Building up the Population III initial mass function from cosmological initial conditions

We simulate the growth of a Population III stellar system, starting from cosmological initial conditions at z=100. We follow the formation of a minihalo and the subsequent collapse of its central gas to high densities, resolving scales as small as ~ 1 AU. Using sink particles to represent the growing protostars, we model the growth of the photodissociating and ionizing region around the first sink, continuing the simulation for ~ 5000 yr after initial protostar formation. Along with the first-forming sink, several tens of secondary sinks form before an ionization front develops around the most massive star. The resulting cluster has high rates of sink formation, ejections from the stellar disc, and sink mergers during the first ~ 2000 yr, before the onset of radiative feedback. By this time a warm ~ 5000 K phase of neutral gas has expanded to roughly the disc radius of 2000 AU, slowing mass flow onto the disc and sinks. By 5000 yr the most massive star grows to 20 M_sol, while the total stellar mass approaches 75 M_sol. Out of the ~ 40 sinks, approximately 30 are low-mass (M_* < 1 M_sol), and if the simulation had resolved smaller scales an even greater number of sinks might have formed. Thus, protostellar radiative feedback is insufficient to prevent rapid disc fragmentation and the formation of a high-member Pop III cluster before an ionization front emerges. Throughout the simulation, the majority of stellar mass is contained within the most massive stars, further implying that the Pop III initial mass function is top-heavy.