COLLAPSE OF PRIMORDIAL CLOUDS AND THE FORMATION OF A CENTRAL CORE TORU TSURIBE Kyoto University, Kyoto, 606-8502, Japan SHU-ICHIRO INUTSUKA National Astronomical Observatory, Mitaka, 181-8588, Japan Abstract. The collapse of rotating clouds is investigated using three-dimensional self-gravitating hy- drodynamical 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, ∼ 4π , 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 × 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 ∼ < 10 6 M ⊙ , central core formation is expected and will have a significant effect on the later evolution of the whole system. 1. Introduction The primordial initial mass function (IMF) has no reason to be the same as the present-day IMF. The fragmentation process during the first collapse of the pre- galactic clouds should be understood to predict the primordial IMF and primordial star formation rates (SFR). The first generation astronomical objects will have a significant effect on subsequent star and galaxy formation through ionization, UV radiation, metal ejection and so on. Thus, it is very important to investigate the formation mechanism of these kinds of primordial objects. Our primary interest is to study and identify the physics responsible during the formation of the first astronomical objects in the Universe. Especially, we invest- igate how and what kind of pre-galactic clouds collapse into massive cores and/or fragment into less massive objects. The purpose of the present paper is to suggest the general criterion that divides fragmentation and massive core formation in the self-gravitating stage of the baryonic components. Astrophysics and Space Science 276: 1097–1105, 2001. © 2001 Kluwer Academic Publishers. Printed in the Netherlands.