Vertical Shear Instability in Thermally-Stratified Protoplanetary Disks: II. Hydrodynamic Simulations and Observability

Abstract

We conduct three-dimensional hydrodynamic simulations to investigate the nonlinear outcomes and observability of vertical shear instability (VSI) in protoplanetary disks. Our models include both vertically isothermal and thermally stratified disks, with the latter representing realistic conditions featuring a hotter atmosphere above the midplane. We find that the VSI grows more rapidly and becomes stronger in thermally stratified disks due to enhanced shear, resulting in higher levels of turbulence. At saturation, the turbulence stress reaches $α_{Rϕ}\gtrsim 10^{-3}$, more than an order of magnitude stronger than the isothermal case. The saturated turbulence is more pronounced near the disk surfaces than at the midplane. On synthetic velocity residual maps, obtained by subtracting the Keplerian rotational velocity, perturbations driven by the VSI manifest as axisymmetric rings in isothermal disks and as ring segments in thermally stratified disks. The latter are visible at disk inclinations as high as $45^\circ$ in thermally stratified disks. The amplitudes of these residual velocities range from $\sim 50$ to $\sim100$ $\mathrm{m\ s}^{-1}$ at a $20^\circ$ inclination, with larger values corresponding to greater thermal stratification. The magnitude of the observed velocity residual increases with the optical depth of the tracer used, as optically thick lines probe the regions near the disk surfaces.