It’s not that old stars are bunching up in globular clusters, but that the clusters themselves are old. Globular clusters formed many billions of years ago and very quickly ran out of gas for star formation. This means that the only stars left in them are either very old, or were formed by stellar collisions which are very rare.
The exact mechanism which forms globular clusters is poorly understood. We know it’s definitely to do with gravity, and is related to the formation or interaction of galaxies. But an exact mechanism for formation of them all is not known.
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