The gravitational instability of a dust layer is one of the scenarios for planetesimal formation. If the density of a dust layer becomes sufficiently high as a result of the sedimentation of dust grains toward the midplane of a protoplanetary disk, the layer becomes gravitationally unstable and spontaneously fragments into planetesimals. Using a shearing box method, we performed local $N$-body simulations of gravitational instability of a dust layer and subsequent coagulation without gas and investigated the basic formation process of planetesimals. In this paper, we adopted the accretion model as a collision model. A gravitationally bound pair of particles is replaced by a single particle with the total mass of the pair. This accretion model enables us to perform long-term and large-scale calculations. We confirmed that the formation process of planetesimals is the same as that in the previous paper with the rubble pile models. The formation process is divided into three stages: the formation of non-axisymmetric structures, the creation of planetesimal seeds, and their collisional growth. We investigated the dependence of the planetesimal mass on the simulation domain size. We found that the mean mass of planetesimals formed in simulations is proportional to $L_y^{3/2}$, where $L_y$ is the size of the computational domain in the direction of rotation. However, the mean mass of planetesimals is independent of $L_x$, where $L_x$ is the size of the computational domain in the radial direction if $L_x$ is sufficiently large. We presented the estimation formula of the planetesimal mass taking into account the simulation domain size.
Streaming instability can be a very efficient way of overcoming growth and drift barriers to planetesimal formation. However, it was shown that strong clumping, which leads to planetesimal formation, requires a considerable number of large grains. State-of-the-art streaming instability models do not take into account realistic size distributions resulting from the collisional evolution of dust. We investigate whether a sufficient quantity of large aggregates can be produced by sticking and what the interplay of dust coagulation and planetesimal formation is. We develop a semi-analytical prescr…
We investigate formation mechanisms for icy super-Earth mass planets orbiting at 2-20 AU around 0.1-0.5 solar mass stars. A large ensemble of coagulation calculations demonstrates a new formation channel: disks composed of large planetesimals with radii of 30-300 km form super-Earths on time scales of roughly 1 Gyr. In other gas-poor disks, a collisional cascade grinds planetesimals to dust before the largest planets reach super-Earth masses. Once icy Earth-mass planets form, they migrate through the leftover swarm of planetesimals at rates of 0.01-1 AU per Myr. On time scales of 10 Myr to 1 G…
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…
Inside-Out Planet Formation (IOPF) is a theory addressing the origin of Systems of Tightly-Packed Inner Planets (STIPs) via {\it in situ} formation and growth of the planets. It predicts that a pebble ring is established at the pressure maximum associated with the dead zone inner boundary (DZIB) with an inner disk magnetorotational instability (MRI)-active region. Using direct $N$-body simulations, we study the collisional evolution of planetesimals formed from such a pebble ring, in particular examining whether a single dominant planet emerges. We consider a variety of models, including some …
The early stages of planet formation are still not well understood. Coagulation models have revealed numerous obstacles to the dust growth, such as the bouncing, fragmentation and radial drift barriers. We study the interplay between dust coagulation and drift in order to determine the conditions in protoplanetary disk that support the formation of planetesimals. We focus on planetesimal formation via sweep-up and investigate whether it can take place in a realistic protoplanetary disk. We have developed a new numerical model that resolves spatial distribution of dust in the radial and vertica…
Rapid Formation of Gas-giant Planets via Collisional Coagulation from Dust Grains to Planetary Cores. II. Dependence on Pebble Bulk Density and Disk Temperature
Context. The growth process of dust particles in protoplanetary disks can be modeled via numerical dust coagulation codes. In this approach, physical effects that dominate the dust growth process often must be implemented in a parameterized form. Due to a lack of these parameterizations, existing studies of dust coagulation have ignored the effects a hydrodynamical gas flow can have on grain growth, even though it is often argued that the flow could significantly contribute either positively or negatively to the growth process. Aims. We intend to provide a quantification of hydrodynamical effe…
We investigate dust growth due to settling in a 1D vertical column of a protoplanetary disk. It is known from the observed 10 micron feature in disk SEDs, that small micron-sized grains are present at the disk atmosphere throughout the lifetime of the disk. We hope to explain such questions as what process can keep the disk atmospheres dusty for the lifetime of the disk and how does the particle properties change as a function of height above the midplane. We use a Monte Carlo code to follow the mass and porosity evolution of the particles in time. The used collision model is based on laborato…
