Rossby wave instability in locally isothermal and polytropic disks: three-dimensional linear calculations

TL;DR

This paper presents three-dimensional linear calculations confirming the Rossby wave instability (RWI) in stratified disks, showing it is mainly a two-dimensional phenomenon with vertical motions being perturbative.

Contribution

The study extends RWI analysis to 3D disks with different equations of state, revealing that 3D effects are minor and primarily perturbative to the dominant 2D instability.

Findings

RWI operates in 3D with similar growth rates to 2D.

Vertical motions are perturbative, not dominant.

Vortex centers in polytropic disks have upward vertical velocities.

Abstract

Numerical calculations of the linear Rossby wave instability (RWI) in global three-dimensional (3D) disks are presented. The linearized fluid equations are solved for vertically stratified, radially structured disks with either a locally isothermal or polytropic equation of state, by decomposing the vertical dependence of the perturbed hydrodynamic quantities into Hermite and Gegenbauer polynomials, respectively. It is confirmed that the RWI operates in 3D. For perturbations with vertical dependence assumed above, there is little difference in growth rates between 3D and two-dimensional (2D) calculations. Comparison between 2D and 3D solutions of this type suggest the RWI is predominantly a 2D instability and that three-dimensional effects, such as vertical motion, to be interpreted as a perturbative consequence of the dominant 2D flow. The vertical flow around co-rotation, where vortex-formation is expected, is examined. In locally isothermal disks the expected vortex center remains in approximate vertical hydrostatic equilibrium. For polytropic disks the vortex center has positive vertical velocity, whose magnitude increases with decreasing polytropic index $n$.