Instruments achieve sharper and finer observations of micron-in-size dust grains in the top layers of young stellar discs. To provide accurate models, we revisit the theory of dust settling for small grains, when gas stratification, dust inertia and finite correlation times for the turbulence should be handled simultaneously. We start from a balance of forces and derive distributions at steady-state. Asymptotic expansions require caution since limits do not commute. In particular, non-physical bumpy distributions appear when turbulence is purely diffusive. This excludes very short correlation times for real discs, as predicted by numerical simulations.
The interaction between settling of dust grains and magnetorotational instability (MRI) turbulence in protoplanetary disks is analyzed. We use a reduced system of coupled ordinary differential equations to represent the interaction between the diffusion of grains and the inhibition of the MRI. The coupled equations are styled on a Landau equation for the turbulence and a Fokker-Planck equation for the diffusion. The turbulence-grain interaction is probably most relevant near the outer edge of the disk's quiescent, or "dead" zone. Settling is most pronounced near the midplane, where a high dust…
We aim to derive a simple analytic model to understand the essential properties of vertically settling growing dust grains in laminar protoplanetary discs. Separating the vertical dynamics from the motion in the disc midplane, we integrate the equations of motion for both a linear and an exponential grain growth rate. Numerical integrations are performed for more complex growth models. We find that the settling efficiency depends on the value of the dimensionless parameter gamma, which characterises the relative efficiency of grain growth with respect to the gas drag. Since gamma is expected t…
In protoplanetary disks, the distribution and abundance of small (sub)micron grains are important for a range of physical and chemical processes. For example, they dominate the optical depth at short wavelengths and their surfaces are the sites of many important chemical reactions such as the formation of water. Based on their aerodynamical properties (i.e., their strong dynamical coupling with the surrounding gas) it is often assumed that these small grains are well-mixed with the gas. Our goal is to study the vertical (re)distribution of grains taking into account settling, turbulent diffusi…
We present Spitzer/IRS spectra of 31 TTS and IRAM/1.3mm observations for 34 low- and intermediate-mass stars in the Cep OB2 region. Including our previously published data, we analyze 56 TTS and the 3 intermediate-mass stars with silicate features in Tr 37 (~4 Myr) and NGC 7160 (~12 Myr). The silicate emission features are well reproduced with a mixture of amorphous (with olivine, forsterite, and silica stoichiometry) and crystalline grains (forsterite, enstatite). We explore grain size and disk structure using radiative transfer disk models, finding that most objects have suffered substantial…
In protoplanetary disks, the differential gravity-driven settling of dust grains with respect to gas and with respect to grains of varying sizes determines the observability of grains, and sets the conditions for grain growth and eventually planet formation. In this work we explore the effect of photophoresis on the settling of large dust grains in the inner regions of actively accreting protoplanetary disks. Photophoretic forces on dust grains result from the collision of gas molecules with differentially heated grains. We undertake one dimensional dust settling calculations to determine the …
The polarimetric observations on the protoplanetary disk around HL Tau have shown the scattering-induced polarization at ALMA Band 7, which indicates that the maximum dust size is $\sim 100~{\rm μm}$, while the Spectral Energy Distribution (SED) has suggested that the maximum dust size is $\sim$ mm. To solve the contradiction, we investigate the impact of differential settling of dust grains on the SED and polarization. If the disk is optically thick, longer observing wavelength traces more interior layer which would be dominated by larger grains. We find that, the SED of the center part of th…
We propose the possibility of a new phenomenon affecting the settling of dust grains at the terrestrial region in early protoplanetary disks. Sinking dust grains evaporate in a hot inner region during the early stage of disk evolution, and the effects of condensation and evaporation on vertical dust settling can be significant. A 1-D dust settling model considering both physical and chemical aspects is presented in this paper. Modeling results show that dust grains evaporate as they descend into the hotter interior and form a "condensation front," above which dust-composing major elements, Mg,…