Rapid orbital drift of macroscopic dust particles is one of the major obstacles against planetesimal formation in protoplanetary disks. We reexamine this problem by considering porosity evolution of dust aggregates. We apply a porosity model based on recent N-body simulations of aggregate collisions, which allows us to study the porosity change upon collision for a wide range of impact energies. As a first step, we neglect collisional fragmentation and instead focus on dust evolution outside the snow line, where the fragmentation has been suggested to be less significant than inside the snow l…
Planetesimal accretion is a key source for heavy-element enrichment in giant planets. It has been suggested that Jupiter's enriched envelope is a result of planetesimal accretion during its growth assuming it formed in a massive planetesimal disk. In this study, we simulate Jupiter's formation in this scenario. We assume in-situ formation and perform N-body simulations to infer the solid accretion rate. We find that tens-Earth masses of planetesimals can be captured by proto-Jupiter during the rapid gas accretion phase. However, if several embryos are formed near Jupiter's core, which is an ex…
The journey from dust particle to planetesimal involves physical processes acting on scales ranging from micrometers (the sticking and restructuring of aggregates) to hundreds of astronomical units (the size of the turbulent protoplanetary nebula). Considering these processes simultaneously is essential when studying planetesimal formation. We develop a novel, global, semi-analytical model for the evolution of the mass-dominating dust particles in a turbulent protoplanetary disk that takes into account the evolution of the dust surface density while preserving the essential characteristics of …
We review the basic dynamics and accretion of planetesimals by showing N-body simulations. The orbits of planetesimals evolve through two-body gravitational relaxation: viscous stirring increases the random velocity and dynamical friction realizes the equiparation of the random energy. In the early stage of planetesimal accretion the growth mode of planetesimals is runaway growth where larger planetesimals grow faster than smaller ones. When a protoplanet (runaway-growing planetesimal) exceeds a critical mass the growth mode shifts to oligarchic growth where similar-sized protoplanets grow kee…
Late-infall-induced formation of giant planets, multigenerational planetesimals, and disk substructures
Max Planck Institute for Solar System Research（马克斯·普朗克太阳系研究所）；University of Chicago（芝加哥大学）；Ludwig-Maximilians-Universität München（慕尼黑大学）；Exzellenzcluster ORIGINS（ORIGINS卓越集群）
The growth and migration of planetesimals in a young protoplanetary disc are fundamental to planet formation. In all models of early growth, there are several processes that can inhibit grains from reaching larger sizes. Nevertheless, observations suggest that growth of planetesimals must be rapid. If a small number of 100 km sized planetesimals do manage to form in the disc, then gas drag effects could enable them to efficiently accrete small solids from beyond their gravitationally focused cross-section. This gas drag-enhanced accretion can allow planetesimals to grow at rapid rates, in prin…
We investigate whether coagulation models of planet formation can explain the observed size distributions of transneptunian objects (TNOs). Analyzing published and new calculations, we demonstrate robust relations between the size of the largest object and the slope of the size distribution for sizes 0.1 km and larger. These relations yield clear, testable predictions for TNOs and other icy objects throughout the solar system. Applying our results to existing observations, we show that a broad range of initial disk masses, planetesimal sizes, and fragmentation parameters can explain the data. …
We explore the growth of planetary embryos by planetesimal accretion up to and beyond the point where pebble accretion becomes efficient at the so-called Hill-transition mass. Both the transition mass and the characteristic mass of planetesimals formed by the streaming instability increase with increasing distance from the star. We developed a model for the growth of a large planetesimal (embryo) embedded in a population of smaller planetesimals formed in a filament by the streaming instability. The model includes in a self-consistent way the collisional mass growth of the embryo, the fragment…
When protoplanets growing by accretion of planetesimals have atmospheres, small planetesimals approaching the protoplanets lose their energy by gas drag from the atmospheres, which leads them to be captured within the Hill sphere of the protoplanets. As a result, growth rates of the protoplanets are enhanced. In order to study the effect of an atmosphere on planetary growth rates, we performed numerical integration of orbits of planetesimals for a wide range of orbital elements and obtained the effective accretion rates of planetesimals onto planets that have atmospheres. Numerical results are…
Planet formation models begin with proto-embryos and planetesimals already fully formed, missing out a crucial step, the formation of planetesimals/proto-embryos. In this work, we include prescriptions for planetesimal and proto-embryo formation arising from pebbles becoming trapped in short-lived pressure bumps, in thermally evolving viscous discs to examine the sizes and distributions of proto-embryos and planetesimals throughout the disc. We find that planetesimal sizes increase with orbital distance, from ~10 km close to the star to hundreds of kilometres further away. Proto-embryo masses …
