Numerical Simulations of Planetesimal Formation in Protoplanetary Disks

Abstract

In the first step of planet formation micrometer-sized dust grains grow in a protoplanetary disk through collisional sticking. This growth becomes inefficient at several centimeters up to meters in size, depending on the distance to the star. The resulting agglomerates are concentrated by turbulence in the disk up to densities at which they fragment through self-gravitaty to $100\,\textrm{km}$ sized planetesimals. In my PhD thesis I simulate the concentration of dust particles in the turbulent gas flow of protoplanetary disks. Here I treat the gas as a fluid and solve the magnetohydrodynamic equations with the {\sc Pencil code}. Dust particles are simulated as non-collisional point particles, decoupled from the grid. At first I test the particle representation of the {\sc Pencil code} by comparing a Rayleigh-Taylor instability (RTI) simulation of a dust-laden fluid with a classical two-layer fluid RTI simulation. Additionally I simulate the sedimentation of a dust clump in a fluid which can be compared with experiments. Further I study zonal flows and the resulting long-lived axisymmetric pressure bumps that are created in magnetorotational instability simulations. Zonal flows are described by annuli of gas rotating faster or slower than the pressure-supported Keplerian rotation. They are created by temporal and spacial variances in the magnetic pressure. In a convergence study I measured a typical radial size of $5$ to $7$ vertical gas pressure scale heights with a life time of up to $50$ local orbits ($T_{\textrm{orb}} = 2 \pi \Omega^{-1}$). Particles get captured by these pressure bumps. For dust particles with a friction time $\tau_{\textrm{f}} \ge 0.1 \Omega^{-1}$ I found concentrations that are some hundred times higher than initially. Larger particles ($\tau_{\textrm{f}} \ge 0.5 \Omega^{-1}$) reach densities $10$,$000$ times higher than their initial densities, sufficient to trigger secondary instabilities such as the streaming instability and gravitational collapse. I study the streaming instability in a zonal flow environment in simulations of higher resolution including the back-reaction drag from particles to the gas. These simulations show that the axisymmetric pressure bumps can accumulate enough particles to trigger the streaming instability, even with small particles ($\tau_{\textrm{f}} = 0.1 \Omega^{-1}$). Allowing for self-gravity dust clumps form, yet they are not stable against tidal forces. This is due to the insufficient resolution here. For my last project I studied the final collapse of a spherical dust cloud with a much higher resolution than in the above simulations. In this study I investigate a dust cloud with an initial density ranging from Roche density $\rho\Roche$ down to $10^{-3} \rho_{\textrm{Roche}}$. Dust spheres with $0.1 \rho_{\textrm{Roche}}$, like I typically get from large scale simulations, fragment to a swarm of bound objects with a size distribution that is comparable to the observed size distribution of asteroids.