Chris W. Ormel

The outcome of protoplanetary dust growth: pebbles, boulders, or planetesimals? II. Introducing the bouncing barrier

Context. The evolution of dust particles in protoplanetary disks determines many observable and structural properties of the disk, such as the spectral energy distribution (SED), appearance of disks, temperature profile, and chemistry. Dust coagulation is also the first step towards planet formation. Aims. We investigate dust growth due to settling in a 1D vertical column of a disk. It is known from the ten micron feature in disk SEDs, that small micron-sized grains are present at the disk atmosphere throughout the lifetime of the disk. We hope to explain such questions as what process can keep the disk atmospheres dusty for the lifetime of the disk and how the particle properties change as a function of height above the midplane. Methods. We used a Monte Carlo code to follow the mass and porosity evolution of the particles in time. We gradually build up the complexity of the models by considering the effects of porosity, different collision models, turbulence, and different gas models, respectively. This way we can distinguish the effects of these physical processes on particle growth and motion. The collision model used is based on laboratory experiments performed on dust aggregates. As the experiments cannot cover all possible collision scenarios, the largest uncertainty of our model comes from the necessary extrapolations we had to perform. We simultaneously solved for the particle growth and motion. Particles can move vertically due to settling and turbulent mixing. We assumed that the vertical profile of the gas density is fixed in time and that only the solid component evolves. Results. We find that the used collision model strongly influences the masses and sizes of the particles. The laboratory-experiment based collision model greatly reduces the particle sizes compared to models that assume sticking at all collision velocities. We find that a turbulence parameter of α = 10−2 is needed to keep the dust atmospheres dusty, but such strong turbulence can produce only small particles at the midplane, which does not favor for planetesimal formation models. We also see that the particles are larger at the midplane and smaller at the upper layers of the disk. At 3–4 pressure-scale heights, micron-sized particles are produced. These particle sizes are needed to explain the ten micron feature of disk SEDs. Turbulence may therefore help keep small dust particles in the disk atmosphere.

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

Context. 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. Aims. 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. Methods. We use literature data, perform laboratory experiments, and apply simple physical models to get a complete picture of the collisional interaction of protoplanetary dust aggregates. Results. We found four different kinds of sticking, two kinds of bouncing, and three kinds of fragmentation as possible outcomes in collisions among protoplanetary dust aggregates. Our best collision model distinguishes between porous and compact dust. We also differentiate between collisions among similar-sized and different-sized bodies. All in all, eight combinations of porosity and mass ratio can be discerned. 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 of 10 −4 ... 10 4 cm s −1 for arbitrary porosities. This model comprises the collisional outcome, the mass(es) of the resulting aggregate(s) and their porosities. Conclusions. 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.

The effect of gas drag on the growth of protoplanets - Analytical expressions for the accretion of small bodies in laminar disks

Planetary bodies form by accretion of smaller bodies. It has been suggested that a very efficient way to grow protoplanets is by ac- creting particles of sizekm (e.g., chondrules, boulders, or fragments of larger bodies) as they can be kept dynamically cold. We investigate the effects of gas drag on the impact radii and the accretion rates of these particles. As simplifying assumptions we restrict our analysis to 2D settings, a gas drag law linear in velocity, and a laminar disk characterized by a smooth (global) pressure gradient that causes particles to drift in radially. These approximations, however, enable us to cover an arbitrary large parameter space. The framework of the circularly restricted three body problem is used to numerically integrate particle trajectories and to derive their impact parameters. Three accretion modes can be distinguished: hyperbolic encounters, where the 2-body gravitational focusing en- hances the impact parameter; three-body encounters, where gas drag enhances the capture probability; and settling encounters ,w here particles settle towards the protoplanet. An analysis of the observed behavior is presented; and we provide a recipe to analytically calculate the impact radius, which confirms the numerical findings. We apply our results to the sweepup of fragments by a protoplanet at a distance of 5 AU. Accretion of debris on small protoplanets (<50 km) is found to be slow, because the fragments are distributed over a rather thick layer. However, the newly found settling mechanism, which is characterized by much larger impact radii, becomes relevant for protoplanets of ∼10 3 km in size and provides a much faster channel for growth.

