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We present a review of Saturn's interior structure and thermal evolution, with a particular focus on work in the past 5 years. Data from the Cassini mission, including a precise determination of the gravity field from the Grand Finale orbits, and the still ongoing identification of ring wave features in Saturn's C-ring tied to seismic modes in the planet, have led to dramatic advances in our understanding of Saturn's structure. Models that match the gravity field suggest that differential rotation, as seen in the visible atmosphere, extends down to at least a depth of 10,000 km (1/6$^{\rm th}$ the planet's radius). At greater depths, a variety of different investigations all now point to a deep Saturn rotation rate of 10 hours and 33 minutes. There is very compelling evidence for a central heavy element concentration (``core''), that in most recent models is 12-20 Earth masses. Ring seismology strongly suggests that the core is not entirely compact, but is dilute (mixed in with the overlying H/He), and has a substantial radial extent, perhaps out to around one-half of the planet's radius. A wide range of thermal evolution scenarios can match the planet's current luminosity, with progress on better quantifying the helium rain scenario hampered by Saturn's poorly known atmospheric helium abundance. We discuss the relevance of magnetic field data on understanding the planet's current interior structure. We point towards additional future work that combines seismology and gravity within a framework that includes differential rotation, and the utility of a Saturn entry probe., Comment: Invited review. Accepted for publication in "Saturn: The Grand Finale", K. H. Baines et al., eds., Cambridge University Press. All-new follow-up to previous 2016 (pre-Grand Finale) review chapter here: arXiv:1609.06324

The Juno mission has provided measurements of Jupiter s gravity field with an outstanding level of accuracy, leading to better constraints on the interior of the planet. Improving our knowledge of the internal structure of Jupiter is key to understanding its formation and evolution but is also important in the framework of exoplanet exploration. In this study, we investigated the differences between the state-of-the-art equations of state and their impact on the properties of interior models. Accounting for uncertainty on the hydrogen and helium equation of state, we assessed the span of the interior features of Jupiter. We carried out an extensive exploration of the parameter space and studied a wide range of interior models using Markov chain Monte Carlo (MCMC) simulations. To consider the uncertainty on the equation of state, we allowed for modifications of the equation of state in our calculations. Our models harbour a dilute core and indicate that Jupiter s internal entropy is higher than what is usually assumed from the Galileo probe measurements. We obtain solutions with extended dilute cores, but contrary to other recent interior models of Jupiter, we also obtain models with small dilute cores. The dilute cores in such solutions extend to 20% of Jupiter s mass, leading to better agreement with formation evolution models. We conclude that the equations of state used in Jupiter models have a crucial effect on the inferred structure and composition. Further explorations of the behaviour of hydrogen helium mixtures at the pressure and temperature conditions in Jupiter will help to constrain the interior of the planet, and therefore its origin.

In order to accurately model giant planets, a whole set of observational constraints is needed. As the conventional constraints for extrasolar planets like mass, radius, and temperature allow for a large number of acceptable models, a new planetary parameter is desirable in order to further constrain planetary models. Such a parameter may be the tidal Love number k2. In this paper we aim to study the capability of k2 to reveal further information about the interior structure of a planet. With theoretical planetary models we investigate how the tidal Love number k2 responds to the internal density distribution of a planet. In particular, we demonstrate the effect of the degeneracy of k2 due to a density discontinuity in the envelope of a three-layer planetary model. The effect of a possible outer density discontinuity masks the effect of the core mass on the Love number k2. Hence, there is no unique relationship between the Love number k2 and the core mass of a planet. We show that the degeneracy of k2 with respect to a layer boundary in the envelope also occurs in existing planets, e.g. Saturn and the Hot Neptune GJ436b. As a result of the degeneracy, the planetary parameter k2 cannot be used to further constrain Saturnian models and for GJ436b only a maximum possible core mass can be derived from a given k2. To significantly narrow the uncertainty about the core mass of GJ436b the combined knowledge of k2 and atmospheric metallicity and temperature profile is necessary., Comment: 7 pages, 4 figures, accepted

Galileo, the first artificial satellite of an outer planet, has been orbiting Jupiter since Dec 7, 1995. The spacecraft encounters one of the four Galilean satellites on each orbit.

A large self-gravitating body does not easily lose significant mass because the escape velocity is much larger than the sound speed of atmosphere-forming species under ambient thermal conditions. The most significant exceptions to this are giant impacts or impact jetting by fast-moving projectiles. A very small object (e.g. a comet) also does not easily lose significant volatile mass upon formation because the energy release associated with its accretion is so small. (It can however lose a great deal of mass if it is subsequently moved closer to the Sun.) I argue that there is an intermediate mass range (corresponding to bodies with radii of approximately 300-800 km) for which the ambient steady-state mass loss is a maximum. By ambient, I mean those conditions pertaining to the formation region of the body. By steady state, I mean to exclude infrequent traumas (giant impacts). The existence of a preferred intermediate mass arises through the competition of growing gravitational containment and growing energy release by accretion; it corresponds typically to GM/(Rc(sub s)(exp 2)) approximately equals 2 to 4, where M is the protoplanet mass of radius R, and c(sub s) is the sound speed. Several factors determine the amount of volatile loss is this vulnerable zone during accretion but in general the loss is a substantial fraction of the volatiles, sometimes approaching 100 percent. The principal implication is that bodies larger than a few hundred kilometers in radius will not have a 'primitive' (i.e. cometary) composition. This is relevant for understanding Triton, Pluto, Charon, and perhaps Chiron.

