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Published online by Cambridge University Press: 12 April 2016
Numerical calculations of the collapse of adiabatic clouds from uniform density and rotation initial conditions show that when restricted to axisymmetry, the clouds form either near-equilibrium spheroids or rings. Rings form in the collapse of low thermal energy clouds and have β = T/|w|≳ 0.43. When the axisymmetric constraint is removed and an initial m=2 density variation is introduced, clouds either collapse to form near-equilibrium ellipsoids or else fragment into binary systems through a bar phase. Ellipsoids form in the collapse of high thermal energy clouds and have β ≲ 0.27. The results are consistent with the critical values of β for instabilities in Maclaurin spheroids, and suggest that protostellar clouds may undergo a dynamic fragmentation in the nonisothermal collapse regime.