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 local fragmentation rates. The freshly produced sub-mm grains pass through the barrier, elevate the effective dust opacity and reduce the radiative flux in the cores envelope. These effects alone are adequate to suppress the transition to runaway accretion and preserve super-Earths in the stellar proximity (0.1 AU), albeit entropy advection between the envelope and the disk can further reduce the accretion rate. At intermediate distance (1AU) from their host stars, the escalation in the dust opacity dominates over entropy advection in stalling the transition to runaway accretion for marginally pebble-isolated cores. Beyond a few AU, the transformation of more massive cores to gas giants is reachable before severe depletion of disk gas. This requirement can be satisfied either in extended disks with large scale height via orderly accretion of migrating pebbles or through the mergers of oligarchic protoplanetary embryos, and can account for the correlated occurrence of long-period gas giants and close-in super-Earths.
The growth of a planetary core by pebble accretion stops at the so called pebble isolation mass, when the core generates a pressure bump that traps drifting pebbles outside its orbit. If the isolation mass is very small, then gas accretion is protracted and the planet remains at a few Earth masses with a mainly solid composition. For larger values of the pebble isolation mass, the planet might be able to accrete gas from the protoplanetary disc and grow into a gas giant. Previous works have determined a scaling of the pebble isolation mass with cube of the disc aspect ratio. Here we expand on …
The growth of a pebble accreting planetary core is stopped when reaching its \textit{isolation mass} that is due to a pressure maximum emerging at the outer edge of the gap opened in gas. This pressure maximum traps the inward drifting pebbles stopping the accretion of solids onto the core. On the other hand, a large amount of pebbles ($\sim 100M_\oplus$) should flow through the orbit of the core until reaching its isolation mass. The efficiency of pebble accretion increases if the core grows in a dust trap of the protoplanetary disc. Dust traps are observed as ring-like structures by ALMA sug…
We investigate the pebble isolation mass for a planet on a fixed eccentric orbit in its protoplanetary disc by conducting a set of 2D hydrodynamical simulations including dust turbulent diffusion. A range of planet eccentricities up to $e=0.2$ is adopted. Our simulations also cover a range of $α-$turbulent viscosities, and for each pair $\{α,e\}$ the pebble isolation mass is estimated as the minimum planet mass in our simulations such that solids with a Stokes number $\gtrsim 0.05$ do not flow across the planet orbit and remain trapped around a pressure bump outside the planet gap. For $α<10^{…
When a planet becomes massive enough, it gradually carves a partial gap around its orbit in the protoplanetary disk. A pressure maximum can be formed outside the gap where solids that are loosely coupled to the gas, typically in the pebble size range, can be trapped. The minimum planet mass for building such a trap, which is called the pebble isolation mass (PIM), is important for two reasons: it marks the end of planetary growth by pebble accretion, and the trapped dust forms a ring that may be observed with millimetre observations. We study the effect of disk turbulence on the pebble isolati…
The conditions in the protoplanetary disc are determinant for the various planet formation mechanisms. We present a framework which combines self-consistent disc structures with the calculations of the growth rates of planetary embryos via pebble accretion, in order to study the formation of Super-Earths. We first perform 2D hydrodynamical simulations of the inner discs, considering a grain size distribution with multiple chemical species and their corresponding size and composition dependent opacities. The resulting aspect ratios are almost constant with orbital distance, resulting in radiall…
Planetary migration is a major challenge for planet formation theories. The speed of Type I migration is proportional to the mass of a protoplanet, while the final decade of growth of a pebble-accreting planetary core takes place at a rate that scales with the mass to the two-thirds power. This results in planetary growth tracks (i.e., the evolution of a protoplanet's mass versus its distance from the star) that become increasingly horizontal (migration-dominated) with rising mass of the protoplanet. It has been shown recently that the migration torque on a protoplanet is reduced proportional …
