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abstract:

The spatial distribution of dust in protoplanetary disks plays a key role in dust evolution and planetesimal formation. The vertical shear instability (VSI) is a potential mechanism for driving turbulence in the outer disk, affecting dust diffusion and settling. Our study presents a semi-analytic model that determines the vertical dust distribution and VSI-driven turbulence strength in a self-consistent manner. Using an empirical formula for the vertical diffusion coefficient based on recent hydrodynamical simulations, we explore equilibrium dust profiles where turbulent diffusion is balanced by settling. We find that for small grains, a stable equilibrium dust distribution exists, allowing VSI-driven turbulence to be sustained at alpha_z ~10^{-3}, where alpha_z is the dimensionless vertical diffusion coefficient. However, for larger grains, this equilibrium solution vanishes, leading to runaway settling, potentially explaining the highly settled dust rings observed in some disks.