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 1mm size, evolved for 400 orbits. Stellar irradiation heating is included with opacities for 0.1-to 10-µm-sized dust. Saturated VSI turbulence produces a stress-to-pressure ratio of α 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 mm size grains are strongly vertically mixed by the VSI. The scale height aspect ratio for 1mm 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 non-ideal MHD models. In our VSI turbulence model, the mm grains drift radially inwards and many are trapped and concentrated inside the vortex. The turbulence induces a velocity dispersion of ∼ 12 m/s for the mm grains, indicating that grain-grain collisions could lead to fragmentation.

Several protoplanetary disks observed by ALMA show dust concentrations consistent with particle trapping in giant vortices. The formation and survival of vortices is of major importance for planet formation, because vortices act as particle traps and are therefore preferred locations of planetesimal formation. Recent studies showed that the vertical shear instability (VSI) is capable of generating turbulence and small vortices in protoplanetary disks that have the proper radial and vertical stratification and thermally relax on sufficiently short time scales. But the effect of the azimuthal extend of the disk is often neglected as the disks azimuth is limited to ∆φ ≤ π/2. We aim to investigate the influence of the azimuthal extent of the disk on the longterm evolution of a protoplanetary disk and the possibility of large vortices forming. To this end, we perform 3-dimensional simulations for up to 1000 local orbits using different values of ∆φ = π/2 to 2π for VSI in disks with a prescribed radial density and temperature gradient cooling on short timescales. We find the VSI capable of forming large vortices which can exist at least several hundred orbits in simulations covering a disk with ∆φ ≥ π. This suggests the VSI to be capable to form vortices or at least to trigger vortex formation via a secondary instability, e.g. Rossby Wave Instability or Kelvin Helmholtz Instability.

Theoretical models of protoplanetary disks have shown the Vertical Shear Instability (VSI) to be a prime candidate to explain turbulence in the dead zone of the disk. However, simulations of the VSI have yet to show consistent levels of key disk turbulence parameters like the stress-to-pressure ratio α. We aim to reconcile these different values by performing a parameter study on the VSI with focus on the disk density gradient p and aspect ratio h ≔ H/R. We use full 2π 3D simulations of the disk for chosen set of both parameters. All simulations are evolved for 1000 reference orbits, at a resolution of 18 cells per h. We find that the saturated stress-to-pressure ratio in our simulations is dependent on the disk aspect ratio with a strong scaling of α∝h2.6, in contrast to the traditional α model, where viscosity scales as ν∝αh2 with a constant α. We also observe consistent formation of large scale vortices across all investigated parameters. The vortices show uniformly aspect ratios of χ ≈ 10 and radial widths of approximately 1.5 H. With our findings we can reconcile the different values reported for the stress-to-pressure ratio from both isothermal and full radiation hydrodynamics models, and show long-term evolution effects of the VSI that could aide in the formation of planetesimals.

A certain appeal to the alpha model for turbulence and related viscosity in accretion disks was that one scales the Reynolds stresses simply on the thermal pressure, assuming that turbulence driven by a certain mechanism will attain a characteristic Mach number in its velocity fluctuations. Besides the notion that there are different mechanism driving turbulence and angular momentum transport in a disk, we also find that within a single instability mechanism, here the Vertical Shear Instability, stresses do not linearly scale with thermal pressure. Here we demonstrate in numerical simulations the effect of the gas temperature gradient and the thermal relaxation time on the average stresses generated in the non-linear stage of the instability. We find that the stresses scale with the square of the exponent of the radial temperature profile at least for a range of dlog T/dlog R = [ − 0.5, −1], beyond which the pressure scale height varies too much over the simulation domain, to provide clear results. Stresses are also dependent on thermal relaxation times, provided they are longer than 10−3 orbital periods. The strong dependence of viscous transport of angular momentum on the local conditions in the disk (especially temperature, temperature gradient, and surface density/optical depth) challenges the ideas of viscosity leading to smooth density distributions, opening a route for structure (ring) formation and time variable mass accretion.