A Framework to Calibrate a Semianalytic Model of the First Stars and Galaxies to the Renaissance Simulations

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We present a method that calibrates a semianalytic model to the Renaissance Simulations, a suite of cosmological hydrodynamical simulations with high-redshift galaxy formation. This approach combines the strengths of semianalytic techniques and hydrodynamical simulations, enabling the extension to larger volumes and lower redshifts that are inaccessible to simulations due to computational expense. Using a sample of Renaissance star formation histories from an average density region of the Universe, we construct a four-parameter prescription for metal-enriched star formation characterized by an initial bursty stage followed by a steady stage where stars are formed at constant efficiencies. Our model also includes a treatment of Pop III star formation where a minimum halo mass and log-normal distribution of stellar mass are adopted to match the numerical simulations. Star formation is generally well reproduced for halos with masses ≲109 M ⊙. Between 11 < z < 25 our model produces metal-enriched star formation rate densities (SFRDs) that typically agree with Renaissance within a factor of ∼2 for the average density region. Additionally, the total metal-enriched stellar mass only differs from Renaissance by about 10% at z ∼ 11. For regions that are either more overdense or rarefied and not included in the calibration, we produce metal-enriched SFRDs that agree with Renaissance within a factor of ∼2 at high-z but eventually differ by higher factors for later times. This is likely due to environmental dependencies not included in the model. Our star formation prescriptions can easily be adopted in other analytic or semianalytic works to match our calibration to Renaissance.