Recent studies of chondrites have found a tungsten isotopic anomaly between chondrules and matrix. Given the refractory nature of tungsten, this implies that W was carried into the solar nebula by at least two distinct families of pre-solar grains. The observed chondrule/matrix split requires that the distinct families were kept separate during the dust coagulation process, and that the two families of grain interacted with the chondrule formation mechanism differently. We take the co-existence of different families of solids in the same general orbital region at the chondrule-precursor size a…
The dust sublimation walls of disks around T Tauri stars represent a directly observable cross-section through the disk atmosphere and midplane. Their emission properties can probe the grain size distribution and composition of the innermost regions of the disk, where terrestrial planets form. Here we calculate the inner dust sublimation wall properties for four classical T Tauri stars with a narrow range of spectral types and inclination angles and a wide range of mass accretion rates to determine the extent to which the walls are radially curved. Best-fits to the near- and mid-IR excesses ar…
Giant protoplanets formed by gravitational instability in the outer regions of circumstellar disks go through an early phase of quasi-static contraction during which radii are large and internal temperatures are low. The main source of opacity in these objects is dust grains. We investigate two problems involving the effect of opacity on the evolution of planets of 3, 5, and 7 M_J. First, we pick three different overall metallicities for the planet and simply scale the opacity accordingly. We show that higher metallicity results in slower contraction as a result of higher opacity. It is found …
Diverse dust vertical height and settling strength conditions in protoplanetary discs
Mullard Space Science Laboratory, University College London（穆拉德太空科学实验室，伦敦大学学院）；Purple Mountain Observatory, Chinese Academy of Sciences（中国科学院紫金山天文台）；School of Astronomy and Space Science, University of Science and Technology of China（中国科学技术大学天文与空间科学学院）；Univ. Grenoble Alpes, CNRS, IPAG（格勒诺布尔阿尔卑斯大学，法国国家科学研究中心，IPAG）；School of Physical Science and Technology, Southwest Jiaotong University（西南交通大学物理科学与技术学院）；School of Natural Sciences, Center for Astronomy, University of Galway（戈尔韦大学自然科学与天文学中心）；Max-Planck Institute for Astronomy (MPIA)（马克斯·普朗克天文学研究所）
Planetary migration provides a theoretical basis for the observed diversity of exoplanetary systems. We demonstrate that dust settling - an inescapable feature of disk evolution - gives even more rapid type I migration by up to a factor of about 2 than occurs in disks with fully mixed dust. On the other hand, type II migration becomes slower by a factor of 2 due to dust settling. This even more problematic type I migration can be resolved by the presence of a dead zone; the inner, high density region of a disk which features a low level of turbulence. We show that enhanced dust settling in the…
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,…
The irradiation of protoplanetary discs by central stars is the main heating mechanism for discs, resulting in their flared geometric structure. In a series of papers, we investigate the deep links between 2D self-consistent disc structure and planetary migration in irradiated discs, focusing particularly on those around M stars. In this first paper, we analyse the thermal structure of discs that are irradiated by an M star by solving the radiative transfer equation by means of a Monte Carlo code. Our simulations of irradiated hydrostatic discs are realistic and self-consistent in that they in…
Circumstellar discs are expected to be the nursery of planets. Grain growth within such discs is the first step in the planet formation process in the core-accretion gas-capture scenario. We aim at providing selected criteria on observational quantities derived from multi-wavelength imaging observations that allow to identify dust grain growth and settling. We define a wide-ranged parameter space of discs in various states of their evolution. Using a parametrised model set-up and radiative transfer techniques we compute multi-wavelength images of discs at different inclinations. Using millimet…
Observations of protoplanetary disks (PPDs) at sub-mm wavelengths suggest that polarisation is caused by scattering of thermal radiation. Most of the dust models that are used to explain these observations have major drawbacks: They either use much smaller grains than expected from dust evolution models, or result in lower polarisations than observed. We investigate the effect of dust grain porosity on the polarisation due to scattering at sub-mm wavelengths arising from grains of up to mm sizes, as they are expected to be present in the midplane of PPDs. Using the effective medium theory, we …
