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, $M_{200} \sim 3\times 10^{8} M_{\odot}$; 100\%
occupation at $M_{200} > 5\times 10^9 M_{\odot}$; and a population of starless
gaseous haloes of present-day mass in the range $10^{6} \lesssim M_{200} /
M_{\odot}\lesssim 5\times 10^{9}$, 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.
