---
title: "AGN Bubbles and Pressure Waves Interactive Lab | Sandbox Physics"
description: "How does energy from a black hole reach the surrounding gas? A light cavity expands as the surrounding pressure falls."
canonical_url: "https://sandboxphysics.com/labs/agn-cavity-transport/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/agn-cavity-transport/"
last_modified: "2026-11-12"
---

Energy leaving a cluster core

# AGN Bubbles and Pressure Waves

**How does energy from a black hole reach the surrounding gas?** A light cavity expands as the surrounding pressure falls. Its enthalpy decreases along the rise, supplying motion and a wake in the gas. Heat appears after that motion dissipates, so the cavity position and the heating profile need not coincide.

Follow two buoyant cavities, turn their axis and compare the dark patches they leave in projection. Then sample a gentle pressure wave as it crosses the cluster gas.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

Model assumptions

The bubble calculation follows two spherical pressure-balanced cavities in a fixed, fully ionized pure-hydrogen atmosphere. They receive ninety-five percent of the prescribed input, expand adiabatically and rise at terminal speed; a specified wake timescale converts released enthalpy into heat. The projection removes thermal emission inside the same two spheres and shows unabsorbed bolometric free-free radiation, with surface lighting for geometry. It is not a Chandra band image or a Perseus fit. The separate spherical Euler calculation includes gravity, free-free cooling and a five-percent central thermal release at one fixed power and duration. Its actual cell means pass spatial and time-step checks; its weak-shock tests fail, so the wave is labelled a compression wave. Bubble power controls do not rescale the gas record. Jet hydrodynamics, cavity displacement in the Euler gas, radio emission, bright rims, mixing, conduction, multiphase condensation and a self-regulating feedback cycle are omitted. The physical observer is fixed when the display camera turns. Every live bubble request checks numerical refinement and the stated weak-inflation and small-cavity limits; a refused request retains the preceding complete state.

Physics tutorial

## Follow the energy beyond the black hole

**Background** The hot gas in a cluster core shines in X-rays and loses energy. Jets from the central black hole can inflate light cavities. A rising cavity and an outward pressure pulse carry energy in different ways.

**Why it matters** A moving ring or a growing bubble is easy to see. Finding where gas has actually gained heat takes another step.

Start with the essentials

- **Focus question**: When energy leaves the centre, has it already become heat?
- **One-sentence intuition**: Cavities can carry enthalpy and waves can reversibly compress gas. Dissipation determines how much of that transported energy becomes heat.

### Core mathematical model

#### A cavity stores enthalpy

$$
H=\frac{\gamma_b}{\gamma_b-1}pV=4pV,\qquad\gamma_b=\frac43
$$

Enthalpy includes internal energy and the work needed to make room for the cavity. A relativistic cavity at pressure balance has four times pressure times volume.

#### A rising bubble releases some of that energy

$$
\frac{H(r)}{H_d}=\left[\frac{p(r)}{p_d}\right]^{1/4},\qquad\dot K_k=\dot W_k-\frac{K_k}{\tau_d},\quad\dot Q_k=\frac{K_k}{\tau_d}
$$

A falling external pressure lets the cavity expand. Released power $\dot W_k$ enters motion in a radial shell. The wake energy $K_k$ gradually dissipates into heat $Q_k$. Halving the pressure leaves about 84.1 percent of the cavity enthalpy.

#### Compression and entropy answer different questions

$$
K=\frac{p}{\rho^{5/3}},\qquad \Delta\ln K=\frac56(M-1)^3+O((M-1)^4)
$$

Reversible compression raises pressure and temperature while keeping the entropy index unchanged. A very weak ideal-gas shock produces entropy only at third order in its excess Mach number. In this gentle gas calculation, that excess entropy does not clear the numerical and cooling-control floor.

### Common difficulties

#### A dark patch changes with the view

**Typical misconception** A deeper projected hole means the gas received more heat.

**Better mental model** The viewing angle changes how much ordinary gas lies in front of and behind a cavity. The physical rise and energy release can remain the same.

