Criteria for collapse and fragmentation of rotating, isothermal clouds

Isothermal collapse of a rotating interstellar cloud is computed three dimensionally with a so-called smoothed particle method. Initial clouds are rigidly rotating homogeneous spheres with small density fluctuations. To find a condition for fragmentation of a cloud, the authors test a wide range of initial conditions in the α₀ - β₀ plane, where α₀ and β₀ are the initial ratios of thermal and rotational energies to gravitational energy, respectively. The characteristics of collapse and fragmentation are determined essentially by the product α₀β₀. For α₀β₀ ⪆ 0.20, a cloud does not shrink appreciably and oscillates about an equilibrium configuration which is not very flattened. For α₀β₀ ⪉ 0.20, the inner part of a cloud contracts greatly to form a flattened disklike configuration. A cloud with α₀β₀ ⪉ 0.12 fragments and forms a multiple system, the multiplicitiy being larger for a cloud with smaller α₀β₀.