Submillimetre-sized dust aggregate collision and growth properties

The collisional and sticking properties of sub-mm-sized aggregates composed of protoplanetary dust analogue material are measured, including the statistical threshold velocity between sticking and bouncing, their surface energy and tensile strength within aggregate clusters. We performed an experiment on the REXUS 12 suborbital rocket. The protoplanetary dust analogue materials were micrometre-sized monodisperse and polydisperse SiO2 particles prepared into aggregates with sizes around 120 $\mu$m and 330 $\mu$m, respectively and volume filling factors around 0.37. During the experimental run of 150 s under reduced gravity conditions, the sticking of aggregates and the formation and fragmentation of clusters of up to a few millimetres in size was observed. The sticking probability of the sub-mm-sized dust aggregates could be derived for velocities decreasing from 22 to 3 cm/s. The transition from bouncing to sticking collisions happened at 12.7 cm/s for the smaller aggregates composed of monodisperse particles and at 11.5 and 11.7 cm/s for the larger aggregates composed of mono- and polydisperse dust particles, respectively. Using the pull-off force of sub-mm-sized dust aggregates from the clusters, the surface energy of the aggregates composed of monodisperse dust was derived to be 1.6x10-5 J/m2, which can be scaled down to 1.7x10-2 J/m2 for the micrometre-sized monomer particles and is in good agreement with previous measurements for silica particles. The tensile strengths of these aggregates within the clusters were derived to be 1.9 Pa and 1.6 Pa for the small and large dust aggregates, respectively. These values are in good agreement with recent tensile strength measurements for mm-sized silica aggregates. Using our data on the sticking-bouncing threshold, estimates of the maximum aggregate size can be given. For a minimum mass solar nebula model, aggregates can reach sizes of 1 cm.Comment: 21 pages (incl. 6 pages of appendix), 23 figure

Low-velocity collision behaviour of clusters composed of sub-mm sized dust aggregates

The experiments presented aim to measure the outcome of collisions between sub-mm sized protoplanetary dust aggregate analogues. We also observed the clusters formed from these aggregates and their collision behaviour. The experiments were performed at the drop tower in Bremen. The protoplanetary dust analogue materials were micrometre-sized monodisperse and polydisperse SiO$_2$ particles prepared into aggregates with sizes between 120~$\mu$m and 250~$\mu$m. One of the dust samples contained aggregates that were previously compacted through repeated bouncing. During three flights of 9~s of microgravity each, individual collisions between aggregates and the formation of clusters of up to a few millimetres in size were observed. In addition, the collisions of clusters with the experiment cell walls leading to compaction or fragmentation were recorded. We observed collisions amongst dust aggregates and collisions between dust clusters and the cell aluminium walls at speeds ranging from about 0.1 cm/s to 20 cm/s. The velocities at which sticking occurred ranged from 0.18 to 5.0 cm/s for aggregates composed of monodisperse dust, with an average value of 2.1 cm/s for reduced masses ranging from 1.2x10-6 to 1.8x10-3 g with an average value of 2.2x10-4 g. From the restructuring and fragmentation of clusters composed of dust aggregates colliding with the aluminium cell walls, we derived a collision recipe for dust aggregates ($\sim$100 $\mu$m) following the model of Dominik \& Thielens (1997) developed for microscopic particles. We measured a critical rolling energy of 1.8x10-13 J and a critical breaking energy of 3.5x10-13 J for 100 $\mu$m-sized non-compacted aggregates.Comment: 12 pages, 13 figure