We explore dust flow in the hottest parts of protoplanetary discs using the forces of gravity, gas drag and radiation pressure. Our main focus is on the optically thin regions of dusty disc, where the dust is exposed to the most extreme heating conditions and dynamical perturbations: the surface of optically thick disc and the inner dust sublimation zone. We utilise results from two numerically strenuous fields of research. The first is the quasi-stationary solutions on gas velocity and density distributions from mangetohydrodynamical (MHD) simulations of accretion discs. This is critical for …
The tensile strength of small dusty bodies in the solar system is determined by the interaction between the composing grains. In the transition regime between small and sticky dust ($\rm μm$) and non cohesive large grains (mm), particles still stick to each other but are easily separated. In laboratory experiments we find that thermal creep gas flow at low ambient pressure generates an overpressure sufficient to overcome the tensile strength. For the first time it allows a direct measurement of the tensile strength of individual, very small (sub)-mm aggregates which consist of only tens of gra…
We apply ionization balance and MHD calculations to investigate whether magnetic activity moderated by recombination on dust can account for the mass accretion rates and the mid-infrared spectra and variability of protostellar disks. The MHD calculations use the stratified shearing-box approach and include grain settling and the feedback from the changing dust abundance on the resistivity of the gas. The two-decade spread in accretion rates among T Tauri stars is too large to result solely from variety in the grain size and stellar X-ray luminosity, but can be produced by varying these togethe…
Context. We investigate the grain opacity k_gr in the atmosphere of protoplanets. This is important for the planetary mass-radius relation since k_gr affects the H/He envelope mass of low-mass planets and the critical core mass of giant planets. Aims. The goal of this study is to derive an analytical model for k_gr. Methods. Our model is based on the comparison of the timescales of microphysical processes like grain settling in the Stokes and Epstein regime, growth by Brownian motion coagulation and differential settling, grain evaporation, and grain advection due to envelope contraction. With…
It is known that the millimeter dust thermal emission of protoplanetary disks is affected by scattering, such that for optically thick disks the emission decreases with respect to the pure absorption case and the spectral indices can reach values below 2. The latter can also be obtained with temperature gradients. Using simple analytical models of radiative transfer in thin slabs, we quantify the effect of scattering, vertical temperature gradients, and dust settling on the emission and spectral indices of geometrically thin face-on accretion disks around young stars. We find that in verticall…
We derive the single-fluid evolution equations describing a mixture made of a gas phase and an arbitrary number of dust phases, generalising the approach developed in Laibe & Price (2014a). A generalisation for continuous dust distributions as well as analytic approximations for strong drag regimes are also provided. This formalism lays the foundation for numeri- cal simulations of dust populations in a wide range of astrophysical systems while avoiding limitations associated with a multiple-fluid treatment. The usefulness of the formalism is illustrated on a series of analytical problems, nam…
In spite of making a small contribution to total protoplanetary disk mass, dust affects the disk temperature by controlling absorption of starlight. As grains grow from their initial ISM-like size distribution, settling depletes the disk's upper layers of dust and decreases the optical depth, cooling the interior. Here we investigate the effect of collisional growth of dust grains and their dynamics on the thermal and optical profile of the disk, and explore the possibility that cooling induced by grain growth and settling could lead to gravitational instability. We develop a Monte Carlo dust …
Context: Circumstellar disks are considered to be the environment for the formation of planets. The growth of dust grains in these disks is the first step in the core accretion-gas capture planet formation scenario. Indicators and evidence of disk evolution can be traced in spatially resolved images and the spectral energy distribution (SED) of these objects. Aims: We develop a model for the dust phase of the edge-on oriented circumstellar disk of the Butterfly Star which allows one to fit observed multi-wavelength images and the SED simultaneously. Methods: Our model is based on spatially res…
As the earliest stage of planet formation, massive, optically thick, and gas rich protoplanetary disks provide key insights into the physics of star and planet formation. When viewed edge-on, high resolution images offer a unique opportunity to study both the radial and vertical structures of these disks and relate this to vertical settling, radial drift, grain growth, and changes in the midplane temperatures. In this work, we present multi-epoch HST and Keck scattered light images, and an ALMA 1.3 mm continuum map for the remarkably flat edge-on protoplanetary disk SSTC2DJ163131.2-242627, a y…