As part of our ongoing initiative on accurately calculating the accretion rate of planetesimals in the core-accretion model, we demonstrated in a recent article that when the calculations include the gravitational force of the Sun (the original core-accretion model did not include solar gravity), results change considerably [ApJ, 899:45]. In this paper, we have advanced our previous study by including the effect of Saturn. To maintain focus on the effect of this planet, and in order to be consistent with previous studies, we did not include the effect of the nebular gas. Results demonstrated t…
Streaming instability is a key mechanism in planet formation, clustering pebbles into planetesimals. It is triggered at a particular disk location where the local volume density of solids exceeds that of the gas. After their formation, planetesimals can grow by feeding from other planetesimals in the birth ring as well as by accreting inwardly drifting pebbles from the outer disk. To investigate the growth of planetesimals at a single location by the streaming instability, we test the conditions under which super-Earths are able to form within the lifetime of the gaseous disk. We modify the \t…
Several hundred stars older than 10 million years have been observed to have infrared excesses. These observations are explained by dust grains formed by the collisional fragmentation of hidden planetesimals. Such dusty planetesimal discs are known as debris discs. In a dynamically cold planetesimal disc, collisional coagulation of planetesimals produces planetary embryos which then stir the surrounding leftover planetesimals. Thus, the collisional fragmentation of planetesimals that results from planet formation forms a debris disc. We aim to determine the properties of the underlying planete…
This paper explores how the stochastic accretion of planetesimals onto white dwarfs would be manifested in observations of their atmospheric pollution. Archival observations of pollution levels for unbiased samples of DA and non-DA white dwarfs are used to derive the distribution of accretion rates, confirming that rates become systematically lower as sinking time is decreased, with no discernable dependence on cooling age. The accretion rates expected from planetesimals that are all the same mass (ie, a mono-mass distribution) are explored both analytically and using a Monte Carlo model, quan…
We present a new instability driven by a combination of coagulation and radial drift of dust particles. We refer to this instability as ``coagulation instability" and regard it as a promising mechanism to concentrate dust particles and assist planetesimal formation in the very early stages of disk evolution. Because of dust-density dependence of collisional coagulation efficiency, dust particles efficiently (inefficiently) grow in a region of positive (negative) dust density perturbations, which lead to a small radial variation of dust sizes and as a result radial velocity perturbations. The r…
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…
After 25 years of laboratory research on protoplanetary dust agglomeration, a consistent picture of the various processes that involve colliding dust aggregates has emerged. Besides sticking, bouncing and fragmentation, other effects, like, e.g., erosion or mass transfer, have now been extensively studied. Coagulation simulations consistently show that $\rm μ$m-sized dust grains can grow to mm- to cm-sized aggregates before they encounter the bouncing barrier, whereas sub-$\rm μ$m-sized water-ice particles can directly grow to planetesimal sizes. For siliceous materials, other processes have t…
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…
A remarkable discovery of NASA's Kepler mission is the wide diversity in the average densities of planets of similar mass. After gas disk dissipation, fully formed planets could interact with nearby planetesimals from a remnant planetesimal disk. These interactions would often lead to planetesimal accretion due to the relatively high ratio between the planet size and the hill radius for typical planets. We present calculations using the open-source stellar evolution toolkit MESA (Modules for Experiments in Stellar Astrophysics) modified to include the deposition of planetesimals into the H/He …
We present results of a detailed study of the rate of the accretion of planetesimals by a growing proto-Jupiter in the core-accretion model. Using a newly developed code, we accurately combine a detailed three-body trajectory calculation with gas drag experienced during the passage of planetesimals in the protoplanet's envelope. We find that the motion of planetesimals is excited to the extent that encounters with the proto-planetary envelope become so fast that ram pressure breaks up the planetesimals in most encounters. As a result, the accretion rate is largely independent of the planetesim…
Observations of dusty debris disks can be used to test theories of planetesimal coagulation. Planetesimals of sizes up to a couple thousand kms are embedded in these disks and their mutual collisions generate the small dust grains that are observed. The dust luminosities, when combined with information on the dust spatial extent and the system age, can be used to infer initial masses in the planetesimal belts. Carrying out such a procedure for a sample of debris disks around Sun-like stars, we reach the following two conclusions. First, if we assume that colliding planetesimals satisfy a primo…
