We present a new numerical framework to model the formation and evolution of giant planets. The code is based on the further development of the stellar evolution toolkit Modules for Experiments in Stellar Astrophysics. The model includes the dissolution of the accreted planetesimals/pebbles, which are assumed to be made of water ice, in the planetary gaseous envelope, and the effect of envelope enrichment on the planetary growth and internal structure is computed self-consistently. We apply our simulations to Jupiter and investigate the impact of different heavy-element and gas accretion rates on its formation history. We show that the assumed runaway gas accretion rate significantly affects the planetary radius and luminosity. It is confirmed that heavy-element enrichment leads to shorter formation timescales due to more efficient gas accretion. We find that with heavy-element enrichment Jupiter’s formation timescale is compatible with typical disks’ lifetimes even when assuming a low heavy-element accretion rate (oligarchic regime). Finally, we provide an approximation for the heavy-element profile in the innermost part of the planet, providing a link between the internal structure and the planetary growth history.

In the standard model for giant planet formation, the planetary growth begins with accretion of solids followed by a buildup of a gaseous atmosphere as more solids are accreted, and finally, by rapid accretion of gas. The interaction of the solids with the gaseous envelope determines the subsequent planetary growth and the final internal structure. In this work we simulate the interaction of planetesimals with a growing giant planet (proto-Jupiter) and investigate how different treatments of the planetesimal-envelope interaction affect the heavy-element distribution, and the inferred core mass. We consider various planetesimal sizes and compositions as well as different ablation and radiation efficiencies, and fragmentation models. We find that in most cases the core reaches a maximum mass of ∼ 2 M ⊕ . We show that the value of the core's mass mainly depends on the assumed size and composition of the solids, while the heavy-element distribution is also affected by the fate of the accreted planetesimals (ablation/fragmentation). Fragmentation, which is found to be important for planetesimals > 1 km, typically leads to enrichment of the inner part of the envelope while ablation results in enrichment of the outer atmosphere. Finally, we present a semi-analytical prescription for deriving the heavy-element distribution in giant protoplanets.

Determining the heavy-element accretion rate of growing giant planets is crucial for understanding their formation and bulk composition. The solid (heavy-element) accretion rate should be carefully modeled during the various stages of giant planet formation and therefore, the planetary capture radius must be determined. In some simulations that model the heavy-element accretion rate, such as in N-body simulations, the presence of the gaseous envelope is either neglected, or treated in an over-simplified manner. In this paper, we present an approximation for the capture radius that does not require the numerical solution of the stellar structure equations. Our approximation for the capture radius works extremely well for various planetesimal sizes and compositions. We show that the commonly assumed constant density assumption for inferring the capture radius leads to a large error in the calculated capture radius and we therefore suggest that our approximation should be implemented in future simulations.

Observations and models of giant planets indicate that such objects are enriched in heavy elements compared to solar abundances. The prevailing view is that giant planets accreted multiple Earth masses of heavy elements after the end of core formation. Such late solid enrichment is commonly explained by the accretion of planetesimals. Planetesimals are expected to form at the edges of planetary gaps, and here we address the question of whether these planetesimals can be accreted in large enough amounts to explain the inferred high heavy element contents of giant planets. We performed a series of N-body simulations of the dynamics of planetesimals and planets during the planetary growth phase, taking gas drag into account as well as the enhanced collision cross section caused by the extended envelopes. We considered the growth of Jupiter and Saturn via gas accretion after reaching the pebble isolation mass and we included their migration in an evolving disk. We find that the accretion efficiency of planetesimals formed at planetary gap edges is very low: less than 10% of the formed planetesimals are accreted even in the most favorable cases, which in our model corresponds to a few Earth masses. When planetesimals are assumed to form beyond the feeding zone of the planets, extending to a few Hill radii from a planet, accretion becomes negligible. Furthermore, we find that the accretion efficiency increases when the planetary migration distance is increased and that the efficiency does not increase when the planetesimal radii are decreased. Based on these results, we conclude that it is difficult to explain the large heavy element content of giant planets with planetesimal accretion during the gas accretion phase. Alternative processes most likely are required, such as accretion of vapor deposited by drifting pebbles.

The origin of Uranus and Neptune is still unknown. In particular, it has been challenging for planet formation models to form the planets in their current radial distances within the expected lifetime of the solar nebula. In this paper, we simulate the in situ formation of Uranus and Neptune via pebble accretion and show that both planets can form within ∼3 Myr at their current locations, and have final compositions that are consistent with the heavy element to H–He ratios predicted by structure models. We find that Uranus and Neptune could have been formed at their current locations. In several cases a few earth masses (M ⊕ ) of heavy elements are missing, suggesting that Uranus and/or Neptune may have accreted ∼1–3 M⊕ of heavy elements after their formation via planetesimal accretion and/or giant impacts.