How supermassive black holes shape central entropies in galaxy clusters

TL;DR

This paper explains how supermassive black holes influence the central entropy of galaxy clusters through AGN feedback, deriving a scaling relation and confirming it with hydrodynamical simulations, with implications for cluster evolution.

Contribution

It introduces a new analytic model linking SMBH mass and cluster entropy, supported by hydrodynamical simulations, to explain cool core cluster properties.

Findings

Derived a scaling relation for entropy with SMBH and cluster mass.

Identified a limiting SMBH mass that prevents cool core formation.

Hydrodynamical simulations support the analytic model's predictions.

Abstract

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.