In the traditional view of planetary magnetism, a planet either has a core dynamo (Earth, Jupiter, Saturn, Uranus, Neptune, maybe Mercury) or does not (Mars, Venus, Moon...) I argue that this view is simplistic in two respects. First, mantle convection in terrestrial planets is invariably ata high enough Rayleigh number that it is time variable; this leads to the intermittent arrival of mantle 'cold fingers' at the core-mantle boundary promoting at least local core convection and dynamo action even when the planetary core is stably stratified on average. Thus, I predict an intermittent dynamo regime in addition to the simple dynamo-on (Earth) and dynamo-off regimes. Second, the mantle convection-driven horizontal temperature gradients just below the core-mantle boundary can lead to unstable flows that will convert thermoelectric or electrochemical toroidal fields into externally detectable poloidal fields, even when a dynamo is not possible. It is likely that Mars possesses an interesting core magnetic field of the latter kind, complex but with a dipole that might be approximately aligned with the rotation axis and a surface field of a few to tens of gammas.

Laboratory simulations of Martian CO2 storage address whether carbonate formation could have reduced CO2 pressure from a hypothetical greater than 1 bar to the present 7 mbar in less than or equal to 3 to 4 billion years. This problem is addressed with experiments and analysis designed to verify and improve previous kinetic measurements, reaction mechanisms, and product characterizations, with the goal of improving existing models of Martian CO2 history. A sensitive manometer monitored the pressure drop of CO2 due to uptake by powdered silicate for periods of 3 to 100+ days. Pressure drops for diopside 1 and basalt show rapid short-term (approximately one day) CO2 uptake and considerably slower long-term pressure drops. Curves for diopside 2, olivine 1, and olivine 2 are qualitatively similar to those for diopside 1, whereas quartz and plagioclase show near-zero short-term pressure drops and very slow long-term signals, indistinguishable from a leak (less than 10(exp 11) mol/sq m/s).

Various arguments suggest that Venus probably has no asthenosphere, and it is likely that beneath the crust there is a highly depleted and highly viscous mantle layer which was probably formed in the early history of the planet when it was partially or completely molten. Models of crystallization of magma oceans suggest that just after crystallization of a hypothetical magma ocean, the internal structure of Venus consists of a crust up to about 70 km thickness, a depleted layer up to about 500 km, and an enriched lower layer which probably consists of an undepleted 'lower mantle' and heavy enriched accumulates near the core-mantle boundary. Partial or even complete melting of Venus due to large impacts during the formation period eventually results in differentiation. However, the final result of such a differentiation can vary from a completely differentiated mantle to an almost completely preserved homogeneous mantle depending on competition between convection and differentiation: between low viscosity ('liquid') convection and crystal settling at small crystal fractions, or between high viscosity ('solid') convection and percolation at large crystal fractions.

The evolution of an initially totally molten magma ocean is constrained on the basis of analysis of various physical problems in the magma ocean. First of all an equilibrium thermodynamics of the magma ocean is developed in the melting temperature range. The equilibrium thermodynamical parameters are found as functions only of temperature and pressure and are used in the subsequent models of kinetics and convection. Kinematic processes determine the crystal size and also determine a non-equilibrium thermodynamics of the system. Rheology controls all dynamical regimes of the magma ocean. The thermal convection models for different rheological laws are developed for both the laminar convection and for turbulent convection in the case of equilibrium thermodynamics of the multiphase system. The evolution is estimated on the basis of all the above analysis.

A large number of volcanic features exist on Venus, ranging from tens of thousands of small domes to large shields and coronae. It is difficult to reconcile all these with an explanation involving deep mantle plumes, since a number of separate arguments lead to the conclusion that deep mantle plumes reaching the base of the lithosphere must exceed a certain size. In addition, the fraction of basal heating in Venus' mantle may be significantly lower than in Earth's mantle reducing the number of strong plumes from the core-mantle boundary. In three-dimensional convection simulations with mainly internal heating, weak, distributed upwellings are usually observed. We present an alternative mechanism for such volcanism, originally proposed for the Earth and for Venus, involving Rayleigh-Taylor instabilities driven by melt buoyancy, occurring spontaneously in partially or incipiently molten regions.

The prevailing view of very large impacts during earth accretion suggests an initial state for earth evolution that was totally molten or nearly so. The problem confronted is to understand the evolution from this state to an almost completely solidified mantle. Two crucial questions are asked by the author: (1) is the resulting endstate of magma ocean freezing compatible with geological record, inferred mantle structure and evidence from geochemistry; and (2) does the freezing event leave a signature that can be discerned in the present earth. The emphasis on this keynote introduction will be to set the stage for the more detailed analyses to follow and to clarify the crucial questions and uncertainties.