Energetics of X-ray cavities and radio lobes in galaxy clusters

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, in which cavities are formed by injecting ultrahot but nonrelativistic gas, cavity formation contributes thermal energy that may offset radiative losses in the gas, thereby helping to solve the cooling flow problem. Contrary to these results, we find that X-ray cavities formed solely from cosmic rays have a global cooling effect. Most cosmic rays in our cavity evolutions do not move beyond the cooling radius, and, as cluster gas is displaced by cosmic rays, it expands and globally cools. As cosmic rays diffuse away from the cavities, the nearby gas becomes buoyant, resulting in a significant outward mass transfer within the cooling radius, carrying relatively low entropy gas containing cosmic rays to outer regions in the cluster, where it remains for times exceeding the local cooling time in the hot gas. This postcavity mass outflow due to cosmic-ray buoyancy may contribute significantly toward solving the cooling flow problem. Cavities formed with cosmic rays are more stable and more long-lived than those formed from ultrahot gas. The product of pressure and volume, PV, varies with time and is a very inaccurate measure of the total energy released. We describe the energetics, size, and buoyant rise of X-ray cavities in detail, showing how each depends on the rate of cosmic-ray diffusion.