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The vertical shear instability (VSI) is a hydrodynamical instability thatrequires rapid gas cooling and has been suggested to operate in outer regionsof protoplanetary disks. The VSI drives turbulence with strong verticalmotions, which could regulate the dust growth and settling. However, dustgrowth and settling can regulate the VSI because dust depletion makes gascooling inefficient in outer disk regions that are optically thin to their ownthermal emission. In this study, we quantify this potentially stabilizingeffects of dust evolution on the VSI based on the linear analysis. We constructa model for calculating the cooling timescale, taking into account dust growthbeyond micron sizes and size-dependent settling. Combining the model with thelinear stability analysis, we map the region where the VSI operates, which wecall the VSI zone, and estimate the maximum growth rate at each radialposition. We find that dust growth as well as settling makes the VSI zone moreconfined around the midplane. This causes a decrease in the growth rate becausethe vertical shear of the rotation velocity, which is the source of theinstability, is weaker at lower altitude. In our default disk model with 0.01solar masses, dust growth from 10 micron to 1 mm causes a decrease in thegrowth rate by a factor of more than 10. The suppression of VSI-driventurbulence by dust evolution may promote further dust evolution in the outerregions and also explain a high degree of dust settling observed in the diskaround HL Tau.

Effects of Dust Evolution on the Vertical Shear Instability in the Outer Regions of Protoplanetary Disks