On the Stability of Elliptical Vortices in Accretion Discs

TL;DR

This paper investigates the 3D stability of elliptical vortices in accretion discs, revealing that they are generally unstable due to resonance effects, with implications for their long-term existence in astrophysical environments.

Contribution

It provides a linear stability analysis and nonlinear simulations demonstrating the inherent instability of elliptical vortices in accretion discs across various aspect ratios.

Findings

Most anticyclonic vortices are unstable due to resonance mechanisms.

Vertical stratification reduces growth rates of instabilities.

Elliptical vortices are always unstable regardless of aspect ratio.

Abstract

(Abriged) The existence of large-scale and long-lived 2D vortices in accretion discs has been debated for more than a decade. They appear spontaneously in several 2D disc simulations and they are known to accelerate planetesimal formation through a dust trapping process. However, the issue of the stability of these structures to the imposition of 3D disturbances is still not fully understood, and it casts doubts on their long term survival. Aim: We present new results on the 3D stability of elliptical vortices embedded in accretion discs, based on a linear analysis and several non-linear simulations. Methods: We derive the linearised equations governing the 3D perturbations in the core of an elliptical vortex, and we show that they can be reduced to a Floquet problem. We solve this problem numerically in the astrophysical regime and we present several analytical limits for which the mechanism responsible for the instability can be explained. Finally, we compare the results of the linear analysis to some high resolution simulations. Results: We show that most anticyclonic vortices are unstable due to a resonance between the turnover time and the local epicyclic oscillation period. In addition, we demonstrate that a strong vertical stratification does not create any additional stable domain of aspect ratio, but it significantly reduces growth rates for relatively weak (and therefore elongated) vortices. Conclusions: Elliptical vortices are always unstable, whatever the horizontal or vertical aspect-ratio is. The instability can however be weak and is often found at small scales, making it difficult to detect in low-order finite-difference simulations.