two-body relaxation

Stars in a cluster almost never actually collide — space is far too empty for that. But over very long times, the countless tiny gravitational nudges that stars give each other as they pass slowly reshuffle their orbits, like a deck of cards being shuffled one faint flick at a time. This gradual scrambling of stellar motions by accumulated close encounters is two-body relaxation.

Each near-miss between two stars deflects them only slightly, and a single passage barely matters. But add up an enormous number of such gentle gravitational tugs and a star's velocity is randomly redirected and its energy nudged up or down, until the cluster slowly forgets its original orbits and settles toward a more thermal, equilibrium distribution of speeds. The characteristic time for this to take hold is the relaxation time, which for a typical globular cluster is hundreds of millions to billions of years — long, but shorter than the cluster's age, so relaxation has had time to act.

Relaxation drives the slow evolution of dense stellar systems. It tends to share energy among stars (pushing toward equipartition), let heavy stars sink and light stars rise (mass segregation), and gradually evaporate the fastest stars off the cluster's edge. Carried to its extreme it produces 'gravothermal collapse,' a runaway shrinking of the cluster core. Galaxies, by contrast, are so vast that their relaxation time exceeds the age of the universe — they are effectively 'collisionless,' which is exactly why galaxies and globular clusters evolve along very different paths.