Much recent work on planet formation has focused on the growth of planets by accretion of grains whose aerodynamic properties make them marginally coupled to the nebular gas, a theory commonly referred to as "pebble accretion". While pebble accretion can ameliorate some of the issues presented by growth by purely gravitational processes, it has other issues when compared with observations of exoplanetary systems. A particular concern is the preponderance of planets that end their growth as "super-Earths" or "sub-Neptunes", with masses in the range 2-10 $M_\oplus$. Once planets reach this mass …
The majority of gas giants (planets of masses $\gtrsim10^2 M_\oplus$) are found to reside at distances beyond $\sim1$ au from their host stars. Within 1 au, the planetary population is dominated by super-Earths of $2-20 M_\oplus$. We show that this dichotomy between inner super-Earths and outer gas giants can be naturally explained should they form in nearly inviscid disks. In laminar disks, a planet can more easily repel disk gas away from its orbit. The feedback torque from the pile-up of gas inside the planet's orbit slows down and eventually halts migration. A pressure bump outside the pla…
In the general classical picture of pebble-based core growth, planetary cores grow by accretion of single pebble species. The growing planet may reach the so-called pebble isolation mass, at which it induces a pressure bump that blocks inward drifting pebbles exterior to its orbit, thereby stalling core growth by pebble accretion. In recent hydrodynamic simulations, pebble filtration by the pressure bump depends on several parameters including core mass, disc structure, turbulent viscosity and pebble size. We investigated how accretion of multiple, instead of single, pebble species affects cor…
We develop a pebble-driven model to study the formation and evolution of planets around stars in the mass range of 0.08 and 1 solar mass. The growth and migration of a large number of individual protoplanetary embryos are simulated in a population synthesis manner. We test two hypotheses for the birth locations of embryos: at the water ice line or log-uniformly distributed over entire protoplanetary disks. Two types of disks with different turbulent viscous parameters alpha of 1e-3 and 1e-4 are investigated, to shed light on the role of outward migration of protoplanets. The forming planets ar…
We model the early stages of planet formation in the Solar System, including continual planetesimal formation, and planetesimal and pebble accretion onto planetary embryos in an evolving disk driven by a disk wind. The aim is to constrain aspects of planet formation that have large uncertainties by matching key characteristics of the Solar System. The model produces a good fit to these characteristics for a narrow range of parameter space. Planetary growth beyond the ice line is dominated by pebble accretion. Planetesimal accretion is more important inside the ice line. Pebble accretion inside…
The formation of super-Earths is strongly linked to the structure of the protoplanetary disc, which determines growth and migration. In the pebble accretion scenario, planets grow to the pebble isolation mass, at which the planet carves a small gap in the gas disc halting the pebble flux and thus its growth. The pebble isolation mass scales with the disc's aspect ratio, which directly depends on the disc structure. I compare the growth of super-Earths in viscously heated discs and discs purely heated by the central star with super-Earth observations. This allows two formation pathways of super…
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…
Giant planets migrate though the protoplanetary disc as they grow. We investigate how the formation of planetary systems depends on the radial flux of pebbles through the protoplanetary disc and on the planet migration rate. Our N-body simulations confirm previous findings that Jupiter-like planets in orbits outside the water ice line originate from embryos starting out at 20-40 AU when using nominal type-I and type-II migration rates and a pebble flux of 100-200 Earth masses per million years, enough to grow Jupiter within the lifetime of the solar nebula. The planetary embryos placed up to 3…
Recent detailed observations of protoplanetary discs revealed a lot of sub-structures which are mostly ring-like. One interpretation is that these rings are caused by growing planets. These potential planets are not yet opening very deep gaps in their discs. These planets instead form small gaps in the discs to generate small pressure bumps exterior to their orbits that stop the inflow of the largest dust particles. In the pebble accretion paradigm, this planetary mass corresponds to the pebble isolation mass, where pebble accretion stops and efficient gas accretion starts. We perform planet p…
