Elena Lega

Streaming instability (SI) is currently the leading model for planetesimal formation in protoplanetary disks, but it typically operates on the radial drift timescale of solids toward the star, that is, within approximately the first million years. In the Solar System, however, some planetesimals (i.e., the parent bodies of chondritic meteorites) formed 2–4 Myr after disk formation, implying that dust must have been retained in the disk for extended periods. Pressure bumps provide an efficient mechanism for trapping dust. However, dust trapping alone does not guarantee planetesimal formation: even modest levels of gas turbulence can inhibit strong vertical settling and radial concentration, preventing the dust density from reaching the threshold required for gravitational collapse. This motivates the exploration of alternative dust–gas instabilities, such as the dusty Rossby wave instability (DRWI), which was first studied in 2D shearing-box simulations. We aim to investigate the viability of such alternative instabilities in global disk simulations under realistic physical conditions. We used the numerical code fargOCA, where the treatment of dust as a pressureless fluid was recently implemented. We first recovered the results of previous 2D shearing-box simulations using global 2D disk simulations and extended the analysis to fully 3D disks in both viscous and inviscid regimes. We reproduced prior 2D results and extended them by characterizing the dust clumping produced by the DRWI in a viscous disk (α=10^-4). We find that this instability does not develop in fully 3D viscous disks, quenched by high-z gas layers that remain unperturbed due to the settling of dust near the midplane. Motivated by this suppression, we explored the inviscid limit and found that multiple dust subrings form, concentrating solids into several thin ring-like structures. These structures would remain unresolved in observations and would therefore appear as a single radially broad and vertically thin ring. This explains the geometry of the rings observed in protoplanetary disks without any need to invoke anisotropic turbulence. With regard to planetesimal formation, dust concentrations in the subrings might remain smaller than the threshold for gravitational collapse. However, gas photoevaporation enhances dust settling and (partially) radial concentration, eventually triggering the formation of dust clumps of increasingly large density, in both the viscous and inviscid cases. We conclude that planetesimal formation within dust-trapping pressure bumps is favored in very low-viscosity disks at late evolutionary stages, when sufficient gas has been removed by photoevaporation. This result is consistent with the inferred late formation of the parent bodies of chondritic meteorites in the Solar System.

Context. Isotopic properties of meteorites provide evidence that multiple dust trap or pressure bumps had to form and persist in the inner Solar System on a timescale of millions of years. The formation of a pressure bump at the outer edge of the gap opened by Jupiter would be effective in blocking particles drifting from the outer to the inner disc. Yet this would not be enough to preserve dust in the inner disc. However, in low-viscosity discs and under specific conditions governing the gas cooling time, it has been shown that massive planets can also open secondary gaps, separated by density bumps, inwards of the main gap. The majority of studies of the process of secondary gap formation have been done in two dimensional equatorial simulations with prescribed disc cooling or by approximating the cooling from the disc photosphere. Recent results have shown that an appropriate computation of the disc cooling by including the treatment of radiation transport is key to determining the formation of secondary gaps. Aims. Our aim is to extend previous studies to three dimensional discs by also including radiative effects. Moreover, we also consider non-ideal magnetohydrodynamic effects in discs with a prescribed cooling time to explore the feedback of the magnetic field on secondary gap formation. Methods. We performed three dimensional hydrodynamical numerical simulations with a self-consistent treatment of radiative effects making use of a flux-limited diffusion approximation. We then extended our study to a similar disc including the magnetic field and non-ideal Ohmic and ambipolar effects. Results. We show that in the hydrodynamical model, a disc with low bulk viscosity (α_ν = 10⁻⁴) and consistent treatment of radiative effects, a Jupiter-mass planet is capable of opening multiple gaps. We also show that multiple gaps and rings are formed by planetary masses close to the pebble isolation mass. In the presence of non-ideal MHD effects, multiple gaps and rings are also formed by a Jupiter-mass planet. Conclusions. A solid Jupiter core in low-viscosity discs blocks particles drifting towards and within the inner disc. The formation of multiple gaps and rings inside the planetary orbit at this stage is crucial to preserving dust reservoirs. Such reservoirs are pushed towards the inner part of the disc during Jupiter runaway growth and they are shown to be persistent after Jupiter’s growth. Multiple dust reservoirs could therefore be present in the inner Solar System since the formation of Jupiter’s solid core when the disc is characterised by low viscosity.

