Letter to the Editor

How supermassive black holes shape central entropies in galaxy clusters

Leibniz Institute for Astrophysics Potsdam (AIP) An der Sternwarte 16 14482 Potsdam, Germany

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Received: 20 December 2025
Accepted: 26 January 2026

Abstract

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 ∝ M_∙^4/3M_500c⁻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.