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

Abstract

Abstract 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. VSI drives turbulence with strong vertical motions, which could regulate 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 these potentially stabilizing effects of dust evolution on the VSI based on 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 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 altitudes. In our default disk model with 0.01 solar masses, dust growth from 10 μm 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 the high degree of dust settling observed in the disk around HL Tau.