Overcoming type I migration and preventing low-mass planets from spiralling into the central star is a long-studied topic. It is well known that outward migration is possible in viscous-heated discs relatively close to the central star because the entropy gradient can be sufficiently steep that the positive corotation torque overcomes the negative Lindblad torque. Yet efficiently trapping planets in this region remains elusive. Here we study disc conditions that yield outward migration for low-mass planets under specific planet migration prescriptions. Using a steady-state disc model with a co…
Reading between the rings: observed dust ring properties as probes of planet masses
University of Warwick（华威大学）；Centre for Exoplanets and Habitability, University of Warwick（华威系外行星与宜居性中心）；University of Victoria（维多利亚大学）；Massachusetts Institute of Technology（麻省理工学院）；McMaster University（麦克马斯特大学）；Origins Institute, McMaster University（麦克马斯特大学起源研究所）
The physics of planet formation is investigated using a population synthesis approach. We develop a simple model for planetary growth including pebble and gas accretion, and orbital migration in an evolving protoplanetary disk. The model is run for a population of 2000 stars with a range of disk masses and radii, and initial protoplanet orbits. The resulting planetary distribution is compared with the observed population of extrasolar planets, and the model parameters are improved iteratively using a particle swarm optimization scheme. The characteristics of the final planetary systems are mai…
We present an analytical model to investigate the production of pebbles and their radial transport through a protoplanetary disk (PPD) with magnetically driven winds. While most of the previous analytical studies in this context assume that the radial turbulent coefficient is equal to the vertical dust diffusion coefficient, in the light of the results of recent numerical simulations, we relax this assumption by adopting effective parametrisations of the turbulent coefficients involved in terms of the strength of the magnetic fields driving the wind. Theoretical studies have already pointed ou…
It is generally accepted that the four major (Galilean) satellites formed out of the gas disk that accompanied Jupiter's formation. However, understanding the specifics of the formation process is challenging as both small particles (pebbles) as well as the satellites are subject to fast migration processes. Here, we hypothesize a new scenario for the origin of the Galilean system, based on the capture of several planetesimal seeds and subsequent slow accretion of pebbles. To halt migration, we invoke an inner disk truncation radius, and other parameters are tuned for the model to match physic…
We study the effect of a migrating planet ($10<M_p<20$ Earth mass) on the dynamics of pebbles in a radiative disk using 2D two-fluid simulations carried out with the RoSSBi code. The combined action of the waves induced by the migrating planet and drag back-reaction on the gas produces a complex evolution of the flux of pebbles. The waves excite zonal flows which act as dust traps, and accumulate pebbles. Owing to drag back-reaction, a Kelvin-Helmholtz instability develops, generating turbulent dust rings containing several Earth masses of solids, where planetesimal formation is likely. The mo…
Super-Earths are found in tighter orbits than the Earth's around more than one third of main sequence stars. It has been proposed that super-Earths are scaled-up terrestrial planets that formed similarly, through mutual accretion of planetary embryos, but in discs much denser than the solar protoplanetary disc. We argue instead that terrestrial planets and super-Earths have two distinct formation pathways that are regulated by the disc's pebble reservoir. Through numerical integrations, which combine pebble accretion and N-body gravity between embryos, we show that a difference of a factor of …
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…
We study the formation of rocky planets by dry pebble accretion from self-consistent dust-growth models. In particular, we aim at computing the maximum core mass of a rocky planet that can sustain a thin H-He atmosphere to account for the second peak of the Kepler's size distribution. We simulate planetary growth by pebble accretion inside the ice line. The pebble flux is computed self-consistently from dust growth by solving the advection-diffusion equation for a representative dust size. Dust coagulation, drift, fragmentation and sublimation at the water iceline are included. The disc evolut…
