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Star formation in the first galaxies - III. Formation, evolution, and characteristics of the first stellar cluster

We simulate the formation of a low metallicity (0.01 Zsun) stellar cluster in a dwarf galaxy at redshift z~14. Beginning with cosmological initial conditions, the simulation utilizes adaptive mesh refinement and sink particles to follow the collapse and evolution of gas past the opacity limit for fragmentation, thus resolving the formation of individual protostellar cores. A time- and location-dependent protostellar radiation field, which heats the gas by absorption on dust, is computed by integration of protostellar evolutionary tracks with the MESA code. The simulation also includes a robust non-equilibrium chemical network that self-consistently treats gas thermodynamics and dust-gas coupling. The system is evolved for 18 kyr after the first protostellar source has formed. In this time span, 30 sink particles representing protostellar cores form with a total mass of 81 Msun. Their masses range from ~0.1 Msun to 14.4 Msun with a median mass ~0.5-1 Msun. Massive protostars grow by competitive accretion while lower-mass protostars are stunted in growth by close encounters and many-body ejections. In the regime explored here, the characteristic mass scale is determined by the temperature floor set by the cosmic microwave background and by the onset of efficient dust-gas coupling. It seems unlikely that host galaxies of the first bursts of metal-enriched star formation will be detectable with the James Webb Space Telescope or other next-generation infrared observatories. Instead, the most promising access route to the dawn of cosmic star formation may lie in the scrutiny of metal-poor, ancient stellar populations in the Galactic neighborhood. The observable targets that correspond to the system simulated here are ultra-faint dwarf satellite galaxies such as Bootes II, Segue I and II, and Willman I.