Investigating the dynamical evolution of dust grains in proto-planetary disks is a key issue to understand how planets should form. We identify under which conditions dust settling can be constrained by high angular resolution observations at mm wavelengths, and which observational strategies are suited for such studies. Exploring a large range of models, we generate synthetic images of disks with different degrees of dust settling, and simulate high angular resolution (~ 0.05-0.3") ALMA observations of these synthetic disks. The resulting data sets are then analyzed blindly with homogeneous d…
We explore the induction of circular polarization (CP) of near-infrared light in star-forming regions using three-dimensional radiative transfer calculations. The simulations trace the change of Stokes parameters at each scattering/absorption process in a dusty gas slab composed of aligned grains. We find that the CP degree enlarges significantly according as the size of dust grains increases and exceeds $\sim 20$ percent for micron-size grains. Therefore, if micron-size grains are dominant in a dusty gas slab, the high CP observed around luminous young stellar objects can be accounted for. Th…
The recent ALMA observations of the disc surrounding HL Tau reveal a very complex dust spatial distribution. We present a radiative transfer model accounting for the observed gaps and bright rings as well as radial changes of the emissivity index. We find that the dust density is depleted by at least a factor 10 in the main gaps compared to the surrounding rings. Ring masses range from 10-100 M$_{\oplus}$ in dust, and, we find that each of the deepest gaps is consistent with the removal of up to 40 M$_{\oplus}$ of dust. If this material has accumulated into rocky bodies, these would be close t…
Dusty disks around young stars are formed out of interstellar dust that consists of amorphous, submicrometre grains. Yet the grains found in comets and meteorites, and traced in the spectra of young stars, include large crystalline grains that must have undergone annealing or condensation at temperatures in excess of 1,000 K, even though they are mixed with surrounding material that never experienced temperatures as high as that. This prompted theories of large-scale mixing capable of transporting thermally altered grains from the inner, hot part of accretion disks to outer, colder disk region…
Scattering of re-emitted flux is considered to be at least partially responsible for the observed polarisation in the (sub-)millimetre wavelength range of several protoplanetary disks. Although the degree of polarisation produced by scattering is highly dependent on the dust model, early studies investigating this mechanism relied on the assumption of single grain sizes and simple density distribution of the dust. However, in the dense inner regions where this mechanism is usually most efficient, the existence of dust grains with sizes ranging from nanometres to millimetres has been confirmed.…
Streaming instability is a privileged channel to bridge the gap between collisional growth of dust grains and planetesimal formation triggered by gravity. This instability is thought to develop through its secular mode, which is long-time growing and may not develop easily in real discs. We address this point by revisiting its perturbation analysis. A third-order expansion with respect to the Stokes number reveals important features over-looked so far. The secular mode can be stable. Epicycles can be unstable, more resistant to viscosity and are identified by Green's function analysis as promi…
The inner-most regions of circumbinary discs are unstable to a parametric instability whose non-linear evolution is hydrodynamical turbulence. This results in significant particle stirring, impacting on planetary growth processes such as the streaming instability or pebble accretion. In this paper, we present the results of three-dimensional, inviscid global hydrodynamical simulations of circumbinary discs with embedded particles of 1 cm size. Hydrodynamical turbulence develops in the disc, and we examine the effect of the particle back-reaction on vertical dust. We find that higher solid-to-g…
In an earlier letter, we reported that dust settling in protoplanetary discs may lead to a dynamical dust-gas instability that produces global toroidal vortices. In this letter, we investigate the evolution of a dusty protoplanetary disc with two different dust species (1 mm and 50 cm dust grains), under the presence of the instability. We show how toroidal vortices, triggered by the interaction of mm grains with the gas, stop the radial migration of metre-sized dust, potentially offering a natural and efficient solution to the dust migration problem.
