Dynamics and stability of magnetized AGN-blown bubbles in clusters of galaxies

We perform MHD simulations of AGN-blown bubbles in the Intercluster Medium (ICM) containing large-scale coherent magnetic fields. We assume that bubbles, created by the intermittent jets from Active Galactic Nuclei, quickly relax to the Woltjer-Taylor spheromak-like state, with internal plasma beta-parameter $\sim 1$. We demonstrate that such bubbles rising through hydrostatically-stratified atmosphere are magnetically stabilized against fluid interface instabilities, remaining coherent for a long time. Typical velocity is $v /c_s \sim \sqrt{R/H} \leq 1$ ($c_s$ is sound speed, $R$ is the bubble size, $H$ is the scale height). Current-driven instabilities (internal kinks) lead to bubble's tilting, but develop on long time scales, and remain unimportant, leading to minor modifications of the internal structure. Our results explain apparent long-term stability of ICM cavities. Subsonically rising stable bubbles dissipate in their wake approximately the energy initially injected by the jet, and may efficiently reheat the clusters cores in a ``gentle'' way.