The detailed structure and the onset of galaxy formation in low-mass gaseous dark matter haloes

We present a model for the formation of the first galaxies before and after the reionization of hydrogen in the early universe. In this model, galaxy formation can only take place in dark matter haloes whose mass exceeds a redshift-dependent critical value, which, before reionization, is equal (in the simplest case) to the mass at which atomic hydrogen cooling becomes effective and, after reionization, is equal to the mass above which gas cannot remain in hydrostatic equilibrium. We define the Halo Occupation Fraction (HOF) as the fraction of haloes that host a luminous galaxy as a function of halo mass. The HOF is established by the interplay between the evolution of the critical mass and the assembly history of haloes and depends on three factors: the minimum halo mass for galaxy formation before reionization, the redshift of reionization, and the intensity of the (evolving) external photoheating rate. Our fiducial model predicts a cutoff in the galaxy mass function at a present-day halo mass, $M_{200} \sim 3\times 10^{8} \, \mathrm{M}_{\odot }$ ; 100 per cent occupation at $M_{200} \gt 5\times 10^9 \, \mathrm{M}_{\odot }$ ; and a population of starless gaseous haloes of present-day mass in the range 10⁶ ≲ M₂₀₀/M_⊙ ≲ 5 × 10⁹, in which the gas is in thermal equilibrium with the ultraviolet background radiation and in hydrostatic equilibrium in the gravitational potential of the halo. The transition between HOF = 0 and HOF = 1 reflects the stochastic nature of halo mass growth. We explore how these characteristic masses vary with model assumptions and parameter values. The results of our model are in excellent agreement with cosmological hydrodynamic simulations of galaxy formation.