The final orbital position of growing planets is determined by their migration speed, which is essentially set by the planetary mass. Small mass planets migrate in type I migration, while more massive planets migrate in type II migration, which is thought to depend mostly on the viscous evolution rate of the disc. A planet is most vulnerable to inward migration before it reaches type II migration and can lose a significant fraction of its semi-major axis at this stage. We investigated the influence of different disc viscosities, the dynamical torque and gas accretion from within the horseshoe region as mechanisms for slowing down planet migration. Our study confirms that planets growing in low viscosity environments migrate less, due to the earlier gap opening and slower type II migration rate. We find that taking the gas accretion from the horseshoe region into account allows an earlier gap opening and this results in less inward migration of growing planets. Furthermore, this effect increases the planetary mass compared to simulations that do not take the effect of gas accretion from the horseshoe region. Moreover, combining the effect of the dynamical torque with the effect of gas accretion from the horseshoe region, significantly slows down inward migration. Taking these effects into account could allow the formation of cold Jupiters (a > 1 au) closer to the water ice line region compared to previous simulations that did not take these effects into account. We thus conclude that gas accretion from within the horseshoe region and the dynamical torque play crucial roles in shaping planetary systems.
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…
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…
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 …
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…
Simulating the interplay between the snowline pebble flux and ongoing planet formation and migration
University of Exeter（埃克塞特大学）；Space Telescope Science Institute（太空望远镜科学研究所）；Max Planck Institute for Astronomy（马克斯·普朗克天文学研究所）；University College Cork（科克大学学院）
Quantifying the Impact of the Dust Torque on the Migration of Low-mass Planets II: The Role of Pebble Accretion in Planet Growth within a Global Planet Formation Model
Recent observations have found a valley in the size distribution of close-in super-Earths that is interpreted as a signpost that close-in super-Earths are mostly rocky in composition. However, new models predict that planetesimals should first form at the water ice line such that close-in planets are expected to have a significant water ice component. Here we investigate the water contents of super-Earths by studying the interplay between pebble accretion, planet migration and disc evolution. Planets' compositions are determined by their position relative to different condensation fronts (ice …
A key process in planet formation is the exchange of angular momentum between a growing planet and the protoplanetary disc, which makes the planet migrate through the disc. Several works show that in general low-mass and intermediate-mass planets migrate towards the central star, unless corotation torques become dominant. Recently, a new kind of torque, called the thermal torque, was proposed as a new source that can generate outward migration of low-mass planets. While the Lindblad and corotation torques depend mostly on the properties of the protoplanetary disc and on the planet mass, the th…
Fast inward migration of planetary cores is a common problem in the current planet formation paradigm. Even though dust is ubiquitous in protoplanetary disks, its dynamical role in the migration history of planetary embryos has not been assessed. In this Letter, we show that the scattered pebble-flow induced by a low-mass planetary embryo leads to an asymmetric dust-density distribution that is able to exert a net torque. By analyzing a large suite of multifluid hydrodynamical simulations addressing the interaction between the disk and a low-mass planet on a fixed circular orbit, and neglectin…
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…
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…
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 …
Current models of (exo)planet formation often rely on a large influx of so-called `pebbles' from the outer disk into the planet formation region. In this paper, we investigate how the formation of pebbles in the cold outer regions of protoplanetary disks and their subsequent migration to the inner disk can alter the gas-phase CO distribution both interior and exterior to the midplane CO snowline. By simulating the resulting CO abundances in the midplane as well as the warm surface layer, we identify observable signatures of large-scale pebble formation and migration that can be used as `smokin…
