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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 $η_{\rm cp}$, the fraction of AGN jet energy transferred to the ICM. We first estimate the values of $η_{\rm cp}$ 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 $η_{\rm cp}$ 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, $η_{\rm cp}$ 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.