We present three-dimensional numerical simulations of particle clumping and planetesimal formation in protoplanetary disks with varying amounts of solid material. As centimeter-size pebbles settle to the mid-plane, turbulence develops through vertical shearing and streaming instabilities. We find that when the pebble-to-gas column density ratio is 0.01, corresponding roughly to solar metallicity, clumping is weak, so the pebble density rarely exceeds the gas density. Doubling the column density ratio leads to a dramatic increase in clumping, with characteristic particle densities more than ten times the gas density and maximum densities reaching several thousand times the gas density. This is consistent with unstratified simulations of the streaming instability that show strong clumping in particle dominated flows. The clumps readily contract gravitationally into interacting planetesimals of order 100 km in radius. Our results suggest that the correlation between host star metallicity and exoplanets may reflect the early stages of planet formation. We further speculate that initially low metallicity disks can be particle enriched during the gas dispersal phase, leading to a late burst of planetesimal formation.
The streaming instability (SI) provides a promising mechanism for planetesimal formation because of its ability to concentrate solids into dense clumps. The degree of clumping strongly depends on the height-integrated solid to gas mass ratio Z in protoplanetary disks (PPDs). In this letter, we show that the magnitude of the radial pressure gradient (RPG) which drives the SI (characterized by $q\equivηv_K/c_s$, where $ηv_K$ is the reduction of Keplerian velocity due to the RPG and $c_s$ is the sound speed) also strongly affects clumping. We present local two-dimensional hybrid numerical simulat…
Planetesimal formation is a crucial yet poorly understood process in planet formation. It is widely believed that planetesimal formation is the outcome of dust clumping by the streaming instability (SI). However, recent analytical and numerical studies have shown that the SI can be damped or suppressed by external turbulence, and at least the outer regions of protoplanetary disks are likely weakly turbulent due to magneto-rotational instability (MRI). We conduct high-resolution local shearing-box simulations of hybrid particle-gas magnetohydrodynamics (MHD), incorporating ambipolar diffusion a…
The streaming instability (SI) is a mechanism to aerodynamically concentrate solids in protoplanetary disks and trigger the formation of planetesimals. The SI produces strong particle clumping if the ratio of solid to gas surface density -- an effective metallicity -- exceeds a critical value. This critical value depends on particle sizes and disk conditions such as radial drift-inducing pressure gradients and levels of turbulence. To quantify these thresholds, we perform a suite of vertically-stratified SI simulations over a range of dust sizes and metallicities. We find a critical metallicit…
Planetesimal Formation under Realistic Gas Dynamics: Dust Concentration in Turbulent and Windy Protoplanetary Disks
CAS Key Laboratory of Planetary Sciences, Purple Mountain Observatory, Chinese Academy of Sciences（中国科学院行星科学重点实验室、紫金山天文台）；Institute for Advanced Study, Tsinghua University（清华大学高等研究院）；Department of Astronomy, Tsinghua University（清华大学天文学系）
Recent observations of protoplanetary disks (PPDs) in the sub-mm have revealed the ubiquity of annular substructures, indicative of pebble-sized dust particles trapped in turbulent ring-like gas pressure bumps. This major paradigm shift also challenges the leading theory of planetesimal formation from such pebbles by the streaming instability, which operates in a pressure gradient and can be suppressed by turbulence. Here we conduct three-dimensional local shearing-box, non-ideal magnetohydrodynamic (MHD) simulations of dust trapping in enforced gas pressure bumps including dust backreaction. …
We present numerical simulations of dust clumping and planetesimal formation initiated by the streaming instability with self-gravity. We examine the variability in the planetesimal formation process by employing simulation domains with large radial and azimuthal extents and a novel approach of re-running otherwise identical simulations with different random initializations of the dust density field.We find that the planetesimal mass distribution and the total mass of dust that is converted to planetesimals can vary substantially between individual small simulations and within the domains of l…
Conditions for planetesimal formation via the streaming instability persist under turbulence driven by magnetorotational instability
American Museum of Natural History（美国自然历史博物馆）；University of Copenhagen（哥本哈根大学）；Iowa State University（爱荷华州立大学）；The University of Alabama（阿拉巴马大学）；Chinese Academy of Sciences（中国科学院）
The Streaming Instability (SI) is a mechanism to concentrate solids in protoplanetary disks. Nonlinear particle clumping from the SI can trigger gravitational collapse into planetesimals. To better understand the numerical robustness of the SI, we perform a suite of vertically-stratified 3D simulations with fixed physical parameters known to produce strong clumping. We vary the numerical implementation, namely the computational domain size and the vertical boundary conditions (vBCs), comparing newly-implemented outflow vBCs to the previously-used periodic and reflecting vBCs. We find strong pa…