The link between the chemistry of the protoplanetary disk and the properties of the resulting planets have long been a subject of interest in the effort to understand planet formation. These connections have generally been made between mature planets and young protoplanetary disks through the carbon-to-oxygen (C/O) ratio. In a rare number of systems, young protoplanets have been found within their natal protoplanetary disks. These systems offer a unique opportunity to directly study the delivery of gas from the protoplanetary disk to the planet. In this work we post-process 3D numerical simulations of an embedded Jupiter-mass planet in its protoplanetary disk to explore the chemical evolution of gas as it flows from the disk to the planet. The relevant dust to this chemical evolution is assumed to be small co-moving grains with a reduced dust-to-gas ratio indicative of the upper atmosphere of a protoplanetary disk. We find that as the gas enters deep into the planet’s gravitational well, it warms significantly (up to ~800 K), releasing all of the volatile content from the ice phase. This change in phase can influence our understanding of the delivery of volatile species to the atmospheres of giant planets. The primary carbon, oxygen, and sulphur carrying ices (CO₂, H₂O, and H₂S) are released into the gas phase and along with the warm gas temperatures near the embedded planets lead to the production of unique species such as CS, SO, and SO₂ compared to the protoplanetary disk. We compute the column densities of SO, SO₂, CS, and H₂CS in our model and find that their values are consistent with previous observational studies.

Context. Giant planets grow and acquire their gas envelope during the disk phase. At the time of the discovery of giant planets in their host disk, it is important to understand the interplay between the host disk and the envelope and circum-planetary disk properties of the planet. Aims. Our aim is to investigate the dynamical and physical structure of the gas in the vicinity of a Jupiter-mass planet and study how protoplanetary disk properties, such as disk mass and viscosity, determine the planetary system as well as the accretion rate inside the planet’s Hill sphere. Methods. We ran global 3D simulations with the grid-based code fargOCA, using a fully radiative equation of state and a dust-to-gas ratio of 0.01. We built a consistent disk structure starting from vertical thermal equilibrium obtained by including stellar irradiation. We then let a gap open with a sequence of phases, whereby we deepened the potential and increased the resolution in the planet’s neighbourhood. We explored three models. The nominal one features a disk with surface density, ∑, corresponding to the minimum mass solar nebula at the planet’s location (5.2 au), characterised by an α viscosity value of 4 10⁻³ at the planet’s location. The second model has a surface density that is ten times smaller than the nominal one and the same viscosity. In the third model, we also reduced the viscosity value by a factor of 10. Results. During gap formation, giant planets accrete gas inside the Hill sphere from the local reservoir. Gas is heated by compression and cools according to opacity, density, and temperature values. This process determine the thermal energy budget inside the Hill sphere. In the analysis of our disks, we find that the gas flowing into the Hill sphere is approximately scaled as the product ∑ν, as expected from viscous transport. The accretion rate of the planetary system (envelope plus circum-planetary disk) is instead scaled as √Σv, with its efficiency depending on the thermal energy budget inside the Hill sphere. Conclusions. Previous studies have shown that pressure-supported or rotationally supported structures are formed around giant planets, depending on the equation of state (EoS) or on the opacity; namely, on the dust content within the Hill sphere. In the case of a fully radiative EoS and a constant dust to gas ratio of 0.01, we find that low-mass and low-viscosity circum-stellar disks favour the formation of a rotationally supported circum-planetary disk. Gas accretion leading to the doubling time of the planetary system of > 10⁵ years has only been found in the case of a low-viscosity disk.

