How supermassive black holes shape central entropies in galaxy clusters

A significant fraction of galaxy clusters show central cooling times of less than 1 Gyr and associated central cluster entropies below 30 keV cm2. We provide a straightforward explanation for these low central entropies in cool core systems and how this is related to accretion onto supermassive black holes (SMBHs). Assuming a time-averaged equilibrium between active galactic nucleus (AGN) jet heating of the radiatively cooling intracluster medium and Bondi accretion, we derived an equilibrium entropy that scales with the SMBH and cluster mass as $ K\propto M_\bullet^{4/3}M_{500\mathrm{c}}^{-1} $. At fixed cluster mass, overly massive SMBHs would raise the central entropy above the cool core threshold, thus implying a novel way of limiting SMBH masses in cool-core clusters. We find a limiting mass of 1.4 × 1010 M⊙ in a cool-core cluster of mass 1015 M⊙. We carried out three-dimensional hydrodynamical simulations of an idealised Perseus-like cluster with AGN jets and find that they reproduce the predictions of our analytic model, once corrections for elevated jet entropies are applied when calculating X-ray emissivity-weighted cluster entropies. Our findings have significant implications for modelling galaxy clusters in cosmological simulations: a combination of overmassive SMBHs and high heating efficiencies precludes the formation of cool-core clusters.