Evading the dust fragmentation barrier with the streaming instability in protoplanetary disks
Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM（巴黎萨克雷大学，巴黎西岱大学，法国原子能和替代能源委员会，法国国家科学研究中心，天体分子研究所）；American Museum of Natural History（美国自然历史博物馆）
The size distribution of asteroids and Kuiper belt objects in the solar system is difficult to reconcile with a bottom-up formation scenario due to the observed scarcity of objects smaller than $\sim$100 km in size. Instead, planetesimals appear to form top-down, with large $100-1000$ km bodies forming from the rapid gravitational collapse of dense clumps of small solid particles. In this paper we investigate the conditions under which solid particles can form dense clumps in a protoplanetary disk. We use a hydrodynamic code to model the interaction between solid particles and the gas inside a…
The streaming instability (SI) has been extensively studied in the linear and non-linear regimes as a mechanism to concentrate solids and trigger planetesimal formation in the midplane of protoplanetary discs. A related dust settling instability (DSI) applies to particles while settling towards the midplane. The DSI has previously been studied in the linear regime, with predictions that it could trigger particle clumping away from the midplane. This work presents a range of linear calculations and non-linear simulations, performed with FARGO3D, to assess conditions for DSI growth. We expand on…
The composition of giant planets reflects their formation history. Planetesimal accretion during the phase of planetary migration could lead to the delivery of heavy elements into giant planets. In our previous paper (Shibata et al. 2020) we showed that planetesimal accretion during planetary migration occurs in a rather narrow region of the protoplanetary disk, which we refer as "the sweet spot for accretion". The goal of this paper is to reveal the nature of the sweet spot and investigate the role of the sweet spot in determining the composition of gas giant planets. We analytically derive t…
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…
Planetesimal formation facilitated by streaming instability in weak pressure bumps
Center for Star and Planet Formation, Globe Institute, University of Copenhagen（哥本哈根大学恒星与行星形成中心全球研究所）；Niels Bohr Institute, University of Copenhagen（哥本哈根大学尼尔斯·玻尔研究所）；Anton Pannekoek Institute for Astronomy, University of Amsterdam（阿姆斯特丹大学安东·潘内科克天体物理研究所）；Division of Astrophysics, Department of Physics, Lund University（隆德大学物理系天体物理学部）
We study the gravitational instability (GI) of small solids in a gas disk as a mechanism to form planetesimals. Dissipation from gas drag introduces secular GI, which proceeds even when standard GI criteria for a critical density or Toomre's $Q$ predict stability. We include the stabilizing effects of turbulent diffusion, which suppresses small scale GI. The radially wide rings that do collapse contain up to $\sim 0.1$ Earth masses of solids. Subsequent fragmentation of the ring (not modeled here) would produce a clan of chemically homogenous planetesimals. Particle radial drift time scales (a…
Dust at the midplane of a circumstellar disk can become gravitationally unstable and fragment into planetesimals if the local dust-to-gas density ratio mu is sufficiently high. We simulate how dust settles in passive disks and ask how high mu can become. We settle the dust using a 1D code and test for dynamical stability using a 3D shearing box code. This scheme allows us to explore the behavior of small particles having short but non-zero stopping times in gas: 0 < t_stop << the orbital period. The streaming instability is thereby filtered out. Dust settles until shearing instabilities in the…
Context.Recent studies suggest that many giant exoplanets are highly enriched with heavy elements compared to their host star andcontain several tens of Earth masses or more of heavy elements. Such enrichment is considered to have been brought by accretionof planetesimals in late formation stages. Previous dynamical simulations, however, show that planets are unable to collect so muchheavy elements throughin situplanetesimal accretion. Aims.We investigate whether a giant planet migrating inward can capture planetesimals efficiently to significantly increase its metal-licity. Methods.We perform…
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…
The streaming instability and Kelvin--Helmholtz instability are considered the two major sources causing clumping of dust particles and turbulence in the dust layer of a protoplanetary disk as long as we consider the dead zone where the magneto-rotational instability does not grow. Extensive numerical simulations have been carried out in order to elucidate the condition for the development of particle clumping caused by the streaming instability. In this paper, a set of two parameters suitable for classifying the numerical results is proposed. One is the Stokes number that has been employed in…
