X-ray signatures of evolving radio galaxies

We present a simple model for an evolving radio galaxy as it expands into the hot, X-ray-emitting interstellar medium (ISM) of its host galaxy or similarly into the hot intracluster medium (TCM) of its host cluster. We solve the governing equations numerically on a grid of model parameters in order to present simple analytical tools for X-ray observations of the shocked shell that is pushed out by the cocoon and the associated cavity in the cluster emission. We apply these tools to the well-known example of Perseus A to show that its time-averaged kinetic luminosity probably exceeds 10(46) ergs s(-1), much larger than the estimated current power. We show how future observations can be used to extract useful source parameters such as the average kinetic power and the source age, and discuss detectability of sources at various stages of their lives.