The non-linear evolution of baryonic overdensities in the early universe: initial conditions of numerical simulations

We run very large cosmological N-body hydrodynamical simulations in order to study statistically the baryon fractions in early dark matter haloes. We critically examine how differences in the initial conditions affect the gas fraction in the redshift range z = 11-21. We test three different linear power spectra for the initial conditions. (1) A complete heating model, which is our fiducial model; this model follows the evolution of overdensities correctly, according to Naoz & Barkana (2005), in particular including the spatial variation of the speed of sound of the gas due to Compton heating from the CMB. (2) An equal-delta model, which assumes that the initial baryon fluctuations are equal to those of the dark matter, while conserving sigma(8) of the total matter. (3) A mean c(s) model, which assumes a uniform speed of sound of the gas. The latter two models are often used in the literature. We calculate the baryon fractions for a large sample of haloes in our simulations. Our fiducial model implies that before reionization and significant stellar heating took place, the minimum mass needed for a minihalo to keep most of its baryons throughout its formation was similar to 3 x 10(4) M-circle dot. However, the alternative models yield a wrong (higher by about 50 per cent) minimum mass, since the system retains a memory of the initial conditions. We also demonstrate this using the 'filtering mass' from linear theory, which accurately describes the evolution of the baryon fraction throughout the simulated redshift range.