Interior Models of Saturn: Including the Uncertainties in Shape and Rotation

The accurate determination of Saturn's gravitational coefficients by Cassini could provide tighter constrains on Saturn's internal structure. Also, occultation measurements provide important information on the planetary shape which is often not considered in structure models. In this paper we explore how wind velocities and internal rotation affect the planetary shape and the constraints on Saturn's interior. We show that within the geodetic approach (Lindal et al., 1985, ApJ, 90, 1136) the derived physical shape is insensitive to the assumed deep rotation. Saturn's re-derived equatorial and polar radii at 100 mbar are found to be 54,445 $\pm$10 km and 60,365$\pm$10 km, respectively. To determine Saturn's interior we use {\it 1 D} three-layer hydrostatic structure models, and present two approaches to include the constraints on the shape. These approaches, however, result in only small differences in Saturn's derived composition. The uncertainty in Saturn's rotation period is more significant: with Voyager's 10h39mns period, the derived mass of heavy elements in the envelope is 0-7 M$_{\oplus}$. With a rotation period of 10h32mns, this value becomes $<4$ $M_{\oplus}$, below the minimum mass inferred from spectroscopic measurements. Saturn's core mass is found to depend strongly on the pressure at which helium phase separation occurs, and is estimated to be 5-20 M$_{\oplus}$. Lower core masses are possible if the separation occurs deeper than 4 Mbars. We suggest that the analysis of Cassini's radio occultation measurements is crucial to test shape models and could lead to constraints on Saturn's rotation profile and departures from hydrostatic equilibrium.Comment: Accepted for publication in Ap

The Effects of Metallicity, and Grain Growth and Settling on the Early Evolution of Gaseous Protoplanets

Giant protoplanets formed by gravitational instability in the outer regions of circumstellar disks go through an early phase of quasi-static contraction during which radii are large and internal temperatures are low. The main source of opacity in these objects is dust grains. We investigate two problems involving the effect of opacity on the evolution of planets of 3, 5, and 7 M_J. First, we pick three different overall metallicities for the planet and simply scale the opacity accordingly. We show that higher metallicity results in slower contraction as a result of higher opacity. It is found that the pre-collapse time scale is proportional to the metallicity. In this scenario, survival of giant planets formed by gravitational instability is predicted to be more likely around low-metallicity stars, since they evolve to the point of collapse to small size on shorter time scales. But metal-rich planets, as a result of longer contraction times, have the best opportunity to capture planetesimals and form heavy-element cores. Second, we investigate the effects of opacity reduction as a result of grain growth and settling, for the same three planetary masses and for three different values of overall metallicity. When these processes are included, the pre-collapse time scale is found to be of order 1000 years for the three masses, significantly shorter than the time scale calculated without these effects. In this case the time scale is found to be relatively insensitive to planetary mass and composition. However, the effects of planetary rotation and accretion of gas and dust, which could increase the timescale, are not included in the calculation. The short time scale we find would preclude metal enrichment by planetesimal capture, as well as heavy-element core formation, over a large range of planetary masses and metallicities.Comment: 22 pages, accepted to Icaru

The formation of mini-Neptunes

Mini-Neptunes seem to be common planets. In this work we investigate the possible formation histories and predicted occurrence rates of mini-Neptunes assuming the planets form beyond the iceline. We consider pebble and planetesimal accretion accounting for envelope enrichment and two different opacity conditions. We find that the formation of mini-Neptunes is a relatively frequent output when envelope enrichment by volatiles is included, and that there is a "sweet spot" for mini-Neptune formation with a relatively low solid accretion rate of ~10^{-6} Earth masses per year. This rate is typical for low/intermediate-mass protoplanetary disks and/or disks with low metallicities. With pebble accretion, envelope enrichment and high opacity favor the formation of mini-Neptunes, with more efficient formation at large semi-major axes (~30 AU) and low disk viscosity. For planetesimal accretion, such planets can form also without enrichment, with the opacity being a key aspect in the growth history and favorable formation location. Finally, we show that the formation of Neptune-like planets remains a challenge for planet formation theories.Comment: Accepted for publication in Ap

On the mass of gas giant planets: Is Saturn a failed gas giant?

The formation history of giant planets inside and outside the solar system remains unknown. We suggest that runaway gas accretion is initiated only at a mass of ~100 M_Earth and that this mass corresponds to the transition to a gas giant, a planet that its composition is dominated in hydrogen and helium. Delaying runaway accretion to later times (a few Myr) and higher masses is likely to be a result of an intermediate stage of efficient heavy-element accretion (at a rate of ~10^-5 M_Earth/yr) that provides sufficient energy to hinder rapid gas accretion. This may imply that Saturn has never reached runaway gas accretion, and that it is a "failed giant planet". The transition to a gas giant planet above Saturn's mass naturally explains the differences between the bulk metallicities and internal structures of Jupiter and Saturn. The transition mass to a gas giant planets strongly depends on the exact formation history and birth environment of the planets, which are still not well constrained for our Solar System. In terms of giant exoplanets, delaying runaway gas accretion to planets beyond Saturn's mass can explain the transitions in the mass-radius relations of observed exoplanets and the high metallicity of intermediate-mass exoplanets.Comment: accepted for publication in A&A Letter

The Interiors of Jupiter and Saturn

Probing the interiors of the gas giant planets in our Solar System is not an easy task. It requires a set of accurate measurements combined with theoretical models that are used to infer the planetary composition and its depth dependence. The masses of Jupiter and Saturn are 317.83 and 95.16 Earth masses, respectively, and since a few decades, we know that they mostly consist of hydrogen and helium. It is the mass of heavy elements (all elements heavier than helium) that is not well determined, as well as their distribution within the planets. While the heavy elements are not the dominating materials in Jupiter and Saturn they are the key for our understanding of their formation and evolution histories. The planetary internal structure is inferred from theoretical models that fit the available observational constraints by using theoretical equations of states (EOSs) for hydrogen, helium, their mixtures, and heavier elements (typically rocks and/or ices). However, there is no unique solution for the planetary structure and the results depend on the used EOSs and the model assumptions imposed by the modeler. Major model assumptions that can affect the derived internal structure include the number of layers, the heat transport mechanism within the planet (and its entropy), the nature of the core (compact vs. diluted), and the location (pressure) of separation between the two envelopes. Alternative structure models assume a less distinct division between the layers and/or a non-homogenous distribution of the heavy elements. Today, with accurate measurements of the gravitational fields of Jupiter and Saturn from the Juno and Cassini missions, structure models can be further constrained. At the same time, these measurements introduce new challenges for planetary modellers.Comment: Invited review. Accepted for publication in the Oxford Research Encyclopedia of Planetary Science. Oxford University Pres