Closed-form expressions for particle relative velocities induced by turbulence (Research Note)

In this note we present complete, closed-form expressions for random relative velocities between colliding particles of arbitrary size in nebula turbulence. These results are exact for very small particles (those with stopping times much shorter than the large eddy overturn time) and are also surprisingly accurate in complete generality (that is, also apply for particles with stopping times comparable to, or much longer than, the large eddy overturn time). We note that some previous studies may have adopted previous simple expressions, which we find to be in error regarding the size dependence in the large particle regime.

Breaking through: The effects of a velocity distribution on barriers to dust growth

It is unknown how far dust growth can proceed by coagulation. Obstacles to collisional growth are the fragmentation and bouncing barriers. However, in all previous simulations of the dust-size evolution in protoplanetary disks, only the mean collision velocity has been considered, neglecting that a small but possibly important fraction of the collisions will occur at both much lower and higher velocities. We study the effect of the probability distribution of impact velocities on the collisional dust growth barriers. Assuming a Maxwellian velocity distribution for colliding particles to determine the fraction of sticking, bouncing, and fragmentation, we implement this in a dust-size evolution code. We also calculate the probability of growing through the barriers and the growth timescale in these regimes. We find that the collisional growth barriers are not as sharp as previously thought. With the existence of low-velocity collisions, a small fraction of the particles manage to grow to masses orders of magnitude above the main population. A particle velocity distribution softens the fragmentation barrier and removes the bouncing barrier. It broadens the size distribution in a natural way, allowing the largest particles to become the first seeds that initiate sweep-up growth towards planetesimal sizes.

Dust coagulation and fragmentation in molecular clouds. II. The opacity of the dust aggregate size distribution

The dust size distribution in molecular clouds can be strongly affected by ice-mantle formation and (subsequent) grain coagulation. Following previous work where the dust size distribution has been calculated from a state-of-the art collision model for dust aggregates that involves both coagulation and fragmentation (Paper I), the corresponding opacities are presented in this study. The opacities are calculated by applying the effective medium theory assuming that the dust aggregates are a mix of 0.1{\mu}m silicate and graphite grains and vacuum. In particular, we explore how the coagulation affects the near-IR opacities and the opacity in the 9.7{\mu}m silicate feature. We find that as dust aggregates grow to {\mu}m-sizes both the near-IR color excess and the opacity in the 9.7 {\mu}m feature increases. Despite their coagulation, porous aggregates help to prolong the presence of the 9.7{\mu}m feature. We find that the ratio between the opacity in the silicate feature and the near-IR color excess becomes lower with respect to the ISM, in accordance with many observations of dark clouds. However, this trend is primarily a result of ice mantle formation and the mixed material composition of the aggregates, rather than being driven by coagulation. With stronger growth, when most of the dust mass resides in particles of size 10{\mu}m or larger, both the near-IR color excess and the 9.7{\mu}m silicate feature significantly diminish. Observations at additional wavelengths, in particular in the sub-mm range, are essential to provide quantitative constraints on the dust size distribution within dense cores. Our results indicate that the sub-mm index {\beta} will increase appreciably, if aggregates grow to ~100{\mu}m in size.

Make Super-Earths, Not Jupiters: Accreting Nebular Gas onto Solid Cores at 0.1?AU and Beyond

Close-in super-Earths having radii 1--4

Testing the theory of grain growth and fragmentation by millimeter observations of protoplanetary disks

R_\oplus

Co-accretion of chondrules and dust in the solar nebula

may possess hydrogen atmospheres comprising a few percent by mass of their rocky cores. We determine the conditions under which such atmospheres can be accreted by cores from their parent circumstellar disks. Accretion from the nebula is problematic because it is too efficient: we find that 10-

The outcome of protoplanetary dust growth: pebbles, boulders, or planetesimals? - III. Sedimentation driven coagulation inside the snowline

M_\oplus