Dust settling against hydrodynamic turbulence in protoplanetary discs

Enhancing the local dust-to-gas ratio in protoplanetary discs is a necessary first step to planetesimal formation. In laminar discs, dust settling is an efficient mechanism to raise the dust-to-gas ratio at the disc mid-plane. However, turbulence, if present, can stir and lift dust particles, which ultimately hinders planetesimal formation. In this work, we study dust settling in protoplanetary discs with hydrodynamic turbulence sustained by the vertical shear instability. We perform axisymmetric numerical simulations to investigate the effect of turbulence, particle size, and solid abundance or metallicity on dust settling. We highlight the positive role of drag forces exerted on to the gas by the dust for settling to overcome the vertical shear instability. In typical disc models we find particles with a Stokes number ∼10^-3 can sediment to ≲ 10 per cent of the gas scaleheight, provided that Σ_d/Σ_g ≳ 0.02-0.05, where Σ_d,g are the surface densities in dust and gas, respectively. This coincides with the metallicity condition for small particles to undergo clumping via the streaming instability. Supersolar metallicities, at least locally, are thus required for a self-consistent picture of planetesimal formation. Our results also imply that dust rings observed in protoplanetary discs should have smaller scaleheights than dust gaps, provided that the metallicity contrast between rings and gaps exceed the corresponding contrast in gas density.