Feedback by active galactic nuclei (AGN) is frequently invoked to explain the
cut-off of the galaxy luminosity function at the bright end and the absence of
cooling flows in galaxy clusters. Meanwhile, there are recent observations of
shock fronts around radio-loud AGN. Using realistic 3D simulations of jets in a
galaxy cluster, we address the question what fraction of the energy of active
galactic nuclei is dissipated in shocks. We find that weak shocks that
encompass the AGN have Mach numbers of 1.1-1.2 and dissipate at least 2% of the
mechanical luminosity of the AGN. In a realistic cluster medium, even a
continuous jet can lead to multiple shock structures, which may lead to an
overestimate of the AGN duty cycles inferred from the spatial distribution of
waves.Comment: accepted by MNRAS Letter