Seeding Cores: A Pathway for Nuclear Star Clusters from Bound Star Clusters in the First Billion Years

We model the formation of star clusters in a dwarf galaxy progenitor during the first 700 Myr of cosmic history using a cosmological radiation-hydrodynamic simulation with a sub-grid star formation efficiency (SFE) model calibrated from AU-scale radiation-MHD simulations of molecular clouds with varying mass, density, and metallicity. In comparison to a constant SFE model, our model yields more bursty star formation, a more abundant massive star cluster population, and overall a higher stellar mass. Clouds reach SFEs up to 80%, forming bound star clusters (densities \(\sim10^{2-4} ~{\rm M_\odot\:pc^{-2}}\), radii \(\lesssim 3~{\rm pc}\)) resembling those observed by the James Webb Space Telescope (JWST) in strongly lensed galaxies. Star clusters follow a flat power-law mass function \({\rm d}N/{\rm d}\log M \propto M^\Gamma\) with slope \(\Gamma \sim -0.4\). The most massive star clusters (\(10^{4-5} ~{\rm M_\odot}\)) grow through mergers and have metallicity spreads of \(0.05 - 0.1\) dex that roughly scale with mass. The second burst of star formation produce loosely bound star clusters with higher metallicities: \(-1.95 < \log(Z/{\rm Z_\odot}) < -1.50\) at lower SFEs (2 - 20%). At \(z \sim 8.7\), a nuclear star cluster (NSC) is seeded, growing 83% of its mass (\(2.4 \times 10^5 ~{\rm M_\odot}\), \(20\%\) of the galaxy’s stellar mass) through mergers with pre-existing clusters and the rest through in-situ star formation. The early formation of NSCs has interesting implications for seeding supermassive black holes and the population of little red dots recently discovered by JWST at \(z \gtrsim 5\).