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 parameters $α\gtrsim \mathrm{St} ^{1.5}$, where $\mathrm{St}$ is the particle Stokes number. We explore the effect of non-linear drag laws, which may be applicable to porous dust particles, and find growth rates are modestly reduced. We also find that gas compressibility increase growth rates by reducing the effect of diffusion. We then apply linear theory to global models of viscous protoplanetary disks. For minimum-mass Solar nebula disk models, we find the streaming instability only grows within disk lifetimes beyond $\sim 10$s of AU, even for cm-sized particles and weak turbulence ($α\sim 10^{-4}$). Our results suggest it is rather difficult to trigger the streaming instability in non-laminar protoplanetary disks, especially for small particles.
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…
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 study the dynamics of a viscous protoplanetary disc hosting a population of dust grains with a range of sizes. We compute steady-state solutions, and show that the radial motion of both the gas and the dust can deviate substantially from those for a single-size dust population. Although the aerodynamic drag from the dust on the gas is weaker than in the case where all grains are optimally coupled to the gas, the cumulative "back-reaction" of the dust particles can still alter the gas dynamics significantly. In typical protoplanetary discs, the net effect of the dust back-reaction decreases …
Protoplanetary disks are believed to evolve on Myr timescales in a diffusive (viscous) manner as a result of angular momentum transport driven by internal stresses. Here we use a sample of 26 protoplanetary disks resolved by ALMA with measured (dust-based) masses and stellar accretion rates to derive the dimensionless $α$-viscosity values for individual objects, with the goal of constraining the angular momentum transport mechanism. We find that the inferred values of $α$ do not cluster around a single value, but instead have a broad distribution extending from $10^{-4}$ to $0.04$. Moreover, t…
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…
In order to understand which mechanism is responsible for accretion in protoplanetary discs, a robust knowledge of the observed disc radius using gas tracers such as $^{12}$CO and other CO isotopologues is pivotal. Indeed, the two main theories proposed, viscous accretion and wind-driven accretion, predict different time evolution for the disc radii. In this Letter, we present an analytical solution for the evolution of the disc radii in viscously evolving protoplanetary discs using $^{12}$CO as a tracer, under the assumption that the $^{12}$CO radius is the radius where the surface density of…
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 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 mut…
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…
Layered accretion is one of the inevitable ingredients in protoplanetary disks when disk turbulence is excited by magnetorotational instabilities (MRIs). In the accretion, disk surfaces where MRIs fully operate have a high value of disk accretion rate ($\dot{M}$), while the disk midplane where MRIs are generally quenched ends up with a low value of $\dot{M}$. Significant progress on understanding MRIs has recently been made by a number of dedicated MHD simulations, which requires improvement of the classical treatment of $α$ in 1D disk models. To this end, we obtain a new expression of $α$ by …
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…
We calculate the chemical evolution of protoplanetary disks considering radial viscous accretion, vertical turbulent mixing and vertical disk winds. We study the effects on the disk chemical structure when different models for the formation of molecular hydrogen on dust grains are adopted. Our gas-phase chemistry is extracted from the UMIST Database for Astrochemistry (Rate06) to which we have added detailed gas-grain interactions. We use our chemical model results to generate synthetic near- and mid-infrared LTE line emission spectra and compare these with recent Spitzer observations. Our res…
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
Based on the viscous disk theory, a number of recent studies have suggested there is large scale meridional circulation in protoplanetary disks. Such a flow could account for the presence of crystalline silicates, including calcium- and aluminum-rich inclusions (CAIs), at large distances from the sun. This paper aims at examining whether such large-scale flows exist in turbulent protoplanetary disks. High-resolution global hydrodynamical and magnetohydrodynamical (MHD) numerical simulations of turbulent protoplanetary disks were used to infer the properties of the flow in such disks. By perfor…
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…
Secular evolution of viscous and self-gravitating protoplanetary discs with magnetic winds
Research Institute of Physics, Southern Federal University（南联邦大学物理研究所）；Faculty of Physics, Southern Federal University（南联邦大学物理学院）；Institut für Astro- und Teilchenphysik, Universität Innsbruck（因斯布鲁克大学天体与粒子物理研究所）；Mullard Space Science Laboratory, University College London（伦敦大学学院穆拉德太空科学实验室）
Protoplanetary disks often appear as multiple concentric rings in dust continuum emission maps and scattered light images. These features are often associated with possible young planets in these disks. Many non-planetary explanations have also been suggested, including snow lines, dead zones and secular gravitational instabilities in the dust. In this paper we suggest another potential origin. The presence of copious amounts of dust tends to strongly reduce the conductivity of the gas, thereby inhibiting the magneto-rotational instability, and thus reducing the turbulence in the disk. From vi…
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…
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 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…
