The composition of Jupiter and the primordial distribution of the heavy elements are determined by its formation history. As a result, in order to constrain the primordial internal structure of Jupiter the growth of the core and the deposition and settling of accreted planetesimals must be followed in detail. In this paper we determine the distribution of the heavy elements in proto-Jupiter and determine the mass and composition of the core. We find that while the outer envelope of proto-Jupiter is typically convective and has an homogeneous composition, the innermost regions have compositional gradients. In addition, the existence of heavy elements in the envelope leads to much higher internal temperatures (several times 10 4 K) than in the case of a hydrogen-helium envelope. The derived core mass depends on the actual definition of the core: if the core is defined as the region in which the heavy-element mass fraction is above some limit (say 0.5), then it can be much more massive (∼ 15 M ⊕ ) and more extended (10% of the planet's radius) than in the case where the core is just the region with 100% heavy elements. In the former case Jupiter's core also consists of hydrogen and helium. Our results should be taken into account when constructing internal structure models of Jupiter and when interpreting the upcoming data from the Juno (NASA) mission.Subject headings: planets and satellites: individual (Jupiter) -planets and satellites:interiors -planets and satellites: composition -planets and satellites: formation -planets and satellites: gaseous planets 1

Constraining the planetary composition is essential for exoplanetary characterization. In this paper, we use a statistical analysis to determine the characteristic maximum (threshold) radii for various compositions for exoplanets with masses up to 25 Earth masses (M ⊕ ). We confirm that most planets with radii larger than 1.6 Earth radius (R ⊕ ) are not rocky, and must consist of lighter elements, as found by previous studies. We find that planets with radii above 2.6 R ⊕ cannot be pure-water worlds, and must contain significant amounts of hydrogen and helium (H-He). We find that planets with radii larger than about 3 R ⊕ , 3.6 R ⊕ , and 4.3 R ⊕ are expected to consist of 2%, 5% and 10% of H-He, respectively. We investigate the sensitivity of the results to the assumed internal structure, the planetary temperature and albedo, and the accuracy of the mass and radius determination. We show that the envelope's metallicity, the percentage of H-He and the distribution of the elements play a significant role in the determination of the threshold radius. Finally, we conclude that despite the degenerate nature of the problem, it is possible to put limits on the possible range of compositions for planets with well-measured mass and radius.

The interiors of giant planets remain poorly understood. Even for the planets in the Solar System, difficulties in observation lead to major uncertainties in the properties of planetary cores. Exoplanets that have undergone rare evolutionary pathways provide a new route to understanding planetary interiors. We present the discovery of TOI-849b, the remnant core of a giant planet, with a radius smaller than Neptune but an anomalously high mass M p =40.8 +2.4 −2.5 M ⊕ and density of 5.5 ± 0.8 gcm −3 , similar to the Earth. Interior structure models suggest that any gaseous envelope of pure hydrogen and helium consists of no more than 3.9 +0.8 −0.9 % of the total mass of the planet. TOI-849b transits a late G type star (T mag = 11.5) with an orbital period of 18.4 hours, leading to an equilibrium temperature of 1800K. The planet's mass is larger than the theoretical threshold mass for runaway gas accretion. As such, the planet could have been a gas giant before undergoing extreme mass loss via thermal self-disruption or giant planet collisions, or it avoided substantial gas accretion, perhaps through gap opening or late formation. Photoevaporation rates cannot provide the mass loss required to reduce a Jupiter-like gas giant, but can remove a few M ⊕ hydrogen and helium envelope on timescales of several Gyr, implying that any remaining atmosphere is likely to be enriched by water or other volatiles from the planetary interior. TOI-849b represents a unique case where material from the primordial core is left over from formation and available to study.

We suggest the existence of a correlation between the planetary radius and orbital period for planets with radii smaller than 4 R ⊕ . Using the Kepler data, we find a correlation coefficient of 0.5120, and suggest that the correlation is not caused solely by survey incompleteness. While the correlation coefficient could change depending on the statistical analysis, the statistical significance of the correlation is robust. Further analysis shows that the correlation originates from two contributing factors. One seems to be a power-law dependence between the two quantities for intermediate periods (3-100 days), and the other is a dearth of planets with radii larger than 2 R ⊕ in short periods. This correlation may provide important constraints for small-planet formation theories and for understanding the dynamical evolution of planetary systems.