The streaming instability is a leading candidate mechanism to explain the formation of planetesimals. Yet, the role of this instability in the driving of turbulence in protoplanetary disks, given its fundamental nature as a linear hydrodynamical instability, has so far not been investigated in detail. We study the turbulence that is induced by the streaming instability as well as its interaction with the vertical shear instability. For this purpose, we employ the FLASH Code to conduct two-dimensional axisymmetric global disk simulations spanning radii from $1$ au to $100$ au, including the mutual drag between gas and dust as well as the radial and vertical stellar gravity. If the streaming instability and the vertical shear instability start their growth at the same time, we find the turbulence in the dust mid-plane layer to be primarily driven by the streaming instability. It gives rise to vertical gas motions with a Mach number of up to ${\sim}10^{-2}$. The dust scale height is set in a self-regulatory manner to about $1\%$ of the gas scale height. In contrast, if the vertical shear instability is allowed to saturate before the dust is introduced into our simulations, then it continues to be the main source of the turbulence in the dust layer. The vertical shear instability induces turbulence with a Mach number of ${\sim}10^{-1}$ and thus impedes dust sedimentation. Nonetheless, we find the vertical shear instability and the streaming instability in combination to lead to radial dust concentration in long-lived accumulations which are significantly denser than those formed by the streaming instability alone. Thus, the vertical shear instability may promote planetesimal formation by creating weak overdensities that act as seeds for the streaming instability.
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 is one of the most promising pathways to the formation of planetesimals from pebbles. Understanding how this instability operates under realistic conditions expected in protoplanetary disks is therefore crucial to assess the efficiency of planet formation. Contemporary models of protoplanetary disks show that magnetic fields are key to driving gas accretion through large-scale, laminar magnetic stresses. However, the effect of such magnetic fields on the streaming instability has not been examined in detail. To this end, we study the stability of dusty, magnetized gas…
The streaming instability is a popular candidate for planetesimal formation by concentrating dust particles to trigger gravitational collapse. However, its robustness against physical conditions expected in protoplanetary disks is unclear. In particular, particle stirring by turbulence may impede the instability. To quantify this effect, we develop the linear theory of the streaming instability with external turbulence modelled by gas viscosity and particle diffusion. We find the streaming instability is sensitive to turbulence, with growth rates becoming negligible for alpha-viscosity paramet…
We develop simple, physically motivated models for drag-induced dust-gas streaming instabilities, which are thought to be crucial for clumping grains to form planetesimals in protoplanetary disks. The models explain, based on the physics of gaseous epicyclic motion and dust-gas drag forces, the most important features of the streaming instability and its simple generalisation, the disk settling instability. Some of the key properties explained by our models include the sudden change in the growth rate of the streaming instability when the dust-to-gas-mass ratio surpasses one, the slow growth r…
We revisit, via a very simplified set of equations, a linear streaming instability (technically an overstability), which is present in, and potentially important for, dusty protoplanetary disks (Youdin & Goodman 2005). The goal is a better understanding of the physical origin of such instabilities, which are notoriously subtle. Rotational dynamics seem to be essential to this type of instability, which cannot be captured by one-dimensional Cartesian models. Dust `pileups' in moving pressure maxima are an important triggering mechanism of the instability, and drag feedback of dust upon the gas …
Under the right conditions, the streaming instability between imperfectly coupled dust and gas is a powerful mechanism for planetesimal formation as it can concentrate dust grains to the point of gravitational collapse. In its simplest form, the streaming instability can be captured by analyzing the linear stability of unstratified disk models, which represent the midplane of protoplanetary disks. We extend such studies by carrying out vertically-global linear stability analyses of dust layers in protoplanetary disks. We find the dominant form of instability in stratified dust layers is one dr…
We investigate streaming instability using two-fluid approximation (neutral gas and dust) in a quasi-global, unstratified protoplanetary disc, with the help of PIERNIK code. We compare amplification rate of the eigen-mode in numerical simulations, with the corresponding growth resulting from the linear stability analysis of full system of Euler's equation including aerodynamic drag. Following Youdin & Goodman (2005) we show that (1) rapid dust clumping occurs due to the difference in azimuthal velocities of gas and dust, coupled by the drag force, (2) initial density perturbations are amplifie…
