In the tails of galaxies that resemble jellyfish, two types of glow are observed: red (from cold hydrogen, discovered by Balmer) and X-ray (from gas at millions of degrees). Surprisingly, their brightnesses almost always relate as 3:1, despite varying conditions.
Simulations showed: cold gas shatters into dense droplets, while hot gas wraps them in a cocoon. The hot glow is a transit zone: gas rapidly cools and mixes without lingering. Hence, the X-ray emission time is nearly constant, and the brightness ratio stays around three. Even with a thousandfold pressure difference, the ratio holds thanks to geometry. The mix involves oxygen and carbon. This process generates entropy.
Now astronomers can, without seeing the flows, estimate the gas mixing rate in distant galaxies by analyzing light (spectroscopy) and brightness (photometry) with telescopes like James Webb.
Johann Balmer, who discovered the series of hydrogen lines (including H-alpha), was a schoolteacher and made this discovery simply by studying numerical patterns.