The solid accretion rate, necessary to grow gas giant planetary cores within the disk lifetime, has been a major constraint for theories of planet formation. We tested the solid accretion rate efficiency on planetary cores of different masses embedded in their birth disk, by means of 3D radiation-hydrodynamics, where we followed the evolution of a swarm of embedded solids of different sizes. We found that using a realistic equation of state and radiative cooling, the disk at 5 au is able to cool efficiently and reduce its aspect ratio. As a result, the pebble isolation mass is reached before t…
Context: Pebble accretion is expected to be the dominant process for the formation of massive solid planets, such as the cores of giant planets and super-Earths. So, far, this process has been studied under the assumption that dust coagulates and drifts throughout the full protoplanetary disk. However, observations show that many disks are structured in rings that may be due to pressure maxima, preventing the global radial drift of the dust. Aims: We study how the pebble-accretion paradigm changes if the dust is confined in a ring. Results: Planet Type-I migration is stopped in a ring, but not…
Recent observations of protoplanetary disks have revealed ring-like structures that can be associated to pressure maxima. Pressure maxima are known to be dust collectors and planet migration traps. Most of planet formation works are based either on the pebble accretion model or on the planetesimal accretion model. However, recent studies proposed the possible formation of Jupiter by the hybrid accretion of pebbles and planetesimals. We aim to study the full process of planet formation consisting of dust evolution, planetesimal formation and planet growth at a pressure maximum in a protoplaneta…
Protoplanets of Super-Earth sizes may get trapped in convergence zones for planetary migration and form gas giants there. These growing planets undergo accretion heating, which triggers a hot-trail effect that can reverse migration directions, increase eccentricities and prevent resonant captures (Chrenko et al. 2017). We study populations of embryos accreting pebbles using Fargo-Thorin 2D hydrocode. We find that embryos in a disk with high surface density ($Σ_0 = 990\,{\rm g}\,{\rm cm}^{-2}$) undergo `unsuccessful' two-body encounters which do not lead to a merger. Only when a 3rd protoplanet…
The compact multi-transiting planet systems discovered by Kepler challenge planet formation theories. Formation in situ from disks with radial mass surface density, $Σ$, profiles similar to the minimum mass solar nebula (MMSN) but boosted in normalization by factors $\gtrsim 10$ has been suggested. We propose that a more natural way to create these planets in the inner disk is formation sequentially from the inside-out via creation of successive gravitationally unstable rings fed from a continuous stream of small (~cm--m size) "pebbles", drifting inwards via gas drag. Pebbles collect at the pr…
Recent ALMA observations have identified a variety of dust gaps in protoplanetary disks, which are commonly interpreted to be generated by unobserved planets. Predicting mass of such embedded planets is of fundamental importance in comparing those disk architectures with the observed diversity of exoplanets. The prediction, however, depends on the assumption that whether the same gap structure exists in the dust component alone or in the gas component as well. We assume a planet can only open a gap in the gas component when its mass exceeds the pebble isolation mass by considering the core acc…
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…
Eccentric gaseous discs are unstable to a parametric instability involving the resonant interaction between inertial-gravity waves and the eccentric mode in the disc. We present 3D global hydrodynamical simulations of inviscid circumbinary discs that form an inner cavity and become eccentric through interaction with the central binary. The parametric instability grows and generates turbulence that transports angular momentum with stress parameter $α\sim 5 \times 10^{-3}$ at distances $\lesssim 7 \;a_{bin} $, where $a_{bin}$ is the binary semi-major axis. Vertical turbulent diffusion occurs at …
We propose a planet formation scenario to explain the elevated occurrence rates of transiting planets around M dwarfs compared to sun-like stars discovered by Kepler. We use a pebble drift and accretion model to simulate the growth of planet cores inside and outside of the snow line. A smaller pebble size interior to the snow line delays the growth of super-Earths, allowing giant planet cores in the outer disk to form first. When those giant planets reach pebble isolation mass they cut off the flow of pebbles to the inner disk and prevent the formation of close-in super-Earths. We apply this m…