Streaming instabilities in weakly ionized protoplanetary discs: the Ambipolar Streaming Instability (AmSI)
Laboratoire d’astrophysique de Bordeaux, Univ. Bordeaux, CNRS（波尔多天体物理实验室，波尔多大学，法国国家科学研究中心）；Institute of Astronomy and Astrophysics, Academia Sinica（中央研究院天文及天文物理研究所）；Physics Division, National Center for Theoretical Sciences（国家理论科学中心物理组）
We identify and study a number of new, rapidly growing instabilities of dust grains in protoplanetary disks, which may be important for planetesimal formation. The study is based on the recognition that dust-gas mixtures are generically unstable to a Resonant Drag Instability (RDI), whenever the gas, absent dust, supports undamped linear modes. We show that the "streaming instability" is an RDI associated with epicyclic oscillations; this provides simple interpretations for its mechanisms and accurate analytic expressions for its growth rates and fastest-growing wavelengths. We extend this ana…
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, …
Laboratory experiments indicate that direct growth of silicate grains via mutual collisions can only produce particles up to roughly millimeters in size. On the other hand, recent simulations of the streaming instability have shown that mm/cm-sized particles require an excessively high metallicity for dense filaments to emerge. Using a numerical algorithm for stiff mutual drag force, we perform simulations of small particles with significantly higher resolutions and longer simulation times than in previous investigations. We find that particles of dimensionless stopping time $τ_\mathrm{s} = 10…
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…
The recently discovered resonant drag instability (RDI) of dust streaming in protoplanetary disc is considered as the mode coupling of subsonic gas-dust mixture perturbations. This mode coupling is coalescence of two modes with nearly equal phase velocities: inertial wave (IW) having positive energy and a streaming dust wave (SDW) having negative energy as measured in the frame of gas environment being at rest in vertical hydrostatic equilibrium. SDW is a trivial mode produced by the bulk streaming of dust, which transports perturbations of dust density. In this way, settling combined with rad…
The streaming instability (SI) is one of the most promising candidates for triggering planetesimal formation by producing dense dust clumps that undergo gravitational collapse. Understanding how the SI operates in realistic protoplanetary disks (PPDs) is therefore crucial to assess the efficiency of planetesimal formation. Modern models of PPDs show that large-scale magnetic torques or winds can drive laminar gas accretion near the disk midplane. In a previous study, we identified a new linear dust-gas instability, the azimuthal drift SI (AdSI), applicable to such accreting disks and is powere…
In this paper, we investigate whether overdensity formation via streaming instability is consistent with recent multi-wavelength ALMA observations in the Lupus star forming region. We simulate the local action of streaming instability in 2D using the code ATHENA, and examine the radiative properties at mm wavelengths of the resulting clumpy dust distribution by focusing on two observable quantities: the optically thick fraction $ff$ (in ALMA band 6) and the spectral index $α$ (in bands 3-7). By comparing the simulated distribution in the $ff-α$ plane before and after the action of streaming in…
Azimuthal Dust Polarization from Aerodynamically Aligned Grains as Evidence for the Streaming Instability in Protoplanetary Disks
National Radio Astronomy Observatory（国家射电天文台）；Iowa State University（爱荷华州立大学）；University of Virginia（弗吉尼亚大学）；New Mexico State University（新墨西哥州立大学）；Institut de Ciències de l’Espai (ICE), CSIC（空间科学研究所（ICE），西班牙高等科学研究委员会）；Instituto Argentino de Radioastronomía (CCT-La Plata, CONICET（阿根廷射电天文研究所）；UNLP（拉普拉塔国立大学天文与地球物理科学学院）；CICPBA)（莱斯大学）；Facultad de Ciencias Astronómicas y Geofísicas, Universidad Nacional de La Plata；Rice University
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…
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…
The radial drift and diffusion of dust particles in protoplanetary disks affect both the opacity and temperature of such disks as well as the location and timing of planetesimal formation. In this paper, we present results of numerical simulations of particle-gas dynamics in protoplanetary disks that include dust grains with various size distributions. We consider three scenarios in terms of particle size ranges, one where the Stokes number $τ_{\rm{s}} = 10^{-1} - 10^0$, one where $τ_{\rm{s}} = 10^{-4} - 10^{-1}$ and finally one where $τ_{\rm{s}} = 10^{-3} - 10^{0}$. Moreover, we consider both…
Recent years have seen growing interest in the streaming instability as a candidate mechanism to produce planetesimals. However, these investigations have been limited to small-scale simulations. We now present the results of a global protoplanetary disk evolution model that incorporates planetesimal formation by the streaming instability, along with viscous accretion, photoevaporation by EUV, FUV, and X-ray photons, dust evolution, the water ice line, and stratified turbulence. Our simulations produce massive (60-130 $M_\oplus$) planetesimal belts beyond 100 au and up to $\sim 20 M_\oplus$ of…
