Bubble wrap for bullets: The stability imparted by a thin magnetic layer

There has been significant recent work by several authors 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 in a bubble rising from the cluster center. 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 apply 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. We consider here the stability imparted by a thin magnetized layer. We investigate this question in the most favorable case, that of two dimensions, where the magnetic field can most strongly affect the stability. We find that in this case such a layer can have a significant stabilizing effect even on modes with wavelengths lambda much larger than the thickness of the layer l. To stabilize modes with lambda approximate to 10l requires only that the Alfven speed in the magnetized layer is comparable to or greater than 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- TaylorYlike instability. We confirm our calculations with two- dimensional numerical experiments using the Athena code.