#### A temperature rise can be temporary

**Typical misconception** Every warm pressure ring must be a shock that heated the gas.

**Better mental model** Gas can warm during compression and cool again as the pulse passes. A shock classification also requires consistent jumps, a speed separated from the sonic limit and detectable excess entropy.

### Run the experiment

1. 01

   #### Watch the rising pair

   Choose Rising pair and watch the representative late state. Drag the physical-time slider back toward detachment.

   **What to observe:** The same two spheres determine their positions, sizes and projected X-ray deficit. Heat continues to grow after energy has entered the wake.

2. 02

   #### Let the wake hold energy longer

   Compare Heat arrives later and Rising pair at the same time.

   **What to observe:** The rise is unchanged. A longer dissipation time retains more energy in motion and leaves less heat behind.

3. 03

   #### Turn the physical axis

   Choose Look along the outburst, then return to Rising pair. Drag the background to turn only the display camera.

   **What to observe:** The physical axis changes the projected deficit. The display camera reveals depth without changing that observation.

4. 04

   #### Sample the passing wave

   Choose A pressure pulse leaves. Drag the green probe across a warm and a cool band; pause and step through the recorded times.

   **What to observe:** Pressure and velocity are measured relative to matching gas that only cools. The time sequence shows actual complete snapshots at the fixed source setting.

5. 05

   #### See what reaches larger radii

   Choose The wave reaches the outskirts, inspect the radial profile and open the shock explanation.

   **What to observe:** A travelling compression remains visible at the final time. The calculation accepts this gentle wave, while the original shock tests remain failed.

Physical conclusion

Follow both transport and dissipation: a cavity or a pressure wave can move energy before the surrounding gas gains heat.

## Related experiments and articles

Black holes and cluster gas · Reading path

### From cavities to the heating question

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **What fills the dark holes in Perseus?**](https://sandboxphysics.com/stories/agn-feedback/holes-in-xray-gas/)
2. [Article **Does a passing pressure wave leave heat behind?**](https://sandboxphysics.com/stories/agn-feedback/pressure-is-not-heat/)
3. [Article **How much enthalpy does a rising bubble transfer?**](https://sandboxphysics.com/stories/agn-feedback/enthalpy-of-a-rising-bubble/)
4. [Article **Compare radial transport with radiative cooling**](https://sandboxphysics.com/stories/agn-feedback/cooling-and-transport/)
5. [Article **Replay a Perseus cavity pair against cooling losses**](https://sandboxphysics.com/stories/agn-feedback/perseus-cavity-replay/)
6. [Article **How to check whether a numerical wave is a shock**](https://sandboxphysics.com/stories/agn-feedback/reading-wave-and-shock-evidence/)
7. [Lab **Supernova Remnant Shocks and Particle Cycles** Compare a different shock problem](https://sandboxphysics.com/labs/supernova-remnant-shocks/)
8. [Article **Follow heating through condensation, cosmic rays and XRISM**](https://sandboxphysics.com/stories/agn-feedback/condensation-feedback-and-nonthermal-pressure/)

Fields & matter · Starter path

## From a field to an electron microscope

Map an electric field and steer a charged particle. Then find the electron's wavelength and use electron beams to see a crystal and a surface.

[Start here → **Make an Electric Field Visible** Move the probe around a dipole and check that the field always points downhill on the potential landscape. Observe · 8 min](https://sandboxphysics.com/labs/electric-field/)

1. [1 Make an Electric Field Visible](https://sandboxphysics.com/labs/electric-field/)
2. [2 A Charge Bending through Fields](https://sandboxphysics.com/labs/charged-particle/)
3. [3 Electron Wavelength & Voltage](https://sandboxphysics.com/labs/electron-wavelength/)
4. [4 Electron Diffraction & Reciprocal Space](https://sandboxphysics.com/labs/electron-diffraction/)
5. [5 TEM Bright Field, Dark Field & SAED](https://sandboxphysics.com/labs/tem-mode-selector/)
6. [6 SEM Secondary-Electron Topography](https://sandboxphysics.com/labs/sem-topography/)

[View the full path →](https://sandboxphysics.com/topics/fields-and-matter/#starter-path)