Kelvin-Helmholtz Instability of Counter-Rotating Discs

TL;DR

This paper investigates the linear stability of counter-rotating galactic discs, revealing a strong, primarily three-dimensional Kelvin-Helmholtz instability that causes mixing, heating, and angular momentum annihilation.

Contribution

It provides a detailed analysis of the Kelvin-Helmholtz instability in counter-rotating discs, highlighting its three-dimensional nature and nonlinear evolution effects.

Findings

Strong Kelvin-Helmholtz instability identified

Instability growth rates comparable to rotation rate

Nonlinear evolution leads to mixing and heating

Abstract

Observations of galaxies and models of accreting systems point to the occurrence of counter-rotating discs where the inner part of the disc ($r<r_0$) is co-rotating and the outer part is counter-rotating. This work analyzes the linear stability of radially separated co- and counter-rotating thin discs. The strong instability found is the supersonic Kelvin-Helmholtz instability. The growth rates are of the order of or larger than the angular rotation rate at the interface. The instability is absent if there is no vertical dependence of the perturbation. That is, the instability is essentially three-dimensional. The nonlinear evolution of the instability is predicted to lead to a mixing of the two components, strong heating of the mixed gas, and vertical expansion of the gas, and annihilation of the angular momenta of the two components. As a result the heated gas will free-fall towards the disc's center over the surface of the inner disc.