Porous Dust Aggregates Research Articles

PLANETESIMAL FORMATION BY GRAVITATIONAL INSTABILITY OF A POROUS DUST DISK

ABSTRACT It has recently been proposed that porous icy dust aggregates are formed by the pairwise accretion of dust aggregates beyond the snowline. We calculate the equilibrium random velocity of porous dust aggregates, taking into account mutual gravitational scattering, collisions, gas drag, and turbulent stirring and scattering. We find that the disk of porous dust aggregates becomes gravitationally unstable as the aggregates evolve through gravitational compression in the minimum-mass solar nebula model for a reasonable range of turbulence strength, which leads to rapid formation of planetesimals.

LIGHT SCATTERING BY FRACTAL DUST AGGREGATES. I. ANGULAR DEPENDENCE OF SCATTERING

ABSTRACT In protoplanetary disks, micron-sized dust grains coagulate to form highly porous dust aggregates. Because the optical properties of these aggregates are not completely understood, it is important to investigate how porous dust aggregates scatter light. In this study, the light scattering properties of porous dust aggregates were calculated using a rigorous method, the T-matrix method, and the results were then compared with those obtained using the Rayleigh–Gans–Debye (RGD) theory and Mie theory with the effective medium approximation (EMT). The RGD theory is applicable to moderately large aggregates made of nearly transparent monomers. This study considered two types of porous dust aggregates—ballistic cluster–cluster agglomerates (BCCAs) and ballistic particle–cluster agglomerates. First, the angular dependence of the scattered intensity was shown to reflect the hierarchical structure of dust aggregates; the large-scale structure of the aggregates is responsible for the intensity at small scattering angles, and their small-scale structure determines the intensity at large scattering angles. Second, it was determined that the EMT underestimates the backward scattering intensity by multiple orders of magnitude, especially in BCCAs, because the EMT averages the structure within the size of the aggregates. It was concluded that the RGD theory is a very useful method for calculating the optical properties of BCCAs.

GRAIN SIZE CONSTRAINTS ON HL TAU WITH POLARIZATION SIGNATURE

ABSTRACT The millimeter-wave polarization of the protoplanetary disk around HL Tau has been interpreted as the emission from elongated dust grains aligned with the magnetic field in the disk. However, the self-scattering of thermal dust emission may also explain the observed millimeter-wave polarization. In this paper, we report a modeling of the millimeter-wave polarization of the HL Tau disk with the self-polarization. Dust grains are assumed to be spherical and to have a power-law size distribution. We change the maximum grain size with a fixed dust composition in a fixed disk model to find the grain size to reproduce the observed signature. We find that the direction of the polarization vectors and the polarization degree can be explained with the self-scattering. Moreover, the polarization degree can be explained only if the maximum grain size is ∼150 μm. The obtained grain size from the polarization is different from that which has been previously expected from the spectral index of the dust opacity coefficient (a millimeter or larger) if the emission is optically thin. We discuss that porous dust aggregates may solve the inconsistency of the maximum grain size between the two constraints.

DUST AND POLYCYCLIC AROMATIC HYDROCARBON IN THE PRE-TRANSITIONAL DISK AROUND HD 169142

ABSTRACT The pre-transitional disk around the Herbig Ae star HD 169142 shows a complex structure of possible ongoing planet formation in dust thermal emission from the near-infrared (IR) to millimeter wavelength range. Also, a distinct set of broad emission features at 3.3, 6.2, 7.7, 8.6, 11.3, and 12.7 &mgr; m ?> , commonly attributed to polycyclic aromatic hydrocarbons (PAHs), is detected prominently in the HD 169142 disk. We model the spectral energy distribution (SED) as well as the PAH emission features of the HD 169142 disk simultaneously with porous dust and astronomical-PAHs, taking into account the spatially resolved disk structure. Our porous dust model, consisting of three distinct components that are primarily concentrated in the inner ring, middle ring, and outer disk, provides an excellent fit to the entire SED, and the PAH model closely reproduces the observed PAH features. The accretion of ice mantles onto porous dust aggregates occurs between ∼16 and 60 AU ?> , which overlaps with the spatial extent (∼ 50 AU ?> ) of the observed PAH emission features. Finally, we discuss the role of PAHs in the formation of planets possibly taking place in the HD 169142 system.

