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 profiles, we reduce the problem to that of numerically integrating a system of chemical equations. The results agree well with numerically expensive 3D simulations, and our approach has the advantage of rapidly being able to explore large regions of parameter space. The minimum baryonic mass Mb is found to be strongly redshift dependent, dropping from 10⁶ Msun at z=15 to 5000 Msun at z=100 as molecular cooling becomes effective. For z>>100, Mb rises again, as CMB photons inhibit H₂-formation through the H^- channel. Finally, for z>>200, the H₂^+ channel for H₂-formation becomes effective, driving Mb down towards 10³ Msun. With a standard CDM power spectrum withsigma₈=0. 7, this implies that a fraction 10^-3 of all baryons may have formed luminous objects by z=30, which could be sufficient to reheat the universe.