  The vertical shear instability (VSI) is a hydrodynamical instability that
requires rapid gas cooling and has been suggested to operate in outer regions
of protoplanetary disks. The VSI drives turbulence with strong vertical
motions, which could regulate the dust growth and settling. However, dust
growth and settling can regulate the VSI because dust depletion makes gas
cooling inefficient in outer disk regions that are optically thin to their own
thermal emission. In this study, we quantify this potentially stabilizing
effects of dust evolution on the VSI based on the linear analysis. We construct
a model for calculating the cooling timescale, taking into account dust growth
beyond micron sizes and size-dependent settling. Combining the model with the
linear stability analysis, we map the region where the VSI operates, which we
call the VSI zone, and estimate the maximum growth rate at each radial
position. We find that dust growth as well as settling makes the VSI zone more
confined around the midplane. This causes a decrease in the growth rate because
the vertical shear of the rotation velocity, which is the source of the
instability, is weaker at lower altitude. In our default disk model with 0.01
solar masses, dust growth from 10 micron to 1 mm causes a decrease in the
growth rate by a factor of more than 10. The suppression of VSI-driven
turbulence by dust evolution may promote further dust evolution in the outer
regions and also explain a high degree of dust settling observed in the disk
around HL Tau.
