Proto-planets embedded in their natal disks acquire hot envelopes as they grow and accrete solids. This ensures that the material they accrete - pebbles, as well as (small) planetesimals - will vaporize to enrich their atmospheres. Enrichment modifies an envelope's structure and significantly alters its further evolution. Our aim is to describe the formation of planets with polluted envelopes from the moment that impactors begin to sublimate to beyond the disk's eventual dissipation. We constructed an analytical interior structure model, characterized by a hot and uniformly mixed high-Z vapor layer surrounding the core, located below the usual unpolluted radiative-convective regions. The evolution of planets with uniformly mixed polluted envelopes follows four potential phases. Initially, the central core grows directly through impacts and rainout until the envelope becomes hot enough to vaporize and absorb all incoming solids. We find that a planet reaches runaway accretion when the sum of its core and vapor mass exceeds a value that we refer to as the critical metal mass - a criterion that supersedes the traditional critical core mass. It scales positively with both the pollutant's evaporation temperature and with the planet's core mass. Hence, planets at shorter orbital separations require the accretion of more solids to reach runaway as they accrete less volatile materials. If the solids accretion rate dries up, we identify the decline of the mean molecular weight - dilution - as a mechanism to limit gas accretion during a polluted planet's embedded cooling phase. When the disk ultimately dissipates, the envelope's inner temperature declines and its vapor eventually rains out, augmenting the mass of the core. The energy release that accompanies this does not result in significant mass-loss, as it only occurs after the planet has substantially contracted.
The amount of nebular gas that a planet can bind is limited by its cooling rate, which is set by the opacity of its envelope. Accreting dust and pebbles contribute to the envelope opacity and, thus, influence the outcome of planet formation. Our aim is to model the size evolution and opacity contribution of solids inside planetary envelopes. We then use the resultant opacity relations to study emergent trends in planet formation. We design a model for the opacity of solids in planetary envelopes that accounts for the growth, fragmentation and erosion of pebbles during their sedimentation. We f…
We analyse the size evolution of pebbles accreted into the gaseous envelope of a protoplanet growing in a protoplanetary disc, taking into account collisions driven by the relative sedimentation speed as well as the convective gas motion. Using a simple estimate of the convective gas speed based on the pebble accretion luminosity, we find that the speed of the convective gas is higher than the sedimentation speed for all particles smaller than 1 mm. This implies that both pebbles and pebble fragments are strongly affected by the convective gas motion and will be transported by large-scale conv…
In the Solar System giant planets come in two flavours: 'gas giants' (Jupiter and Saturn) with massive gas envelopes and 'ice giants' (Uranus and Neptune) with much thinner envelopes around their cores. It is poorly understood how these two classes of planets formed. High solid accretion rates, necessary to form the cores of giant planets within the life-time of protoplanetary discs, heat the envelope and prevent rapid gas contraction onto the core, unless accretion is halted. We find that, in fact, accretion of pebbles (~ cm-sized particles) is self-limiting: when a core becomes massive enoug…
Wind erosion is a destructive mechanism that completely dissolves a weakly bound object like a planetesimal into its constituent particles, if the velocity relative to the ambient gas and the local gas pressure are sufficiently high. In numerical simulations we study the influence of such wind erosion on pebble and planetesimal accretion by a planetary body up to $10 R_\mathrm{Earth}$. Due to the rapid size reduction of an in-falling small body, the accretion outcome changes significantly. Erosion leads to a strong decrease in the accretion efficiency below a threshold size of the small body o…
Context: Planet formation by pebble accretion is an alternative to planetesimal-driven core accretion. In this scenario, planets grow by accreting cm-to-m-sized pebbles instead of km-sized planetesimals. One of the main differences with planetesimal-driven core accretion is the increased thermal ablation experienced by pebbles. This provides early enrichment to the planet's envelope, which changes the process of core growth. Aims: We aim to predict core masses and envelope compositions of planets that form by pebble accretion and compare mass deposition of pebbles to planetesimals. Methods: We…
