Modeling AGN Feedback in Cool-Core Clusters: The Balance between Heating and Cooling

We study the long-term evolution of an idealized cool-core galaxy cluster under the influence of momentum-driven AGN feedback using three-dimensional high-resolution (60 pc) adaptive mesh refinement (AMR) simulations. The momentum-driven AGN feedback is modeled with a pair of (small-angle) precessing jets, and the jet power is calculated based on the accretion rate of the cold gas in the vicinity of the Supermassive Black Hole (SMBH). The ICM first cools into clumps along the propagation direction of the AGN jets. As the jet power increases, gas condensation occurs isotropically, forming spatially extended (up to a few tens kpc) structures that resemble the observed $\rm H\alpha$ filaments in Perseus and many other cool-core cluster. Jet heating elevates the gas entropy and cooling time, halting clump formation. The cold gas that is not accreted onto the SMBH settles into a rotating disk of $\sim 10^{11}$ M$_{\odot}$. The hot gas cools directly onto the cold disk while the SMBH accretes from the innermost region of the disk, powering the AGN that maintains a thermally balanced steady state for a few Gyr. The mass cooling rate averaged over 7 Gyr is $\sim 30$ M$_{\odot}$/yr, an order of magnitude lower than the classic cooling flow value (which we obtain in runs without the AGN). Medium resolution simulations produce similar results, but when the resolution is lower than 0.5 kpc, the cluster experiences cycles of gas condensation and AGN outbursts. Owing to its self-regulating mechanism, AGN feedback can successfully balance cooling with a wide range of model parameters. Besides suppressing cooling, our model produces cold structures in early stages (up to $\sim 2$ Gyr) that are in good agreement with the observations. However, the long-lived massive cold disk is unrealistic, suggesting that additional physical processes are still needed.