We present evidence that it is unlikely that the streaming instability (SI) can form planetesimals from mm grains inside axisymmetric pressure bumps. We conducted the largest simulation of the SI so far (7 million CPU hours), consisting of a large slice of the disk with mm grains, a solar-like dust-to-gas ratio ($Z = 0.01$), and the largest pressure bump that does not cause gravitational instability (GI) in the particle layer. We used a high resolution of $1000/H$ to resolve as many SI unstable modes as possible. The simulation produced a long-lived particle over-density far exceeding the SI c…
The streaming instability is a promising mechanism to induce the formation of planetesimals. Nonetheless, this process has been found in previous studies to require either a dust-to-gas surface density ratio or a dust size that is enhanced compared to observed values. Employing two-dimensional global simulations of protoplanetary disks, we show that the vertical shear instability and the streaming instability in concert can cause dust concentration that is sufficient for planetesimal formation for lower surface density ratios and smaller dust sizes than the streaming instability in isolation, …
Planets are built from planetesimals: solids larger than a kilometer which grow by colliding pairwise. Planetesimals themselves are unlikely to form by two-body collisions; sub-km objects have gravitational fields individually too weak, and electrostatic attraction is too feeble for growth beyond a few cm. We review the possibility that planetesimals form when self-gravity brings together vast ensembles of small particles. Even when self-gravity is weak, aerodynamic processes can accumulate solids relative to gas, paving the way for gravitational collapse. Particles pile up as they drift radia…
Gravitational instability (GI) of a dust-rich layer at the midplane of a gaseous circumstellar disk is one proposed mechanism to form planetesimals, the building blocks of rocky planets and gas giant cores. Self-gravity competes against the Kelvin-Helmholtz instability (KHI): gradients in dust content drive a vertical shear which risks overturning the dusty subdisk and forestalling GI. To understand the conditions under which the disk can resist the KHI, we perform 3D simulations of stratified subdisks in the limit that dust particles are small and aerodynamically well coupled to gas. This lim…
Using self-consistent models of turbulent particle growth in an evolving protoplanetary nebula of solar composition we find that recently proposed local metallicity and Stokes number criteria necessary for the streaming instability to generate gravitationally bound particle overdensities are generally not approached anywhere in the disk during the first million years, an epoch in which meteoritic and observational evidence strongly suggests that the formation of the first planetesimals and perhaps giant planet core accretion is already occurring.
The streaming instability concentrates solid particles in protoplanetary disks, leading to gravitational collapse into planetesimals. Despite its key role in producing particle clumping and determining critical length scales in the instability's linear regime, the influence of the disk's radial pressure gradient on planetesimal properties has not been examined in detail. Here, we use streaming instability simulations that include particle self-gravity to study how the planetesimal initial mass function depends on the radial pressure gradient. Fitting our results to a power-law, ${\rm d}N / {\r…
The goal of this work is to investigate Jupiter's growth focusing on the amount of heavy elements accreted by the planet, and its comparison with recent structure models. Our model assumes an initial core growth dominated by pebble accretion, and a second growth phase that is characterized by a moderate accretion of both planetesimals and gas. The third phase is dominated by runaway gas accretion during which the planet becomes detached from the disk. The second and third phases are computed in detail, considering two different prescriptions for the planetesimal accretion and fits from hydrody…
The final composition of giant planets formed as a result of gravitational instability in the disk gas depends on their ability to capture solid material (planetesimals) during their 'pre-collapse' stage, when they are extended and cold, and contracting quasi-statically. The duration of the pre-collapse stage is inversely proportional roughly to the square of the planetary mass, so massive protoplanets have shorter pre-collapse timescales and therefore limited opportunity for planetesimal capture. The available accretion time for protoplanets with masses of 3, 5, 7, and 10 Jupiter masses is fo…
(Abridged) We present local 2D and 3D hybrid numerical simulations of particles and gas in the midplane of protoplanetary disks (PPDs) using the Athena code. The particles are coupled to gas aerodynamically, with particle-to-gas feedback included. Magnetorotational turbulence is ignored as an approximation for the dead zone of PPDs, and we ignore particle self-gravity to study the precursor of planetesimal formation. Our simulations include a wide size distribution of particles, ranging from strongly coupled particles with dimensionless stopping time tau_s=Omega t_stop=1e-4 to marginally coupl…
