Three-dimensional Magnetohydrodynamic Simulations of Buoyant Bubbles in
  Galaxy Clusters
  We report results of 3D MHD simulations of the dynamics of buoyant bubbles in
magnetized galaxy cluster media. The simulations are three dimensional
extensions of two dimensional calculations reported by Jones & De Young (2005).
Initially spherical bubbles and briefly inflated spherical bubbles all with
radii a few times smaller than the intracluster medium (ICM) scale height were
followed as they rose through several ICM scale heights. Such bubbles quickly
evolve into a toroidal form that, in the absence of magnetic influences, is
stable against fragmentation in our simulations. This ring formation results
from (commonly used) initial conditions that cause ICM material below the
bubbles to drive upwards through the bubble, creating a vortex ring; that is,
hydrostatic bubbles develop into "smoke rings", if they are initially not very
much smaller or very much larger than the ICM scale height. Even modest ICM
magnetic fields with beta = P_gas/P_mag ~ 10^3 can influence the dynamics of
the bubbles, provided the fields are not tangled on scales comparable to or
smaller than the size of the bubbles. Quasi-uniform, horizontal fields with
initial beta ~ 10^2 bifurcated our bubbles before they rose more than about a
scale height of the ICM, and substantially weaker fields produced clear
distortions. On the other hand, tangled magnetic fields with similar, modest
strengths are generally less easily amplified by the bubble motions and are
thus less influential in bubble evolution. Inclusion of a comparably strong,
tangled magnetic field inside the initial bubbles had little effect on our
bubble evolution, since those fields were quickly diminished through expansion
of the bubble and reconnection of the initial field.
