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 three-dimensional simulations, and our approach has the advantage of being able to explore large regions of parameter space rapidly. The minimum baryonic mass M_b is found to be strongly redshift dependent, dropping from 10⁶ M_☉ at z ~ 15 to 5 × 10³ M_☉ at z ~ 100 as molecular cooling becomes effective. For z ≫ 100, M_b rises again, as cosmic microwave background photons inhibit H₂ formation through the H^- channel. Finally, for z ≫ 200, the H⁺₂ channel for H₂ formation becomes effective, driving M_b down toward M_b ~ 10³ M_☉. With a standard cold dark matter power spectrum with σ₈ = 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.