The streaming instability for solid particles in protoplanetary disks is re-examined assuming the familiar alpha ($α$) model for isotropic turbulence. Turbulence always reduces the growth rates of the streaming instability relative to values calculated for globally laminar disks. While for small values of the turbulence parameter, $α< 10^{-5}$, the wavelengths of the fastest-growing disturbances are small fractions of the local gas vertical scale height $H$, we find that for moderate values of the turbulence parameter, i.e., $α\sim 10^{-5}-10^{-3}$, the lengthscales of maximally growing distur…
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…
Axisymmetric dust rings are a ubiquitous feature of young protoplanetary disks. These rings are likely caused by pressure bumps in the gas profile; a small bump can induce a traffic jam-like pattern in the dust density, while a large bump may halt radial dust drift entirely. The resulting increase in dust concentration may trigger planetesimal formation by the streaming instability (SI), as the SI itself requires some initial concentration. Here we present the first 3D simulations of planetesimal formation in the presence of a pressure bump modeled specifically after those observed by ALMA. In…
A critical step toward the emergence of planets in a protoplanetary disk consists in accretion of planetesimals, bodies 1-1000 km in size, from smaller disk constituents. This process is poorly understood partly because we lack good observational constraints on the complex physical processes that contribute to planetesimal formation. In the outer solar system, the best place to look for clues is the Kuiper belt, where icy planetesimals survived to this day. Here we report evidence that Kuiper belt planetesimals formed by the streaming instability, a process in which aerodynamically concentrate…
Turbulence acting on mixes of gas and particles generally evenly diffuses the latter through the former. However, in the presence of background gas temperature gradients a phenomenon known as turbulent thermal diffusion appears as a particle drift velocity (rather than a diffusive term). This process moves particles from hot regions to cold ones. We rederive turbulent thermal diffusion using astrophysical language and demonstrate that it could play a major role in protoplanetary discs by concentrating particles by factors of tens. Such a concentration would set the stage for collective behavio…
Damping of the previously discovered resonant drag instability (RDI) of dust streaming in protoplanetary disc is studied using the local approach to dynamics of gas-dust perturbations in the limit of the small dust fraction. Turbulence in a disc is represented by the effective viscosity and diffusivity in equations of motion for gas and dust, respectively. In the standard case of the Schmidt number (ratio of the effective viscosity to diffusivity) Sc = 1, the reduced description of RDI in terms of the inertial wave (IW) and the streaming dust wave (SDW) falling in resonance with each other rev…
In the recent years, sub/mm observations of protoplanetary disks have discovered an incredible diversity of substructures in the dust emission. An important result was the finding that dust grains of mm size are embedded in very thin dusty disks. This implies that the dust mass fraction in the midplane becomes comparable to the gas, increasing the importance of the interaction between the two components there. We address this problem by means of numerical 2.5D simulations in order to study the gas and dust interaction in fully global stratified disks. To this purpose, we employ the recently de…
Instabilities of the dust layer in a protoplanetary disk are investigated. It is known that the streaming instability develops and dust density concentration occurs in a situation where the initial dust density is uniform. This work considers the effect of initial dust density gradient vertical to the midplane. Dust and gas are treated as different fluids. Pressure of dust fluid is assumed to be zero. The gas friction time is assumed to be constant. Axisymmetric two-dimensional numerical simulation was performed using the spectral method. We found that an instability develops with a growth rat…
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…
Protoplanets may be born into dust-rich environments if planetesimals formed through streaming or gravitational instabilities, or if the protoplanetary disc is undergoing mass loss due to disc winds or photoevaporation. Motivated by this possibility, we explore the interaction between low mass planets and dusty protoplanetary discs with focus on disc-planet torques. We implement Lin & Youdin's newly developed, purely hydrodynamic model of dusty gas into the PLUTO code to simulate dusty protoplanetary discs with an embedded planet. We find that for imperfectly coupled dust and high metallicity,…
More than a decade of dedicated experimental work on the collisional physics of protoplanetary dust has brought us to a point at which the growth of dust aggregates can - for the first time - be self-consistently and reliably modelled. In this article, the emergent collision model for protoplanetery dust aggregates (Güttler et al. 2010) as well as the numerical model for the evolution of dust aggregates in protoplanetary disks (Zsom et al. 2010) are reviewed. It turns out that, after a brief period of rapid collisional growth of fluffy dust aggregates to sizes of a few centimeters, the protopl…
(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…
