---
title: "Does a passing pressure wave leave heat behind?"
description: "Reversible compression explains why a warm ring, a sound wave and irreversible shock heating need different evidence."
canonical_url: "https://sandboxphysics.com/stories/agn-feedback/pressure-is-not-heat/"
language: "en"
page_type: "story"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/stories/agn-feedback/pressure-is-not-heat/"
last_modified: "2026-11-12"
---

[How black holes move energy through cluster gas](https://sandboxphysics.com/stories/agn-feedback/)

L1 · Bubbles, waves and cluster heating

# Does a passing pressure wave leave heat behind?

Sandbox Physics · 2026-11-12

Compression can warm gas temporarily. As the gas expands again, that temperature rise can disappear. A warm ripple in a cluster may be carrying energy outward; dissipation determines how much remains as heat.

## Begin with a piston that can return the work

Imagine gas in an insulated cylinder with a frictionless piston. Insulated means that heat does not cross its walls during the experiment. Pushing the piston inward does work on the gas and raises its temperature. If the motion is smooth enough, the gas can push the piston back and return to its starting state.

The gas was warmer during compression, but the round trip need not leave additional thermal energy. A real bicycle pump also has friction and heat transfer through its walls. The ideal piston isolates one point: being hotter at a particular instant differs from retaining irreversible heating after a process ends.

## One layer of gas pushes the next

A local pressure increase pushes adjacent gas, which then pushes gas farther away. Compression and rarefaction travel outward. Individual gas parcels may move mainly back and forth near their original positions while energy travels a long distance. This is the basic picture of a sound wave.

Cluster atmospheres provide the gas through which such disturbances propagate. Expanding cavities can launch pressure disturbances into that atmosphere. Turning an observed ripple into a heating estimate requires its speed, amplitude and dissipation distance.

The periods are enormously longer than audible sound. Sonification shifts pressure-wave information into a range we can hear. The original measurements are X-ray images and spectra.

Reading: Fabian et al. (2003)

## Entropy keeps track of the process

Temperature alone includes the effect of reversible compression. Entropy tracks a change that a reversible cycle cannot erase. For the ideal monatomic gas used here, a useful entropy index combines pressure and mass density as follows. Keep the units of both quantities fixed when comparing it.

$$
K=\frac{p}{\rho^{5/3}}
$$

Pressure is divided by mass density to the five-thirds power. The exponent follows from the heat capacities of an ideal monatomic gas. Reversible adiabatic motion preserves this index for a gas parcel; shock dissipation raises it.

Reading: Kaiser & Binney (2002)

## A very weak shock makes little entropy

A shock is a thin transition through which some flow energy becomes heat irreversibly. Its density and pressure jumps must agree with the propagation speed. In M87, for example, observed density and temperature jumps support a shock Mach number near 1.2. This Mach number measures the shock speed relative to upstream gas in units of the upstream sound speed.

As a shock approaches the sound-speed limit, its entropy jump becomes small much faster than its pressure and density jumps. A conspicuous compression band can therefore have an entropy excess hidden beneath observational or numerical uncertainty. Calling it a compression wave states the established result.

In the gentle calculation accompanying this reading, the pressure wave survives grid refinement while the original shock tests fail. Energy reaches larger radii; determining how it subsequently dissipates into enough heat requires additional physical processes.

Reading: Forman et al. (2007) · Sandbox Physics

## Try the observation

### [Hold a probe still as the wave passes](https://sandboxphysics.com/labs/agn-cavity-transport/)

1. Choose A pressure pulse leaves and pause with the probe in an orange band.
2. Keep its radius fixed and step through actual frames, comparing pressure sign and velocity direction.
3. Open the shock explanation and distinguish jump consistency from detectable entropy production.

## Exercises and explained answers

A parcel is warmer at a wave crest and cooler in the following trough. What else would you compare to test irreversible heating?

Follow the same parcel and compare its pressure, density and entropy index, accounting for actual heating and radiative losses. The crest temperature also includes reversible compression.

[Previous: What fills the dark holes in Perseus?](https://sandboxphysics.com/stories/agn-feedback/holes-in-xray-gas/) [Next: How much enthalpy does a rising bubble transfer?](https://sandboxphysics.com/stories/agn-feedback/enthalpy-of-a-rising-bubble/)

## Primary sources and calculation notes

1. [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.

2. [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.

3. [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.

4. [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.