How Small Were the First Cosmological Objects?

The minimum mass that a virialized gas cloud must have in order to be able tocool in a Hubble time is computed, using a detailed treatment of the chemistryof molecular hydrogen. With a simple model for halo profiles, we reduce theproblem to that of numerically integrating a system of chemical equations. Theresults agree well with numerically expensive 3D simulations, and our approachhas the advantage of rapidly being able to explore large regions of parameterspace. The minimum baryonic mass M_b is found to be strongly redshiftdependent, dropping from 10^6 solar masses at z=15 to 5000 solar masses atz=100 as molecular cooling becomes effective. For z>>100, M_b rises again, asCMB photons inhibit H_2-formation through the H^- channel. Finally, for z>>200,the H_2^+ channel for H_2-formation becomes effective, driving M_b down towards10^3 solar masses. With a standard CDM power spectrum with sigma_8=0.7, thisimplies that a fraction 10^{-3} of all baryons may have formed luminous objectsby z=30, which could be sufficient to reheat the universe.