Molecules at high Redshift: The Evolution of the Cool Phase of Protogalactic Disks

We study the formation of molecular hydrogen, after the epoch of re-ionization, in the context of canonical galaxy formation theory due to hierarchical clustering. There is an initial epoch of $H_2$ production in the gas phase through the $H^-$ route which ends at a redshift of order unity. Star formation in the protogalactic disks can become self-regulated. The process responsible for the feedback is heating of the gas by the internal stellar radiation field which can dominate the background radiation field at various epochs. It is possible to define a maximum star formation rate during this epoch. Plausible estimates give a rate of 0.2-2 Mo yr-1 for condensations corresponding to 1 sigma and 2 sigma initial density fluctuations. Therefore, the production of metals and dust proceeds slowly in this phase. This moderate epoch is terminated by a phase transition to a cold dense and warm neutral/ionized medium once the metals and dust have increased to a level Z=0.03-0.1 Z_o. Then: (1) atoms and molecules such as C, O and CO become abundant and cool the gas to below $300 K$ ; (2) the dust abundance has become sufficiently high to allow shielding of the molecular gas and; (3) molecular hydrogen formation can occur rapidly on grain surfaces. This phase transition occurs at a redshift of approximately 1.5, with a fiducial range of 1.2<z<2. The combination of feedback and a phase transition provides a natural resolution of the G-dwarf problem.