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 arrives to the convergence zone, three-body encounters lead to mergers. For a low-viscosity disk ($ν= 5\times10^{13}\,{\rm cm}^2\,{\rm s}^{-1}$) a massive coorbital is a possible outcome, for which a pebble isolation develops and the coorbital is stabilised. For more massive protoplanets ($5\,M_\oplus$), the convergence radius is located further out, in the ice-giant zone. After a series of encounters, there is an evolution driven by a dynamical torque of a tadpole region, which is systematically repeated several times, until the coorbital configuration is disrupted and planets merge. This may be a pathway how to solve the problem that coorbitals often form in simulations but they are not observed in nature.
In contrast, the joint evolution of 120 low-mass protoplanets ($0.1\,M_\oplus$) reveals completely different dynamics. The evolution is no longer smooth, but rather a random walk. This is because the spiral arms, developed in the gas disk due to Lindblad resonances, overlap with each other and affect not only a single protoplanet but several in the surroundings. Our hydrodynamical simulations may have important implications for N-body simulations of planetary migration that use simplified torque prescriptions and are thus unable to capture protoplanet dynamics in its full glory.
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…
We perform hydrodynamical simulations of the accretion of pebbles and rocks onto protoplanets of a few hundred kilometres in radius, including two-way drag force coupling between particles and the protoplanetary disc gas. Particle streams interacting with the gas far out within the Hill sphere of the protoplanet spiral into a prograde circumplanetary disc. Material is accreted onto the protoplanet due to stirring by the turbulent surroundings. We speculate that the trend for prograde rotation among the largest asteroids is primordial and that protoplanets accreted 10%-50% of their mass from pe…
A notable challenge of planet formation is to find a path to directly form planetesimals from small particles. We aim to understand how drifting pebbles pile up in a protoplanetary disk with a non-uniform turbulence structure. We consider a disk structure in which the midplane turbulence viscosity is increasing with radius in protoplanetary disks as in the outer region of a dead zone. We perform 1D diffusion-advection simulations of pebbles that include back-reaction (the inertia) to radial drift and vertical/radial diffusion of pebbles for a given pebble-to-gas mass flux. We report a new mech…
Nearly-axisymmetric gaps and rings are commonly observed in protoplanetary discs. The leading theory regarding the origin of these patterns is that they are due to dust trapping at the edges of gas gaps induced by the gravitational torques from embedded planets. If the concentration of solids at the gap edges becomes high enough, it could potentially result in planetesimal formation by the streaming instability. We test this hypothesis by performing global 1-D simulations of dust evolution and planetesimal formation in a protoplanetary disc that is perturbed by multiple planets. We explore dif…
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…
We introduce collisions of solids as a new and efficient ionization mechanism for gas in protoplanetary disks, which especially operates in the dense midplane of protoplanetary disks. This idea is sparked by laboratory experiments where we found that charge, which is exchanged by grains in mutual collision (tribocharging), is not tied to their surfaces alone. As kind of collateral effect, charges also become entrained into the gas phase, i.e. collisions ionize the protoplanetary disk. Therefore, solids are not only sinks of charges in disks but also sources. A first estimate shows that ionizat…
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…
The formation of the first planetesimals and the final growth of planetary cores relies on the abundance of small pebbles. The efficiencies of both the streaming instability (SI) process, suggested to catalyze the early growth of planetesimals, and the pebble-accretion process, suggested to accelerate the growth of planetary cores, depend on the sizes of solids residing in the disk. In particular, these processes were found to be sensitive to size distribution of solids, and efficient planetesimal formation and growth through these channels require a limited pebble size distribution. Here we s…
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…
Pebble accretion is one of the major theories in planet formation. Aerodynamically small particles, called pebbles, are highly affected by the gas flow. A growing planet embedded in a protoplanetary disk induces three-dimensional (3D) gas flow. In our previous study, Paper I, we focused on the shear regime of pebble accretion, and investigated the influence of planet-induced gas flow on pebble accretion. In Paper I, we found that pebble accretion is inefficient in the planet-induced gas flow compared to that in the unperturbed flow, in particular when ${\rm St}\lesssim10^{-3}$, where St is the…
It has been realized in recent years that the accretion of pebble-sized dust particles onto planetary cores is an important mode of core growth, which enables the formation of giant planets at large distances and assists planet formation in general. The pebble accretion theory is built upon the orbit theory of dust particles in a laminar protoplanetary disk (PPD). For sufficiently large core mass (in the "Hill regime"), essentially all particles of appropriate sizes entering the Hill sphere can be captured. However, the outer regions of PPDs are expected to be weakly turbulent due to the magne…
