Thermal instabilities in accretion disks II: Numerical Experiments for the Goldreich-Schubert-Fricke Instability and the Convective Overstability in disks around young stars

TL;DR

This paper uses numerical experiments to analyze the growth and behavior of thermal instabilities, specifically GSF and COS, in stratified rotating disks around young stars, revealing their growth rates, saturation, and flow patterns.

Contribution

It demonstrates the numerical reproduction of analytic growth rates for GSF and COS instabilities in disks, and explores their independent growth, saturation, and flow dynamics in a stratified rotating disk model.

Findings

GSF modes grow faster than COS modes.

Near the midplane, GSF modes saturate while COS modes dominate.

Away from the midplane, GSF saturates with eddy formation.

Abstract

The linear stability analysis of a stratified rotating fluid (see paper I) showed that disks with a baroclinic stratification under the influence of thermal relaxation will become unstable to thermal instabilities. One instability is the Goldreich-Schubert-Fricke instability (GSF), which is the local version of the Vertical Shear Instability (VSI) and the other is a thermal overstability, the Convective Overstability (COS). In the present paper we reproduce the analytic predicted growth rates for both instabilities in numerical experiments of small axisymmetric sections of vertically isothermal disks with a radial temperature gradient, especially for cooling times longer than the critical cooling time for VSI. In this cooling time regime our simulations reveal the simultaneous and independent growth of both modes: COS and GSF. We consistently observe that GSF modes exhibit a faster growth rate compared to COS modes. Near the midplane, GSF modes eventually stop growing, while COS modes continue to grow and ultimately dominate the flow pattern. Away from the midplane, we find GSF modes to saturate, when bands of constant angular momentum have formed. In these bands we observe the formation and growth of eddies driven by the baroclinic term, further enhancing the velocity perturbations. In geophysics this effect is known as horizontal convection or sea-breeze instability. Three-dimensional simulations will have to show whether similar effects will occur when axisymmetry is not enforced. Our local simulations help to reveal the numerical resolution requirements to observe thermal instabilities in global simulations of disks around young stars.