Formation of Proto-globular Cluster Clouds by Thermal Instability

Many models of globular cluster formation assume the presence of cold dense clouds in early universe. Here we re-examine the Fall & Rees (1985) model for formation of proto-globular cluster clouds (PGCCs) via thermal instabilities in a protogalactic halo. We first argue, based on the previous study of two-dimensional numerical simulations of thermally unstable clouds in a stratified halo of galaxy clusters by Real et al. (1991), that under the protogalactic environments only nonlinear (δ ∼> 1) density inhomogeneities can condense into PGCCs without being disrupted by the buoyancy-driven dynamical instabilities. We then carry out numerical simulations of the collapse of overdense clouds in one-dimensional spherical geometry, including self-gravity and radiative cooling down to T = 10 K. Since imprinting of Jeans mass at 10 K is essential to this model, here we focus on the cases where external UV background radiation prevents the formation of H2 molecules and so prevent the cloud from cooling below 10 4 K. The quantitative results from these simulations can be summarized as follows: 1) Perturbations smaller thanMmin ∼ (10 M⊙)(nh/0.05 cm ) cool isobarically, where nh is the unperturbed halo density, while perturbations larger than Mmax ∼ (10 8 M⊙)(nh/0.05 cm ) cool isochorically and thermal instabilities do not operate. On the other hand, intermediate size perturbations (Mmin < Mpgcc < Mmax) are compressed supersonically, accompanied by strong accretion shocks. 2) For supersonically collapsing clouds, the density compression factor after they cool to Tc = 10 4 K range 10 − 10, while the isobaric compression factor is only 10. 3) Isobarically collapsed clouds (M < Mmin) are too small to be gravitationally bound. For supersonically collapsing clouds, however, the Jeans mass can be reduced to as small as 10 M⊙(nh/0.05 cm ) at the maximum compression owing to the increased density compression. 4) The density profile of simulated PGCCs can be approximated by a constant core with a halo of ρ ∝ r rather than a singular isothermal sphere.