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.
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