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

Metallicity of the Massive Protoplanets Around HR 8799 If Formed by Gravitational Instability

The final composition of giant planets formed as a result of gravitational instability in the disk gas depends on their ability to capture solid material (planetesimals) during their 'pre-collapse' stage, when they are extended and cold, and contracting quasi-statically. The duration of the pre-collapse stage is inversely proportional roughly to the square of the planetary mass, so massive protoplanets have shorter pre-collapse timescales and therefore limited opportunity for planetesimal capture. The available accretion time for protoplanets with masses of 3, 5, 7, and 10 Jupiter masses is found to be 7.82E4, 2.62E4, 1.17E4 and 5.67E3 years, respectively. The total mass that can be captured by the protoplanets depends on the planetary mass, planetesimal size, the radial distance of the protoplanet from the parent star, and the local solid surface density. We consider three radial distances, 24, 38, and 68 AU, similar to the radial distances of the planets in the system HR 8799, and estimate the mass of heavy elements that can be accreted. We find that for the planetary masses usually adopted for the HR 8799 system, the amount of heavy elements accreted by the planets is small, leaving them with nearly stellar compositions.Comment: accepted for publication in Icaru