In the innermost regions of protoplanerary discs, the solid-to-gas ratio can be increased considerably by a number of processes, including photoevaporative and particle drift. MHD disc models also suggest the existence of a dead-zone at $R\lesssim 10$ AU, where the regions close to the midplane remain laminar. In this context, we use two-fluid hydrodynamical simulations to study the interaction between a low-mass planet ($\sim 1.7 \;{\rm M_\oplus}$) on a fixed orbit and an inviscid pebble-rich disc with solid-to-gas ratio $ε\ge 0.5$. For pebbles with Stokes numbers St=0.1, 0.5, multiple dusty …
We propose a pebble-driven planet formation scenario to form giant planets with high multiplicity and large orbital distances in the early gas disk phase. We perform N-body simulations to investigate the growth and migration of low-mass protoplanets in the disk with inner viscously heated and outer stellar irradiated regions. The key feature of this model is that the giant planet cores grow rapidly by a combination of pebble accretion and planet-planet collisions. This consequently speeds up their gas accretion. Because of efficient growth, the planet transitions from rapid type I migration to…
We examine the migration of luminous low-mass cores in laminar protoplanetary discs where accretion occurs mainly because of disc winds and where the planet luminosity is generated by pebble accretion. Using 2D hydrodynamical simulations, we determine the eccentricities induced by thermal forces as a function of gas and pebble accretion rates, and also evaluate the importance of the torque exerted by the solid component relative to the gas torque. For a gas accretion rate $\dot M= 2\times 10^{-8}$ $M_\odot/$yr and pebble flux $\dot M_{peb}=170$ $M_\oplus$/Myr, we find that embryo eccentricitie…
At least 30\% of main sequence stars host planets with sizes of between 1 and 4 Earth radii and orbital periods of less than 100 days. We use N-body simulations including a model for gas-assisted pebble accretion and disk--planet tidal interaction to study the formation of super-Earth systems. We show that the integrated pebble mass reservoir creates a bifurcation between hot super-Earths or hot-Neptunes ($\lesssim15M_{\oplus}$) and super-massive planetary cores potentially able to become gas giant planets ($\gtrsim15M_{\oplus}$). Simulations with moderate pebble fluxes grow multiple super-Ear…
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…
Context: Planetary embryos can continue to grow by pebble accretion until they become giant planet cores. Simultaneously, these embryos mutually interact and also migrate due to torques arising from the protoplanetary disk. Aims: Our aim is to investigate how pebble accretion alters the orbital evolution of embryos undergoing the Type-I migration. In particular, we study whether they establish resonant chains, whether these chains are prone to instabilities and if giant planet cores form through embryo merging, thus occurring more rapidly than by pebble accretion alone. Methods: For the first …
Massive cores of the giant planets are thought to have formed in a gas disk by accretion of pebble-size particles whose accretional cross-section is enhanced by aerodynamic gas drag [1][2]. A commonly held view is that the terrestrial planet system formed later (30-200 Myr after the dispersal of the gas disk) by giant collisions of tens of roughly Mars-size protoplanets [3]. Here we propose, instead, that the terrestrial planets formed earlier by gas-driven convergent migration of protoplanets toward $\sim\!1\,{\rm au}$ (related ref. [4] invoked a different process to concentrate planetesimals…
Pebble accretion has become a popular component to core accretion models of planet formation, and is especially relevant to the formation of compact, resonant terrestrial planetary systems. Pebbles initially form in the inner protoplanetary disc, sweeping outwards in a radially expanding front, potentially forming planetesimals and planetary cores via migration and the streaming instability. This pebble front appears at early times, in what is typically assumed to be a low mass disc. We argue this picture is in conflict with the reality of young circumstellar discs, which are massive and self-…
We present a synergic study of protoplanetary disks to investigate links between inner disk gas molecules and the large-scale migration of solid pebbles. The sample includes 63 disks where two types of measurements are available: i) spatially-resolved disk images revealing the radial distribution of disk pebbles (mm-cm dust grains), from millimeter observations with ALMA or the SMA, and ii) infrared molecular emission spectra as observed with Spitzer. The line flux ratios of H2O with HCN, C2H2, and CO2 all anti-correlate with the dust disk radius R$_{dust}$, expanding previous results found by…
The origins of the Galilean satellites - namely Io, Europa, Ganymede, and Callisto - is not fully understood yet. Here we use N-body numerical simulations to study the formation of Galilean satellites in a gaseous circumplanetary disk around Jupiter. Our model includes the effects of pebble accretion, gas-driven migration, and gas tidal damping and drag. Satellitesimals in our simulations first grow via pebble accretion and start to migrate inwards. When they reach the trap at the disk inner edge, scattering events and collisions take place promoting additional growth. Growing satellites event…
