  The Chandra X-ray Observatory is finding a surprisingly large number of
cavities in the X-ray emitting intracluster medium, produced by the release of
radio plasma from active galactic nuclei. In this Letter, we present simple
analytic formulae for the evolution of the X-ray deficit and for the radio
spectrum of a buoyantly rising bubble. The aim of this work is to provide a
theoretical framework for the planning and the analysis of X-ray and radio
observations of galaxy clusters. We show that the cluster volume tested for the
presence of cavities by X-ray observations is a strongly rising function of the
sensitivity.

Astrophysics