How Small Were the First Cosmological Objects?

The minimum mass that a virialized gas cloud must have in order to be able to cool in a Hubble time is computed, using a detailed treatment of the chemistry of molecular hydrogen. With a simple model for halo proÐles, we reduce the problem to that of numerically integrating a system of chemical equations. The results agree well with numerically expensive three-dimensional simulations, and our approach has the advantage of being able to explore large regions of parameter space rapidly. The minimum baryonic mass is found to be strongly redshift dependent, dropping from at zD 15 to at M b 106 M _ 5 ] 103 M _ zD 100 as molecular cooling becomes e†ective. For z? 100, rises again, as cosmic microwave backM b ground photons inhibit formation through the H~ channel. Finally, for z? 200, the channel for 2 2 formation becomes e†ective, driving down toward With a standard cold dark 2 Mb Mb D 103 M_. matter power spectrum with this implies that a fraction 10~3 of all baryons may have formed p8\ 0.7, luminous objects by z\ 30, which could be sufficient to reheat the universe. Subject heading : cosmology : theory È early universe È galaxies : formation