Testing the Jeans, Toomre, and Bonnor–Ebert Concepts for Planetesimal Formation: 3D Streaming-instability Simulations of Diffusion-regulated Formation of Planetesimals

Abstract

Abstract We perform streaming-instability simulations at Hill density and beyond to demonstrate that planetesimal formation is not completed when pebble accumulations exceed the local Hill density. We find that Hill density is not a sufficient criterion for further gravitational collapse of a pebble cloud into a planetesimal, but that additionally the accumulated mass has to be large enough to overcome turbulent diffusion. A Toomre analysis of the system indicates that linear self-gravity modes play no role on the scale of our numerical simulation. We nevertheless find that self-gravity, by vertically contracting the pebble layer, increases the strength of turbulence, which is either an indication of Kelvin–Helmholtz instability or a boost of the streaming instability. We furthermore determine the Bonnor–Ebert central density to which a pebble cloud of a given mass has to be compressed before it would be able to continue contraction against internal diffusion. As the equivalent “solid body” size of the pebble cloud 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 one of 10 km for the same level of turbulent diffusion. This can explain the lack of small bodies in the solar system and predicts small objects will form at large pebble-to-gas ratios, so either in the outskirts of the solar nebula or at late times of generally reduced gas mass.