Vortex formation in protoplanetary discs induced by the vertical shear instability

Abstract

We present the results of 2D and 3D hydrodynamic simulations of idealized protoplanetary discs that examine the formation and evolution of vortices by the vertical shear instability (VSI). In agreement with recent work, we find that discs with radially decreasing temperature profiles and short thermal relaxation time-scales, are subject to the axisymmetric VSI. In three dimensions, the resulting velocity perturbations give rise to quasi-axisymmetric potential vorticity perturbations that break up into discrete vortices, in a manner that is reminiscent of the Rossby wave instability. Discs with very short thermal evolution time-scales (i.e. τ ≤ 0.1 local orbit periods) develop strong vorticity perturbations that roll up into vortices that have small aspect ratios (χ ≤ 2) and short lifetimes (∼ a few orbits). Longer thermal time-scales give rise to vortices with larger aspect ratios (6 ≤ χ ≤ 10), and lifetimes that depend on the entropy gradient. A steeply decreasing entropy profile leads to vortex lifetimes that exceed the simulation run times of hundreds of orbital periods. Vortex lifetimes in discs with positive or weakly decreasing entropy profiles are much shorter, being 10s of orbits at most, suggesting that the subcritical baroclinic instability plays an important role in sustaining vortices against destruction through the elliptical instability. Applied to the outer regions of protoplanetary discs, where the VSI is most likely to occur, our results suggest that vortices formed by the VSI are likely to be short-lived structures.