How Small Were the First Cosmological

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 106M at z ∼ 15 to 5×103M 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 H 2 -channel for H2-formation becomes effective, driving Mb down towards Mb ∼ 10 3M . With a standard CDM 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. Published in ApJ, 474, 1-12 (January 1, 1997). Available from h t t p://www.mpa-garching.mpg.de/̃ max/minmass.html (faster from Europe) and from from h t t p ://www.sns.ias.edu/ ̃max/minmass.html (faster from the US). Figures 5 and 6 will print in color if your printer supports it.