On the nature of the magnetic Rayleigh-Taylor instability in Astrophysical Plasma: The case of uniform magnetic field strength

TL;DR

This paper critically examines the growth rates of the magnetic Rayleigh-Taylor instability in astrophysical plasmas, revealing that common estimation methods are flawed and emphasizing the importance of magnetic shear in interpreting observations.

Contribution

It provides a new analysis of the instability's growth rates, clarifies misconceptions about the most unstable modes, and extends the analysis to sheared magnetic fields.

Findings

Growth rate $\sigma^2$ is independent of magnetic field strength.

Most unstable modes are associated with small scales.

Magnetic shear significantly affects instability behavior.

Abstract

The magnetic Rayleigh-Taylor instability has been shown to play a key role in many astrophysical systems. The equation for the growth rate of this instability in the incompressible limit, and the most-unstable mode that can be derived from it, are often used to estimate the strength of the magnetic field that is associated with the observed dynamics. However, there are some issues with the interpretations given. Here we show that the class of most unstable modes $k_u$ for a given $\theta$, the class of modes often used to estimate the strength of the magnetic field from observations, for the system leads to the instability growing as $\sigma^2=1/2 A g k_u$, a growth rate which is independent of the strength of the magnetic field and which highlights that small scales are preferred by the system, but not does not give the fastest growing mode for that given $k$. We also highlight that outside of the interchange ($\mathbf{k}\cdot\mathbf{B}=0$) and undular ($\mathbf{k}$ parallel to $\mathbf{B}$) modes, all the other modes have a perturbation pair of the same wavenumber and growth rate that when excited in the linear regime can result in an interference pattern that gives field aligned filamentary structure often seen in 3D simulations. The analysis was extended to a sheared magnetic field, where it was found that it was possible to extend the results for a non-sheared field to this case. We suggest that without magnetic shear it is too simplistic to be used to infer magnetic field strengths in astrophysical systems.