  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 by others,
that under the protogalactic environments only nonlinear density
inhomogeneities can condense into PGCCs. 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=10^4 K. Since
imprinting of Jeans mass at 10^4 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 than M_min ~ (10^{5.6} M_sun) (n_h/0.05 cm3)^{-2} cool isobarically,
while perturbations larger than M_max ~ (10^8 M_sun) (n_h/0.05 cm3)^{-2} cool
isochorically. On the other hand, intermediate size perturbations (M_min<
M_pgcc < M_max) are compressed supersonically. 2) For supersonically collapsing
clouds, the density compression factor after they cool to T_c=10^4 K range
10^{2.5}-10^6. 3) For supersonically collapsing clouds the Jeans mass can be
reduced to as small as 10^{5.5} M_sun (n_h/0.05 cm3)^{-1/2} at the maximum
compression. 4) The density profile of simulated PGCCs can be approximated by a
constant core with a halo of rho ~ r^{-2} rather than a singular isothermal
sphere.
