From Primordial Stars to Early Galaxies: A Semi-Analytic Model Calibrated with Aeos and Renaissance

TL;DR

The study tackles how to reliably model the birth of the first stars and galaxies by coupling a fast semi-analytic framework to two complementary hydrodynamic simulations, Aeos and Renaissance, using DM merger trees and reionization feedback. The authors calibrate the SAM to Aeos for detailed Pop III and metal-enriched Pop II behavior and to Renaissance for broader, high-mass halos, enabling accurate tracking of early star formation over a wide halo mass range. A key finding is that incorporating scatter in the critical mass $M_{ m crit}$ requires a modified, mass- and redshift-aware prescription to avoid spurious low-mass Pop III halos, while a delay distribution $t_{ m delay}$ governs the Pop III-to-Pop II transition accounting for feedback and metal mixing. The calibrated SAM reproduces Aeos results at $z>17$, extends predictions to DM-only volumes (e.g., predicting $\sim 10$ Pop III sources in the MACS J0416 lensed area by $z\sim10$), and offers a computationally efficient tool to forecast the earliest stages of cosmic star formation and its observables with JWST. This framework thus bridges small-scale primordial physics and large-scale structure, enabling rapid exploration of reionization, metal enrichment, and early galaxy formation with practical relevance to upcoming observations.

Abstract

We present an extension of our semi-analytic model that follows the formation of Population III stars and their metal-enriched descendants, incorporating dark matter halo merger trees from cosmological $N$-body simulations and feedback from reionization. Our extended model is calibrated using two complementary cosmological hydrodynamical simulations: Aeos, which resolves individual Population III and II stars to $z\sim14.6$, and Renaissance, which is lower resolution but follows large-scale metal-enriched star formation to $z \sim 11$. With a combined calibration, we capture small-scale physics of primordial star formation over a large range in halo mass. We find good agreement between our calibrated model and Aeos, reproducing the evolution in number of star-forming halos and total stellar mass. Achieving this agreement requires increasing the normalization of, flattening the redshift dependence of, and adding scatter to the commonly used critical mass threshold $M_{\mathrm{crit}}$. Our treatment of the delay between Pop III stellar death and subsequent Pop II star formation emphasizes the need to account for halos that have yet to transition to Pop II, since incomplete sampling of this delay in simulations limits physically motivated calibrations. Finally, we apply our model to larger-volume dark matter only simulations and predict $\sim10$ active Pop III sources at $z = 10$ lie within the area strongly lensed by galaxy cluster MACS J0416 with a magnification exceeding $μ> 30$. These results demonstrate that semi-analytic approaches, when calibrated to hydrodynamical simulations, can provide accurate, computationally efficient predictions for the earliest stages of cosmic star formation.

Figures (7)

• Figure 1: Virial masses for halos hosting the first Pop III stars in A eos(black points) compared to a single realization of our semi-analytic model (orange diamonds) and a realization of the SAM using an unmodified $M_{\mathrm{crit}}$ from Kulkarni2021, shown with purple crosses. The green dashed line shows our modified $M_{\mathrm{crit}}$ from Equation (\ref{['eq:MCrit']}), while the purple dash-dotted line shows the unmodified $M_{\mathrm{crit}}$ from Kulkarni2021. Our modification corrects for the effect introduced by applying scatter to $M_{\mathrm{crit}}$, which otherwise produces an artificial excess of low mass Pop III forming halos. This adjustment brings the distribution of Pop III host halos into closer agreement with A eos.
• Figure 2: The delay period before the formation of metal-enriched Pop II stars following the death of the first Pop III star for A eos(black) and a single realization of the SAM (orange). Open points are the Pop III formation redshift and filled points are the redshift of Pop II formation for a single halo.
• Figure 3: Metal-enriched Pop II starburst masses for the A eos halos (black points) and the sample of Renaissance halos (green crosses) from Hazlett2025 during the bursty stage compared with the halo virial mass and redshift at the starburst. The best fit power law (solid) along with 1$\sigma$ lines (dashed) is shown. Overall, the A eos halos extend the burst mass relation to lower mass halos than Renaissance.
• Figure 4: Total number of halos hosting Pop III (blue) and Pop II stars (yellow). The results from A eos are shown by thick solid lines for Pop III and Pop II, respectively. The results of 10 realizations of our fiducial SAM for Pop III and Pop II are also shown, with the dashed line representing the average and the shaded region extending between the maximum and minimum total stellar masses of the 10 simulations. The HighEsc densely dot-dashed lines show a realization using higher ionizing radiation escape fractions. The NoReionExt densely dashed lines show the impact of excluding reionization and external enrichment from the SAM. The Hazlett+2025 dotted lines show results from the SAM calibrated only to the Renaissance simulations. The Kulkarni+2021 dot-dashed lines show the impact of using the unmodified $M_{\mathrm{crit}}$ from Kulkarni2021.
• Figure 5: Total stellar masses for Pop III and metal-enriched Pop II stars following the same convention for lines as the previous figure.