First structure formation. I. Primordial star-forming regions in hierarchical models

We investigate the formation of the first primordial star clusters from hig h-a perturbations in a cold dark matter-dominated universe. For this purpos e, we have developed a powerful two-level hierarchical cosmological code wi th a realistic and robust treatment of multispecies primordial gas chemistr y, paying special attention to the formation and destruction of H-2 molecul es, nonequilibrium ionization, and cooling processes. We performed three-di mensional simulations at small scales and at high redshifts and find that? analogous to simulations of large-scale structure, a complex system of void s, filaments, sheets, and spherical knots form at the intersections of fila ments. On the total mass scales covered by our simulations (1 x 10(5) to 1 x 10(9) M-.), which collapse at redshifts z > 25, we find that only within the spherical knots can enough H-2 be formed (n(H2)/n(H) greater than or si milar to 5 x 10(-4)) to cool the gas appreciably. The time dependence of th e 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. remarkabl y well. Using a different H-2 cooling function (that of Lepp & Shull), we r epeat the calculations of Tegmark et al. We find a minimum mass that is abl e to collapse and cool via H-2 for a given redshift that is an order of mag nitude lower than that found by Tegmark et al. Furthermore, we discuss the possible implications for theories of primordial star formation from the ex tensive 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 m odel for star formation, our results would predict the very first stellar s ystems to be as small as similar to 50 M-.. Some implications for primordia l globular cluster formation scenarios are also discussed.