Long Term Evolution of Magnetized Bubbles in Galaxy Clusters

We have performed nonlinear ideal magnetohydrodynamic simulations of the long term evolution of a magnetized low-density ``bubble" plasma formed by a radio galaxy in a stratified cluster medium. It is found that about 3.5\% of the initial magnetic energy remains in the bubble after $\sim 8 \times 10^{9}$~years, and the initial magnetic bubble expansion is adiabatic. The bubble can survive for at least $8 \times 10^9$~years due to the stabilizing effect of the bubble magnetic field on Rayleigh-Taylor and Kelvin-Holmholtz instabilities, possibly accounting for ``ghost cavities" as observed in Perseus-A\@. A filament structure spanning about 500~kpc is formed along the path of bubble motion. The mean value of the magnetic field inside this structure is $\sim 0.57$~$\mu$G at $\sim8\times10^9$~years. Finally, the initial bubble momentum and rotation have limited influence on the long term evolution of the bubble.