  We describe the formation and evolution of X-ray cavities in the hot gas of
galaxy clusters. The cavities are formed only with relativistic cosmic rays
that eventually diffuse into the surrounding gas. We explore the evolution of
cavities formed with a wide range of cosmic ray diffusion rates. In previous
numerical simulations cavities are formed by injecting ultra-hot but
non-relativistic gas which increases the global thermal energy, offsetting
radiative losses in the gas and helping to solve the cooling flow problem.
Contrary to these results, we find that X-ray cavities formed solely by cosmic
rays have a global cooling effect. As the cluster gas is displaced by cosmic
rays, a global expansion of the cluster gas occurs with associated cooling that
exceeds the heating by shock waves as the cavity forms. Most cosmic rays in our
cavity evolutions do not move beyond the cooling radius even after 1 Gyr. The
gas density is depressed by cosmic rays, becomes buoyant, and undergoes a
significant outward mass transfer within the cooling radius, carrying cosmic
rays and relatively low entropy gas to distant regions in the cluster where it
remains for times exceeding the local cooling time in the hot gas. This
post-cavity mass outflow due to cosmic ray buoyancy may contribute toward
solving the cooling flow problem. We describe the energetics, size, stability
and buoyant rise of X-ray cavities in detail, showing how each depends on the
rate of cosmic ray diffusion.
