Gravoturbulent Planetesimal Formation
Max-Planck-Institut für Astronomie, Heidelberg (Germany)
Local Project ID:
HPC Platform used:
JUQUEEN and JUWELS of JSC
Planet formation is a beneficial side effect of star formation. When a large gas cloud collapses under its own weight creating a star, some of the material forms a disk out of dust and gas around this newborn star. Such disks can be found around stars younger than 10 million years, and we believe they are the origin of planetary systems like our own. They are composed mainly out of hydrogen and helium, plus 1-2% heavier elements which astronomers simply call metals. The initial metal abundance is 13 orders of magnitude lower than typical planet densities. Thus, the planet formation process must be very efficient in concentrating metals locally. Therefore, we focused on simulating the early gas and dust mixture in an effort to understand the scales and size distributions of early planetary material.
The first step towards planet formation requires the coagulation of dusty ice grains. By sticking, these grains grow up to centimeters in size. Larger sizes are not possible since collisions then lead to destruction rather than to sticking. What follows is unfortunately not observable because meter-sized or even kilometer-sized objects are not detectable. Yet, having discovered thousands of planets around other stars the planet formation process must be very efficient in overcoming this and other growth barriers.
From our own solar system we know that planetesimals must have been formed, which are planetary building blocks of 100 kilometers in size. They subsequently then form cores of gas giants and terrestrial planets. Planetesimal leftovers can still be found today in the form of asteroids and comets. Thus, we would have a relatively clear evolutionary path from dust up to the final planetary system if we could explain how centimeter-sized pebbles can grow to planetesimals considering the effects of self-gravity and turbulence. We required a model which can include these large scale but still resolve the necessary physics, means powerful computational resources were required.
We used high-resolution simulations to model disk turbulence and its two effects on the dust, the mixing and diffusion of the dust on large scales but also the concentration of dust on small scales . Reaching a dust concentration of unity the streaming instability sets in, in which the gas starts feeling a significant back reaction from the dust. Moreover, in regions with densities larger than Roche density, at which tidal forces no longer prevent a gravitational collapse, the particle heap collapses into 100 – 1,000 km sized planet embryos [2,3].
Additionally, we studied the possibility that early self-gravitating disks fragment into gas giant planets through gravitational instabilities. We had previously studied the criterion for fragmentation  and looked at the potential for metallicity enrichment of these fragments during and after formation . While it is well known that the spiral arms induced by these gravitational instabilities collect solid material, potentially forming planetesimals, it is currently unknown how efficiently fragments themselves collect dust and particles of various sizes. We found that gas giant planet formed by gravitational instabilities can have significant
Our simulations used the Pencil Code , a high order finite difference MHD code. Particles are treated as Lagrangian swarm particles and include the effects of mutual drag and self-gravity. Our streaming instability runs used up to 5,123 grid-cells and 64 million particles , while the disk fragmentation simulations use more than 1 billion grid-cells . They run for millions of computational steps before planetesimals start to form because the concentrations develop on viscous time scales, which are much longer than the dynamical time scales.
Over the last years we developed a planetesimal formation model based on the simulations we perform on the Jülich supercomputer JUQUEEN/JUWELS. These high-resolution hydro-dynamical simulations are completed in reasonable times due to the many thousands of cores available at JUQUEEN/JUWELS.
We were able to push our simulations to understand the efficiency of these processes and to derive initial mass functions for planetesimals and gas giant planets. We aimed to better model the turbulence in disks and using the high-resolution studies of the collapsing and possibly fragmenting particle clouds and gas clouds. With both results in hand we can predict when and where planetesimals and Jupiter-like planets should form and of which size they will be . This is a fundamental step forward in understanding the formation of our own solar system as well as of the many planetary systems around other stars.
This project has received funding from the Deutsche Forschungsgemeinschaft within the Schwerpunktprogrammen (DFG SPP) 1385 "The first ten million years of the solar system" and 1833 “Building a habitable earth”. The authors gratefully acknowledge the Gauss Centre for Supercomputing (GCS) for providing computing time for a GCS Large Scale Project on the GCS share of the supercomputers JUQUEEN and JUWELS at Jülich Supercomputing Centre (JSC).
 Schreiber, A., Klahr, H. The Astrophysical Journal, 861, 47, 2018
 Klahr, H., Schreiber, A. The Astrophysical Journal, 901, 54, 2020
 Klahr, H., Schreiber, A. The Astrophysical Journal submitted, 2021, arXiv:2011.07849
 Baehr, H., Klahr, H., Kratter, K. M., The Astrophysical Journal, 484, 40, 2017
 Baehr, H., Klahr, H., The Astrophysical Journal, 881, 162, 2019
 Johansen, A., Klahr, H., Henning, Th. Astronomy and Astrophysics, 529, 62, 2011
 Klahr H., Pfeil T., Schreiber A. (2018) Instabilities and Flow Structures in Protoplanetary Disks: Setting the Stage for Planetesimal Formation. In: Deeg H., Belmonte J. (eds) Handbook of Exoplanets. Springer, Cham.
Dr. Hans Baehr & Prof. Dr. H. Hubertus Klahr
Max-Planck-Institut für Astronomie
Königstuhl 17, D-69117 Heidelberg (Germany)
e-mail: klahr [@] mpia.de
Local project ID: chhd19