Vertical Shear Instability in Thermally-Stratified Protoplanetary Disks: I. A Linear Stability Analysis

TL;DR

This paper conducts a linear stability analysis of the vertical shear instability in thermally stratified protoplanetary disks, revealing the characteristics and growth behaviors of surface and body modes influenced by thermal stratification.

Contribution

It provides a semi-global linear stability framework distinguishing surface and body modes, highlighting the effects of thermal stratification on VSI growth rates and mode dominance.

Findings

Surface modes grow rapidly with high radial wave number

Body modes grow faster at lower radial wave numbers

Thermal stratification enhances VSI growth rates

Abstract

Vertical shear instability (VSI), driven by a vertical gradient of rotational angular velocity, is a promising source of turbulence in protoplanetary disks. We examine the semi-global stability of thermally stratified disks and find that the VSI consists of surface and body modes: surface modes are confined to regions of strong shear, while body modes extend perturbations across the disk, consistent with the previous findings. In thermally stratified disks, surface modes bifurcate into two branches. The branch associated with the strongest shear at mid-height exhibits a higher growth rate compared to the branch near the surfaces. Surface modes generally grow rapidly and require a high radial wave number $k_R$, whereas body mode growth rates increase as $k_R$ decreases. Thermal stratification enhances the growth rates of both surface and body modes and boosts VSI-driven radial kinetic energy relative to vertical energy. Our results suggest that simulations will initially favor surface modes with large $k_R$, followed by an increase in body modes with smaller $k_R$, with faster progression in more thermal stratified disks.