Gas and Dust Dynamics in Starlight-heated Protoplanetary Disks

Theoretical models of the ionization state in protoplanetary disks suggest the existence of large areas with low ionization and weak coupling between the gas and magnetic fields. In this regime hydrodynamical instabilities may become important. In this work we investigate the gas and dust structure and dynamics for a typical T Tauri system under the influence of the vertical shear instability (VSI). We use global 3D radiation hydrodynamics simulations covering all 360° of azimuth with embedded particles of 0.1 and 1 mm size, evolved for 400 orbits. Stellar irradiation heating is included with opacities for 0.1–10 μm sized dust. Saturated VSI turbulence produces a stress-to-pressure ratio of $\alpha \simeq {10}^{-4}$. The value of α is lowest within 30 au of the star, where thermal relaxation is slower relative to the orbital period and approaches the rate below which VSI is cut off. The rise in α from 20 to 30 au causes a dip in the surface density near 35 au, leading to Rossby wave instability and the generation of a stationary, long-lived vortex spanning about 4 au in radius and 40 au in azimuth. Our results confirm previous findings that millimeter-sized grains are strongly vertically mixed by the VSI. The scale height aspect ratio for 1 mm grains is determined to be 0.037, much higher than the value H/r = 0.007 obtained from millimeter-wave observations of the HL Tau system. The measured aspect ratio is better fit by nonideal MHD models. In our VSI turbulence model, the millimeter grains drift radially inwards and many are trapped and concentrated inside the vortex. The turbulence induces a velocity dispersion of ∼12 m s⁻¹ for the millimeter grains, indicating that grain–grain collisions could lead to fragmentation.