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.Comment: 12 pages, 9 figures, 4 table

The four-populations 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.Comment: 14 pages, 11 figures, 5 tables, to be published in Astronomy and 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&

Towards a Dynamical Collision Model of Highly Porous Dust Aggregates

In the recent years we have performed various experiments on the collision dynamics of highly porous dust aggregates and although we now have a comprehensive picture of the micromechanics of those aggregates, the macroscopic understanding is still lacking. We are therefore developing a mechanical model to describe dust aggregate collisions with macroscopic parameters like tensile strength, compressive strength and shear strength. For one well defined dust sample material, the tensile and compressive strength were measured in a static experiment and implemented in a Smoothed Particle Hydrodynamics (SPH) code. A laboratory experiment was designed to compare the laboratory results with the results of the SPH simulation. In this experiment, a mm-sized glass bead is dropped into a cm-sized dust aggregate with the previously measured strength parameters. We determine the deceleration of the glass bead by high-speed imaging and the compression of the dust aggregate by x-ray micro-tomography. The measured penetration depth, stopping time and compaction under the glass bead are utilized to calibrate and test the SPH code. We find that the statically measured compressive strength curve is only applicable if we adjust it to the dynamic situation with a 'softness' parameter. After determining this parameter, the SPH code is capable of reproducing experimental results, which have not been used for the calibration before.Comment: Accepted by "Proc. Powders and Grains 2009", Publisher AI

The outcome of protoplanetary dust growth: pebbles, boulders, or planetesimals? I. Mapping the zoo of laboratory collision experiments

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.Comment: accepted by Astronomy and Astrophysic

The Physics of Protoplanetesimal Dust Agglomerates. IV. Towards 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 article, 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.Comment: accepted by The astrophysical Journa

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

Crossing barriers in planetesimal formation: The growth of mm-dust aggregates with large constituent grains

Collisions of mm-size dust aggregates play a crucial role in the early phases of planet formation. We developed a laboratory setup to observe collisions of dust aggregates levitating at mbar pressures and elevated temperatures of 800 K. We report on collisions between basalt dust aggregates of from 0.3 to 5 mm in size at velocities between 0.1 and 15 cm/s. Individual grains are smaller than 25 \mum in size. We find that for all impact energies in the studied range sticking occurs at a probability of 32.1 \pm 2.5% on average. In general, the sticking probability decreases with increasing impact parameter. The sticking probability increases with energy density (impact energy per contact area). We also observe collisions of aggregates that were formed by a previous sticking of two larger aggregates. Partners of these aggregates can be detached by a second collision with a probability of on average 19.8 \pm 4.0%. The measured accretion efficiencies are remarkably high compared to other experimental results. We attribute this to the rel. large dust grains used in our experiments, which make aggregates more susceptible to restructuring and energy dissipation. Collisional hardening by compaction might not occur as the aggregates are already very compact with only 54 \pm 1% porosity. The disassembly of previously grown aggregates in collisions might stall further aggregate growth. However, owing to the levitation technique and the limited data statistics, no conclusive statement about this aspect can yet be given. We find that the detachment efficiency decreases with increasing velocities and accretion dominates in the higher velocity range. For high accretion efficiencies, our experiments suggest that continued growth in the mm-range with larger constituent grains would be a viable way to produce larger aggregates, which might in turn form the seeds to proceed to growing planetesimals.Comment: 9 pages, 20 figure