How big were the first cosmological objects?

We calculate the cooling times at constant density for haloes with virial temperatures from 100 K to 1 × 105 K that originate from a 3σfluctuation of a CDM power spectrum in three different cosmologies. Our intention is to determine the first objects that can cool to low temperatures, but not to follow their dynamical evolution. We identify two generations of haloes: those with low virial temperatures, Tvir ≲ 9000 K that remain largely neutral, and those with larger virial temperatures that become ionized. The lower temperature, lower mass haloes are the first to cool to 75 per cent of their virial temperature. The precise temperature and mass of the first objects are dependent upon the molecular hydrogen (H2) cooling function and the cosmological model. The higher mass haloes collapse later but, in this paradigm, cool much more efficiently once they have done so, first via electronic transitions and then via molecular cooling: in fact, a greater residual ionization once the haloes cool below 9000 K results in an enhanced H2 production and hence a higher cooling rate at low temperatures than for the lower mass haloes, so that within our constant-density model it is the former that are the first to cool to really low temperatures. We discuss the possible significance of this result in the context of CDM models in which the shallow slope of the initial fluctuation spectrum on small scales leads to a wide range of halo masses (of differing overdensities) collapsing over a small redshift interval. This ‘crosstalk’ is sufficiently important that both high- and low-mass haloes collapse during the lifetimes of the massive stars which may be formed at these epochs. Further investigation is thus required to determine which generation of haloes plays the dominant role in early structure formation.