Criteria for fragmentation of rotating isothermal clouds revisited

The collapse of rotating isothermal clouds is investigated by three-dimensional self-gravitating hydrodynamical calculations. The criterion that predicts the outcome after the collapse is presented for the initially uniform-density rigid-rotating sphere. It is shown that the central flatness, that is, the axial ratio of the isodensity contour in the central region, is a good indicator for the fate of the cloud. If the central flatness is greater than the critical value similar to 4 pi, a collapsing cloud with moderate perturbations is unstable for fragmentation, while if the central flatness is smaller than the critical value, it does not fragment at least before adiabatic core formation. The relation between the central flatness and the initial value of the ratio of the thermal (alpha(0)) and rotational energy (beta(0)) to the gravitational energy is also presented. Warm clouds (alpha(0) greater than or equal to 0.5) are not expected to fragment before adiabatic core formation almost independent of the initial rotation (beta(0)) and the properties of the initial perturbation.