Numerical models of the early stages of planet formation

Abstract

This PhD thesis deals with the early stages of planet formation and the growth from micrometer dust grains to kilometer-sized planetesimals. Dust grains are diffused by the turbulence in the protoplanetary disc. We measure the diffusion coefficient of magnetorotational turbulence and relate it to the turbulent viscosity. Diffusion is surprisingly as strong as viscosity, even though most of the viscosity comes from magnetic stresses that do not directly affect diffusion. The ratio between turbulent viscosity and turbulent diffusion (the Schmidt number) is found to depend strongly on the strength of an imposed vertical magnetic field. Large field strengths yield a Schmidt number that is much larger than unity. Larger solid particles, i.e. rocks and boulders, are not only diffused by magnetorotational turbulence, but also experience concentrations in transient high pressure regions of the turbulent gas, reaching local densities two orders of magnitude higher than the average. Discs that are not susceptible to the magnetorotational instability can develop turbulence due to the sedimentation of solids. The radial pressure gradient of the gas, together with a vertical gradient in the solids-to-gas ratio, leads to a vertical shear in the orbital velocity of the gas, unstable to the Kelvin-Helmholtz instability. The turbulent state is characterised by a number of dense clumps of solids that form due to the dependence of the orbital velocity on the local solids-to-gas ratio, making denser regions plough through less dense regions and scoop up the material at the full Keplerian speed. Isolating the effect of this streaming instability, by ignoring vertical stratification, we find that the turbulent state depends strongly on the background solids-to-gas ratio and on the friction time of the particles. Marginally coupled solids display huge overdensities and a diffusion coefficient that approaches that of the magnetorotational turbulence, more tightly coupled solids develop only a very weak non-linear state.