Bubbles in planetary nebulae and clusters of galaxies: Instabilities at bubble' fronts

I study the stability of off-center low-density more or less spherical (fat) bubbles in clusters of galaxies and in planetary nebulae (PNs) to Rayleigh-Taylor (RT) instability. As the bubble expands and decelerates, the interface between the low-density bubble's interior and the dense shell formed from the accreted ambient medium is RT-stable. If, however, in a specific direction the density decreases such that this segment is accelerated by the pressure inside the bubble, then this accelerated region is RT-unstable. The outermost region, relative to the center of the system, is the most likely to become unstable because there the density gradient is the steepest. Using simple analytical analysis, I find that off-center fat bubbles in PNs are much less stable than in clusters. In PNs bubbles become unstable when they are very small relative to their distance from the center; they can be stabilized somewhat if the mass loss rate from the stellar progenitor decreases for a time, such that the negative density gradient is much shallower. In clusters fat bubbles become unstable when their size is comparable to their distance from the center. I discuss some implications of this instability in clusters and in PNs.