On the Energy Coupling Efficiency of AGN Outbursts in Galaxy Clusters
  Active galactic nucleus (AGN) jets are believed to be important in solving
the cooling flow problem in the intracluster medium (ICM), while the detailed
mechanism is still in debate. Here we present a systematic study on the energy
coupling efficiency $\eta_{\rm cp}$, the fraction of AGN jet energy transferred
to the ICM. We first estimate the values of $\eta_{\rm cp}$ analytically in two
extreme cases, which are further confirmed and extended with a parameter study
of spherical outbursts in a uniform medium using hydrodynamic simulations. We
find that $\eta_{\rm cp}$ increases from $\sim 0.4$ for a weak isobaric
injection to $\gtrsim 0.8$ for a powerful point injection. For any given
outburst energy, we find two characteristic outburst powers that separate these
two extreme cases. We then investigate the energy coupling efficiency of AGN
jet outbursts in a realistic ICM with hydrodynamic simulations, finding that
jet outbursts are intrinsically different from spherical outbursts. For both
powerful and weak jet outbursts, $\eta_{\rm cp}$ is typically around $0.7-0.9$,
partly due to the non-spherical nature of jet outbursts, which produce
backflows emanating from the hotspots, significantly enhancing the ejecta-ICM
interaction. While for powerful outbursts a dominant fraction of the energy
transferred from the jet to the ICM is dissipated by shocks, shock dissipation
only accounts for $\lesssim 30\%$ of the injected jet energy for weak
outbursts. While both powerful and weak outbursts could efficiently heat
cooling flows, powerful thermal-energy-dominated jets are most effective in
delaying the onset of the central cooling catastrophe.
