Protostellar disks fragment into multiple stars when local parts of the disk become gravitationally unstable and can cool fast enough to collapse before shear and pressure disperse them. The classic stability measure is Toomre Q, introduced by Alar Toomre Massachusetts Institute of Technology, which compares stabilizing forces (thermal pressure and rotation) to self-gravity. When Toomre Q drops below a value near unity, the disk is prone to axisymmetric collapse; in practice, non-axisymmetric modes and three-dimensional effects make the threshold and outcome dependent on local conditions.
Physical criteria for fragmentation
A second, complementary requirement is rapid cooling. The theoretical cooling-time criterion was formulated by Charles F. Gammie University of Chicago, who showed that even a disk with low Toomre Q will avoid fragmenting if it cannot radiate away compressional heat quickly. Gammie found that collapse proceeds when the local cooling time is shorter than a few orbital periods, allowing density perturbations to contract rather than being sheared apart. Disk mass and radial location matter: higher disk-to-star mass ratios increase self-gravity, and the outer, colder regions of disks are more likely to satisfy both low Toomre Q and fast cooling. These combined criteria explain why fragmentation is most common at tens to hundreds of astronomical units from the central protostar in many models.
Numerical simulations by Matthew R. Bate University of Exeter have reinforced these theoretical thresholds while showing important complications. Bate’s simulations demonstrate that turbulence, magnetic fields, and radiative feedback from young protostars modify where and when fragmentation occurs; magnetic braking or strong irradiation can suppress fragmentation, whereas infall of material from the parent cloud can drive the disk into the unstable regime. Thus the simple Q-plus-cooling picture is a useful guide but not an absolute rule.
Observational and environmental context
Observationally, arrays like the Atacama Large Millimeter/submillimeter Array in Chile have imaged massive, structured disks and young multiple systems consistent with fragmentation. Fragmentation has direct consequences for stellar multiplicity and the mass distribution of stars: it produces wide companions, hierarchical systems, and can create brown dwarfs or very low-mass stars by direct collapse of disk clumps. In dense star-forming environments such as the Orion Nebula, tidal interactions and external irradiation from nearby massive stars further influence disk stability and the survival of fragments, adding a territorial and environmental dimension to where fragmentation yields stable multiple systems.
Consequences extend to planet formation as well. Disk fragmentation competes with core accretion: a fragment may become a companion star or a massive planet formed by disk instability, altering the architecture of any inner planetary system. Culturally and practically, understanding fragmentation informs surveys of stellar multiplicity and guides the placement and design of observatories in dry, high-altitude locations where cold dust emission can be resolved. The balance of gravity, cooling, and environmental influence determines whether a protostellar disk quietly feeds a single star or breaks into a family of siblings.