Hot gas in elliptical galaxies and clusters emits X-rays, but its observed luminosity is lower than predicted by a self-similar model with purely gravitational heating. This discrepancy is known as the 'entropy problem' in galaxy groups. Alongside this work, the archive hosts studies of hot gas in groups, black holes as tugs and thermometers, and dust battered by invisible waves. All of them touch on the influence of active nuclei on their environment, but this paper is the first to span the entire mass range from individual elliptical galaxies to massive clusters, using optically selected samples free of X-ray biases.
The authors started from an entropy profile derived from adiabatic cosmological simulations, characterized by a central parameter η, and assumed that black hole activity only increases this parameter. Gas density and temperature were described by a polytropic equation of state with index γ=1.19±0.02, taken from X-COP cluster observations. The central entropy was calibrated using the observed bolometric luminosity–halo mass relation obtained from stacked eRosita X-ray observations of optically selected systems. The entropy excess ΔS was computed as the difference between the model entropy and the baseline simulation entropy, integrated over gas mass rather than radius to account for gas expansion upon heating. The heat $Q_{heat}$ was found from the equation ΔS = $Q_{heat}$/$T_{heat}$ + $Q_{cool}$/$T_{cool}$, where the heating and cooling temperatures were estimated from semi-analytic and semi-empirical models of black hole accretion history.
For a canonical accretion efficiency of 10%, supermassive black holes thermalize 1 to 3% of their energy into the surrounding gas. This value is nearly constant across the entire mass range from $10^{12}$ to $10^{15}$ solar masses. Comparing the heat injected by black holes with the heat radiated by the gas over a Hubble time reveals two regimes. In elliptical galaxies and groups with masses below $10^{14}$ solar masses, the accumulated heat significantly exceeds radiative losses, and the gas remains in a high-entropy state long after the quasar epoch. In clusters with masses above $10^{14}$ solar masses, heating and cooling are in self-regulated equilibrium, and most of the injected energy has already been radiated away. Numerically, $Q_{heat}$ ranges from 2×$10^4$ to 4×$10^7$ solar masses times c², depending on halo mass.
This work is the first to quantitatively link the entropy excess of hot gas to the energy output of supermassive black holes across the full mass range, from elliptical galaxies to clusters. Unlike neighboring studies that either focused on clusters or used X-ray-selected samples biased toward bright objects, this work uses optically selected systems and stacked eRosita observations, eliminating systematic errors. The derived heating efficiency of 1–3% is consistent with the fraction of mechanical energy in jets, pointing to a mechanical rather than radiative feedback mechanism.
The proposed method can be extended to higher redshifts using future X-ray instruments such as HUBS, AXIS, and NewAthena. This would allow tracking the evolution of entropy and heating over cosmic time and testing how feedback efficiency changes. The model could also be refined by accounting for gas inhomogeneity and a possible dependence of the polytropic index on central entropy.
The results will inform semi-analytic models of galaxy formation and cosmological hydrodynamical simulations by providing realistic feedback parameters for active galactic nuclei. They will also aid in interpreting X-ray observations of groups and clusters.
Test the prediction of low accretion rates in elliptical galaxies using the demographics of active galactic nuclei. Compare the model with high-resolution entropy profiles of individual systems.
This work directly links two unresolved problems in astrophysics: the suppression of star formation in massive galaxies and the prevention of cooling in hot cluster gas. The derived heating efficiency closes the energy budget in galaxy formation models, but the exact mechanism of energy transfer from jets to the gas remains an open question.
This section is addressed to the author of the paper and their colleagues. Neighbouring works were found by meaning-based search across our archive, not by word overlap. We do not review: we show the field around the work.
What the work does
The authors built a model with a single free parameter, the central entropy, and calibrated it against the relation between X-ray luminosity and halo mass from optically selected samples. Comparing with adiabatic simulations allowed them to estimate the heat injected by active galactic nuclei and to show that black holes thermalize 1–3% of their energy in the surrounding gas.
Where its strength is
This work is the first to quantitatively link the entropy excess of hot gas to the energy output of supermassive black holes across the full mass range, from elliptical galaxies to clusters, using samples free of X-ray selection biases.
Where it could go next
Worth trying
Why this may matter
If the heating efficiency is indeed universal, it provides a simple parameter for models of galaxy and cluster formation, connecting black hole growth to the thermal history of the gas.
Nearby works in our archive
The archive is sparse around this work: the closest review is only 0.56, against a usual 0.64. It looks like few have drilled nearby.
In the cluster Abell 85, the central black hole has a mass of 4×$10^{10}$ solar masses, making it one of the most massive dynamically confirmed black holes. If all its rest energy were converted to heat, it would be enough to heat the entire cluster gas to incredible temperatures.
In Dan Simmons's novel 'Hyperion', the TechnoCore uses black hole energy for its own purposes. Here, black holes act as natural heat regulators, preventing galaxies from cooling uncontrollably.