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We perform streaming instability simulations at Hill density and beyond, todemonstrate that Planetesimal formation is not completed when pebbleaccumulations exceed the local Hill density. We find that Hill density is not asufficient criterion for further gravitational collapse of a pebble cloud intoa planetesimal, but that additionally the accumulated mass has to be largeenough to overcome turbulent diffusion. A Toomre analysis of the systemindicates that linear self-gravity modes play no role on the scale of ournumerical simulation. We nevertheless find that self-gravity, by verticallycontracting the pebble layer, increases the strength of turbulence, which iseither an indication of Kelvin Helmholtz Instability or a boost of thestreaming-instability. We furthermore determine the Bonnor-Ebert centraldensity to which a pebble cloud of given mass has to be compressed before itwould be able to continue contraction against internal diffusion. As theequivalent "solid body" size of the pebble cloud scales with the centraldensity to the power of -1/6, it is much easier to have a pebble cloud of 100km equivalent size to collapse than one of 10 km for the same level ofturbulent diffusion. This can explain the lack of small bodies in the solarsystem and predicts to have small objects formed by gravitational collapse atlarge pebble to gas ratios, in the outskirts of the solar nebula and at latetimes of generally reduced gas mass.

astrophysical journal/the astrophysical journal

Testing the Jeans, Toomre and Bonnor-Ebert concepts for planetesimal  formation: 3D streaming instability simulations of diffusion regulated  formation of planetesimals