Porosity evolution of dust aggregates is crucial in understanding dust evolution in protoplanetary disks. In this study, we present useful tools to study the coagulation and porosity evolution of dust aggregates. First, we present a new numerical method for simulating dust coagulation and porosity evolution as an extension of the conventional Smoluchowski equation. This method follows the evolution of the mean porosity for each aggregate mass simultaneously with the evolution of the mass distribution function. This method reproduces the results of previous Monte Carlo simulations with much less computational expense. Second, we propose a new collision model for porous dust aggregates on the basis of our N-body experiments on aggregate collisions. We first obtain empirical data on porosity changes between the classical limits of ballistic cluster-cluster and particle-cluster aggregation. Using the data, we construct a recipe for the porosity change due to general hit-and-stick collisions as well as formulae for the aerodynamical and collisional cross sections. Simple coagulation simulations using the extended Smoluchowski method show that our collision model explains the fractal dimensions of porous aggregates observed in a full N-body simulation and a laboratory experiment. Besides, we discover that aggregates at the high-mass end of the distribution can have a considerably small aerodynamical cross section per unit mass compared with aggregates of lower masses. We point out an important implication of this discovery for dust growth in protoplanetary disks.
Dust coagulation in interstellar space and protoplanetary disks is usually treated as one of 2 extreme cases: Particle-Cluster Aggregation and Cluster-Cluster Aggregation. In this paper we study the process of hierarchical growth, where aggregates are built from significantly smaller aggregates (but not monomers). We show that this process can be understood as a modified, PCA-like process that produces porous, but non-fractal particles whose filling factor is chiefly determined by the porosity of the building blocks. We also show that in a coagulation environment where relative velocities are …
In this work, we study the light scattering properties of dust aggregates ($0.7μm \lesssim R_c \lesssim 2.0μm$) having a wide range of porosity ($\mathcal{P}$ = 0.59 to 0.98). The simulations are executed using the Superposition T-matrix code with BCCA, BA, BAM1 and BAM2 clusters of varying porosity. We investigate the nature and dependencies of the different scattering parameters on porosity, size and composition of the aggregated particles for wavelengths 0.45 $μ$m and 0.65 $μ$m. We find that the scattering parameters are strongly correlated with the porosity of the aggregated structures. Ou…
Dust coagulation in a protoplanetary disk is the first step of planetesimal formation. However, a pathway from dust aggregates to planetesimals remains unclear. Both numerical simulations and laboratory experiments have suggested the importance of dust structure in planetesimal formation, but it is not well constrained by observations. We study how dust structure and porosity alters polarimetric images at millimeter wavelength by performing 3D radiative transfer simulations. Aggregates with different porosity and fractal dimension are considered. As a result, we find that dust aggregates with …
We study the light scattering properties of moderately large dust aggregates ($0.8μm \lesssim R \lesssim 2.0μm$) with a wide variation of porosity ($\mathcal{P}$) from 0.57 to 0.98. The computations are performed using the Superposition T-matrix code with BAM2 cluster ($\mathcal{P} \sim 0.57-0.64$), BAM1 cluster ($\mathcal{P} \sim 0.74$), BA or BPCA cluster ($\mathcal{P} \sim 0.85-0.87$) and BCCA cluster ($\mathcal{P} \sim 0.98$). The effect of aggregate size parameter ($X$) on the light scattering properties of aggregates (BA and BAM2) having different porosities is explored in this study. We…
Ring structures are observed by (sub-)millimeter dust continuum emission in various circumstellar disks from early stages of Class 0 and I to late stage of Class II young stellar objects (YSOs). In this paper, we study one of the possible scenarios of such ring formation in early stage, which is coagulation of dust aggregates. The dust grains grow in an inside-out manner because the growth timescale is roughly proportional to the orbital period. The boundary of the dust evolution can be regarded as the growth front, where the growth time is comparable to the disk age. With radiative transfer c…
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…