The omnipresence of super-Earths suggests that they are able to be retained in natal disks around low-mass stars, whereas exoplanets' mass distribution indicates that some cores have transformed into gas giants through runaway gas accretion at 1AU from solar-type stars. In this paper, we show that transition to runaway gas accretion by cores may be self-impeded by an increase of the grain opacity in their envelope after they have acquired sufficient mass (typically 10Mearth) to enter a pebble-isolation phase. The accumulation of mm-m size pebbles in their migration barriers enhances their loca…
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 sub-solar 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 sub…
We compute the maximum mass a growing planetary embryo can reach depending on the size of accreted planetesimals or pebbles, to infer the possibility of growing the cores of giant planets, and giant planets themselves. We compute the internal structure of the gas envelope of planetary embryos, to determine the core mass that is necessary to bind an envelope large enough to destroy planetesimals or pebbles while they are gravitationally captured. We also consider the effect of the advection wind originating from the protoplanetary disk, following the results of Ormel et al. (2015). We show that…
This paper identifies constraints on the growth of a small planetary core (0.3 M$_{\oplus}$) that accretes millimeter-sized pebbles from a gaseous disk. We construct time-dependent spherical envelope models that capture physical processes not included in existing global hydrodynamic simulations, including particle size evolution, dust transport, and realistic gas equations of state. We assume a low enough disk density that pebbles are marginally coupled to the gas and are trapped efficiently near the core Bondi radius. Pebbles then drift rapidly enough to experience erosion by sandblasting, mu…
Pebbles of millimeter sizes are abundant in protoplanetary discs around young stars. Chondrules inside primitive meteorites - formed by melting of dust aggregate pebbles or in impacts between planetesimals - have similar sizes. The role of pebble accretion for terrestrial planet formation is nevertheless unclear. Here we present a model where inwards-drifting pebbles feed the growth of terrestrial planets. The masses and orbits of Venus, Earth, Theia (which later collided with the Earth to form the Moon) and Mars are all consistent with pebble accretion onto protoplanets that formed around Mar…
During their formation, planets form large, hot atmospheres due to the ongoing accretion of solids. It has been customary to assume that all solids end up at the center constituting a "core" of refractory materials, whereas the envelope remains metal-free. Recent work, as well as observations by the JUNO mission, indicate however that the distinction may not be so clear cut. Indeed, small silicate, pebble-sized particles will sublimate in the atmosphere when they hit the sublimation temperature (T ~ 2,000 K). In this paper we extend previous analytical work to compute the properties of planets…
We investigate possible pathways for the formation of the low density Neptune-mass planet HAT-P-26b. We use two formation different models based on pebbles and planetesimals accretion, and includes gas accretion, disk migration and simple photoevaporation. The models tracks the atmospheric oxygen abundance, in addition to the orbital period, and mass of the forming planets, that we compare to HAT-P-26b. We find that pebbles accretion can explain this planet more naturally than planetesimals accretion that fails completely unless we artificially enhance the disk metallicity significantly. Pebbl…
In the core accretion scenario, a massive core forms first and then accretes an envelope. When discussing how this core forms some divergences appear. First scenarios of planet formation predict the accretion of km-sized bodies, called planetesimals, while more recent works suggest growth by accretion of pebbles, which are cm-sized objects. These two accretion models are often discussed separately and we aim here at comparing the outcomes of the two models with identical initial conditions. We use two distinct codes: one computing planetesimal accretion, the other pebble accretion. Using a pop…
The formation of planets depends on the underlying protoplanetary disc structure, which influences both the accretion and migration rates of embedded planets. The disc itself evolves on time-scales of several Myr during which both temperature and density profiles change as matter accretes onto the central star. Here we use a detailed model of an evolving disc to determine the growth of planets by pebble accretion and their migration through the disc. Cores that reach their pebble isolation mass accrete gas to finally form giant planets with extensive gas envelopes, while planets that do not re…
