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 $10^{-3}\, Z_{\odot}$.
