Star Formation in the First Galaxies - II: Clustered Star Formation and the Influence of Metal Line Cooling

Population III stars are believed to have been more massive than typical stars today and to have formed in relative isolation. The thermodynamic impact of metals is expected to induce a transition leading to clustered, low-mass Population II star formation. In this work, we present results from three cosmological simulations, only differing in gas metallicity, that focus on the impact of metal fine-structure line cooling on the formation of stellar clusters in a high-redshift atomic cooling halo. Introduction of sink particles allows us to follow the process of gas hydrodynamics and accretion onto cluster stars for 4 Myr corresponding to multiple local free-fall times. At metallicities at least $10^{-3}\, Z_{\odot}$, gas is able to reach the CMB temperature floor and fragment pervasively resulting in a stellar cluster of size $\sim1$ pc and total mass $\sim1000\, M_{\odot}$. The masses of individual sink particles vary, but are typically $\sim100\, M_{\odot}$, consistent with the Jeans mass when gas cools to the CMB temperature, though some solar mass fragments are also produced. At the low metallicity of $10^{-4}\, Z_{\odot}$, fragmentation is completely suppressed on scales greater than 0.01 pc and total stellar mass is lower by a factor of 3 than in the higher metallicity simulations. The sink particle accretion rates, and thus their masses, are determined by the mass of the gravitationally unstable gas cloud and the prolonged gas accretion over many Myr. The simulations thus exhibit features of both monolithic collapse and competitive accretion. Even considering possible dust induced fragmentation that would occur at higher densities, the formation of a bona fide stellar cluster seems to require metal line cooling and metallicities of at least $10^{-3}\, Z_{\odot}$.