The onset of star formation in primordial haloes

Context. Star formation remains an unsolved problem in astrophysics. Numerical studies of large-scale structure simulations cannot resolve the process and their approach usually assumes that only gas denser than a typical threshold can host and form stars. Aims. We investigate the onset of cosmological star formation and compare several very-high-resolution, three-dimensional, N-body/SPH simulations that include non-equilibrium, atomic and molecular chemistry, star formation prescriptions, and feedback effects. Methods. We study how primordial star formation depends on gas density threshold, cosmological parameters, and initial set-ups. Results. For mean-density initial conditions, we find that standard low-density star-formation threshold (0.2 h(2) cm(-3)) models predict the onset of star formation at z similar to 25-31, depending on the adopted cosmology. In these models, stars are formed automatically when the gas density increases above the adopted threshold, regardless of the time between the moment when the threshold is reached and the effective runaway collapse. While this is a reasonable approximation at low redshift, at high redshift this time interval represents a significant fraction of the Hubble time and thus this assumption can induce large artificial offsets to the onset of star formation. Choosing higher density thresholds (135 h(2) cm(-3)) allows the entire cooling process to be followed, and the onset of star formation is then estimated to be at redshift z similar to 12-16. When isolated, rare, high-density peaks are considered, the chemical evolution is much faster and the first star formation episodes occur at z greater than or similar to 40, almost regardless of the choice of the density threshold. Conclusions. These results could have implications for the formation redshift of the first cosmological objects, as inferred from direct numerical simulations of mean-density environments and studies of the reionization history of the universe.