Evolution of initially localized perturbations in stratified ionized disks

TL;DR

This paper analyzes how localized perturbations evolve in stratified, magnetized disks, showing stability depends on disk thickness and that localized disturbances grow more slowly than eigenmode predictions.

Contribution

It provides an explicit solution to the initial value problem for localized perturbations in stratified disks using WKB approximation and numerical verification.

Findings

Localized perturbations remain confined within the disk.

Thinner disks are stable; thicker disks exhibit unstable modes.

Growth time of perturbations is longer than inverse eigenmode growth rates.

Abstract

A detailed solution of an initial value problem of a vertically localized initial perturbation in rotating magnetized vertically stratified disk is presented. The appropriate linearized MHD equations are solved by employing the WKB approximation and the results are verified numerically. The eigenfrequencies as well as eigenfunctions are explicitly obtained. It is demonstrated that the initial perturbation remains confined within the disk. It is further shown that thin enough disks are stable but as their thickness grows increasing number of unstable modes participate in the solution of the initial value problem. However it is demonstrated that due to the localization of the initial perturbation the growth time of the instability is significantly longer than the calculated inverse growth rate of the individual unstable eigenfunctions.