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…
We present a basic, fast, and flexible planet formation model, called SimAb (Simulating Abundances), to form giant planets and study their primary atmospheric composition soon after their formation. In SimAb we introduce parameters to simplify the assumptions about the complex physics involved in the formation of a planet. This approach allows us to trace and understand the influence of complex physical processes on the formed planets. We focus on the C/O ratio and the metallicity of the planetary atmosphere as an indicator of their compositions. We show that the initial protoplanet core mass …
We develop a simple model to predict the radial distribution of planetesimal formation. The model is based on the observed growth of dust to mm-sized particles, which drift radially, pile-up, and form planetesimals where the stopping time and dust-to-gas ratio intersect the allowed region for streaming instability-induced gravitational collapse. Using an approximate analytic treatment, we first show that drifting particles define a track in metallicity--stopping time space whose only substantial dependence is on the disk's angular momentum transport efficiency. Prompt planetesimal formation is…
A Dichotomy of the Mass-Metallicity Relation of Exoplanetary Atmospheres Demarcated by their Birthplace
Division of Science, National Astronomical Observatory of Japan（日本国立天文台科学部）；Graduate Institute for Advanced Studies, SOKENDAI（综合研究大学院大学）；Astrobiology Center（天体生物学中心）；Department of Earth and Planetary Science, The University of Tokyo（东京大学地球行星科学系）；Department of Earth and Planetary Sciences, Institute of Science Tokyo（东京科学大学地球行星科学系）；UTokyo Organization for Planetary Space Science (UTOPS), University of Tokyo（东京大学宇宙行星科学研究组织）；Kapteyn Astronomical Institute, University of Groningen（格罗宁根大学卡普坦天文研究所）
The formation of planetesimals is an unsolved problem in planet formation theory. A prominent scenario for overcoming dust growth barriers in dead zones is the gravitational collapse of locally over-dense regions, shown to robustly produce $\sim$100 km sized objects. Still, the conditions under which planetesimal formation occurs remain unclear. For collapse to proceed, the self-gravity of an overdensity must overcome stellar tidal disruption on large scales and turbulent diffusion on small scales. Here, we relate the scales of streaming and Kelvin-Helmholtz instability, which both regulate pa…
Recent observations of debris discs, believed to be made up of remnant planetesimals, brought a number of surprises. Debris disc presence does not correlate with the host star's metallicity, and may anti-correlate with the presence of gas giant planets. These observations contradict both assumptions and predictions of the highly successful Core Accretion model of planet formation. Here we explore predictions of the alternative Tidal Downsizing (TD) scenario of planet formation. In TD, small planets and planetesimal debris is made only when gas fragments, predecessors of giant planets, are tida…
Enhancing the local dust-to-gas ratio in protoplanetary discs is a necessary first step to planetesimal formation. In laminar discs, dust settling is an efficient mechanism to raise the dust-to-gas ratio at the disc midplane. However, turbulence, if present, can stir and lift dust particles, which ultimately hinders planetesimal formation. In this work, we study dust settling in protoplanetary discs with hydrodynamic turbulence sustained by the vertical shear instability. We perform axisymmetric numerical simulations to investigate the effect of turbulence, particle size, and solid abundance o…
The formation of planetesimals is expected to occur via particle-gas instabilities that concentrate dust into self-gravitating clumps. Triggering these instabilities requires the prior pileup of dust in the protoplanetary disk. Until now, this has been successfully modeled exclusively at the disk's snowline, whereas rocky planetesimals in the inner disk were obtained only by assuming either unrealistically large particle sizes or an enhanced global disk metallicity. However, planetesimal formation solely at the snowline is difficult to reconcile with the early and contemporaneous formation of …
The Athena MHD code has been extended to integrates the motion of particles coupled with the gas via aerodynamic drag, in order to study the dynamics of gas and solids in protoplanetary disks and the formation of planetesimals. Our particle-gas hybrid scheme is based on a second order predictor-corrector method. Careful treatment of the momentum feedback on the gas guarantees exact conservation. The hybrid scheme is stable and convergent in most regimes relevant to protoplanetary disks. We describe a semi-implicit integrator generalized from the leap-frog approach. In the absence of drag force…
