3D Simulations of Diffusion Limited Planetesimal Formations
Hubert Klahr and Andreas Schreiber
Max-Planck-Institute for Astronomy
Planetesimal formation in simulations of the streaming instability is typically completed when the individual pebble accumulations exceed the local Hill density. Here, we perform high resolution, non-stratified streaming instability simulations at the scales of the pebble accumulations. We find that reaching the Hill density is not a sufficient criterion for the gravitational collapse of a pebble cloud into a planetesimal, but that also the accumulated mass has to be large enough to overcome turbulent diffusion. This mass of pebbles is related to the Jeans mass in star formation. A Toomre analysis of the system indicates that linear self-gravity modes play no role in our system. The increased turbulence is either an indication of Kelvin Helmholtz Instability or a boost of the streaming instability. We determine the critical length scale respectively mass for a pebble cloud collapse based on a dimensionally averaged diffusivity and successfully test this criterion in our numerical experiments. We furthermore determine the Bonnor-Ebert central density to which a pebble cloud of given mass would have to be compressed before it would be able to continue contraction against internal diffusion. As the equivalent mass diameter scales with the central density to the power of $-1/6$, it is much easier to have a pebble cloud of $100$ km equivalent size to collapse than those of $10$ km. This can explain the lack of small bodies in the solar system and predicts to have them formed rather late at times of reduced gas mass in the nebula.