Radiation hydrodynamical turbulence in protoplanetary disks: Numerical models and observational constraints

Planets are born in protostellar disks, which are now observed with enough resolution to address questions about internal gas flows. Magnetic forces are possibly drivers of the flows, but ionization state estimates suggest that much of the gas mass decouples from magnetic fields. Thus, hydrodynamical instabilities could play a major role. We investigate disk dynamics under conditions typical for a T Tauri system, using global 3D radiation-hydrodynamics simulations with embedded particles and a resolution of 70 cells per scale height. Stellar irradiation heating is included with realistic dust opacities. The disk starts in joint radiative balance and hydrostatic equilibrium. The vertical shear instability (VSI) develops into turbulence that persists up to at least 1600 inner orbits (143 outer orbits). Turbulent speeds are a few percent of the local sound speed at the midplane, increasing to 20%, or 100 m s(-1), in the corona. These are consistent with recent upper limits on turbulent speeds from optically thin and thick molecular line observations of TW Hya and HD 163296. The predominantly vertical motions induced by the VSI efficiently lift particles upward. Grains 0.1 and 1 mm in size achieve scale heights greater than expected in isotropic turbulence. We conclude that while kinematic constraints from molecular line emission do not directly discriminate between magnetic and nonmagnetic disk models, the small dust scale heights measured in HL Tau and HD 163296 favor turbulent magnetic models, which reach lower ratios of the vertical kinetic energy density to the accretion stress.European Research Council under the European Union's Seventh Framework Programme (FP7)/ERC, 258729 / NASA Exoplanet Research program, 14XRP14_20153, 16-XRP16 20065 / STFC, ST/P000592/1, ST/M001202/1/ CONICYT through FONDECYT, 3170657 / Millennium Science Initiative (Chilean Ministry of Economy), RC13007 / Space Telescope Science Institute, HST-AR-14572 / National Science Foundation, NSF PHY-112591