Recent cosmological simulations have shown that turbulence should be generally prevailing in clusters because clusters are continuously growing through matter accretion. Using one-dimensional hydrodynamic simulations, we study the heating of cool-core clusters by the ubiquitous turbulence as well as feedback from the central active galactic nuclei (AGNs) for a wide range of cluster and turbulence parameters, focusing on the global stability of the core. We find that the AGN shows intermittent activities in the presence of moderate turbulence similar to the one observed with Hitomi. The cluster core maintains a quasi-equilibrium state for most of the time because the heating through turbulent diffusion is nearly balanced with radiative cooling. The balance is gradually lost because of slight dominance of the radiative cooling, and the AGN is ignited by increased gas inflow. Finally, when the AGN bursts, the core is heated almost instantaneously. Thanks to the pre-existing turbulence, the heated gas is distributed throughout the core without becoming globally unstable and causing catastrophic cooling, and the core recovers the quasi-equilibrium state. The AGN bursts can be stronger in lower-mass clusters. Predictions of our model can be easily checked with future X-ray missions like XRISM and Athena.
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