OUTWARD MOTION OF POROUS DUST AGGREGATES BY STELLAR RADIATION PRESSURE IN PROTOPLANETARY DISKS

We study the dust motion at the surface layer of protoplanetary disks. Dust grains in surface layer migrate outward due to angular momentum transport via gas-drag force induced by the stellar radiation pressure. In this study, we calculate mass flux of the outward motion of compact grains and porous dust aggregates by the radiation pressure. The radiation pressure force for porous dust aggregates is calculated using the T-Matrix Method for the Clusters of Spheres. First, we confirm that porous dust aggregates are forced by strong radiation pressure even if they grow to be larger aggregates in contrast to homogeneous and spherical compact grains to which efficiency of radiation pressure becomes lower when their sizes increase. In addition, we find that the outward mass flux of porous dust aggregates with monomer size of 0.1 $\mu$m is larger than that of compact grains by an order of magnitude at the disk radius of 1 AU, when their sizes are several microns. This implies that large compact grains like calcium-aluminum rich inclusions (CAIs) are hardly transported to outer region by stellar radiation pressure, whereas porous dust aggregates like chondritic-porous interplanetary dust particles (CP-IDPs) are efficiently transported to comet formation region. Crystalline silicates are possibly transported in porous dust aggregates by stellar radiation pressure from inner hot region to outer cold cometary region in the protosolar nebula.

Tensile and shear strength of porous dust agglomerates

Context.Within the sequential accretion scenario of planet formation, planets are build up through a sequence sticking collisions. The outcome of collisions between porous dust aggregates is very important for the growth from very small dust particles to planetesimals. In this work we determine the necessary material properties of dust aggregates as a function the porosity. Aims: Continuum models such as SPH that are capable of simulating collisions of macroscopic dust aggregates require a set of material parameters. Some of them such as the tensile and shear strength are difficult to obtain from laboratory experiments. The aim of this work is to determine these parameters from ab-initio molecular dynamics simulations. Methods: We simulate the behavior of porous dust aggregates using a detailed micro-physical model of the interaction of spherical grains that includes adhesion forces, rolling, twisting, and sliding. Using different methods of preparing the samples we study the strength behavior of our samples with varying porosity and coordination number of the material. Results: For the tensile strength, we can reproduce data from laboratory experiments very well. For the shear strength, there are no experimental data available. The results from our simulations differ significantly from previous theoretical models, which indicates that the latter might not be sufficient to describe porous dust aggregates. Conclusions: We have provided functional behavior of tensile and shear strength of porous dust aggregates as a function of the porosity that can be directly applied in continuum simulations of these objects in planet formation scenarios.

The suborbital particle aggregation and collision experiment (SPACE): Studying the collision behavior of submillimeter-sized dust aggregates on the suborbital rocket flight REXUS 12

The Suborbital Particle Aggregation and Collision Experiment (SPACE) is a novel approach to study the collision properties of submillimeter-sized, highly porous dust aggregates. The experiment was designed, built, and carried out to increase our knowledge about the processes dominating the first phase of planet formation. During this phase, the growth of planetary precursors occurs by agglomeration of micrometer-sized dust grains into aggregates of at least millimeters to centimeters in size. However, the formation of larger bodies from the so-formed building blocks is not yet fully understood. Recent numerical models on dust growth lack a particular support by experimental studies in the size range of submillimeters, because these particles are predicted to collide at very gentle relative velocities of below 1 cm/s that can only be achieved in a reduced-gravity environment. The SPACE experiment investigates the collision behavior of an ensemble of silicate-dust aggregates inside several evacuated glass containers which are being agitated by a shaker to induce the desired collisions at chosen velocities. The dust aggregates are being observed by a high-speed camera, allowing for the determination of the collision properties of the protoplanetary dust analog material. The data obtained from the suborbital flight with the REXUS (Rocket Experiments for University Students) 12 rocket will be directly implemented into a state-of-the-art dust growth and collision model.

Static compression of porous dust aggregates

Context: In protoplanetary disks, dust grains coagulate with each other and grow to form aggregates. As these aggregates grow by coagulation, their filling factor \phi decreases down to \phi << 1. However, comets, the remnants of these early planetesimals, have \phi ~ 0.1. Thus, static compression of porous dust aggregates is important in planetesimal formation. However, the static compression strength has been investigated only for relatively high density aggregates (\phi > 0.1). Aims: We investigate and find the compression strength of highly porous aggregates (\phi << 1). Methods: We perform three dimensional N-body simulations of aggregate compression with a particle-particle interaction model. We introduce a new method of static compression: the periodic boundary condition is adopted and the boundaries move with low speed to get closer. The dust aggregate is compressed uniformly and isotropically by themselves over the periodic boundaries. Results: We empirically derive a formula of the compression strength of highly porous aggregates (\phi << 1). We check the validity of the compression strength formula for wide ranges of numerical parameters, such as the size of initial aggregates, the boundary speed, the normal damping force, and material. We also compare our results to the previous studies of static compression in the relatively high density region (\phi > 0.1) and confirm that our results consistently connect to those in the high density region. The compression strength formula is also derived analytically.