In dead zones of protoplanetary discs, it is assumed that micrometre-sized particles grow Brownian, sediment to the midplane and drift radially inward. When collisional compaction sets in, the growing aggregates collect slower and therefore dynamically smaller particles. This sedimentation and growth phase of highly porous ice and dust aggregates is simulated with laboratory experiments in which we obtained mm- to cm-sized ice aggregates with a porosity of 90\% as well as cm-sized dust agglomerates with a porosity of 85\%. We modelled the growth process during sedimentation in an analytical ca…
Adhesion forces between submicrometer-sized silicate grains play a crucial role in the formation of silicate dust agglomerates, rocky planetesimals, and terrestrial planets. The surface energy of silicate dust particles is the key to their adhesion and rolling forces in a theoretical model based on the contact mechanics. Here we revisit the cohesion of amorphous silica spheres by compiling available data on the surface energy for hydrophilic amorphous silica in various circumstances. It turned out that the surface energy for hydrophilic amorphous silica in a vacuum is a factor of 10 higher tha…
The collisional evolution of solid material in protoplanetary disks is a crucial step in the formation of planetesimals, comets, and planets. Although dense protoplanetary environments favor fast dust coagulation, there are several factors that limit the straightforward pathway from interstellar micron-size grains to pebble-size aggregates. Apart from the grain bouncing, fragmentation, and fast drift to the central star, a notable limiting factor is the electrostatic repulsion of like-charged grains. In this study we aim at theoretical modeling of the dust coagulation coupled with the dust cha…
We analyze the coagulation of dust in and around a gap opened by a Jupiter-mass planet. To this end, we carry out a high-resolution magnetohydrodynamic (MHD) simulation of the gap environment, which is turbulent due to the magnetorotational instability. From the MHD simulation, we obtain values of the gas velocities, densities and turbulent stresses a) close to the gap edge, b) in one of the two gas streams that accrete onto the planet, c) inside the low-density gap, and d) outside the gap. The MHD values are then supplied to a Monte Carlo dust coagulation algorithm, which models grain stickin…
The Influence of the Fractal Dimension on Dust Evolution in Protoplanetary Disks
Institut für Theoretische Astrophysik, Zentrum für Astronomie der Universität Heidelberg（海德堡大学天体物理中心理论天体物理研究所）；Anton Pannekoek Institute for Astronomy, University of Amsterdam（阿姆斯特丹大学安顿·潘内科克天文学研究所）
Dust growth is often neglected when building models of protoplanetary disks due to its complexity and computational expense. However, it does play a major role in shaping the evolution of protoplanetary dust and planet formation. In this paper, we present a numerical model coupling 2-D hydrodynamic evolution of a protoplanetary disk, including a Jupiter-mass planet, and dust coagulation. This is obtained by including multiple dust fluids in a single grid-based hydrodynamic simulation and solving the Smoluchowski equation for dust coagulation on top of solving for the hydrodynamic evolution. We…
Gas-giant planets, such as Jupiter, Saturn and massive exoplanets, were formed via the gas accretion onto the solid cores each with a mass of roughly ten Earth masses. However, rapid radial migration due to disk-planet interaction prevents the formation of such massive cores via planetesimal accretion. Comparably rapid core growth via pebble accretion requires very massive protoplanetary disks because most pebbles fall into the central star. Although planetesimal formation, planetary migration, and gas-giant core formation have been studied with much effort, the full evolution path from dust t…
Incremental particle growth in turbulent protoplanetary nebulae is limited by a combination of barriers that can slow or stall growth. Moreover, particles that grow massive enough to decouple from the gas are subject to inward radial drift which could lead to the depletion of most disk solids before planetesimals can form. Compact particle growth is probably not realistic. Rather, it is more likely that grains grow as fractal aggregates which may overcome this so-called radial drift barrier because they remain more coupled to the gas than compact particles of equal mass. We model fractal aggre…
Evolving the size distribution of solid aggregates challenges simulations of young stellar objects. Among other difficulties, generic formulae for stability conditions of explicit solvers provide severe constrains when integrating the coagulation equation for astrophysical objects. Recent numerical experiments have recently reported that these generic conditions may be much too stringent. By analysing the coagulation equation in the Laplace space, we explain why this is indeed the case and provide a novel stability condition which avoids time over-sampling.
