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 , radii ) 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>Γ</mml:mi> <mml:mo>∼</mml:mo> <mml:mo>−</mml:mo> <mml:mn>0.4</mml:mn> </mml:mrow> </mml:math> . The most massive star clusters () grow through mergers and have metallicity spreads of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mn>0.05</mml:mn> <mml:mo>−</mml:mo> <mml:mn>0.1</mml:mn> </mml:mrow> </mml:math> dex that roughly scale with mass. The second burst of star formation produce loosely bound star clusters with higher metallicities: at lower SFEs (2 - 20%). At <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>z</mml:mi> <mml:mo>∼</mml:mo> <mml:mn>8.7</mml:mn> </mml:mrow> </mml:math> , a nuclear star cluster (NSC) is seeded, growing 83% of its mass (, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mn>20</mml:mn> <mml:mi>%</mml:mi> </mml:mrow> </mml:math> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>z</mml:mi> <mml:mo>≳</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:math> .