Second-Generation Objects in the Universe: Radiative Cooling and Collapse of Halos with Virial Temperatures above 10⁴ K

The first generation of stars is thought to have formed in low-mass halos with T_vir < 10⁴ K where H₂ cooling is paramount. However, the efficiency of H₂ formation and cooling in these halos may have been severely limited by feedback processes. In this paper we investigate the radiative cooling and collapse of halos with virial temperatures T_vir > 10⁴ K, i.e., those that can cool in the absence of H₂ via neutral atomic lines. The evolution of these halos differs from their less massive counterparts. Efficient atomic line radiation allows rapid cooling to ~8000 K; subsequently the gas can contract nearly isothermally at this temperature. In the absence of H₂ molecules, the gas would likely settle into a locally stable disk, and only disks with unusually low spin would be unstable. However, we find that the initial atomic line cooling leaves a large, out-of-equilibrium residual free electron fraction. This allows the molecular fraction to build up to a universal value of x ≈ 10^-3, almost independently of initial density and temperature. We show that this is a nonequilibrium freeze-out value that can be understood in terms of timescale arguments. Unlike in less massive halos, H₂ formation and cooling is largely impervious to feedback from external UV fields, due to the high initial densities achieved by atomic cooling. The newly formed molecules cool the gas further to ~100 K and allow the gas to fragment on scales of a few times 100 M_☉. We investigate the importance of various feedback effects such as H₂ photodissociation from internal UV fields and radiation pressure due to Lyα photon trapping, which are likely to regulate the efficiency of star formation.