This introduces forces of dilatation and friction, and inelastic response. As in our previous studies (Asphaug & Benz 1994,1996) we conclude that the progenitor must have been a rubble-pile, and we obtain approximately the same pre-breakup diameter (about 1.5 km) in our best fits to the data. We find that the inclusion of realistic fragment shapes leads to grain locking and dilatancy, so that even in the absence of friction or other dissipation we find that disruption is overall more difficult than in our spheres-based simulations. We constrain the comet's bulk density at about 300-400 kg/m^3, half that of our spheres-based predictions and consistent with recent estimates derived from spacecraft observations.Comment: Submitted to The Astrophysical Journal (7/16/12) added Acknowledgments (8/29/12) accepted, peer reviewed versio

Theory of Figures to the Seventh Order and the Interiors of Jupiter and Saturn

Interior modeling of Jupiter and Saturn has advanced to a state where thousands of models are generated that cover the uncertainty space of many parameters. This approach demands a fast method of computing their gravity field and shape. Moreover, the Cassini mission at Saturn and the ongoing Juno mission delivered gravitational harmonics up to J12. Here we report the expansion of the theory of figures, which is a fast method for gravity field and shape computation, to the seventh order (ToF7), which allows for computation of up to J14. We apply three different codes to compare the accuracy using polytropic models. We apply ToF7 to Jupiter and Saturn interior models in conjunction with CMS-19 H/He equation of state. For Jupiter, we find that J6 is best matched by a transition from an He-depleted to He-enriched envelope at 2–2.5 Mbar. However, the atmospheric metallicity reaches 1 × solar only if the adiabat is perturbed toward lower densities, or if the surface temperature is enhanced by ∼14 K from the Galileo value. Our Saturn models imply a largely homogeneous-in-Z envelope at 1.5–4 × solar atop a small core. Perturbing the adiabat yields metallicity profiles with extended, heavy-element-enriched deep interior (diffuse core) out to 0.4 RSat, as for Jupiter. Classical models with compact, dilute, or no core are possible as long as the deep interior is enriched in heavy elements. Including a thermal wind fitted to the observed wind speeds, representative Jupiter and Saturn models are consistent with all observed Jn values

Destructive gravitational encounters: outcome and implications of catastrophic collisions and tidal splitting in the post-formation outer solar system

I present results from three theoretical numerical studies relating to destructive events in the lives of outer solar system satellites and smaller bodies. The first project is a study of the implications that a Late Heavy Bombardment in the outer solar system, such as predicted by the Nice model, might have had for the mid sized moons of Jupiter, Saturn, and Uranus. A Monte Carlo calculation shows that Mimas, Enceladus, Tethys, and Miranda each would almost certainly have experienced at least one catastrophic collision after formation. If true, these bodies would have disrupted and then reaccreted as scrambled mixtures of rock and ice -- potentially preserving this signature in their present day structure. Conversely, if these satellites are fully differentiated today then they would have required a heat source sufficient for melting and differentiation in the absence of short half life radioactive elements. Tidal heating may have been sufficient for Tethys, Enceladus, and Miranda, but a differentiated Mimas would present a difficulty to either the Nice model or to the classical formation model of the Saturn system.The second study is a numerical investigation of the expected outcome of destructive collisions between gravity-dominated bodies; in particular of the conditions required for a collision to be catastrophic, defined as one that leaves behind a surviving body with less than half the total colliding mass. In this study I focus on bodies with radii between 100 and 1000 km, a previously neglected size range, and derive a simple scaling law for the threshold impact energy required for disruption in this size range. This scaling law is expected to hold for all projectile-to-target size ratios and is independent of material, so long as elastic strength may be ignored. Compared with scaling laws existing in the literature the newly derived scaling generally predicts lower threshold energy for disruption, except for highly oblique impacts by projectiles much smaller than the target.The third project is a study of the tidal breakup of rubble piles by modeling the breakup of comet Shoemaker-Levy 9 in a rigid body code that, for the first time, treats non-spherical rubble pile elements. This introduces dilatation and grain locking as the major forces acting against gravity tides during the comet's close approach to Jupiter and changes the outcome of tidal encounters compared with that predicted by models using spherical elements. By comparing simulation results to the well-studied post-breakup morphology of comet SL9 we were able to constrain the progenitor's bulk density at 300--400 kg/m^3, half that of previous estimates

Destructive gravitational encounters: outcome and implications of catastrophic collisions and tidal splitting in the post-formation outer solar system

I present results from three theoretical numerical studies relating to destructive events in the lives of outer solar system satellites and smaller bodies. The first project is a study of the implications that a Late Heavy Bombardment in the outer solar system, such as predicted by the Nice model, might have had for the mid sized moons of Jupiter, Saturn, and Uranus. A Monte Carlo calculation shows that Mimas, Enceladus, Tethys, and Miranda each would almost certainly have experienced at least one catastrophic collision after formation. If true, these bodies would have disrupted and then reaccreted as scrambled mixtures of rock and ice -- potentially preserving this signature in their present day structure. Conversely, if these satellites are fully differentiated today then they would have required a heat source sufficient for melting and differentiation in the absence of short half life radioactive elements. Tidal heating may have been sufficient for Tethys, Enceladus, and Miranda, but a differentiated Mimas would present a difficulty to either the Nice model or to the classical formation model of the Saturn system.The second study is a numerical investigation of the expected outcome of destructive collisions between gravity-dominated bodies; in particular of the conditions required for a collision to be catastrophic, defined as one that leaves behind a surviving body with less than half the total colliding mass. In this study I focus on bodies with radii between 100 and 1000 km, a previously neglected size range, and derive a simple scaling law for the threshold impact energy required for disruption in this size range. This scaling law is expected to hold for all projectile-to-target size ratios and is independent of material, so long as elastic strength may be ignored. Compared with scaling laws existing in the literature the newly derived scaling generally predicts lower threshold energy for disruption, except for highly oblique impacts by projectiles much smaller than the target.The third project is a study of the tidal breakup of rubble piles by modeling the breakup of comet Shoemaker-Levy 9 in a rigid body code that, for the first time, treats non-spherical rubble pile elements. This introduces dilatation and grain locking as the major forces acting against gravity tides during the comet's close approach to Jupiter and changes the outcome of tidal encounters compared with that predicted by models using spherical elements. By comparing simulation results to the well-studied post-breakup morphology of comet SL9 we were able to constrain the progenitor's bulk density at 300--400 kg/m^3, half that of previous estimates