Most protoplanetary discs are thought to undergo violent and frequent accretion outbursts, during which the accretion rate and central luminosity are elevated for several decades. This temporarily increases the disc temperature, leading to the sublimation of ice species as snowlines move outwards. In this paper, we investigate how an FUor-type accretion outburst alters the growth and appearance of dust aggregates at different locations in protoplanetary discs. We develop a model based on the Monte Carlo approach to simulate locally the coagulation and fragmentation of icy dust particles and in…
Estimates of the total particulate mass of the plumes of Enceladus are important to constrain theories of particle formation and transport at the surface and interior of the satellite. We revisit the calculations of Ingersoll & Ewald (2011), who estimated the particulate mass of the Enceladus plumes from strongly forward scattered light in Cassini ISS images. We model the plume as a combination of spherical particles and irregular aggregates resulting from the coagulation of spherical monomers, the latter of which allows for plumes of lower particulate mass. Though a continuum of solutions are…
In order to characterize the early growth of fine-grained dust rims (FGRs) that commonly surround chondrules, we perform numerical simulations of dust accretion onto chondrule surfaces. We employ a Monte Carlo algorithm to simulate the collision of dust monomers having radii between 0.5 and 10 $μ$m with chondrules whose radii are between 500 and 1000 $μ$m, in 100-$μ$m increments. The collisions are driven by Brownian motion and solar nebula turbulence. After each collision, the colliding particles either stick at the point of contact, roll or bounce. We limit accretion of dust monomers (and in…
The coagulation of dust particles is a key process in planetesimal formation. However, the radial drift and bouncing barriers are not completely resolved, especially for silicate dust. Since the collision velocities of dust particles are regulated by turbulence in a protoplanetary disk, the turbulent clustering should be properly treated. To that end, direct numerical simulations (DNSs) of the Navier Stokes equations are requisite. In a series of papers, Pan & Padoan used a DNS with the Reynolds number Re~1000. Here, we perform DNSs with up to Re=16100, which allow us to track the motion of pa…
In this work, we introduce a comet dust model that incorporates multiple dust morphologies along with inhomogeneous mixture of silicate minerals and carbonaceous materials under power-law size distribution, to replicate the standard polarization-phase curve observed in several comets in the narrow-band continuum. Following the results from Rosetta/MIDAS and COSIMA, we create high porosity Hierarchical Aggregates (HA) and low porosity (< 10$\%$) Solids in the form of agglomerated debris. We also introduce a moderate porosity structure with solids in the core, surrounded by fluffy aggregates cal…
Highly porous dust aggregates can break through the radial drift barrier, but previous studies assumed disks in their later stage, where the disks have a very small mass and low temperature. In contrast, dust coagulation should begin in the very early stage such as the disk formation stage because the growth timescale of dust is shorter than the disk formation timescale if there is no process to suppress the collisional growth of dust. We investigate the possibility of planetesimal formation via direct collisional growth in the very early stage of a protoplanetary disk. We show that, in the ve…
In protoplanetary discs, the coagulation of dust grains into large aggregates still remains poorly understood. Grain porosity appears to be a promising solution to allow the grains to survive and form planetesimals. Furthermore, dust shattering has generally been considered to come only from collisional fragmentation; however, a new process was recently introduced, rotational disruption. We wrote a one-dimensional code that models the growth and porosity evolution of grains as they drift to study their final outcome when the two shattering processes are included. When simulating the evolution …
After 25 years of laboratory research on protoplanetary dust agglomeration, a consistent picture of the various processes that involve colliding dust aggregates has emerged. Besides sticking, bouncing and fragmentation, other effects, like, e.g., erosion or mass transfer, have now been extensively studied. Coagulation simulations consistently show that $\rm μ$m-sized dust grains can grow to mm- to cm-sized aggregates before they encounter the bouncing barrier, whereas sub-$\rm μ$m-sized water-ice particles can directly grow to planetesimal sizes. For siliceous materials, other processes have t…
Context: The size of the constituent particles (monomers) of dust aggregates is one of the most uncertain parameters directly affecting collisional growth of aggregates in planet-forming disks. Despite its importance, the monomer size has not yet been meaningfully constrained by disk observations. Aims: We attempt to derive the monomer size from optical and near-infrared (IR) polarimetric observations of planet-forming disks. Methods: We perform a comprehensive parameter survey on the degree of linear polarization of light scattered by dust aggregates, using an exact numerical method called th…