Super-Earths possess low-mass H$_2$/He atmospheres (typically less than 10% by mass). However, the origins of super-Earth atmospheres have not yet been ascertained. We investigate the role of rapid disk clearing by photoevaporation during the formation of super-Earths and their atmospheres. We perform unified simulations of super-Earth formation and atmospheric evolution in evolving disks that consider both photoevaporative winds and magnetically driven disk winds. For the growth mode of planetary cores, we consider two cases in which planetary embryos grow with and without pebble accretion. O…
Pebble accretion is a promising process for decreasing growth timescales of planetary cores, allowing gas giants to form at wide orbital separations. However, nebular turbulence can reduce the efficiency of this gas-assisted growth. We present an order of magnitude model of pebble accretion, which calculates the impact of turbulence on the average velocity of small bodies, the radius for binary capture, and the sizes of the small bodies that can be accreted. We also include the effect of turbulence on the particle scale height, which has been studied in previous works. We find that turbulence …
The growth process of proto-planets can be sped-up by accreting a large number of solid, pebble-sized objects that are still present in the protoplanetary disc. It is still an open question on how efficient this process works in realistic turbulent discs. Here, we investigate the accretion of pebbles in turbulent discs that are driven by the purely hydrodynamical vertical shear instability (VSI). For this purpose, we perform global three-dimensional simulations of locally isothermal, VSI turbulent discs with embedded protoplanetary cores from 5 to 100 $M_\oplus$ that are placed at 5.2 au dista…
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…
Pebble accretion is an efficient mechanism able to build up the core of the giant planets within the lifetime of the protoplanetary disc gas-phase. The core grows via this process until the protoplanet reaches its pebble isolation mass and starts to accrete gas. During the growth, the protoplanet undergoes a rapid, large-scale, inward migration due to the interactions with the gaseous protoplanetary disc. In our work, we investigate how this early migration would have affected the minor body populations in our solar system. In particular, we focus on the Jupiter Trojans and the Hildas asteroid…
We present the results of planet formation N-body simulations based on a comprehensive physical model that includes planetary mass growth through mutual embryo collisions and planetesimal/boulder accretion, viscous disc evolution, planetary migration and gas accretion onto planetary cores. The main aim of this study is to determine which set of model parameters leads to the formation of planetary systems that are similar to the compact low mass multi-planet systems that have been discovered by radial velocity surveys and the Kepler mission. We vary the initial disc mass, solids-to-gas ratio an…
Active Galactic Nucleus Tori: Potential Birthplace to Millions of Planets
Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences（波兰科学院尼古拉·哥白尼天文学中心）；New Mexico State University（新墨西哥州立大学）；CUNY Borough of Manhattan Community College（纽约市立大学曼哈顿社区学院）；American Museum of Natural History（美国自然历史博物馆）
When a planet forms a deep gap in a protoplanetary disk, dust grains cannot pass through the gap. As a consequence, the density of the dust grains can increase up to the same level of the density of the gas at the outer edge. The feedback on the gas from the drifting dust grains is not negligible, in such a dusty region. We carried out two-dimensional two-fluid (gas and dust) hydrodynamic simulations. We found that when the radial flow of the dust grains across the gap is halted, a broad ring of the dust grains can be formed because of the dust feedback and the diffusion of the dust grains. Th…
The elemental composition of the gas and dust in a protoplanetary disk influences the compositions of the planets that form in it. We use the Molecules with ALMA at Planet-forming Scales (MAPS) data to constrain the elemental composition of the gas at the locations of potentially forming planets. The elemental abundances are inferred by comparing source-specific gas-grain thermochemical models, with variable C/O ratios and small-grain abundances, from the DALI code with CO and C2H column densities derived from the high-resolution observations of the disks of AS 209, HD 163296, and MWC 480. Ele…
Dust and Gas Transport in Substructured Nonideal MHD Wind-Launching Disks with Embedded Planets
University of Virginia（弗吉尼亚大学）；Virginia Institute of Theoretical Astronomy, University of Virginia（弗吉尼亚大学理论天体物理研究所）；Department of Astronomy, University of Florida（佛罗里达大学天文学系）；Institute of Astronomy and Astrophysics, Academia Sinica（中央研究院天文及天文物理研究所）；Physics Division, National Center for Theoretical Sciences（国家理论科学中心物理学部）；Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交通大学李政道研究所）
