Vertical settling of pebbles in turbulent circumbinary discs and the in situ formation of circumbinary planets

The inner-most regions of circumbinary discs are unstable to a parametric instability whose non-linear evolution is hydrodynamical turbulence. This results in significant particle stirring, impacting on planetary growth processes such as the streaming instability or pebble accretion. In this paper, we present the results of three-dimensional, inviscid global hydrodynamical simulations of circumbinary discs with embedded particles of 1 cm size. Hydrodynamical turbulence develops in the disc, and we examine the effect of the particle back-reaction on vertical dust. We find that higher solid-to-gas ratios lead to smaller gas vertical velocity fluctuations, and therefore to smaller dust scale heights. For a metallicity $Z=0.1$, the dust scale height near the edge of the tidally-truncated cavity is $\sim 80\%$ of the gas scale height, such that growing a Ceres-mass object to a 10 $M_\oplus$ core via pebble accretion would take longer than the disc lifetime. Collision velocities for small particles are also higher than the critical velocity for fragmentation, which precludes grain growth and the possibility of forming a massive planetesimal seed for pebble accretion. At larger distances from the binary, turbulence is weak enough to enable not only efficient pebble accretion but also grain growth to sizes required to trigger the streaming instability. In these regions, an in-situ formation scenario of circumbinary planets involving the streaming instability to form a massive planetesimal followed by pebble accretion onto this core is viable. In that case, planetary migration has to be invoked to explain the presence of circumbinary planets at their observed locations.