Calculations of three-dimensional collapse and fragmentation

Calculations of the fragmentation of an isothermally collapsing cloud have been carried out using a method that follows the motion of individual fluid particles and includes pressure and viscosity forces between neighbouring particles. In a cloud or region whose mass is comparable to the Jeans mass, a highly condensed core forms, surrounded by a diffuse envelope that continues to accrete on to the core; in the presence of rotation, the inner part of the envelope becomes essentially an accretion disc. If the mass exceeds the Jeans mass, several such accreting cores are formed, the number being comparable to the initial number of Jeans masses in the cloud. Binary systems and hierarchical multiple systems are frequently obtained. The mass of the largest object formed is independent of the Jeans mass but depends on the angular momentum and viscosity of the cloud, and is essentially the maximum mass accretable by a single object. The resulting mass spectrum may be determined by the development of a hierarchy of accreting objects of different sizes, such that each object has several smaller ones associated with it. The hypothesis of a self-similar accretion hierarchy predicts a power-law mass spectrum, which in the limit of inefficient accretion has an exponent x = 1, in reasonable agreement with observations.