Atmospheric chemical abundances of giant planets lead to important constraints on planetary formation and migration. Studies have shown that giant planets that migrate through the protoplanetary disk can accrete substantial amounts of oxygen-rich planetesimals, leading to super-solar metallicities in the envelope and solar or subsolar C/O ratios. Pebble accretion has been demonstrated to play an important role in core accretion and to have growth rates that are consistent with planetary migration. The high pebble accretion rates allow planetary cores to start their growth beyond 10 AU and subsequently migrate to cold ( 1 AU), warm (∼0.1 AU-1AU) or hot ( 0.1 AU) orbits. In this work we investigate how the formation of giant planets via pebble accretion influences their atmospheric chemical compositions. We find that under the standard pebble accretion scenario, where the core is isolated from the envelope, the resulting metallicities (O/H and C/H ratios) are sub-solar, while the C/O ratios are super-solar. Planets that migrate through the disk to become hot Jupiters accrete substantial amounts of water vapour, but still acquire slightly sub-solar O/H and super-solar C/O of 0.7-0.8. The metallicity can be substantially sub-solar (∼ 0.2 − 0.5×solar) and the C/O can even approach 1.0 if the planet accretes its envelope mostly beyond the CO 2 ice line, i.e. cold Jupiters or hot Jupiters that form far out and migrate in by scattering. Allowing for core erosion yields significantly super-solar metallicities and solar or sub-solar C/O, which can also be achieved by other means, e.g. photo-evaporation and late-stage planetesimal accretion.

Nearly-axisymmetric gaps and rings are commonly observed in protoplanetary discs. The leading theory regarding the origin of these patterns is that they are due to dust trapping at the edges of gas gaps induced by the gravitational torques from embedded planets. If the concentration of solids at the gap edges becomes high enough, it could potentially result in planetesimal formation by the streaming instability. We test this hypothesis by performing global 1-D simulations of dust evolution and planetesimal formation in a protoplanetary disc that is perturbed by multiple planets. We explore different combinations of particle sizes, disc parameters, and planetary masses, and find that planetesimals form in all these cases. We also compare the spatial distribution of pebbles from our simulations with protoplanetary disc observations. Planets larger than one pebble isolation mass catch drifting pebbles efficiently at the edge of their gas gaps, and depending on the efficiency of planetesimal formation at the gap edges, the protoplanetary disc transforms within a few 100,000 years to either a transition disc with a large inner hole devoid of dust or to a disc with narrow bright rings. For simulations with planetary masses lower than the pebble isolation mass, the outcome is a disc with a series of weak ring patterns but no strong depletion between the rings. Lowering the pebble size artificially to 100 micrometer-sized "silt", we find that regions between planets get depleted of their pebble mass on a longer time-scale of up to 0.5 million years. These simulations also produce fewer planetesimals than in the nominal model with millimeter-sized particles and always have at least two rings of pebbles still visible after 1 Myr.

The presence of rings and gaps in protoplanetary disks are often ascribed to planet–disk interactions, where dust and pebbles are trapped at the edges of planetary-induced gas gaps. Recent works have shown that these are likely sites for planetesimal formation via the streaming instability. Given the large amount of planetesimals that potentially form at gap edges, we address the question of their fate and their ability to radially transport solids in protoplanetary disks. We performed a series of N-body simulations of planetesimal orbits, taking into account the effect of gas drag and mass loss via ablation. We considered two planetary systems: one that is akin to the young Solar System and another inspired by the structures observed in the protoplanetary disk around HL Tau. In both systems, the proximity to the gap-opening planets results in large orbital excitations, causing the planetesimals to leave their birth locations and spread out across the disk soon after formation. We find that collisions between pairs of planetesimals are rare and should not affect the outcome of our simulations. Collisions with planets occur for ~1% of the planetesimals in the Solar System and for ~20% of the planetesimals in the HL Tau system. Planetesimals that end up on eccentric orbits interior of ~10 au experience efficient ablation and lose all mass before they reach the innermost disk region. In our nominal Solar System simulation, with a stellar gas accretion rate of Ṁ0 = 10−7 M⊙ yr−1 and α = 10−2, we find that 70% of the initial planetesimal mass has been ablated after 500 kyr. Since the protoplanets are located further away from the star in the HL Tau system, the ablation rate is lower and only 11% of the initial planetesimal mass has been ablated after 1 Myr using the same disk parameters. The ablated material consist of a mixture of solid grains and vaporized ices, where a large fraction of the vaporized ices re-condense to form solid ice. Assuming that the solid grains and ices grow to pebbles in the disk midplane, this results in a pebble flux of ~10−100 M⊕ Myr−1 through the inner disk. This occurred in the Solar System at a time so early in its evolution that there is not likely to be any record of it. Our results demonstrate that scattered planetesimals can carry a significant flux of solids past planetary-induced gaps in young and massive protoplanetary disks.

Unexpected clustering in the orbital elements of minor bodies beyond the Kuiper belt has led to speculations that our solar system actually hosts nine planets, the eight established plus a hypothetical "Planet Nine". Several recent studies have shown that a planet with a mass of about 10 Earth masses on a distant eccentric orbit with perihelion far beyond the Kuiper belt could create and maintain this clustering. The evolutionary path resulting in an orbit such as the one suggested for Planet Nine is nevertheless not easily explained. Here we investigate whether a planet scattered away from the giant-planet region could be lifted to an orbit similar to the one suggested for Planet Nine through dynamical friction with a cold, distant planetesimal belt. Recent simulations of planetesimal formation via the streaming instability suggest that planetesimals can readily form beyond 100 au. We explore this circularisation by dynamical friction with a set of numerical simulations. We find that a planet that is scattered from the region close to Neptune onto an eccentric orbit has a 20-30% chance of obtaining an orbit similar to that of Planet Nine after 4.6 Gyr. Our simulations also result in strong or partial clustering of the planetesimals; however, whether or not this clustering is observable depends on the location of the inner edge of the planetesimal belt. If the inner edge is located at 200 au the degree of clustering amongst observable objects is significant.

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.