First Structure Formation. I. Primordial Star‐forming Regions in Hierarchical Models

Abstract

We investigate the formation of the first primordial star clusters from high-σ perturbations in a cold dark matter-dominated universe. For this purpose, we have developed a powerful two-level hierarchical cosmological code with a realistic and robust treatment of multispecies primordial gas chemistry, paying special attention to the formation and destruction of H 2 molecules, nonequilibrium ionization, and cooling processes. We performed three-dimensional simulations at small scales and at high redshifts and find that, analogous to simulations of large-scale structure, a complex system of voids, filaments, sheets, and spherical knots form at the intersections of filaments. On the total mass scales covered by our simulations (1 × 10 5 to 1 × 10 9 M ☉ ), which collapse at redshifts z > 25, we find that only within the spherical knots can enough H 2 be formed ( n / n ≳5 × 10 −4 ) to cool the gas appreciably. The time dependence of the formation of H 2 molecules and the final H 2 fraction in the simulations agree with the theoretical predictions of Abel and Tegmark et al. remarkably well. Using a different H 2 cooling function (that of Lepp & Shull), we repeat the calculations of Tegmark et al. We find a minimum mass that is able to collapse and cool via H 2 for a given redshift that is an order of magnitude lower than that found by Tegmark et al. Furthermore, we discuss the possible implications for theories of primordial star formation from the extensive merging of small structure inherent in hierarchical models. In our simulation, typically only 5%-8% percent of the total baryonic mass in the collapsing structures is found to cool significantly. Assuming the Padoan model for star formation, our results would predict the very first stellar systems to be as small as ~50 M ☉ . Some implications for primordial globular cluster formation scenarios are also discussed.