---
title: "How black holes move energy through cluster gas"
description: "Follow cavities, compression and dissipation through worked physics, actual Perseus catalogue values and recent X-ray measurements."
canonical_url: "https://sandboxphysics.com/stories/agn-feedback/"
language: "en"
page_type: "story"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/stories/agn-feedback/"
last_modified: "2026-11-12"
---

AC44 · Bubbles, waves and cluster heating

# How black holes move energy through cluster gas

Sandbox Physics · 2026-11-12

Begin with two dark patches in an X-ray image. Work out what a bubble carries, what a passing wave changes and what the observations tell us about heating.

[01 · L1 What fills the dark holes in Perseus? X-ray cavities, radio lobes and cool bright rims trace how energy from a central black hole reaches cluster gas.](https://sandboxphysics.com/stories/agn-feedback/holes-in-xray-gas/) [02 · L1 Does a passing pressure wave leave heat behind? Reversible compression explains why a warm ring, a sound wave and irreversible shock heating need different evidence.](https://sandboxphysics.com/stories/agn-feedback/pressure-is-not-heat/) [03 · L1 How much enthalpy does a rising bubble transfer? Derive cavity enthalpy from internal energy and displacement work, then follow its adiabatic decline and delayed dissipation.](https://sandboxphysics.com/stories/agn-feedback/enthalpy-of-a-rising-bubble/) [04 · L2 Compare radial transport with radiative cooling Define shells, powers and energies before comparing buoyant transport, delayed dissipation and a spherical thermal pulse.](https://sandboxphysics.com/stories/agn-feedback/cooling-and-transport/) [05 · L3 Replay a Perseus cavity pair against cooling losses Use a fixed Rafferty table slice to calculate inner-cavity enthalpy, age sensitivity and required heating in a truncated aperture.](https://sandboxphysics.com/stories/agn-feedback/perseus-cavity-replay/) [06 · L3 How to check whether a numerical wave is a shock Replay actual finite-volume refinement, then inspect jump consistency, branch association and entropy floors.](https://sandboxphysics.com/stories/agn-feedback/reading-wave-and-shock-evidence/) [07 · L4 Follow heating through condensation, cosmic rays and XRISM Read controlled condensation and cosmic-ray models beside XRISM velocity maps and resonant scattering to test how AGN energy thermalizes.](https://sandboxphysics.com/stories/agn-feedback/condensation-feedback-and-nonthermal-pressure/)

## Primary sources and calculation notes

1. [Bîrzan et al. (2004), A systematic study of radio-induced X-ray cavities in clusters, groups, and galaxies](https://arxiv.org/pdf/astro-ph/0402348v2)

   Frozen 30 April 2004 version: Section 4.1 on three cavity ages; Section 5.2, equations 7–9 on buoyancy and enthalpy transfer; Section 5.3 compares mechanical power with radiative losses. The Perseus input values come from the separate Rafferty 2006 tables.

2. [Fabian et al. (2000), Chandra imaging of the complex X-ray core of the Perseus cluster](https://arxiv.org/abs/astro-ph/0007456)

   Original Chandra images and the cool bright rims around the inner radio lobes. The holes were known from ROSAT before Chandra resolved their surroundings.

3. [Fabian et al. (2003), A deep Chandra observation of the Perseus cluster: shocks and ripples](https://arxiv.org/abs/astro-ph/0306036)

   Deep-observation residual images and ripple interpretation. Its heating argument depends on propagation and dissipation assumptions.

4. [Rafferty et al. (2006), The feedback-regulated growth of black holes and bulges](https://arxiv.org/pdf/astro-ph/0605323v2)

   Frozen 20 July 2006 version: Table A1 Perseus rows, Table 2 Perseus row/footnotes, Sections 3.1.2–3.1.3. The tutorial replays the inner pair with a separately stated age estimator.

5. [Kaiser & Binney (2002), Simple models of cooling flows](https://arxiv.org/pdf/astro-ph/0207111v2)

   Appendix on entropy generation in shocks. Its Mach-number convention differs from the shock-frame upstream Mach used in our RH derivation.

6. [Forman et al. (2007), Filaments, bubbles, and weak shocks in the gaseous atmosphere of M87](https://arxiv.org/abs/astro-ph/0604583v2)

   Density and temperature jumps support the weak-shock interpretation in a different system, M87. Used as an observational contrast, not a calibration of the gentle pulse.

7. [Sharma et al. (2012), Thermal instability and the feedback regulation of hot halos](https://arxiv.org/pdf/1106.4816v1)

   Figures 4–5,8 and 15; idealized versus feedback heating, thermal-instability/free-fall times and unresolved cold-filament widths. Thresholds depend on the physical setup.

8. [Ruszkowski, Yang & Reynolds (2017), Cosmic ray feedback heating of the intracluster medium](https://arxiv.org/abs/1701.07441)

   Table 1 and Figures 2–4 compare cosmic-ray transport and heating prescriptions in 3D magnetized simulations. A conditional model comparison, not a direct measurement of the cosmic-ray pressure.

9. [XRISM Collaboration (2026), Disentangling multiple gas kinematic drivers in the Perseus galaxy cluster](https://doi.org/10.1038/s41586-025-10017-x)

   Published 28 January 2026; accessible manuscript arXiv:2509.04421, Figures 2–4 and Methods on heating/cooling. Broadening and scale assumptions enter the dissipation estimate.

10. [Heinrich et al. (2026 preprint), Chaotic ICM motions probed by resonant scattering](https://arxiv.org/abs/2609.10845)

    Submitted 9 September 2026, PDF version 11 September; Figure 4 and Section 4 test resonant-line transfer, spatial-spectral mixing and velocity anisotropy. Preprint status retained as of 11 November 2026.

11. [Sandbox Physics, frozen gentle-source numerical evidence (2026)](https://sandboxphysics.com/stories/agn-feedback/materials/wave-refinement-manifest.json)

    Actual 512/1024/2048/4096 refinement history, original shock criteria and matching controls. The source power and scientific gates were kept fixed; the final scope remains no resolved AGN shock.