In the past decade, ALMA observations have revealed that a large fraction of protoplanetary discs contains rings in the dust continuum. These rings are the locations where pebbles accumulate, which is beneficial for planetesimal formation and subsequent planet assembly. We investigate the viability of planet formation inside ALMA rings in which pebbles are trapped by either a Gaussian-shape pressure bump or by the strong dust backreaction. Planetesimals form at the midplane of the ring via streaming instability. By conducting N-body simulations, we study the growth of these planetesimals by co…
Gas-giant planets, such as Jupiter, Saturn and massive exoplanets, were formed via the gas accretion onto the solid cores each with a mass of roughly ten Earth masses. However, rapid radial migration due to disk-planet interaction prevents the formation of such massive cores via planetesimal accretion. Comparably rapid core growth via pebble accretion requires very massive protoplanetary disks because most pebbles fall into the central star. Although planetesimal formation, planetary migration, and gas-giant core formation have been studied with much effort, the full evolution path from dust t…
Context. Planet formation with pebbles has been proposed to solve a couple of long-standing issues in the classical formation model. Some sophisticated simulations have been done to confirm the efficiency of pebble accretion. However, there has not been any global N-body simulations that compare the outcomes of planet formation via pebble accretion with observed extrasolar planetary systems. Aims. In this paper, we study the effects of a range of initial parameters of planet formation via pebble accretion, and present the first results of our simulations. Methods. We incorporate the pebble acc…
In the classical core-accretion planet formation scenario, rapid inward migration and accretion timescales of kilometer size planetesimals may not favor the formation of massive cores of giant planets before the dissipation of protoplanetary disks. On the other hand, the existence of pressure maxima in the disk could act as migration traps and locations for solid material accumulation, favoring the formation of massive cores. We aim to study the radial drift of pebbles and planetesimals and planet migration at pressure maxima in a protoplanetary disk and their implications for the formation of…
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…
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…
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…
Models of planetary core growth by either planetesimal or pebble accretion are traditionally disconnected from the models of dust evolution and formation of the first gravitationally-bound planetesimals. The state-of-the-art models typically start with massive planetary cores already present. We aim to study the formation and growth of planetary cores in a pressure bump, motivated by the annular structures observed in protoplanetary disks, starting with sub-micron-sized dust grains. We connect the models of dust coagulation and drift, planetesimal formation in the streaming instability, gravit…
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…
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…
Recent work has shown that aside from the classical view of collisions by increasingly massive planetesimals, the accretion of mm- to m-sized 'pebbles' can also reproduce the mass-orbit distribution of the terrestrial planets. Here, we perform N-body simulations to study the effects of pebble accretion onto growing planetesimals of different diameters located in the inner Solar System. The simulations are run to occur during the lifetime of the gas disc while also simultaneously taking Jupiter's growth into account. We find that pebble accretion can increase the mass in the solid disc by at le…
Atmospheric abundances are thought to constrain the planet formation pathway, because different species evaporate at different temperatures leaving distinct signatures in the accreted atmosphere. The planetary C/O ratio is thought to constrain the planet formation pathway, because of the condensation sequence of H$_2$O, CO$_2$, CH$_4$, and CO, resulting in an increase of the gas phase C/O ratio with increasing distance. Here we use a disc evolution model including pebble growth, drift and evaporation coupled with a planet formation model that includes pebble and gas accretion as well as planet…
Standard accretion disk models suggest that the snow line in the solar nebula migrated interior to the Earth's orbit in a late stage of nebula evolution. In this late stage, a significant amount of ice could have been delivered to 1 AU from outer regions in the form of mm to dm-sized pebbles. This raises the question why the present Earth is so depleted of water (with the ocean mass being as small as 0.023% of the Earth mass). Here we quantify the amount of icy pebbles accreted by terrestrial embryos after the migration of the snow line assuming that no mechanism halts the pebble flow in outer…