One of the main scenarios of planet formation is the core accretion model where a massive core forms first and then accretes a gaseous envelope. This core forms by accreting solids, either planetesimals, or pebbles. A key constraint in this model is that the accretion of gas must proceed before the dissipation of the gas disc. Classical planetesimal accretion scenario predicts that the time needed to form a giant planets core is much longer than the time needed to dissipate the disc. This difficulty led to the development of another accretion scenario, in which cores grow by accretion of pebbl…
We have investigated how envelope pollution by icy planetesimals affects the critical core mass for gas giant formation and the gas accretion time-scales. In the core-accretion model, runaway gas accretion is triggered after a core reaches a critical core mass. All the previous studies on the core-accretion model assumed that the envelope has the solar composition uniformly. In fact, the envelope is likely polluted by evaporated materials of icy planetesimals because icy planetesimals going through the envelope experience mass loss via strong ablation and most of their masses are deposited in …
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…
A Dichotomy of the Mass-Metallicity Relation of Exoplanetary Atmospheres Demarcated by their Birthplace
Division of Science, National Astronomical Observatory of Japan（日本国立天文台科学部）；Graduate Institute for Advanced Studies, SOKENDAI（综合研究大学院大学）；Astrobiology Center（天体生物学中心）；Department of Earth and Planetary Science, The University of Tokyo（东京大学地球行星科学系）；Department of Earth and Planetary Sciences, Institute of Science Tokyo（东京科学大学地球行星科学系）；UTokyo Organization for Planetary Space Science (UTOPS), University of Tokyo（东京大学宇宙行星科学研究组织）；Kapteyn Astronomical Institute, University of Groningen（格罗宁根大学卡普坦天文研究所）
We present a study on the formation of planetary systems around low mass stars similar to Trappist-1, through the accretion of either planetesimals or pebbles. The aim is to determine if the currently observed systems around low mass stars favour one scenario over the other. We ran numerous N-body simulations, coupled to a thermally evolving viscous disc model, including prescriptions for planet migration and photoevaporation. We examine the differences between the pebble and planetesimal accretion scenarios, but also look at the influences of disc mass, planetesimal size, and the percentage o…
The formation of planetary cores must proceed rapidly in order for the giant planets to accrete their gaseous envelopes before the dissipation of the protoplanetary gas disc (<3 Myr). In orbits beyond 10 AU, direct accumulation of planetesimals by the cores is too slow. Fragments of planetesimals could be accreted faster, but planetesimals are likely too large for fragmentation to be efficient, and resonant trapping poses a further hurdle. Here we instead investigate the accretion of small pebbles (mm-cm sizes) that are the natural outcome of an equilibrium between the growth and radial drift …
We study the dynamics and growth of dust particles in circumstellar disks of different masses that are prone to gravitational instability during the critical first Myr of their evolution. The dust component is made up of two different components: micron-sized dust and grown dust of evolving size. For the dust component, we considered the dust coagulation, fragmentation, momentum exchange with the gas, and dust self-gravity. We found that the micron-sized dust particles grow rapidly in the circumstellar disk, reaching a few cm in size in the inner 100 au of the disk during less than 100 kyr aft…
Jupiter's atmosphere is enriched in C, N, S, P, Ar, Kr and Xe with respect to solar abundances by a factor of ~3. Gas Giant envelopes are mainly enriched through the dissolution of solids in the atmosphere, and this constant enrichment factor is puzzling since several of the above elements are not expected to have been in the solid phase in Jupiter's feeding zone; most seriously, Ar and the main carrier of N, N2, only condense at the very low temperatures, 21-26 K, associated with the outer solar nebula. We propose that a plausible solution to the enigma of Jupiter's uniform enrichment pattern…
The compositions of nascent planets depend on the compositions of their birth disks. In particular, the elemental compositions of Gas Giant gaseous envelopes depend on the elemental composition of the disk gas from which the envelope is accreted. Previous models demonstrated that sequential freeze-out of O and C-bearing volatiles in disks will result in an supersolar C/O ratios and subsolar C/H ratios in the gas between water and CO snowlines. This result does not take into account, however, the expected grain growth and radial drift of pebbles in disks, and the accompanying re-distribution of…
