Three-dimensional Numerical Simulations of Thermal-Gravitational Instability in the Protogalactic Halo Environment

We study thermal-gravitational instability in simplified models of protogalactic halos using three-dimensional hydrodynamic simulations. The simulations started with isothermal density perturbations of various power spectra and followed the evolution of gas with radiative cooling down to T = 10 super(4) K, background heating, and self-gravity for up to 620 cooling times. Then cooled and condensed clouds were identified and their physical properties were examined in detail. In our models, the cooling timescale is several times shorter than the gravitational timescale. Hence, during the early stage clouds start to form around initial density peaks as a result of thermal instability. Small clouds appear first, and they are pressure-bound. Subsequently, the clouds grow through compression by the background pressure, as well as through gravitational infall. During the late stage, cloud-cloud collisions become important, and clouds grow mostly through gravitational merging. Gravitationally bound clouds with mass M sub(c) 6 x 10 super(6) M sub( )are found in the late stage. They are approximately in virial equilibrium and have radii R sub(c) 150-200 pc. Those clouds have gained angular momentum through tidal torque, as well as merging, so they have large angular momentum with a spin parameter (l sub(s)) 60.3. The clouds formed in a denser background tend to have smaller spin parameters, since self-gravity, compared to radiative cooling, is relatively less important at higher density. H sub(2) cooling to below T = 10 super(4) K does not drastically change the evolution and properties of clouds, since it is much less efficient than the H Lya cooling. The slope of the initial density power spectrum affects the morphology of the cloud distribution, but the properties of individual clouds do not sensitively depend on it. We point out limitations of our study and mention briefly the implications of our results for the formation of protoglobular cluster clouds in protogalactic halos.