Despite the fact that the observed gradient in water content among the Galilean satellites is globally consistent with a formation in a circum-Jovian disk on both sides of the snowline, the mechanisms that led to a low water mass fraction in Europa ($\sim$$8\%$) are not yet understood. Here, we present new modeling results of solids transport in the circum-Jovian disk accounting for aerodynamic drag, turbulent diffusion, surface temperature evolution and sublimation of water ice. We find that the water mass fraction of pebbles (e.g., solids with sizes of 10$^{-2}$ -- 1 m) as they drift inward …
TRAPPIST-1 is a nearby 0.08 M M-star, which was recently found to harbor a planetary system of at least seven Earth-mass planets, all within 0.1 au. The configuration confounds theorists as the planets are not easily explained by either in situ or migration models. In this Paper we present a scenario for the formation and orbital architecture of the TRAPPIST-1 system. In our model, planet formation starts at the H2O iceline, where pebble-size particles -- whose origin is the outer disk -- concentrate to trigger streaming instabilities. After their formation, planetary embryos quickly mature by…
Context. The classical "planetesimal" accretion scenario for the formation of planets has recently evolved with the idea that "pebbles", centimeter- to meter-sized icy grains migrating in protoplanetary disks, can control planetesimal and/or planetary growth. Aims. We investigate how pebble accretion depends on disk properties and affects the formation of planetary systems Methods. We construct analytical models of pebble accretion onto planetary embryos that consistently account for the mass and orbital evolution of the pebble flow and reflect disk structure. Results. We derive simple formula…
To avoid known difficulties in planetesimal formation such as the drift or fragmentation barriers, many scenarios have been proposed. However, in these scenarios, planetesimals form in general only at some specific locations in protoplanetary discs. On the other hand, it is generally assumed in planet formation models and population synthesis models, that planetesimals are broadly distributed in the protoplanetary disc. Here we propose a new scenario in which planetesimals can form in broad areas of the discs. Planetesimals form at the gas pressure bump formed by a first-generation planet (e.g…
Pebble accretion refers to the assembly of rocky planet cores from particles whose velocity dispersions are damped by drag from circumstellar disc gas. Accretion cross-sections can approach maximal Hill-sphere scales for particles whose Stokes numbers approach unity. While fast, pebble accretion is also lossy. Gas drag brings pebbles to protocores but also sweeps them past; those particles with the largest accretion cross-sections also have the fastest radial drift speeds and are the most easily drained out of discs. We present a global model of planet formation by pebble accretion that keeps …
We present a model in which planetesimal disks are built from the combination of planetesimal formation and accretion of radially drifting pebbles onto existing planetesimals. In this model, the rate of accretion of pebbles onto planetesimals quickly outpaces the rate of direct planetesimal formation in the inner disk. This allows for the formation of a high mass inner disk without the need for enhanced planetesimal formation or a massive protoplanetary disk. Our proposed mechanism for planetesimal disk growth does not require any special conditions to operate. Consequently, we expect that hig…
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 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…
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 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…
The inner-most regions of circumbinary discs are unstable to a parametric instability whose non-linear evolution is hydrodynamical turbulence. This results in significant particle stirring, impacting on planetary growth processes such as the streaming instability or pebble accretion. In this paper, we present the results of three-dimensional, inviscid global hydrodynamical simulations of circumbinary discs with embedded particles of 1 cm size. Hydrodynamical turbulence develops in the disc, and we examine the effect of the particle back-reaction on vertical dust. We find that higher solid-to-g…
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…
Recently, seven Earth-sized planets were discovered around the M-dwarf star TRAPPIST-1. Thanks to transit-timing variations, the masses and therefore the bulk densities of the planets have been constrained, suggesting that all TRAPPIST-1 planets are consistent with water mass fractions on the order of 10%. These water fractions, as well as the similar planet masses within the system, constitute strong constraints on the origins of the TRAPPIST-1 system. In a previous work, we outlined a pebble-driven formation scenario. In this paper we investigate this formation scenario in more detail. We us…
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…
