AC44 · Bubbles, waves and cluster heating
How black holes move energy through cluster gas
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.
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.
02 · L1Does a passing pressure wave leave heat behind?
Reversible compression explains why a warm ring, a sound wave and irreversible shock heating need different evidence.
03 · L1How much enthalpy does a rising bubble transfer?
Derive cavity enthalpy from internal energy and displacement work, then follow its adiabatic decline and delayed dissipation.
04 · L2Compare radial transport with radiative cooling
Define shells, powers and energies before comparing buoyant transport, delayed dissipation and a spherical thermal pulse.
05 · L3Replay 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.
06 · L3How to check whether a numerical wave is a shock
Replay actual finite-volume refinement, then inspect jump consistency, branch association and entropy floors.
07 · L4Follow 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.
Primary sources and calculation notes
- Bîrzan et al. (2004), A systematic study of radio-induced X-ray cavities in clusters, groups, and galaxies
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.
- Fabian et al. (2000), Chandra imaging of the complex X-ray core of the Perseus cluster
Original Chandra images and the cool bright rims around the inner radio lobes. The holes were known from ROSAT before Chandra resolved their surroundings.
- Fabian et al. (2003), A deep Chandra observation of the Perseus cluster: shocks and ripples
Deep-observation residual images and ripple interpretation. Its heating argument depends on propagation and dissipation assumptions.
- Rafferty et al. (2006), The feedback-regulated growth of black holes and bulges
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.
- Kaiser & Binney (2002), Simple models of cooling flows
Appendix on entropy generation in shocks. Its Mach-number convention differs from the shock-frame upstream Mach used in our RH derivation.
- Forman et al. (2007), Filaments, bubbles, and weak shocks in the gaseous atmosphere of M87
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.
- Sharma et al. (2012), Thermal instability and the feedback regulation of hot halos
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.
- Ruszkowski, Yang & Reynolds (2017), Cosmic ray feedback heating of the intracluster medium
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.
- XRISM Collaboration (2026), Disentangling multiple gas kinematic drivers in the Perseus galaxy cluster
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.
- Heinrich et al. (2026 preprint), Chaotic ICM motions probed by resonant scattering
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.
- Sandbox Physics, frozen gentle-source numerical evidence (2026)
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.