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…
MHD turbulence plays a crucial role in the dust dynamics of protoplanetary discs. It affects planet formation, vertical settling and is one possible origin of the large scale axisymmetric structures, such as rings, recently imaged by ALMA and SPHERE. Among the variety of MHD processes, the magnetorotational instability (MRI) has raised particular interest since it provides a source of turbulence and potentially organizes the flow into radial structures. However, the weak ionization of discs prevents the MRI from being excited beyond 1 AU. The strong sedimentation of millimetre dust measured in…
The total amount of dust (or "metallicity") and the dust distribution in protoplanetary disks are crucial for planet formation. Dust grains radially drift due to gas--dust friction, and the gas is affected by the feedback from dust grains. We investigate the effects of the feedback from dust grains on the viscous evolution of the gas, taking into account the vertical dust settling. The feedback from the grains pushes the gas outward. When the grains are small and the dust-to-gas mass ratio is much smaller than unity, the radial drift velocity is reduced by the feedback effect but the gas still…
Full one-fluid dusty gas with multiple grain species in SPH
Munich University of Applied Sciences HM（慕尼黑应用科学大学）；Ludwig-Maximilians-Universität München（慕尼黑大学）；Univ Lyon, Univ Lyon1, Ens de Lyon, CNRS, Centre de Recherche Astrophysique de Lyon UMR5574（里昂大学/里昂第一大学/巴黎高等师范学校里昂分校/CNRS/里昂天体物理研究中心）；CNRS, IPAG, Université Grenoble Alpes（法国国家科学研究中心/IPAG研究所/格勒诺布尔阿尔卑斯大学）；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/CNRS/AIM中心）；School of Physics and Astronomy, Monash University（莫纳什大学物理与天文学院）
We model the dust evolution in protoplanetary disks with full 3D, Smoothed Particle Hydrodynamics (SPH), two-phase (gas+dust) hydrodynamical simulations. The gas+dust dynamics, where aerodynamic drag leads to the vertical settling and radial migration of grains, is consistently treated. In a previous work, we characterized the spatial distribution of non-growing dust grains of different sizes in a disk containing a gap-opening planet and investigated the gap's detectability with the Atacama Large Millimeter/submillimeter Array (ALMA). Here we take into account the effects of grain growth and f…
Super-puffs -- low-mass exoplanets with extremely low bulk density -- are attractive targets for exploring their atmospheres and formation processes. Recent studies suggested that the large radii of super-puffs may be caused by atmospheric dust entrained in the escaping atmospheres. In this study, we investigate how the dust grows in escaping atmospheres and influence the transit radii using a microphysical model of grain growth. Collision growth is efficient in many cases, leading to hinder the upward transport of dust via enhanced gravitational settling. We find that dust abundance in the ou…
Evaporating rocky exoplanets, such as KIC 12557548b, eject large amounts of dust grains, which can trail the planet in a comet-like tail. When such objects occult their host star, the resulting transit signal contains information about the dust in the tail. We aim to use the detailed shape of the Kepler light curve of KIC 12557548b to constrain the size and composition of the dust grains that make up the tail, as well as the mass loss rate of the planet. Using a self-consistent numerical model of the dust dynamics and sublimation, we calculate the shape of the tail by following dust grains fro…
Recently, two exoplanet candidates have been discovered, KIC 12557548b and KOI-2700b, whose transit profiles show evidence for a comet-like tail of dust trailing the planet, thought to be fed by the evaporation of the planet's surface. We aim to put constraints on the composition of the dust ejected by these objects from the shape of their transit light curves. We derive a semi-analytical expression for the attenuation of dust cross-section in the tail, incorporating the sublimation of dust grains as well as their drift away from the planet. This expression shows that the length of the tail is…
Dust Growth in Binary Systems: Inhibition of dust settling and growth in circumbinary discs
Univ. Grenoble Alpes, CNRS, IPAG（格勒诺布尔阿尔卑斯大学）；Université Lyon 1, ENS de Lyon, CNRS, CRAL（里昂第一大学）；School of Physics and Astronomy, Monash University（蒙纳士大学）；Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM（巴黎萨克雷大学）；Homer L. Dodge Department of Physics and Astronomy, The University of Oklahoma（俄克拉荷马大学）；LIRA, Observatoire de Paris, Universite PSL（巴黎天文台）
High dust density in the midplane of protoplanetary disks is favorable for efficient grain growth and can allow fast formation of planetesimals and planets, before disks dissipate. Vertical settling and dust trapping in pressure maxima are two mechanisms allowing dust to concentrate in geometrically thin and high density regions. In this work, we aim to study these mechanisms in the highly inclined protoplanetary disk SSTC2D J163131.2-242627 (Oph163131, i~84deg). We present new high angular resolution continuum and 12CO ALMA observations of Oph163131. The gas emission appears significantly mor…