Context. In the context of low-viscosity protoplanetary discs (PPDs), the formation scenarios of the Solar System should be revisited. In particular, the Jupiter-Saturn pair has been shown to lock in the 2:1 mean motion resonance while migrating generally inwards, making the Grand Tack scenario impossible. Aims. We explore what resonant chains of multiple giant planets can form in a low-viscosity disc, and whether these configurations can evolve into forming the Solar System in the post gas disc phase. Methods. We used hydrodynamical simulations with the code FARGOCA to study the migration of the giant planets in a disc with viscosity parameter of α = 10⁻⁴. After a transition phase to a gas-less configuration, we studied the stability of the obtained resonant chains through their interactions with a disc of leftover planetesimals by performing N-body simulations using rebound. Results. The gaps opened by giant planets are wider and deeper for lower viscosity, reducing the damping effect of the disc. Thus, when planets enter a resonance, the resonant angle remains closer to circulation, making the chain weaker. Exploring numerous configurations, we found five stable resonant chains of four or five planets. In a thin (cold) PPD, the four giant planets revert their migration and migrate outwards. After disc dispersal, under the influence of a belt of planetesimals, some resonant chains undergo an instability phase while others migrate smoothly over a billion years. For three of our resonant chains, about ~1% of the final configurations pass the four criteria to fit the Solar System. The most successful runs are obtained for systems formed in a cold PPD with a massive planetesimal disc. Conclusions. This work provides a fully consistent study of the dynamical history of the Solar System’s giant planets, from the protoplanetary disc phase up to the giant planet instability. Although building resonant configurations is difficult in low-viscosity discs, we find it possible to reproduce the Solar System from a cold, low-viscosity protoplanetary disc.

In a previous paper, we showed that, like the migration speed, the eccentricity damping efficiency is modulated linearly by the depth of the partial gap a planet carves in the disk surface density profile, resulting in less efficient e-damping compared to the prescription commonly used in population synthesis works. Here, we extend our analysis to 3D, refining our e-damping formula and studying how the inclination damping efficiency is also affected. We perform high-resolution 3D locally isothermal hydrodynamical simulations of planets with varying masses embedded in disks with varying aspect ratios and viscosities. We extract the gap profile and orbital damping timescales for fixed eccentricities and inclinations up to the disk scale height. The limit in gap depths below which vortices appear, in the low-viscosity case, happens roughly at the transition between classical type-I and type-II migration regimes. The orbital damping timescales can be described by two linear trends with a break around gap depths ∼80% and with slopes and intercepts depending on the eccentricity and inclination. These trends are understood on physical grounds and are reproduced by simple fitting formulas whose error is within the typical uncertainty of type-I torque formulas. Thus, our recipes for the gap depth and orbital damping efficiencies yield a simple description for planet–disk interactions to use in N-body codes in the case of partial-gap opening planets that is consistent with high-resolution 3D hydrosimulations. Finally, we show examples of how our novel orbital damping prescription can affect the outcome of population synthesis experiments.

The exoplanet population characterized by relatively short orbital periods (P < 100 d) around solar-type stars is dominated by super-Earths and sub-Neptunes. However, these planets are missing in our Solar System and the reason behind this absence is still unknown. Two theoretical scenarios invoke the role of Jupiter as the possible culprit: Jupiter may have acted as a dynamical barrier to the inward migration of sub-Neptunes from beyond the water iceline; alternatively, Jupiter may have considerably reduced the inward flux of material (pebbles) required to form super-Earths inside that iceline. Both scenarios predict an anti-correlation between the presence of small planets and that of cold Jupiters in exoplanetary systems. To test that prediction, we homogeneously analyzed the radial-velocity measurements of 38 Kepler and K2 transiting small planet systems gathered over nearly ten years with the HARPS-N spectrograph, as well as publicly available radial velocities collected with other facilities. We used Bayesian differential evolution Markov chain Monte Carlo techniques, which in some cases were coupled with Gaussian process regression to model non-stationary variations due to stellar magnetic activity phenomena. We detected five cold Jupiters in three systems: two in Kepler-68, two in Kepler-454, and a very eccentric one in K2-312. We also found linear trends caused by bound companions in Kepler-93, Kepler-454, and K2-12, with slopes that are still compatible with a planetary mass for outer bodies in the Kepler-454 and K2-12 systems. By using binomial statistics and accounting for the survey completeness, we derived an occurrence rate of 9.3_−2.9^+7.7% for cold Jupiters with 0.3–13 M_Jup and 1–10 AU, which is lower but still compatible at 1.3σ with the value measured from radial-velocity surveys for solar-type stars, regardless of the presence or absence of small planets. The sample is not large enough to draw a firm conclusion about the predicted anti-correlation between small planets and cold Jupiters; nevertheless, we found no evidence of previous claims of an excess of cold Jupiters in small planet systems. As an important byproduct of our analyses, we homogeneously determined the masses of 64 Kepler and K2 small planets, reaching a precision better than 5, 7.5, and 10σ for 25, 13, and 8 planets, respectively. Finally, we release the 3661 HARPS-N radial velocities used in this work to the scientific community. These radial-velocity measurements mainly benefit from an improved data reduction software that corrects for subtle prior systematic effects.