Numerous circumbinary planets have been discovered in surveys of transiting planets. Often, these planets are found to orbit near to the zone of dynamical instability, close to the central binary. The existence of these planets has been explained by hydrodynamical simulations that show that migrating circumbinary planets, embedded in circumbinary discs, halt at the central cavity that is formed by the central binary. Transit surveys are naturally most sensitive to finding circumbinary planets with the shortest orbital periods. The future promise of detecting longer period systems using radial-…
According to planetary interior models, some giant planets contain large metal masses with large metal-mass fractions. HD 149026b and TOI-849b are characteristic examples of these giant planets. It has been suggested that the envelope mass loss during giant impacts plays a key role in the formation of such giant planets. The aim of the present letter is to propose a mechanism that can explain the origin of such giant planets. We investigate the formation of giant planets in a rapidly dissipating disk using N-body simulations that consider pebble accretion. The results show that although the pe…
The observed lifetimes of gaseous protoplanetary discs place strong constraints on gas and ice giant formation in the core accretion scenario. The approximately 10-Earth-mass solid core responsible for the attraction of the gaseous envelope has to form before gas dissipation in the protoplanetary disc is completed within 1-10 million years. Building up the core by collisions between km-sized planetesimals fails to meet this time-scale constraint, especially at wide stellar separations. Nonetheless, gas-giant planets are detected by direct imaging at wide orbital distances. In this paper, we nu…
We investigate the chemical composition of the solar system's giant planets atmospheres using a physical formation model with chemistry. The model incorporate disk evolution, pebbles and gas accretion, type I and II migration, simplified disk photoevaporation and solar system chemical measurements. We track the chemical compositions of the formed giant planets and compare them to the observed values. Two categories of models are studied: with and without disk chemical enrichment via photoevaporation. Predictions for the Oxygen and Nitrogen abundances, core masses, and total amount of heavy ele…
We compute, for the first time, self-consistent models of planet growth including the effect of envelope enrichment. The change of envelope metallicity is assumed to be the result of planetesimal disruption or icy pebble sublimation. We solve internal structure equations taking into account global energy conservation for the envelope to compute in-situ planetary growth. We consider different opacities and equations of state suited for a wide range of metallicities. We find that envelope enrichment speeds up the formation of gas giants. It also explains naturally the formation of low and interm…
A substantial number of super-Earths have been discovered, and atmospheres of transiting super-Earths have also been observed by transmission spectroscopy. Several lines of observational evidence indicate that most super-Earths do not possess massive H$_2$/He atmospheres. However, accretion and retention of less massive atmospheres on super-Earths challenge planet formation theory. We consider the following three mechanisms: (i) envelope heating by pebble accretion, (ii) mass loss during giant impacts, and (iii) atmospheric loss by stellar X-ray and EUV photoevaporation. We investigate whether…
We present evidence that excesses in Be in polluted white dwarfs (WDs) are the result of accretion of icy exomoons that formed in the radiation belts of giant exoplanets. Here we use excess Be in the white dwarf GALEX J2339-0424 as an example. We constrain the parent body abundances of rock-forming elements in GALEX J2339-0424 and show that the overabundance of beryllium in this WD cannot be accounted for by differences in diffusive fluxes through the WD outer envelope nor by chemical fractionations during typical rock-forming processes. We argue instead that the Be was produced by energetic p…
We explore the heating and differentiation of rocky planets that grow by rapid pebble accretion. Our terrestrial planets grow outside of the ice line and initially accrete 28\% water ice by mass. The accretion of water stops after the protoplanet reaches a mass of $0.01\,M_{\rm E}$ where the gas envelope becomes hot enough to sublimate the ice and transport the vapour back to the protoplanetary disc by recycling flows. The energy released by the decay of $^{26}$Al melts the accreted ice to form clay (phyllosilicates), oxidized iron (FeO), and a water surface layer with ten times the mass of Ea…
