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Abstract

Turbulence in protoplanetary disks affects dust evolution and planetesimal formation. The vertical shear instability (VSI) is one of the candidate turbulence-driving mechanisms in the outer disk region. Since the VSI requires rapid gas cooling, dust grains in disks can influence and potentially control VSI-driven turbulence. However, VSI-driven turbulence has strong vertical motion, causing vertical dust diffusion. As a result, it remains unclear how turbulent structures and dust distributions form. We aim to clarify whether the VSI can achieve a quasi-steady dust profile under cooling rate evolution associated with turbulently diffusing dust. We also elucidate the dependence of the dust size and dust-to-gas mass ratio on the realization and persistence of the equilibrium state. We perform global two-dimensional hydrodynamical simulations of an axisymmetric disk to investigate how the VSI drives turbulence and maintains a balance between dust settling and diffusion. These simulations account for the dynamic interplay between dust distribution, cooling rates, and turbulence. We find that VSI mixing, dust settling, and local cooling reach an equilibrium, forming a thick dust layer with a dimensionless vertical mixing coefficient of approximately 10^{-3}. The ability of the VSI to sustain this state also depends on the dust size and dust-to-gas mass ratio. Larger grains or lower mass ratios weaken turbulence, leading to dust settling. The condition of equilibrium state existence is consistent with the prediction of the semi-analytic model presented by Fukuhara & Okuzumi (2024). Our results indicate that efficient turbulent dust mixing and efficient cooling can occur simultaneously. They also imply that turbulence in VSI-dominated disks has different intensity levels depending on the grain size. This suggests that the efficiency of dust growth can depend on the VSI in protoplanetary disks.