Collisions of inhomogeneous pre-planetesimals

In the framework of the coagulation scenario, kilometre-sized planetesimals form by subsequent collisions of pre-planetesimals of sizes from centimetre to hundreds of metres. Pre-planetesimals are fluffy, porous dust aggregates, which are inhomogeneous owing to their collisional history. Planetesimal growth can be prevented by catastrophic disruption in pre-planetesimal collisions above the destruction velocity threshold. We develop an inhomogeneity model based on the density distribution of dust aggregates, which is assumed to be a Gaussian distribution with a well-defined standard deviation. As a second input parameter, we consider the typical size of an inhomogeneous clump. These input parameters are easily accessible by laboratory experiments. For the simulation of the dust aggregates, we utilise a smoothed particle hydrodynamics (SPH) code with extensions for modelling porous solid bodies. The porosity model was previously calibrated for the simulation of silica dust, which commonly serves as an analogue for pre-planetesimal material. The inhomogeneity is imposed as an initial condition on the SPH particle distribution. We carry out collisions of centimetre-sized dust aggregates of intermediate porosity. We vary the standard deviation of the inhomogeneous distribution at fixed typical clump size. The collision outcome is categorised according to the four-population model. We show that inhomogeneous pre-planetesimals are more prone to destruction than homogeneous aggregates. Even slight inhomogeneities can lower the threshold for catastrophic disruption. For a fixed collision velocity, the sizes of the fragments decrease with increasing inhomogeneity. Pre-planetesimals with an active collisional history tend to be weaker. This is a possible obstacle to collisional growth and needs to be taken into account in future studies of the coagulation scenario.

Free collisions in a microgravity many-particle experiment. I. Dust aggregate sticking at low velocities

Over the past years the processes involved in the growth of planetesimals have extensively been studied in the laboratory. Based on these experiments, a dust-aggregate collision model was developed upon which computer simulations were based to evaluate how big protoplanetary dust aggregates can grow and to analyze which kinds of collisions are relevant in the solar nebula and are worth further studies in the laboratory. The sticking threshold velocity of millimeter-sized dust aggregates is one such critical value that have so far only theoretically been derived, as the relevant velocities could not be reached in the laboratory. We developed a microgravity experiment that allows us for the first time to study free collisions of mm-sized dust aggregates down to velocities of ∼0.1cms−1 to assess this part of the protoplanetary dust evolution model. Here, we present the results of 125 free collisions between dust aggregates of 0.5–2mm diameter. Seven collisions with velocities between 0.2 and 3cms−1 led to sticking, suggesting a transition from perfect sticking to perfect bouncing with a certain sticking probability instead of a sharp velocity threshold. We developed a model to explain the physical processes involved in dust-aggregate sticking, derived dynamical material properties of the dust aggregates from the results of the collisions, and deduced the velocity below which dust aggregates always stick. For millimeter-sized porous dust aggregates this velocity is 8×10−5ms−1.

The four-population model: a new classification scheme for pre-planetesimal collisions

Within the collision growth scenario for planetesimal formation, the growth step from centimetre sized pre-planetesimals to kilometre sized planetesimals is still unclear. The formation of larger objects from the highly porous pre-planetesimals may be halted by a combination of fragmentation in disruptive collisions and mutual rebound with compaction. However, the right amount of fragmentation is necessary to explain the observed dust features in late T Tauri discs. Therefore, detailed data on the outcome of pre-planetesimal collisions is required and has to be presented in a suitable and precise format. We propose and apply a new classification scheme for pre-planetesimal collisions based on the quantitative aspects of four fragment populations: the largest and second largest fragment, a power-law population, and a sub-resolution population. For the simulations of pre-planetesimal collisions, we adopt the SPH numerical scheme with extensions for the simulation of porous solid bodies. By means of laboratory benchmark experiments, this model was previously calibrated and tested for the correct simulation of the compaction, bouncing, and fragmentation behaviour of macroscopic highly porous silica dust aggregates. It is shown that previous attempts to map collision data were much too oriented on qualitatively categorising into sticking, bouncing, and fragmentation events. We show that the four-populations model encompasses all previous categorisations and in addition allows for transitions. This is because it is based on quantitative characteristic attributes of each population such as the mass, kinetic energy, and filling factor. As a demonstration of the applicability and the power of the four-populations model, we utilise it to present the results of a study on the influence of collision velocity in head-on collisions of intermediate porosity aggregates.