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 …
Forming planetesimals from pebbles is a major challenge in our current understanding of planet formation. In a protoplanetary disk, pebbles drift inward near the disk midplane via gas drag and they may enter a dead zone. In this context, we identified that the backreaction of the drag of pebbles onto the gas could lead to a runaway pile-up of pebbles, the so-called no-drift mechanism. We improve upon the previous study of the no-drift mechanism by investigating the nature and characteristics of the resultant planetesimal belt. We performed 1D diffusion-advection simulations of drifting pebbles…
In models of planetary accretion, pebbles form by dust coagulation and rapidly migrate toward the central star. Planetesimals may continuously form from pebbles over the age of the protoplanetary disk by yet uncertain mechanisms. Meanwhile, large planetary embryos grow efficiently by accumulation of leftover pebbles that are not incorporated in planetesimals. Although this process, called pebble accretion, is offering a new promising pathway for formation of giant planets' cores, architectures of planetary systems formed through the process remain elusive. In the present paper, we perform simu…
Aims. Dust plays a crucial role in the evolution of protoplanetary disks. We study the dynamics and growth of initially sub-$μm$ dust particles in self-gravitating young protoplanetary disks with various strengths of turbulent viscosity. We aim to understand the physical conditions that determine the formation and spatial distribution of pebbles when both disk self-gravity and turbulent viscosity can be concurrently at work. Methods. We perform the thin-disk hydrodynamics simulations of self-gravitating protoplanetary disks over an initial time period of 0.5 Myr using the FEOSAD code. Turbulen…
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 …
[abridged] Recent laboratory experiments indicate that destructive collisions of icy dust particles occur with much lower velocities than previously thought. When these new velocities are considered from laboratory experiments in dust evolution models, a growth to pebble sizes in protoplanetary disks (PPDs) is difficult. This may contradict (sub-)mm observations and challenge the formation of planetesimals and planets. We investigate the conditions that are required in dust evolution models for growing and trapping pebbles in PPDs when the fragmentation speed is 1ms$^{-1}$ in the entire disk. …
The composition of planets may be largely determined by the chemical processing and accretion of icy pebbles in protoplanetary disks. Recent observations of protoplanetary disks hint at wide-spread depletion of gaseous carbon. The missing volatile carbon is likely frozen in CO and/or CO$_2$ ice on grains and locked into the disk through pebble trapping in pressure bumps or planetesimals. We present the results of the first successful ACA (Atacama Compact Array) [C I] $J$ = 1-0 mini-survey of seven protoplanetary disks. Using tailored azimuthally symmetric DALI (Dust And LInes) thermo-chemical …
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…
Axisymmetric dust rings containing tens to hundreds of Earth masses of solids have been observed in protoplanetary discs with (sub-)millimetre imaging. Here, we investigate the growth of a planetary embryo in a massive (150M$_\oplus$) axisymmetric dust trap through dust and gas hydrodynamics simulations. When accounting for the accretion luminosity of the planetary embryo from pebble accretion, the thermal feedback on the surrounding gas leads to the formation of an anticyclonic vortex. Since the vortex forms at the location of the planet, this has significant consequences for the planet's gro…
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…
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…
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…
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 …
The pebble accretion model has the potential to explain the formation of various types of planets. A growing planet embedded in a disk induces three-dimensional (3D) gas flow, which may influence pebble accretion. In this study, we investigate the influence of the 3D planet-induced gas flow on pebble accretion. Assuming a non-isothermal, inviscid gas disk, we perform 3D hydrodynamical simulations on the spherical polar grid. Then we numerically integrate the equation of motion of pebbles in 3D using hydrodynamical simulations data. We find that the trajectories of pebbles in the planet-induced…
Observations of protoplanetary disks have revealed them to be complex and dynamic, with vertical and radial transport of gas and dust occurring simultaneously with chemistry and planet formation. Previous models of protoplanetary disks focused primarily on chemical evolution of gas and dust in a static disk, or dynamical evolution of solids in a chemically passive disk. In this paper, we present a new 1D method for modelling pebble growth and chemistry simultaneously. Gas and small dust particles are allowed to diffuse vertically, connecting chemistry at all elevations of the disk. Pebbles are…
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…
This chapter highlights the properties of turbulence and meso-scale flow structures in protoplanetary disks and their role in the planet formation process. Here we focus on the formation of planetesimals from a gravitational collapse of a pebble cloud. Large scale and long lived flow structures - vortices and zonal flows - are a consequence of weak magneto and hydrodynamic instabilities in the pressure and entropy stratified quasi-Keplerian shear flow interacting with the fast rotation of the disk. The vortices and zonal flows on the other hand are particle traps tapping into the radial pebble…
