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

Abstract

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.

Free collisions in a microgravity many-particle experiment. III. The collision behavior of sub-millimeter-sized dust aggregates

“…A second point which should be addressed is the single porosity of our samples (φ ∼ 0.37). Various numerical simulations (Suyama et al 2008;Zsom et al 2011;Okuzumi et al 2012) have shown that the first dust agglomerates might have had a much lower volume filling factor (down to φ ∼ 10 −3 ). Zsom et al (2011) showed that particles with a mass of ∼ 10 −6 g can still have such a low density.…”

“…Various numerical simulations (Suyama et al 2008;Zsom et al 2011;Okuzumi et al 2012) have shown that the first dust agglomerates might have had a much lower volume filling factor (down to φ ∼ 10 −3 ). Zsom et al (2011) showed that particles with a mass of ∼ 10 −6 g can still have such a low density. Their simulations also showed that, after a relatively short time (few hundred years), these particles can become more compact and end with values comparable to our samples.…”

Modeling dust growth in protoplanetary disks: The breakthrough case

“…The Monte Carlo coagulation algorithm with equal-mass representative particles -makes it easy to implement additional particle properties, such as porosity (Zsom & Dullemond 2008;Zsom et al 2010), because the computation time does not depend significantly on the number of properties that are evolved, but only on the number of collisions performed; -is straightforward to develop to further spatial dimensions (Zsom et al 2011;Drążkowska et al 2013), as the representative particles can be treated as Lagrangian tracer bodies; -can be used along with hydrodynamic grid codes (Johansen et al 2012); -experiences no numerical diffusion of the mass function in general, so there is no danger of encountering an artificial speed-up of the growth; -has difficulty resolving features that include low fraction of total mass, which makes it less useful in the case of breaking through the growth barriers or runaway growth modeling, although the algorithm can be developed to overcome this issue (Ormel & Spaans 2008), -makes it hard to model evolution over long timescales in general, because it is impossible to use extremely long timesteps, as every collision needs to be resolved.…”

Dust and gas mixtures with multiple grain species – a one-fluid approach

“…The presence of grains with Stokes number of order unity and dust-to-gas ratios of order unity (ie.. ǫ ≃ 0.5) is expected (e.g. Barrière-Fouchet et al 2005;Zsom et al 2011). In such a situation, the right panel of Fig.…”