Bubble-Wrap for Bullets: The Stability Imparted By A Thin Magnetic Layer

TL;DR

This paper investigates how a thin magnetic layer can stabilize large-scale instabilities in astrophysical plasma interfaces, such as cluster bubbles, by analyzing the conditions under which magnetic fields suppress Kelvin-Helmholtz and Rayleigh-Taylor instabilities.

Contribution

It demonstrates that a thin magnetized layer can significantly stabilize large-scale modes, even when its thickness is much smaller than the wavelength, through analytical and numerical methods.

Findings

Magnetic layers can stabilize modes ten times larger than their thickness.

Alfvén speed comparable to destabilizing velocities is sufficient for stabilization.

Numerical experiments confirm the analytical stability criteria.

Abstract

There has been significant recent work which examines a situation where a thin magnetic layer is `draped' over a core merging into a larger cluster; the same process also appears to be at work at a bubble rising from the cluster centre. Such a thin magnetic layer could thermally isolate the core from the cluster medium, but only if the same shear process which generates the layer does not later disrupt it. On the other hand, if the magnetized layer can stabilize against the shear instabilities, then the magnetic layer can have the additional dynamical effect of reducing the shear-driven mixing of the core's material during the merger process. These arguments could equally well to underdense cluster bubbles, which would be even more prone to disruption. While it is well known that magnetic fields can suppress instabilities, it is less clear that a thin layer can suppress instabilities on scales significantly larger than its thickness. Here we consider the stability imparted by a thin magnetized layer. Such a layer can have a significant stabilizing effect even on modes with wavelengths much larger than the thickness of the layer l; to stabilize modes ten times larger requires only that the Alfv\'en speed in the magnetized layer is comparable to the relevant destabilizing velocity -- the shear velocity in the case of pure Kelvin-Helmholtz like instability, or a typical buoyancy velocity in the case of pure Rayleigh-Taylor. We confirm our calculations with two-dimensional numerical experiments using the Athena code.