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Notes:
In order for a halo to successfully develop star forming regions it must satisfy several criteria: First, the cooling time of the gas must be less than the dynamical collapse time, i.e. the cloud must become gravitationally bound. Second, the fraction of gas in molecular Hydrogen must be higher that 10-4.
In the metal-free gas of the early universe, H2 was the main coolant. For temperatures less than 1000K, collisional excitation of rotational transitions and the subsequent radiative decay dominated. The lowest two rotational transitions of H2 have an energy spacing of E/kb~512 K. At high densities, collisional deexcitiations dominate and the gas does not cool. Once this characteristic temperature and density are reached, the gas begins a slow contraction towards gravitational collapse.