Protoplanetary disks & Planetesimal formation

1. Introduction

Collisions between small (sub-micron) dust and ice grains in the early protoplanetary disk allow the grains to grow to centimetre-scaled particles – often referred to as `pebbles’ (e.g., Dominik and Tielens, 1997; Blum and Wurm, 2000; Wada et al., 2009; Güttler et al., 2010). Subsequently, when sufficiently concentrated within the disk, pebbles form a pebble cloud that can gently collapse under its own gravity. Currently the preferred and most-studied mechanism that can lead to such a pebble concentration is the streaming instability (e.g., Youdin and Goodman, 2005; Johansen et al., 2007; Wahlberg Jansson and Johansen, 2014; Simon et al., 2017) expected to mostly form large (∼100 km) planetesimals (e.g. Simon et al., 2016; Schäfer et al., 2017; Klahr and Schreiber, 2020).

2. Protoplanetary disk model

To study where and under which conditions planetesimals form, we need to simulate the evolution of the gas and dust in the protoplanetary disk. We use the DiskBuild protoplanetary disk model first presented in Morbidelli et al. 2022, which includes dust and gas evolution. Here, we summarise the model’s main features and refer the reader to the methods section of Morbidelli et al. 2022 for a detailed model description.

We typically initiate the model with an empty disk and a protostar with an initial mass of $0.5M_{\odot}$ . This is consistent with a Class-0 protostar. Subsequently, the disk is populated through an infall function describing the amount of mass added to the star-disk system as a function of time and distance to the star. The mass added to the disk decays over time as $\exp(-t/T_{\text{infall}})$ , where $t$ is time and $T_{\text{infall}}$ is the infall timescale, a free parameter of the model. The time-integrated mass of the infall results in a star-disk system with one solar mass. Over time, the gas disk evolves under viscous heating and spreading. We compute the scale height self-consistently at each distance, $r$ , of the disk by measuring the temperature, $T$

Of the infalling mass, 1% is dust, and the rest is gas (hydrogen), corresponding to the solar metallicity. The dust is further split up into three sub-species: 1) all refractory species, 2) silicates, 3) water/ice. When the local disk temperature is above one of these sublimation temperatures, the corresponding dust species are considered to be in the gaseous form and thus evolve in the same way the overall gas does. In the part of the disk where a dust species is in solid form, we track the size of dust particles, or rather its stokes number, ${\text St}$ .

3. Recent results

We have recently published results with this code in Morbidelli et al. 2022 and Marschall & Morbidelli 2023. As an illustration, the two figures below show an example of protoplanetary disks after only 1,000 years of evolution. The purple line shows the gas surface density and the green line shows the dust surface density. The vertical dashed lines show different sublimation lines (purple: refractories, green: silicates, orange: water/ice) and the distance within which material falls into the disk (grey: labelled $R_C$ for centrifugal radius). The two simulations only differ only in the initial viscosity in the disk, the left having a small, while the right having a large viscosity.

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