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…
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 …
Observationally inferred crystalline abundance in silicates in comets, which should have been formed in the outer region of a protoplanetary disk, is relatively high (~ 10-60%), although crystalline silicates would be formed by annealing of amorphous precursors in the disk inner region. In order to quantitatively address this puzzle, we have performed Monte Carlo simulation of advection/diffusion of silicate particles in a turbulent disk, in the setting based on pebble accretion model: pebbles consisting of many small amorphous silicates embedded in icy mantle are formed in the disk outer regi…
Pebble accretion is an emerging paradigm for the fast growth of planetary cores. Pebble flux and pebble sizes are the key parameters used in the pebble accretion models. We aim to derive the pebble sizes and fluxes from state-of-the-art dust coagulation models, understand their dependence on disk parameters and the fragmentation threshold velocity, and the impact of those on the planetary growth by pebble accretion. We use a one-dimensional dust evolution model including dust growth and fragmentation to calculate realistic pebble sizes and mass flux. We use this information to integrate the gr…
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…
Rapid Formation of Gas-giant Planets via Collisional Coagulation from Dust Grains to Planetary Cores. II. Dependence on Pebble Bulk Density and Disk Temperature
Tracing Pebble Drift History in Two Protoplanetary Disks with CO Enhancement
University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；University of Exeter（埃克塞特大学）；University of Leeds（利兹大学）；Massachusetts Institute of Technology（麻省理工学院）；University of Virginia（弗吉尼亚大学）；Boston University（波士顿大学）；Harvard & Smithsonian（哈佛大学与史密森尼学会）；University of Michigan（密歇根大学）
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…
The similar orbital distances and detection rates of debris disks and the prominent rings observed in protoplanetary disks suggest a potential connection between these structures. We explore this connection with new calculations that follow the evolution of rings of pebbles and planetesimals as they grow into planets and generate dusty debris. Depending on the initial solid mass and planetesimal formation efficiency, the calculations predict diverse outcomes for the resulting planet masses and accompanying debris signature. When compared with debris disk incidence rates as a function of lumino…
We conduct a pebble-driven planet population synthesis study to investigate the formation of planets around very low-mass stars and brown dwarfs, in the (sub)stellar mass range between $0.01 \ M_{\odot}$ and $0.1 \ M_{\odot}$. Based on the extrapolation of numerical simulations of planetesimal formation by the streaming instability, we obtain the characteristic mass of the planetesimals and the initial masses of the protoplanets (largest bodies from the planetesimal size distributions), in either the early self-gravitating phase or the later non-self-gravitating phase of the protoplanetary dis…
In parabolic flight experiments we studied the wind induced erosion of granular beds composed of spherical glass beads at low gravity and low ambient pressure. Varying g-levels were set by centrifugal forces. Expanding existing parameter sets to a pressure range between $p=300-1200\,$Pa and to g-levels of $g=1.1-2.2\,\rm m\,s^{-2}$ erosion thresholds are still consistent with the existing model for wind erosion on planetary surfaces by Shao & Lu (2000). These parameters were the lowest values that could technically be reached by the experiment. The experiments decrease the necessary range of e…
The sticking of micron sized dust particles due to surface forces in circumstellar disks is the first stage in the production of asteroids and planets. The key ingredients that drive this process are the relative velocity between the dust particles in this environment and the complex physics of dust aggregate collisions. Here we present the results of a collision model, which is based on laboratory experiments of these aggregates. We investigate the maximum aggregate size and mass that can be reached by coagulation in protoplanetary disks. We model the growth of dust aggregates at 1 AU at the …
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…
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…
Numerical simulations of pebble dynamics inside gas clumps formed by gravitational instability of protoplanetary discs are presented. We find that dust-mediated Rayleigh-Taylor instabilities transport pebbles inward rapidly via dense metal-rich "fingers". This speeds up sedimentation of small pebbles by up to two orders of magnitude and yet does not impede grain growth because grains of all sizes sediment at the same collective speed as long as Stokes number is less than unity. In simulations with a fixed pebble size, solid planetary cores form if pebble size exceeds a few cm. Pebble growth le…
Recent theoretical works suggest that the pebble accretion process is important for planet formation in protoplanetary disks, because it accelerates the growth of planetary cores. While several observations reveal axisymmetric sharp gaps in very young disks, which may be indicative of the existence of planets. We investigate the possibility of planet formation via pebble accretion in much earlier phases, the gravitationally unstable disks of class 0/I young stellar objects. We find that under the conditions of the class 0/I disks, the pebble accretion timescales can be shorter compared to the …