Motivated by recent measurements of deposits of $^{60}$Fe on the ocean floor and the lunar surface, we model the transport of dust grains containing $^{60}$Fe from a near-Earth (i.e., within 100 pc) supernova (SN). We inject dust grains into the environment of an SN remnant (SNR) and trace their trajectories by applying a 1D hydrodynamic description assuming spherical symmetry to describe the plasma dynamics, and include a rudimentary, 3D magnetic field description to examine its influence on charged dust grains. We assume the interstellar medium (ISM) magnetic fields are turbulent, and are am…
Gravitational instability (GI) controls the dynamics of young massive protoplanetary discs. Apart from facilitating gas accretion on to the central protostar, it must also impact on the process of planet formation: directly through fragmentation, and indirectly through the turbulent concentration of small solids. To understand the latter process, it is essential to determine the dust dynamics in such a turbulent flow. For that purpose, we conduct a series of 3D shearing box simulations of coupled gas and dust, including the gas's self-gravity and scanning a range of Stokes numbers, from 0.001 …
We study the secondary electron emissions induced by the impact of electrons on dust grains and the resulting dust charging processes in the nonequilibrium dusty plasma with power-law distributions. We derive new expressions of the secondary emitted electron flux and the dust charging currents that are generalized by the power-law q-distributions, where the nonlinear core functions are numerically studied for the nonextensive parameter q. Our numerical analyses show that the power-law q-distribution of the primary electrons has a significant effect on the secondary emitted electron flux as wel…
Secular gravitational instability (GI) is one of the promising mechanisms for creating annular substructures and planetesimals in protoplanetary disks. We perform numerical simulations of the secular GI in a radially extended disk with inward drifting dust grains. The results show that, even in the presence of the dust diffusion, the dust rings form via the secular GI while the dust grains are moving inward, and the dust surface density increases by a factor of ten. Once the secular GI develops into a nonlinear regime, the total mass of the resultant rings can be a significant fraction of the …
Na I D lines in the spectrum of the young binary KH 15D have been analyzed in detail. We find an excess absorption component that may be attributed to foreground interstellar absorption, and to gas possibly associated with the solids in the circumbinary disk. The derived column density is log N_NaI = 12.5 cm^-2, centered on a radial velocity that is consistent with the systemic velocity. Subtracting the likely contribution of the ISM leaves log N_NaI ~ 12.3 cm^-2. There is no detectable change in the gas column density across the "knife edge" formed by the opaque grain disk, indicating that th…
We model the behaviour of dust grains entrained by photoevaporation-driven winds from protoplanetary discs assuming a non-rotating, plane-parallel disc. We obtain an analytic expression for the maximum entrainable grain size in extreme-UV radiation-driven winds, which we demonstrate to be proportional to the mass loss rate of the disc. When compared with our hydrodynamic simulations, the model reproduces almost all of the wind properties for the gas and dust. In typical turbulent discs, the entrained grain sizes in the wind are smaller than the theoretical maximum everywhere but the inner disc…
Proto-planetary disc surveys conducted with ALMA are measuring disc radii in multiple star forming regions. The disc radius is a fundamental quantity to diagnose whether discs undergo viscous spreading, discriminating between viscosity or angular momentum removal by winds as drivers of disc evolution. Observationally, however, the sub-mm continuum emission is dominated by the dust, which also drifts inwards, complicating the picture. In this paper we investigate, using theoretical models of dust grain growth and radial drift, how the radii of dusty viscous proto-planetary discs evolve with tim…
(abridged) In the core accretion scenario for the formation of planetary rocky cores, the first step toward planet formation is the growth of dust grains into larger and larger aggregates and eventually planetesimals. Although dust grains are thought to grow from the submicron sizes typical of interstellar dust to micron size particles in the dense regions of molecular clouds and cores, the growth from micron size particles to pebbles and kilometre size bodies must occur in protoplanetary disks. This step in the formation of planetary systems is the last stage of solids evolution that can be o…
