High Resolution Parameter Study of the Vertical Shear Instability

TL;DR

This study conducts high-resolution 3D simulations of the Vertical Shear Instability in protoplanetary disks, revealing how turbulence levels depend on disk parameters and showing vortex formation that impacts planetesimal development.

Contribution

It provides a detailed parameter study of VSI, demonstrating the dependence of turbulence on disk aspect ratio and explaining discrepancies in previous turbulence measurements.

Findings

Stress-to-pressure ratio scales with disk aspect ratio as α∝h^{2.6}

Large-scale vortices form consistently across parameters

Vortices have aspect ratio ~10 and radial width ~1.5 H

Abstract

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 $\alpha$. 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 2$\pi$ 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 \review{strong} scaling of $\alpha\propto h^{2.6}$, in contrast to the traditional $\alpha$ model, where viscosity scales as $\nu \propto \alpha h^2$ with a constant $\alpha$. We also observe consistent formation of large scale vortices across all investigated parameters. The vortices show uniformly aspect ratios of $\chi \approx 10$ 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 radiation hydrodynamics models, and show long-term evolution effects of the VSI that could aide in the formation of planetesimals.