Despite many methods developed to find young massive planets in protoplanetary discs, it is challenging to directly detect low-mass planets that are embedded in discs. On the other hand, the core-accretion theory suggests that there could be a large population of embedded low-mass young planets at the Kelvin-Helmholtz (KH) contraction phase. We adopt both 1-D models and 3-D simulations to calculate the envelopes around low-mass cores (several to tens of $M_{\oplus}$) with different luminosities, and derive their thermal fluxes at radio wavelengths. We find that, when the background disc is opt…
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 (MESA). 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 accretio…
Context. We investigate the grain opacity k_gr in the atmosphere of protoplanets. This is important for the planetary mass-radius relation since k_gr affects the H/He envelope mass of low-mass planets and the critical core mass of giant planets. Aims. The goal of this study is to derive an analytical model for k_gr. Methods. Our model is based on the comparison of the timescales of microphysical processes like grain settling in the Stokes and Epstein regime, growth by Brownian motion coagulation and differential settling, grain evaporation, and grain advection due to envelope contraction. With…
Planetary cores are thought to form in proto-planetary disks via the growth of dusty solid material. However, it is unclear how early this process begins. We study the physical structure and grain growth in the edge-on disk that surrounds the ~1 Myr old low-mass (~0.55 Msun) protostar embedded in the Bok Globule CB26 to examine how much grain growth has already occurred in the protostellar phase. We combine the SED between 0.9 $μ$m and 6.4 cm with high angular resolution continuum maps at 1.3, 2.9, and 8.1 mm, and use the radiative transfer code RADMC-3D to conduct a detailed modelling of the …
The formation of planets with gaseous envelopes takes place in protoplanetary accretion discs on time-scales of several millions of years. Small dust particles stick to each other to form pebbles, pebbles concentrate in the turbulent flow to form planetesimals and planetary embryos and grow to planets, which undergo substantial radial migration. All these processes are influenced by the underlying structure of the protoplanetary disc, specifically the profiles of temperature, gas scale height and density. The commonly used disc structure of the Minimum Mass Solar Nebular (MMSN) is a simple pow…
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 perform a series of…
The existence of a Radius Valley in the Kepler size distribution stands as one of the most important observational constraints to understand the origin and composition of exoplanets with radii between that of Earth and Neptune. The goal of this work is to provide insights into the existence of the Radius Valley from, first, a pure formation point of view, and second, a combined formation-evolution model. We run global planet formation simulations including the evolution of dust by coagulation, drift and fragmentation; and the evolution of the gaseous disc by viscous accretion and photoevaporat…
Uranus and Neptune are ice giants with $\sim$ 15% atmospheres by mass, placing them in an intermediate category between rocky planets and gas giants. These atmospheres are too massive to have been primarily outgassed, yet they never underwent runaway gas accretion. The ice giants never reached critical core mass ($M_\text{crit}$) in a full gas disk, yet their cores are $\gtrsim M_\text{crit}$, suggesting that their envelopes were mainly accreted at the end of the disk lifetime. Pebble accretion calls into question traditional slow atmospheric growth during this phase. We show that the full-siz…
The present-day envelope of gaseous planets is a relic of how these giant planets originated and evolved. Measuring their elemental composition therefore presents a powerful opportunity to answer long-standing questions regarding planet formation. Obtaining precise observational constraints on the elemental inventory of giant exoplanets has, however, remained challenging due to the limited simultaneous wavelength coverage of current space-based instruments. Here, we present thermal emission observations of the non-transiting hot Jupiter $τ$ Boo b using the new wide wavelength coverage (0.95$-$…
How Late Solid Enrichment Shapes Atmospheric Abundances in Giant Planets
University of Waterloo（滑铁卢大学）；Waterloo Centre for Astrophysics, University of Waterloo（滑铁卢大学天体物理中心）；University of Guelph（圭尔夫大学）；Western University（韦仕敦大学）
An accumulation of multi-epoch, high-resolution, optical spectra reveal that the nearby star G77-50 is a very cool DAZ white dwarf externally polluted by Mg, Fe, Al, Ca, and possibly Na, Cr, Mn. The metallic and hydrogen absorption features all exhibit multiple components consistent with Zeeman splitting in a B~120kG magnetic field. Ultraviolet through infrared photometry combined with trigonometric parallaxes yield Teff=5310K, M=0.60Msun, and a cooling age of 5.2Gyr. The space velocity of the white dwarf suggests possible membership in the Galactic thick disk, consistent with an estimated tot…