Thermal conductivity measurements of porous dust aggregates: I. Technique, model and first results

We present a non-invasive technique for measuring the thermal conductivity of fragile and sensitive materials. In the context of planet-formation research, the investigation of the thermal conductivity of porous dust aggregates provide important knowledge about the influence of heating processes, like internal heating by radioactive decay of short-lived nuclei, e.g. 26Al, on the evolution and growth of planetesimals. The determination of the thermal conductivity was performed by a combination of laboratory experiments and numerical simulations. An IR camera measured the temperature distribution of the sample surface heated by a well-characterized laser beam. The thermal conductivity as free parameter in the model calculations, exactly emulating the experiment, was varied until the experimental and numerical temperature distributions showed best agreement. Thus, we determined for three types of porous dust samples, consisting of spherical, 1.5 μm-sized SiO 2 particles, with volume filling factors in the range of 15–54%, the thermal conductivity to be 0.002–0.02 W m −1 K −1, respectively. From our results, we can conclude that the thermal conductivity mainly depends on the volume filling factor. Further investigations, which are planned for different materials and varied contact area sizes (produced by sintering), will prove the appropriate dependencies in more detail.

The outcome of protoplanetary dust growth: pebbles, boulders, or planetesimals?

The growth processes from protoplanetary dust to planetesimals are not fully understood. Laboratory experiments and theoretical models have shown that collisions among the dust aggregates can lead to sticking, bouncing, and fragmentation. However, no systematic study on the collisional outcome of protoplanetary dust has been performed so far so that a physical model of the dust evolution in protoplanetary disks is still missing. We intend to map the parameter space for the collisional interaction of arbitrarily porous dust aggregates. This parameter space encompasses the dust-aggregate masses, their porosities and the collision velocity. With such a complete mapping of the collisional outcomes of protoplanetary dust aggregates, it will be possible to follow the collisional evolution of dust in a protoplanetary disk environment. We use literature data, perform own laboratory experiments, and apply simple physical models to get a complete picture of the collisional interaction of protoplanetary dust aggregates. In our study, we found four different types of sticking, two types of bouncing, and three types of fragmentation as possible outcomes in collisions among protoplanetary dust aggregates. We distinguish between eight combinations of porosity and mass ratio. For each of these cases, we present a complete collision model for dust-aggregate masses between 10^-12 and 10^2 g and collision velocities in the range 10^-4 to 10^4 cm/s for arbitrary porosities. This model comprises the collisional outcome, the mass(es) of the resulting aggregate(s) and their porosities. We present the first complete collision model for protoplanetary dust. This collision model can be used for the determination of the dust-growth rate in protoplanetary disks.

Numerical simulations of highly porous dust aggregates in the low-velocity collision regime

A highly favoured mechanism of planetesimal formation is collisional growth. Single dust grains, which follow gas flows in the protoplanetary disc, hit each other, stick due to van der Waals forces and form fluffy aggregates up to centimetre size. The mechanism of further growth is unclear since the outcome of aggregate collisions in the relevant velocity and size regime cannot be investigated in the laboratory under protoplanetary disc conditions. Realistic statistics of the result of dust aggregate collisions beyond decimetre size is missing for a deeper understanding of planetary growth. Joining experimental and numerical efforts we want to calibrate and validate a computer program that is capable of a correct simulation of the macroscopic behaviour of highly porous dust aggregates. After testing its numerical limitations thoroughly we will check the program especially for a realistic reproduction of various benchmark experiments. We adopt the smooth particle hydrodynamics (SPH) numerical scheme with extensions for the simulation of solid bodies and a modified version of the Sirono porosity model. Experimentally measured macroscopic material properties of silica dust are implemented. We calibrate and test for the compressive strength relation and the bulk modulus. SPH has already proven to be a suitable tool to simulate collisions at rather high velocities. In this work we demonstrate that its area of application can not only be extended to low-velocity experiments and collisions. It can also be used to simulate the behaviour of highly porous objects in this velocity regime to a very high accuracy.The result of the calibration process in this work is an SPH code that can be utilised to investigate the collisional outcome of porous dust in the low-velocity regime.