The formation mechanism of planetesimals in protoplanetary discs is hotly debated. Currently, the favoured model involves the accumulation of meter-sized objects within a turbulent disc, followed by a phase of gravitational instability. At best one can simulate a few million particles numerically as opposed to the several trillion meter-sized particles expected in a real protoplanetary disc. Therefore, single particles are often used as super-particles to represent a distribution of many smaller particles. It is assumed that small scale phenomena do not play a role and particle collisions are …
We introduce a new Lagrangian smooth-particle method to model the growth and drift of pebbles in protoplanetary disks. The Lagrangian nature of the model makes it especially suited to follow characteristics of individual (groups of) particles, such as their composition. In this work we focus on the water content of solid particles. Planetesimal formation via streaming instability is taken into account, partly based on previous results on streaming instability outside the water snowline that were presented in Schoonenberg & Ormel (2017). We validate our model by reproducing earlier results from…
The streaming instability is a promising mechanism to drive the formation of planetesimals in protoplanetary disks. To trigger this process, it has been argued that sedimentation of solids onto the mid-plane needs to be efficient and therefore that a quiescent gaseous environment is required. It is often suggested that dead-zone or disk-wind structure created by non-ideal magnetohydrodynamical (MHD) effects meets this requirement. However, simulations have shown that the midplane of a dead zone is not completely quiescent. In order to examine the concentration of solids in such an environment,…
We compute, for the first time, self-consistent models of planet growth including the effect of envelope enrichment. The change of envelope metallicity is assumed to be the result of planetesimal disruption or icy pebble sublimation. We solve internal structure equations taking into account global energy conservation for the envelope to compute in-situ planetary growth. We consider different opacities and equations of state suited for a wide range of metallicities. We find that envelope enrichment speeds up the formation of gas giants. It also explains naturally the formation of low and interm…
The discovery of 1I/`Oumuamua confirmed that planetesimals must exist in great numbers in interstellar space. Originally generated during planet formation, they are scattered from their original systems and subsequently drift through interstellar space. As a consequence they should seed molecular clouds with at least hundred-metre-scale objects. We consider how the galactic background density of planetesimals, enriched from successive generations of star and system formation, can be incorporated into forming stellar systems. We find that at minimum of the order of 10$^{7}$ `Oumuamua-sized and …
Transmission spectroscopy is enabling precise measurements of atmospheric H2O abundances for numerous giant exoplanets. For hot Jupiters, relating H2O abundances to metallicities provides a powerful probe of their formation conditions. However, metallicity measurements for Neptune-mass exoplanets are only now becoming viable. Exo-Neptunes are expected to possess super-solar metallicities from accretion of H2O-rich and solid-rich planetesimals. However, initial investigations into the exo-Neptune HAT-P-26b suggested a significantly lower metallicity than predicted by the core-accretion theory o…
The streaming instability is often invoked as solution to the fragmentation and drift barriers in planetesimal formation, catalyzing the aggregation of dust on kyr timescales to grow km-sized cores. However there remains a lack of consensus on the physical mechanism(s) responsible for initiating it. One potential avenue is disc photoevaporation, wherein the preferential removal of relatively dust-free gas increases the disc metallicity. Late in the disc lifetime, photoevaporation dominates viscous accretion, creating a gradient in the depleted gas surface density near the location of the gap. …
One of the main scenarios of planet formation is the core accretion model where a massive core forms first and then accretes a gaseous envelope. This core forms by accreting solids, either planetesimals, or pebbles. A key constraint in this model is that the accretion of gas must proceed before the dissipation of the gas disc. Classical planetesimal accretion scenario predicts that the time needed to form a giant planets core is much longer than the time needed to dissipate the disc. This difficulty led to the development of another accretion scenario, in which cores grow by accretion of pebbl…
We 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…
Most of our current understanding of the planet formation mechanism is based on the planet metallicity correlation derived mostly from solar-type stars harbouring gas-giant planets. To achieve a far more reaching grasp on the substellar formation process we aim to analyse in terms of their metallicity a diverse sample of stars (in terms of mass and spectral type) covering the whole range of possible outcomes of the planet formation process (from planetesimals to brown dwarfs and low-mass binaries). Our methodology is based on the use of high-precision stellar parameters derived by our own grou…