Context. Radius and mass measurements of short-period giant planets reveal that many of these planets contain a large amount of heavy elements. Although the range of inferred metallicities is broad, planets with more than 100 M_⊕ of heavy elements are not rare. This is in sharp contrast with the expectations of the conventional core-accretion model for the origin of giant planets. Aims. The proposed explanations for the heavy-element enrichment of giant planets fall short of explaining the most enriched planets. We look for additional processes that can explain the full envelope of inferred enrichments. Methods. We revisited the dynamics of pebbles and dust in the vicinity of giant planets using analytic estimates and published results on the profile of a gap opened by a giant planet, the radial velocity of the gas with respect to the planet, the Stokes number of particles in the different parts of the disk, and the consequent dust/gas ratio. Although our results are derived in the framework of a viscous α-disk, we also discuss the case of disks driven by angular momentum removal in magnetized winds. Results. When giant planets are far from the star, dust and pebbles are confined to a pressure bump at the outer edge of the planet-induced gap. When the planets reach the inner part of the disk (r_p ≪ 2 au), dust instead penetrates into the gap together with the gas. The dust/gas ratio can be enhanced by more than an order of magnitude if the radial drift of dust is not impeded farther out by other barriers. Thus, hot planets undergoing runaway gas accretion can swallow a large amount of dust, acquiring ~100 M_⊕ of heavy elements by the time they reach Jupiter masses. Conclusions. Whereas the gas accreted by giant planets in the outer disk is very dust-poor, that accreted by hot planets can be extremely dust-rich. Thus, provided that a large fraction of the atmosphere of hot Jupiters is accreted in situ, a large amount of dust can be accreted as well. We draw a distinction between this process and pebble accretion (i.e., the capture of dust without the accretion of gas), which is ineffective at small stellocentric radii, even for super-Earths. Giant planets farther out in the disk are extremely effective barriers against the flow of pebbles and dust across their gap. Saturn and Jupiter, after locking into a mutual mean motion resonance and reversing their migration, could have accreted small pebble debris.

Context. Numerous studies have shown that a gap-forming Jovian mass planet embedded in a protoplanetary disc, in which a turbulent viscosity operates, can accrete gas efficiently through the gap, and for typical parameters it doubles its mass in ~0.1 Myr. The planet also migrates inwards on a timescale that is closely related to the local viscous evolution timescale, which is also typically 0.1 Myr. These timescales are short compared to protoplanetary disc lifetimes, and raise questions about the origins of the cold gas giant exoplanets that have been discovered in abundance. It is understood that protoplanetary discs are unlikely to be globally turbulent, and instead they may launch magnetised winds such that accretion towards the star occurs in laminar accretion flows located in narrow layers near the surfaces of the disc. Aims. The aim of this study is to examine the rate at which gas accretes onto Jovian mass planets that are embedded in layered protoplanetary discs, and to compare the results with those obtained for viscous models. Methods. We use 3D hydrodynamical simulations of planets embedded in protoplanetary discs, in which a constant radial mass flux towards the star of ṁ = 10⁻⁸ M_⊙ yr⁻¹ is sustained. We consider a classical viscous α disc model, and also models in which an external torque is applied in narrow surface layers to mimic the effects of a magnetised wind. The accreting layers have a variety of depths, as parameterised by their column densities Σ_A, and we consider values of Σ_A in the range 0.1−10 g cm⁻². Results. The viscous disc model gives results in agreement with previous studies. In accord with our recent work that examines the migration of Jovian mass planets in layered models, we find the accretion rate onto the planet in the layered models crucially depends on the ability of the planet to block the wind-induced mass flow towards the star. For Σ_A = 10 g cm⁻², the planet torque can block the mass flow in disc, accretion onto the planet is slow, and a mass doubling time of 10 Myr is obtained. For Σ_A = 0.1 g cm⁻², the flow is not blocked, accretion is fast, and the mass doubling time is 0.2 Myr. Conclusions. Our results show that although the radial mass flow through the layered disc models is always 10⁻⁸ M_⊙ yr⁻¹, adopting different values of Σ_A leads to very different gas accretion rates onto embedded gas giant planets.