Thermal metamorphoses of cosmic dust aggregates: Experiments by furnace, electrical gas discharge, and radiative heating

We experimentally investigated thermal modifications of porous dust aggregates composed of micrometersized grains by furnace, electrical discharge, and laser radiation heating. In the furnace, porous SiO2 aggregates of 95% porosity at first underwent surface diffusion sintering, which led to progressively increasing necking between adjacent particles. Subsequently, viscous flow dissolved the particulate structure of the still porous sample, and finally melting occurred. Exposing aggregates of various grain types to electrical discharges dispersed most of the sample and left it thermally unprocessed. Nevertheless, some material was thermally processed to sintered aggregates and a tiny fraction to solidified melt spherules with diameters of less than 180 μm and most with interior bubbles. In comparison, radiative laser heating turned out to be a much more efficient process to produce melt spherules of chondrule size, and voids were rarer than in discharge heating. Besides providing material data for further applications, our work also allows a direct conclusion to be drawn on chondrule formation. Low energetic efficiency and aggregate destruction exclude chondrule formation from loosely-bound aggregates inside hypothetical nebular lightning channels. However, radiative heating of whatever origin, including possible lightning, remains a candidate process of chondrule formation.

NUMERICAL MODELING OF THE COAGULATION AND POROSITY EVOLUTION OF DUST AGGREGATES

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.

THE PHYSICS OF PROTOPLANETESIMAL DUST AGGLOMERATES. IV. TOWARD A DYNAMICAL COLLISION MODEL

Recent years have shown many advances in our knowledge of the collisional evolution of protoplanetary dust. Based on a variety of dust-collision experiments in the laboratory, our view of the growth of dust aggregates in protoplanetary disks is now supported by a deeper understanding of the physics involved in the interaction between dust agglomerates. However, the parameter space, which determines the collisional outcome, is huge and sometimes inaccessible to laboratory experiments. Very large or fluffy dust aggregates and extremely low collision velocities are beyond the boundary of today's laboratories. It is therefore desirable to augment our empirical knowledge of dust-collision physics with a numerical method to treat arbitrary aggregate sizes, porosities, and collision velocities. In this paper, we implement experimentally determined material parameters of highly porous dust aggregates into a smooth particle hydrodynamics (SPH) code, in particular an omnidirectional compressive-strength and a tensile-strength relation. We also give a prescription of calibrating the SPH code with compression and low-velocity impact experiments. In the process of calibration, we developed a dynamic compressive-strength relation and estimated a relation for the shear strength. Finally, we defined and performed a series of benchmark tests and found the agreement between experimental results and numerical simulations to be very satisfactory. SPH codes have been used in the past to study collisions at rather high velocities. At the end of this work, we show examples of future applications in the low-velocity regime of collisional evolution.

The Physics of Protoplanetesimal Dust Agglomerates. II. Low‐Velocity Collision Properties

For the investigation of collisions among protoplanetesimal dust aggregates, we performed microgravity experiments in which the impacts of high-porosity millimeter-sized dust aggregates into 2.5 cm high-porosity dust aggregates can be studied. The dust aggregates consisted either of monodisperse spherical, quasi-monodisperse irregular, or polydisperse irregular micrometer-sized dust grains and were produced by random ballistic deposition with porosities between 85% and 93%. Impact velocities ranged from ~0.1 to ~3 m s−1, and impact angles were almost randomly distributed. In addition to the smooth surfaces of the target aggregates formed in our experiments, we "molded" target aggregates such that the radii of the local surface curvatures corresponded to the projectile radii, decreasing the targets' porosities to 80%-85%. The experiments showed that impacts into the highest porosity targets almost always led to sticking, whereas for the less porous dust aggregates, consisting of monodisperse spherical dust grains, the collisions with intermediate velocities and high impact angles resulted in the bouncing of the projectile with a mass transfer from the target to the projectile aggregate. Sticking probabilities for the impacts into the "molded" target aggregates were considerably decreased. For the impacts into smooth targets, we measured the depth of intrusion and the crater volume, and were able to derive some interesting dynamical properties which can help to derive a collision model for protoplanetesimal dust aggregates. Future models of the aggregate growth in protoplanetary disks should take into account noncentral impacts, impact compression, the influence of the local radius of curvature on the collisional outcome, and the possible mass transfer between the target and projectile agglomerates in nonsticking collisions.