Two-dimensional axisymmetric collapse of thermally unstable primordial clouds

Abstract

We have performed two-dimensional hydrodynamic simulations of the collapse of isolated axisymmetric clouds condensing via radiative cooling in a primordial background gas. In order to study the development of the so-called shape instability, we have considered two types of axisymmetric clouds, oblate and prolate clouds of various sizes and with axial ratios of 0.5 less than or equal toR(c,R)/R-c,R-z less than or equal to 2. We find that the degree of oblateness or prolateness is enhanced during the initial cooling phase. However, it can be reversed later, if the initial contrast in cooling times between the cloud gas and the background gas is much greater than 1. In such cases an oblate cloud collapses to a structure composed of an outer thin disk and a central prolate component. A prolate cloud, on the other hand, becomes a thin cigar-shaped structure with a central dense oblate component. The reversal of shape in the central part of the cooled clouds is due to supersonic motions either along the disk plane in the case of oblate clouds or along the symmetry axis in the case of prolate clouds. For a background gas of T-h = 1.7 x 10(6) K and n(h) = 0.1 cm(-3) in a protogalactic halo environment, the mean density of the cloud gas that has cooled to 10(4) K increases to 100n(h) or so in our simulations where non-equilibrium cooling is adopted and the background gas cools too. The spherical Jeans mass of such gas is estimated to be about M-J similar to 5 10(7) M-.. In order for cloud mass to exceed the Jeans mass and at the same time in order for the thermal instability to operate, the initial cloud size should be around 1l(cool)-1.5l(cool), where l cool is the cooling length