Using collisions of AGN outflows with ICM shocks as dynamical probes

In this paper, we lay out a simple set of relationships connecting the dynamics of fast plasma jets to the dynamical state of their ambient media. The objective is to provide a tool kit that can be used to connect the morphologies of radio active galactic nuclei (AGNs) in galaxy clusters to the dynamical state of the local intracluster medium (ICM). The formalism is intended to apply to either relativistic or non-relativistic jets. Special attention is paid to interactions involving ICM shocks, although the results can be applied more broadly. Our formalism emphasizes the importance of the relative Mach number of the impacting ICM flow and the internal Mach number of the AGN jet in determining how the AGN outflows evolve.