Jeans Instability

A cloud of interstellar gas is caught in a tug of war. Its own gravity pulls every part toward every other, trying to collapse it; its pressure pushes back, trying to smooth any clump away as a sound wave. Which one wins depends entirely on size. Squeeze a ripple of a given wavelength into the cloud and gravity scales with how much mass that ripple encloses, which grows fast with wavelength, while pressure support does not. So below a critical wavelength, the Jeans length, pressure wins and the ripple just oscillates; above it, gravity wins and the ripple runs away, growing exponentially until that patch collapses into something dense, a star-forming core. The colder and denser the cloud, the smaller that critical size, which is why cold dense clouds fragment into stars. The scene is a patch of that gas cloud: pick a perturbation wavelength and watch it either slosh harmlessly (stable, the cloud stays diffuse) or run away so the gas fragments and drains into dense glowing cores (collapse, the start of star formation). The big banner and the colour, blue for stable and orange for collapse, tell you which regime you are in at a glance; the diagnostic is the growth rate against wavelength, crossing zero exactly at the Jeans length.