What process occurs when a gravitationally unstable core breaks into smaller, denser clumps?

Fragmentation

As a large, gravitationally unstable core begins to contract, it rarely collapses monolithically into a single massive object. Instead, the immense cloud undergoes fragmentation. This process involves the large structure breaking up into numerous smaller, denser clumps or cores scattered throughout the original region. Each of these fragments carries the potential to evolve into one or more individual stars or a component of a multiple-star system. The nature of this fragmentation—whether it produces many small pieces or fewer large pieces—is highly dependent on the initial turbulence within the cloud and ultimately determines the resulting population and size distribution of the stars formed in that cluster.