Critical Metallicities for Second-Generation Stars

The first massive stars may influence the formation of second-generation stars, in part by their metal enrichment of the surrounding gas. We investigate the "critical metallicity", defined as the the value, Z_crit, at which primordial gas cools more efficiently by fine-structure lines of O I (63.18 microns, Si II 34.8 microns, Fe II (25.99 and 35.35 microns), and C II (157.74 microns) than by either H I or H2 line emission. We explore the time-dependent thermodynamics and fragmentation of cooling gas at redshifts z = 10-30, seeded by trace heavy elements expelled from early supernovae. Because different modes of nucleosynthesis (alpha-process, Fe-group) produce abundance ratios far from solar values, these early stellar populations are likely to be influenced by O, Si, and Fe cooling. Our models also include radiative coupling of the fine structure lines and H2 to the cosmic microwave background (CMB), which sets a temperature floor (70-80K at z = 25-30) that may increase the Jeans mass. The H2 forms from catalytic effects of electrons left over from the recombination epoch or produced during virialization. These electrons form the H^- ion (H + e -> H- + gamma), which in turn forms H2 through associative detachment (H- + H -> H2 + e). In virialized halos at z = 10-30, the gas densities (n = 1-100 cm^{-3}) are well below the critical densities, n_cr = 10^{5-6} cm^{-3}, at which (O, Si, Fe) fine-structure lines reach LTE populations and produce their most efficient cooling. Thus, Z_crit may initially exceed 0.01 Z_sun at n = 1-100 cm^{-3}, and then drop to 10^{-3.5} Z_sun at n = 10^6 cm^{-3}, where the Jeans mass may be imprinted on the stellar mass function. Primordial clouds of 10^8 M_sun at 0.01 Z_sun and 200K will produce redshifted fine structure lines, with fluxes between 10^{-22} and 10^{-21} Watts/m^2 at z = 4.