Small solids embedded in gaseous protoplanetary disks are subject to strong dust-gas friction. Consequently, tightly-coupled dust particles almost follow the gas flow. This near conservation of dust-to-gas ratio along streamlines is analogous to the near conservation of entropy along flows of (dust-free) gas with weak heating and cooling. We develop this thermodynamic analogy into a framework to study dusty gas dynamics in protoplanetary disks. We show that an isothermal dusty gas behaves like an adiabatic pure gas; and that finite dust-gas coupling may be regarded as an effective heating/cool…
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,…
Streaming instability is hypothesized to be triggered at particular protoplanetary disk locations where the volume density of the solid particles is enriched comparable to that of the gas. A ring of planetesimals thus forms when this condition is fulfilled locally. These planetesimals collide with each other and accrete inward drifting pebbles from the outer disk to further increase masses. We investigate the growth of the planetesimals that form in a ring-belt at various disk radii. Their initial mass distributions are calculated based on the formula summarized from the streaming instability …
The question of what determines the width of Kuiper belt analogues (exoKuiper belts) is an open one. If solved, this understanding would provide valuable insights into the architecture, dynamics, and formation of exoplanetary systems. Recent observations by ALMA have revealed an apparent paradox in this field, the presence of radially narrow belts in protoplanetary discs that are likely the birthplaces of planetesimals, and exoKuiper belts nearly four times as wide in mature systems. If the parent planetesimals of this type of debris disc indeed form in these narrow protoplanetary rings via st…
The streaming instability is a promising mechanism to overcome the barriers in direct dust growth and lead to the formation of planetesimals. Most previous studies of the streaming instability, however, were focused on a local region of a protoplanetary disk with a limited simulation domain such that only one filamentary concentration of solids has been observed. The characteristic separation between filaments is therefore not known. To address this, we conduct the largest-scale simulations of the streaming instability to date, with computational domains up to 1.6 gas scale heights both horizo…
We analyse the concentration of solid particles in vortices created and sustained by radial buoyancy in protoplanetary disks, i.e. baroclinic vortex growth. Besides the gas drag acting on particles we also allow for back-reaction from dust onto the gas. This becomes important when the local dust-to-gas ratio approaches unity. In our 2D, local, shearing sheet simulations we see high concentrations of grains inside the vortices for a broad range of Stokes numbers, ${\rm St}$. An initial dust-to-gas ratio of 1:100 can easily be reversed to 100:1 for ${\rm St}=1$. The increased dust-to-gas ratio t…
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 is a fundamental process that can drive dust-gas dynamics and ultimately planetesimal formation in protoplanetary discs. As a linear instability, it has been shown that its growth with a distribution of dust sizes can be classified into two distinct regimes, fast- and slow-growth, depending on the dust-size distribution and the total dust-to-gas density ratio $ε$. Using numerical simulations of an unstratified disc, we bring three cases in different regimes into nonlinear saturation. We find that the saturation states of the two fast-growth cases are similar to its si…
Spinning planetesimals in a gaseous protoplanetary disk may experience a hydrodynamical force perpendicular to their relative velocities. We examine the effect this force has on the dynamics of these objects using analytical arguments based on a simple laminar disk model and numerical integrations of the equations of motion for individual grains. We focus in particular on meter-sized boulders traditionally expected to spiral in to the central star in as little as 100 years from 1 A.U. We find that there are plausible scenarios in which this force extends the lifetime of these solids in the dis…
The streaming instability is thought to play a central role in the early stages of planet formation by enabling the efficient bypass of a number of barriers hindering the formation of planetesimals. We present the first study exploring the efficiency of the linear streaming instability when a particle-size distribution is considered. We find that, for a given dust-to-gas mass ratio, the multi-species streaming instability grows on timescales much longer than those expected when only one dust species is involved. In particular, distributions that contain close-to-order-unity dust-to-gas mass ra…
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）
The formation of planets with gaseous envelopes takes place in protoplanetary accretion discs on time-scales of several millions of years. Small dust particles stick to each other to form pebbles, pebbles concentrate in the turbulent flow to form planetesimals and planetary embryos and grow to planets, which undergo substantial radial migration. All these processes are influenced by the underlying structure of the protoplanetary disc, specifically the profiles of temperature, gas scale height and density. The commonly used disc structure of the Minimum Mass Solar Nebular (MMSN) is a simple pow…