Observations of protoplanetary disks show that some characteristics seem recurrent, even in star formation regions that are physically distant such as surface mass density profiles varying as $r^{-1}$, or aspect ratios about 0.03 to 0.23. Accretion rates are also recurrently found around $10^{-8} - 10^{-6}~\mathrm{M_{\odot}~yr^{-1}}$ for disks already evolved (Isella et al., 2009, Andrews et al., 2009, 2010). Several models have been developed in order to recover these properties. However, most of them usually simplify the disk geometry if not its mid-plane temperature. This has major conseque…
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…
Evolution of dust in a protoplanetary disc driven by stellar flybys: implications for the streaming instability
Institute of Astronomy and Astrophysics, Academia Sinica（中央研究院天文及天文物理研究所）；Graduate Institute of Astrophysics, National Taiwan University（國立台灣大學天文研究所）；Homer L. Dodge Department of Physics and Astronomy, The University of Oklahoma（歐克拉荷馬大學霍默·L·道奇物理與天文學系）；Department of Physics and Astronomy, The University of Alabama（阿拉巴馬大學物理與天文學系）；Univ. Grenoble Alpes, CNRS, IPAG（格勒諾布爾阿爾卑斯大學、法國國家科學研究中心、IPAG）
The C/O ratio is a defining feature of both gas giant atmospheric and protoplanetary disk chemistry. In disks, the C/O ratio is regulated by the presence of snowlines of major volatiles at different distances from the central star. We explore the effect of radial drift of solids and viscous gas accretion onto the central star on the snowline locations of the main C and O carriers in a protoplanetary disk, H2O, CO2 and CO, and their consequences for the C/O ratio in gas and dust throughout the disk. We determine the snowline locations for a range of fixed initial particle sizes and disk types. …
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…
Low-mass objects embedded in isothermal protoplanetary discs are known to suffer rapid inward Type I migration. In non-isothermal discs, recent work has shown that a decreasing radial profile of the disc entropy can lead to a strong positive corotation torque which can significantly slow down or reverse Type I migration in laminar viscous disc models. It is not clear however how this picture changes in turbulent disc models. The aim of this study is to examine the impact of turbulence on the torque experienced by a low-mass planet embedded in a non-isothermal protoplanetary disc. We particular…
The nature and rate of (viscous) angular momentum transport in protoplanetary discs (PPDs) has important consequences for the formation process of planetary systems. While accretion rates onto the central star yield constraints on such transport in the inner regions of a PPD, empirical constraints on viscous spreading in the outer regions remain challenging to obtain. Here we demonstrate a novel method to probe the angular momentum transport at the outer edge of the disc. This method applies to PPDs that have lost a significant fraction of their mass due to thermal winds driven by UV irradiati…
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…
Streaming instability is a powerful mechanism which concentrates dust grains in pro- toplanetary discs, eventually up to the stage where they collapse gravitationally and form planetesimals. Previous studies inferred that it should be ineffective in viscous discs, too efficient in inviscid discs, and may not operate in local pressure maxima where solids accumulate. From a linear analysis of stability, we show that streaming instability behaves differently inside local pressure maxima. Under the action of the strong differential advection imposed by the bump, a novel unstable mode develops and …
Vortex formation through the Rossby wave instability (RWI) in protoplanetary discs has been invoked to play a role in planet formation theory, and suggested to explain the observation of large dust asymmetries in several transitional discs. However, whether or not vortex formation operates in layered accretion discs, i.e. models of protoplanetary discs including dead zones near the disc midplane --- regions that are magnetically inactive and the effective viscosity greatly reduced --- has not been verified. As a first step toward testing the robustness of vortex formation in layered discs, we …
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…
Current theories on planetary formation establish that giant planet formation should be contextual to their quick migration towards the central star due to the protoplanets-disc interactions on a timescale of the order of $10^5$ years, for objects of nearly 10 terrestrial masses. Such a timescale should be smaller by an order of magnitude than that of gas accretion onto the protoplanet during the hierarchical growing-up of protoplanets by collisions with other minor objects. These arguments have recently been analysed using N-body and/or fluid-dynamics codes or a mixing of them. In this work, …
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…
In this article, we proceed to study convection as a possible factor of episodic accretion in protoplanetary disks. Within the model presented in Article~I, the accretion history is analyzed at different rates and areas of matter inflow from the envelope onto the disk. It is shown that the burst-like regime occurs in a wide range of parameters. The long-term evolution of the disk is also modeled, including the decreasing-with-time matter inflow from the envelope. It is demonstrated that the disk becomes convectively unstable and maintains burst-like accretion onto the star for several million …
A major uncertainty in accretion disk theory is the nature and properties of gas turbulence, which drives transport in protoplanetary disks. The commonly used viscous prescription for the Maxwell-Reynolds stress tensor gives rise to a meridional circulation where flow is outward near the midplane and inward away from it. This meridional circulation has been proposed as an explanation for the presence of high-temperature minerals (believed to be of inner solar system provenance) in comets. However, it has not been observed in simulations of magnetohydrodynamical (MHD) turbulence so far. In this…
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…