Low-velocity collisions of centimeter-sized dust aggregates

Collisions between centimeter- to decimeter-sized dusty bodies are important to understand the mechanisms leading to the formation of planetesimals. We thus performed laboratory experiments to study the collisional behavior of dust aggregates in this size range at velocities below and around the fragmentation threshold. We developed two independent experimental setups with the same goal to study the effects of bouncing, fragmentation, and mass transfer in free particle-particle collisions. The first setup is an evacuated drop tower with a free-fall height of 1.5 m, providing us with 0.56 s of microgravity time so that we observed collisions with velocities between 8 mm/s and 2 m/s. The second setup is designed to study the effect of partial fragmentation (when only one of the two aggregates is destroyed) and mass transfer in more detail. It allows for the measurement of the accretion efficiency as the samples are safely recovered after the encounter. Our results are that for very low velocities we found bouncing as could be expected while the fragmentation velocity of 20 cm/s was significantly lower than expected. We present the critical energy for disruptive collisions Q*, which showed up to be at least two orders of magnitude lower than previous experiments in the literature. In the wide range between bouncing and disruptive collisions, only one of the samples fragmented in the encounter while the other gained mass. The accretion efficiency in the order of a few percent of the particle's mass is depending on the impact velocity and the sample porosity. Our results will have consequences for dust evolution models in protoplanetary disks as well as for the strength of large, porous planetesimal bodies

\'Free Collisions in a Microgravity Many-Particle Experiment. II. The Collision Dynamics of Dust-Coated Chondrules

The formation of planetesimals in the early Solar System is hardly understood, and in particular the growth of dust aggregates above millimeter sizes has recently turned out to be a difficult task in our understanding [Zsom et al. 2010, A&A, 513, A57]. Laboratory experiments have shown that dust aggregates of these sizes stick to one another only at unreasonably low velocities. However, in the protoplanetary disk, millimeter-sized particles are known to have been ubiquitous. One can find relics of them in the form of solid chondrules as the main constituent of chondrites. Most of these chondrules were found to feature a fine-grained rim, which is hypothesized to have formed from accreting dust grains in the solar nebula. To study the influence of these dust-coated chondrules on the formation of chondrites and possibly planetesimals, we conducted collision experiments between millimeter-sized, dust-coated chondrule analogs at velocities of a few cm/s. For 2 and 3 mm diameter chondrule analogs covered by dusty rims of a volume filling factor of 0.18 and 0.35-0.58, we found sticking velocities of a few cm/s. This velocity is higher than the sticking velocity of dust aggregates of the same size. We therefore conclude that chondrules may be an important step towards a deeper understanding of the collisional growth of larger bodies. Moreover, we analyzed the collision behavior in an ensemble of dust aggregates and non-coated chondrule analogs. While neither the dust aggregates nor the solid chondrule analogs show sticking in collisions among their species, we found an enhanced sicking efficiency in collisions between the two constituents, which leads us to the conjecture that chondrules might act as "catalyzers" for the growth of larger bodies in the young Solar System

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

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

Porosities of Protoplanetary Dust Agglomerates from Collision Experiments

Aggregation of dust through sticking collisions is the first step of planet formation. Basic physical properties of the evolving dust aggregates strongly depend on the porosity of the aggregates, e.g. mechanical strength, thermal conductivity, gas-grain coupling time. Also the outcome of further collisions depends on the porosity of the colliding aggregates. In laboratory experiments we study the growth of large aggregates of $\sim$ 3 mm to 3 cm through continuous impacts of small dust agglomerates of 100 $\mu$m size, consisting of $\mu$m grains at different impact velocities. The experiments show that agglomerates grow by direct sticking as well as gravitational reaccretion. The latter can be regarded as suitable analog to reaccretion of fragments by gas drag in protoplanetary disks. Experiments were carried out in the velocity range between 1.5 m/s and 7 m/s. With increasing impact velocities the volume filling factor of the resulting agglomerates increases from $\phi = 0.2$ for 1.5 m/s to $\phi = 0.32$ for 7 m/s. These values are independent of the target size. Extrapolation of the measured velocity dependence of the volume filling factor implies that higher collision velocities will not lead to more compact aggregates. Therefore, $\phi = 0.32$ marks a degree of compaction suitable to describe structures forming at $\rm v > 6\, m/s$. At small collision velocities below 1 m/s highly porous structures with $\phi \approx 0.10$ will form. For intermediate collision velocities porosities vary. Depending on the disk model and resulting relative velocities, objects in protoplanetary disks up to dm-size might evolve from highly porous ($\phi \approx 0.10$) to compact ($\phi = 0.32$) with a more complex intermediate size range of varying porosity.Comment: Accepted by The Astrophysical Journa

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

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