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 realistic sub-grid star formation efficiency (SFE) model, derived from AU-scale radiation-MHD simulations of molecular clouds with varying mass, density, and metallicity. Using this model for cloud-scale SFEs, the galaxy forms stars stochastically, assembling most of its 10⁶~ M_ in stars by redshift $z=8$ through two star-forming bursts (SFBs), each lasting ~10~ Myr, separated by 80~ Myr of quiescence. Clouds reach SFEs up to $80%$ during the first SFB, forming bound star clusters (densities ~10²⁻⁴ ~ M_\:pc⁻², radii 3~ pc) resembling those observed by the James Webb Space Telescope (JWST) in strongly lensed galaxies. Star clusters follow a flat power-law mass function with slope Γ ~ -0.4. The most massive star clusters (10⁴⁻⁵ ~ M_) grow through mergers and have metallicity spreads of $0.05 - 0.1$ dex that roughly scale with mass. The second SFB forms loosely bound star clusters with higher metallicities: -1.95 < log(Z/ Z_) < -1.50 at lower SFEs ($2 - 20%$). At z ~ 8.7, a nuclear star cluster (NSC) is seeded, growing $83%$ of its mass (2.4 × 10⁵ ~ M_, $20%$ 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 5.