The existence of planets born in environments highly perturbed by a stellar companion represents a major challenge to the paradigm of planet formation. In numerical simulations, the presence of a close binary companion stirs up the relative velocity between planetesimals, which is fundamental in determining the balance between accretion and erosion. However, the recent discovery of circumbinary planets by Kepler establishes that planet formation in binary systems is clearly viable. We perform N-body simulations of planetesimals embedded in a protoplanetary disk, where planetesimal phasing is f…
Forming gas giant planets by the accretion of 100 km diameter planetesimals, a typical size that results from self-gravity assisted planetesimal formation, is often thought to be inefficient. Many models therefore use small km-sized planetesimals, or invoke the accretion of pebbles. Furthermore, models based on planetesimal accretion often use the ad hoc assumption of planetesimals distributed radially in a minimum mass solar nebula fashion. We wish to investigate the impact of various initial radial density distributions in planetesimals with a dynamical model for the formation of planetesima…
Chondrules are primitive materials in the Solar System. They are formed in the first about 3 Myr of the Solar System's history. This timescale is longer than that of Mars formation, and it is conceivable that protoplanets, planetesimals and chondrules might have existed simultaneously in the solar nebula. Due to protoplanets perturbation on the planetesimal dynamics and chondrule accretion on them, all the formed chondrules are unlikely to be accreted by planetesimals. We investigate the amount of chondrules accreted by planetesimals in such a condition. We assume that a protoplanet is in olig…
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…
The accretion of pebbles on planetary cores has been widely studied in recent years and is found to be a highly effective mechanism for planetary growth. While most studies assume planetary cores as an initial condition in their simulation, the question how, where and when these cores form is often neglected. We study the impact of pebble accretion during the formation phase and subsequent evolution of planetary embryos in the early stages of circumstellar disk evolution. In doing so we aim to quantify the timescales and local dependency of planetary embryo formation, based on the solid evolut…
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…
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…
Context: In planetesimal formation theory, several barriers have been proposed, which are bouncing, fragmentation, and radial drift problems. To understand the structure evolution of dust aggregates is a key in the planetesimal formation. Dust grains become fluffy by coagulation in protoplanetary disks. However, once they become fluffy, they are not sufficiently compressed by collisional compression to form compact planetesimals. Aims: We aim to reveal the pathway of the dust structure evolution from dust grains to compact planetesimals. Methods: Using the compressive strength formula, we anal…
The formation of cold gas giants similar to Jupiter and Saturn in orbit and mass is a great challenge for planetesimal-driven core accretion models because the core growth rates far from the star are low. Here we model the growth and migration of single protoplanets that accrete planetesimals and gas. We integrated the core growth rate using fits in the literature to $N$-body simulations, which provide the efficiency of accreting the planetesimals that a protoplanet migrates through. We take into account three constraints from the solar system and from protoplanetary discs: (1) the masses of t…
Mass-independent isotopic anomalies of carbonaceous and non-carbonaceous meteorites show a clear dichotomy suggesting an efficient separation of the inner and outer solar system. Observations show that ring-like structures in the distribution of mm-sized pebbles in protoplanetary disks are common. These structures are often associated with drifting pebbles being trapped by local pressure maxima in the gas disk. Similar structures may also have existed in the sun's natal disk, which could naturally explain the meteorite/planetary isotopic dichotomy. Here, we test the effects of a strong pressur…
We describe an updated version of our hybrid N-body-coagulation code for planet formation. In addition to the features of our 2006-2008 code, our treatment now includes algorithms for the 1D evolution of the viscous disk, the accretion of small particles in planetary atmospheres, gas accretion onto massive cores, and the response of N-bodies to the gravitational potential of the gaseous disk and the swarm of planetesimals. To validate the N-body portion of the algorithm, we use a battery of tests in planetary dynamics. As a first application of the complete code, we consider the evolution of P…
Most protoplanetary discs are thought to undergo violent and frequent accretion outbursts, during which the accretion rate and central luminosity are elevated for several decades. This temporarily increases the disc temperature, leading to the sublimation of ice species as snowlines move outwards. In this paper, we investigate how an FUor-type accretion outburst alters the growth and appearance of dust aggregates at different locations in protoplanetary discs. We develop a model based on the Monte Carlo approach to simulate locally the coagulation and fragmentation of icy dust particles and in…
Recent observations show that planet can reside in close binary systems with stellar separation of only about 20 AU. However, planet formation in such close binary systems is a challenge to current theory. One of the major theoretical problems occurs in the intermediate stage-planetesimals accretion into planetary embryos-during which the companion's perturbations can stir up the relative velocites(dV) of planetesimals and thus slow down or even cease their growth. However, all previous studies assumed a 2-dimentional (2D) disk and a coplanar binary orbit. Extending previous studies by includi…