Dust grains drift through the interstellar medium (ISM) and are aligned with the magnetic field. Here we study the effect of grain alignment and grain motion on grain growth in molecular clouds (MCs). We first discuss the characteristic timescales of alignment of the grain axis of maximum inertia ($\hat{a}_{1}$) with its angular momentum (${\bf J}$) (i.e., {\it internal alignment}) and alignment of ${\bf J}$ with the magnetic field (${\bf B}$, i.e., {\it external alignment}). We determine the maximum grain size with efficient internal ($a_{\rm max,aJ}$) and external alignment ($a_{\rm max,JB}$…
In protoplanetary disks micron-size dust grains coagulate to form larger structures with complex shapes and compositions. The coagulation process changes the absorption and scattering properties of particles in the disk in significant ways. To properly interpret observations of protoplanetary disks and to place these observations in the context of the first steps of planet formation, it is crucial to understand the optical properties of these complex structures. We derive the optical properties of dust aggregates using detailed computations of aggregate structures and compare these computa- ti…
We introduce a possible disruption mechanism of dust grains in planet formation by their spinning motion. This mechanism has been discussed as rotational disruption for the interstellar dust grains. We theoretically calculate whether porous dust aggregates can be disrupted by their spinning motion and if it prohibits dust growth in protoplanetary disks. We assume radiative torque and gas-flow torque as driving sources of the spinning motion, assume that dust aggregates reach a steady-state rigid rotation, and compare the obtained tensile stress due to the centrifugal force with their tensile s…
The journey from dust particle to planetesimal involves physical processes acting on scales ranging from micrometers (the sticking and restructuring of aggregates) to hundreds of astronomical units (the size of the turbulent protoplanetary nebula). Considering these processes simultaneously is essential when studying planetesimal formation. We develop a novel, global, semi-analytical model for the evolution of the mass-dominating dust particles in a turbulent protoplanetary disk that takes into account the evolution of the dust surface density while preserving the essential characteristics of …
Coagulation of dust aggregates plays an important role in the formation of planets and is of key importance to the evolution of protoplanetary disks (PPDs). Characteristics of dust, such as the diversity of particle size, porosity, charge, and the manner in which dust couples to turbulent gas, affect the collision outcome and the rate of dust growth. Here we present a numerical model of the evolution of the dust population within a PPD which incorporates all of these effects. The probability that any two particles collide depends on the particle charge, cross-sectional area and their relative …
Modeling (Sub-)millimeter Scattering Properties of Fractal and Consolidated Porous Particles: Applications to Protoplanetary Disks
Instituto de Astrofísica de Andalucía (IAA-CSIC)（安达卢西亚天体物理研究所）；Universidad Nacional Autónoma de México（墨西哥国立自治大学）；Université Rouen Normandie（鲁昂诺曼底大学）；European Southern Observatory (ESO)（欧洲南方天文台）
The coagulation of microscopic dust into planetesimals is the first step towards planet formation. The size and shape of the growing aggregates determine the efficiency of this early growth. It has been proposed that fluffy ice aggregates can grow very efficiently, suffering less from the bouncing and radial drift barriers. While the collision velocity between icy aggregates of similar size is thought to stay below the fragmentation threshold, they may nonetheless lose mass from collisions with much smaller projectiles. We investigate the effect of these erosive collisions on the ability of po…
Despite rapidly growing disk observations, it remains a mystery what primordial dust aggregates look like and what the physical and chemical properties of their constituent grains (monomers) are in young planet-forming disks. Confrontation of models with observations to answer this mystery has been a notorious task because we have to abandon a commonly used assumption, perfectly spherical grains, and take into account particles with complex morphology. In this Letter, we present the first thorough comparison between near-infrared scattered light of the young planet-forming disk around IM Lup a…
In a protoplanetary disk, dust aggregates in the $μ$m to mm size range possess mean collision velocities of 10 to 60 ms$^{-1}$ with respect to dm- to m-size bodies. We performed laboratory collision experiments to explore this parameter regime and found a size- and velocity-dependent threshold between erosion and growth. By using a local Monte Carlo coagulation calculation and complementary a simple semi-analytical timescale approach, we show that erosion considerably limits particle growth in protoplanetary disks and leads to a steady-state dust-size distribution from $μ$m to dm sized particl…
ALMA observations revealed recently polarised radiation of several protoplanetary disks in the (sub-)millimetre wavelength range. Besides self-scattering of large particles, thermal emission by elongated grains is a potential source for the detected polarisation signal. We calculate the wavelength dependent absorption and intrinsic polarisation of spheroidally shaped, micrometre and sub-millimetre sized dust grains using the discrete dipole approximation. In particular, we analyse the impact of dust grain porosity which appears to be present in disks when small grains coagulate to form larger …
