Collapse of primordial clouds and the formation of a central core

The collapse of rotating clouds is investigated using three-dimensional self-gravitating hydrodynamical simulations. We take into account the detailed non-equilibrium chemical reactions for primordial gas that consists of pure hydrogen. The parameters of the collapse and the condition of the fragmentation are compared with those of isothermal clouds. It is shown that the geometrical flatness of the central region of the disc is a good indicator for predicting whether the clouds fragment or not. If the flatness is greater than the critical value, similar to 4 pi, a cloud fragments into filaments and blobs. On the other hand, if the flatness is smaller than the critical value, fragmentation is not expected before the central core formation even if the cooling is efficient and the total mass becomes much greater than the local Jeans mass at the centre. The critical mass is found to be 3 x 10(6) M . for a typical initial condition. If the initial cloud mass is smaller than this critical value, fragmentation before the central core formation is not expected. For a typically estimated first collapsing cosmological baryonic object, M less than or similar to 10(6) M., central core formation is expected and will have a significant effect on the later evolution of the whole system.