AGN jet feedback on a moving mesh: gentle cluster heating by weak shocks and lobe disruption

While there is overwhelming observational evidence of AGN-driven jets in galaxy clusters and groups, if and how the jet energy is delivered to the ambient medium remains unanswered. Here we perform very high resolution AGN jet simulations within a live, cosmologically evolved cluster with the moving mesh code AREPO. We find that mock X-ray and radio lobe properties are in good agreement with observations with different power jets transitioning from FR-I to FR-II-like morphologies. During the lobe inflation phase, heating by both internal and bow shocks contributes to lobe energetics, and $\sim 40$ per cent of the feedback energy goes into the $PdV$ work done by the expanding lobes. Low power jets are more likely to simply displace gas during lobe inflation, but higher power jets become more effective at driving shocks and heating the intracluster medium (ICM), although shocks rarely exceed $\mathcal{M}\sim 2-3$. Once the lobe inflation phase ceases, cluster weather significantly impacts the lobe evolution. Lower power jet lobes are more readily disrupted and mixed with the ICM, depositing up to $\sim 70$ per cent of the injected energy, however, ultimately the equivalent of $\gtrsim 50$ per cent of the feedback energy ends up as potential energy of the system. Even though the mean ICM entropy is increased up to $80$~Myr after the jets switch off, AGN heating is gentle, inducing no large variations in cluster radial profiles in accord with observations.