Regular satellites of giant planets are formed by accretion of solid bodies in circumplanetary disks. Planetesimals that are moving on heliocentric orbits and are sufficiently large to be decoupled from the flow of the protoplanetary gas disk can be captured by gas drag from the circumplanetary disk. In the present work, we examine the distribution of captured planetesimals in circumplanetary disks using orbital integrations. We find that the number of captured planetesimals reaches an equilibrium state as a balance between continuous capture and orbital decay into the planet. The number of pl…
In the framework of the coagulation scenario, kilometre-sized planetesimals form by subsequent collisions of pre-planetesimals of sizes from centimetre to hundreds of metres. Pre-planetesimals are fluffy, porous dust aggregates, which are inhomogeneous owing to their collisional history. Planetesimal growth can be prevented by catastrophic disruption in pre-planetesimal collisions above the destruction velocity threshold. We develop an inhomogeneity model based on the density distribution of dust aggregates, which is assumed to be a Gaussian distribution with a well-defined standard deviation.…
Adhesion forces between submicrometer-sized silicate grains play a crucial role in the formation of silicate dust agglomerates, rocky planetesimals, and terrestrial planets. The surface energy of silicate dust particles is the key to their adhesion and rolling forces in a theoretical model based on the contact mechanics. Here we revisit the cohesion of amorphous silica spheres by compiling available data on the surface energy for hydrophilic amorphous silica in various circumstances. It turned out that the surface energy for hydrophilic amorphous silica in a vacuum is a factor of 10 higher tha…
Jupiter's atmosphere is enriched with heavy elements by a factor of about 3 compared to proto-solar. The origin of this enrichment and whether it represent the bulk composition of the planetary envelope remain unknown. Internal structure models of Jupiter suggest that its envelope is separated from the deep interior and that the planet is not fully mixed. This implies that Jupiter's atmosphere was enriched with heavy elements just before the end of its formation. Such enrichment can be a result of late planetesimal accretion. However, in-situ Jupiter formation models suggest the decreasing acc…
We consider planets composed of water ice and rock, located far from a central star. In an earlier study, computing the growth of planets by continuous accretion, we found that a large fraction of the ice evaporates upon accretion, creating a water vapor atmosphere. Here we consider accretion as a discrete series of planetesimal impacts (of order $10^8$), at the same time-dependent accretion rate, and investigate the fate of the vapor, as a result of its interaction with the accreting planetesimals. We find that a large fraction of the vapor escapes. The remaining fraction may form an outer la…
Pebble accretion is a new mechanism to quickly grow the cores of planets. In pebble accretion, gravity and gas drag conspire to yield large collisional cross sections for small particles in protoplanetary disks. However, before pebble accretion commences, aerodynamical deflection may act to prevent planetesimals from becoming large, because particles tend to follow gas streamlines. We derive the planetesimal radius where pebble accretion is initiated and determine the growth timescales of planetesimals by sweepup of small particles. We obtain the collision efficiency factor as the ratio of the…
Collisions electrically charge grains which promotes growth by coagulation. We present aggregation experiments with three large ensembles of basalt beads ($150\,μ\mathrm{m} - 180\,μ\mathrm{m})$, two of which are charged, while one remains almost neutral as control system. In microgravity experiments, free collisions within these samples are induced with moderate collision velocities ($0 - 0.2 \,\mathrm{m\,s}^{-1}$). In the control system, coagulation stops at (sub-)mm size while the charged grains continue to grow. A maximum agglomerate size of 5\,cm is reached, limited only by bead depletion …
The formation of planetesimals was a key step in the assemblage of planetary bodies, yet many aspects of their formation remain poorly constrained. Notably, the mechanism by which chondrules -- sub-millimetric spheroids that dominate primitive meteorites -- were incorporated into planetesimals remains poorly understood. Here we classify and analyze particle-size distributions in various CO carbonaceous chondrites found in the Atacama Desert. Our results show that the average circle-equivalent diameters of chondrules define a positive trend with the petrographic grade, which reflects the progre…
In the standard model of core accretion, the cores of the giant planets form by the accretion of planetesimals. In this scenario, the evolution of the planetesimal population plays an important role in the formation of massive cores. Recently, we studied the role of planetesimal fragmentation in the in situ formation of a giant planet. However, the exchange of angular momentum between the planet and the gaseous disk causes the migration of the planet in the disk. In this new work, we incorporate the migration of the planet and globally study the role of planet migration in the formation of a m…
