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 $30,\mathrm{keV},\mathrm{cm}^2$. We provide a straight forward 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 (ICM) as well as Bondi accretion, we derive 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 $1.4\times10^{10},\mathrm{M}\odot$ in a cool core cluster of mass $10^{15},\mathrm{M}\odot$. We carry out three-dimensional hydrodynamical simulations of an idealized 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 in 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 preclude the formation of cool core clusters.

💡 Research Summary

This paper addresses the long‑standing puzzle of why many galaxy clusters exhibit very low central entropies (K < 30 keV cm²) and short cooling times (< 1 Gyr). The authors propose a simple analytic framework in which the intracluster medium (ICM) in a cool‑core cluster is regulated by a balance between heating from active‑galactic‑nucleus (AGN) jets and radiative cooling, while the supermassive black hole (SMBH) at the cluster centre accretes gas at a Bondi‑like rate from kiloparsec‑scale surroundings.

Starting from the Bondi‑Hoyle‑Lyttleton formula, the accretion rate scales as (\dot M \propto M_{\bullet}^{2} K^{-3/2}), where (M_{\bullet}) is the SMBH mass and (K) the pseudo‑entropy of the gas. Assuming a fixed fraction (\epsilon) (≈ 0.2) of the rest‑mass energy of the accreted gas is converted into a collimated jet, the jet power is (\dot E = \epsilon \dot M c^{2}). Radiative cooling is approximated by the observed X‑ray bolometric luminosity–mass scaling (L_{\rm bol} \propto M_{500c}^{3/2}). Equating jet heating and cooling over timescales longer than the jet duty cycle yields an equilibrium central electron entropy

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