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.Comment: accepted by Astronomy & Astrophysic

Compression Behaviour of Porous Dust Agglomerates

The early planetesimal growth proceeds through a sequence of sticking collisions of dust agglomerates. Very uncertain is still the relative velocity regime in which growth rather than destruction can take place. The outcome of a collision depends on the bulk properties of the porous dust agglomerates. Continuum models of dust agglomerates require a set of material parameters that are often difficult to obtain from laboratory experiments. Here, we aim at determining those parameters from ab-initio molecular dynamics simulations. Our goal is to improveon the existing model that describe the interaction of individual monomers. We use a molecular dynamics approach featuring a detailed micro-physical model of the interaction of spherical grains. The model includes normal forces, rolling, twisting and sliding between the dust grains. We present a new treatment of wall-particle interaction that allows us to perform customized simulations that directly correspond to laboratory experiments. We find that the existing interaction model by Dominik & Tielens leads to a too soft compressive strength behavior for uni and omni-directional compression. Upon making the rolling and sliding coefficients stiffer we find excellent agreement in both cases. Additionally, we find that the compressive strength curve depends on the velocity with which the sample is compressed. The modified interaction strengths between two individual dust grains will lead to a different behaviour of the whole dust agglomerate. This will influences the sticking probabilities and hence the growth of planetesimals. The new parameter set might possibly lead to an enhanced sticking as more energy can be stored in the system before breakup.Comment: 11 pages, 14 figures, accepted for publication in A&

Numerical determination of the material properties of porous dust cakes

The formation of planetesimals requires the growth of dust particles through collisions. Micron-sized particles must grow by many orders of magnitude in mass. In order to understand and model the processes during this growth, the mechanical properties, and the interaction cross sections of aggregates with surrounding gas must be well understood. Recent advances in experimental (laboratory) studies now provide the background for pushing numerical aggregate models onto a new level. We present the calibration of a previously tested model of aggregate dynamics. We use plastic deformation of surface asperities as the physical model to bring critical velocities for sticking into accordance with experimental results. The modified code is then used to compute compression strength and the velocity of sound in the aggregate at different densities. We compare these predictions with experimental results and conclude that the new code is capable of studying the properties of small aggregates.Comment: Accepted for publication in A&

Dust coagulation and fragmentation in molecular clouds. I. How collisions between dust aggregates alter the dust size distribution

In dense molecular clouds collisions between dust grains alter the ISM-dust size distribution. We study this process by inserting the results from detailed numerical simulations of two colliding dust aggregates into a coagulation model that computes the dust size distribution with time. All collisional outcomes -- sticking, fragmentation (shattering, breakage, and erosion) -- are included and the effects on the internal structure of the aggregates are also tabulated. The dust aggregate evolution model is applied to an homogeneous and static cloud of temperature 10 K and gas densities between 10^3 and 10^7 cm^-3. The coagulation is followed locally on timescales of ~10^7 yr. We find that the growth can be divided into two stages: a growth dominated phase and a fragmentation dominated phase. Initially, the mass distribution is relatively narrow and shifts to larger sizes with time. At a certain point, dependent on the material properties of the grains as well as on the gas density, collision velocities will become sufficiently energetic to fragment particles, halting the growth and replenishing particles of lower mass. Eventually, a steady state is reached, where the mass distribution is characterized by a mass spectrum of approximately equal amount of mass per logarithmic size bin. The amount of growth that is achieved depends on the cloud's lifetime. If clouds exist on free-fall timescales the effects of coagulation on the dust size distribution are very minor. On the other hand, if clouds have long-term support mechanisms, the impact of coagulation is important, resulting in a significant decrease of the opacity on timescales longer than the initial collision timescale between big grains.Comment: 25 pages, 20 figures, accepted for publication in Astronomy & Astrophysic

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.Comment: 17 pages, 15 figures; v2: version to appear in ApJ (typos corrected

The influence of grain rotation on the structure of dust aggregates

We study the effect of rotation during the collision between dust aggregates, in order to address a mismatch between previous model calculations of Brownian motion driven aggregation and experiments. We show that rotation during the collision does influence the shape and internal structure of the aggregates formed. The effect is limited in the ballistic regime when aggregates can be considered to move on straight lines during a collision. However, if the stopping length of an aggregate becomes smaller than its physical size, extremely elongated aggregates can be produced. We show that this effect may have played a role in the inner regions of the solar nebula where densities were high.Comment: 15 pages, 6 figures, accepted for publication in Icarus, typos correcte

High Velocity Dust Collisions: Forming Planetesimals in a Fragmentation Cascade with Final Accretion

In laboratory experiments we determine the mass gain and loss in central collisions between cm to dm-size SiO2 dust targets and sub-mm to cm-size SiO2 dust projectiles of varying mass, size, shape, and at different collision velocities up to ~56.5 m/s. Dust projectiles much larger than 1 mm lead to a small amount of erosion of the target but decimetre targets do not break up. Collisions produce ejecta which are smaller than the incoming projectile. Projectiles smaller than 1 mm are accreted by a target even at the highest collision velocities. This implies that net accretion of decimetre and larger bodies is possible. Independent of the original size of a projectile considered, after several collisions all fragments will be of sub-mm size which might then be (re)-accreted in the next collision with a larger body. The experimental data suggest that collisional growth through fragmentation and reaccretion is a viable mechanism to form planetesimals