The inviscid (control) case

Figure 2: Mid-plane density slices (upper panels) and simulated X-ray surface brightness maps (lower-panels) for the inviscid control case (Run 1) shown at three times; $t=1$ (left panels), $t=2$ (middle panels) and $t=4$ (right panels). Arrows indicating fluid velocity have been superposed on the density slices. Note how the bubble is rapidly destroyed by the combined action of RT and KH instabilities. At no time would one observe a flattened detached ghost cavity as we see in Per-A.

Initially we discuss the results from our zero-viscosity ($\mu=0$) simulations. These will serve as a crucial comparison for understanding the viscous simulations that we shall discuss next. Our qualitative simulation setup and results are very similar to those previously obtained by Churazov et al. (2001), Brüggen & Kaiser (2001, 2002), Brüggen et al. (2002) and Robinson et al. (2003). Of course, it is important to realize that even in this $\mu=0$ cases, the action of numerical diffusion keeps the effective Reynolds number finite. We determine the effective Reynolds number of these ``zero-viscosity'' cases by performing additional simulations with small values of $\mu$ and visually comparing the smallest scale structures resulting from the $\mu=0$ Run. This exercise suggests that the effective Reynolds numbers of our $\mu=0$ simulations are in the range 2000-5000.

The initially static bubble starts accelerating due to buoyancy. As noted by several previous authors, RT instabilities induce circulatory motions within the bubbles, that then induce ``secondary'' KH instabilities along the contact discontinuity between the low-density bubble and ambient ICM. These KH instabilities are primarily responsible for shredding the bubble within 2-3 time units (i.e. $\sim 5$ sound crossing times of the bubble; top-panels of Fig. 2). Due to the shredding of the bubble, one never observes a detached and flattened but otherwise intact structure such as we appear to see in the ghost cavity of Perseus-A (see bottom panels of Fig. 2).

To further facilitate comparison with observations, we produce simulated X-ray surface brightness maps. In detail, we set the local X-ray emissivity to be proportional to $\rho^2 T^{1/2}$ and integrate along lines of sight through the simulation volume in order to build up a 2-dimensional map of X-ray surface brightness. For definiteness, we show surface brightness maps for the case in which the observer is viewing along the $y$-direction (i.e., the line joining the center of the ICM atmosphere and the center of the initial bubble is perpendicular to the observers line of sight). From these maps, it can be seen that the observed cavity never has the appearance of the Perseus-A ghost cavity (Fig. 2; lower panels).

In addition to morphological problems, we note that zero-viscosity models does not reproduce the H$\alpha$-deduced flow pattern. At early times, while the buoyant bubble is still reasonably intact, we never see a circulatory flow pattern below the bubble. At late times, the buoyant bubble loses integrity and induces complex and disorganized motions in the ICM.