# Self-consistent semi-analytic models of the first stars

## TL;DR

This paper introduces a semi-analytic model that tracks the evolution of the first stars and their transition to metal-enriched star formation, incorporating clustering, feedback, and merger histories to study early cosmic star formation.

## Contribution

It presents a novel semi-analytic framework that combines cosmological simulations with physical prescriptions to model early star formation and feedback processes.

## Key findings

- Varying model parameters significantly alters star formation history.
- Pop III star formation efficiency and delay time are critical factors.
- Clustering effects on feedback mechanisms are generally mild but can be significant with metal enrichment.

## Abstract

We have developed a semi-analytic framework to model the large-scale evolution of the first Population III (Pop III) stars and the transition to metal-enriched star formation. Our model follows dark matter halos from cosmological N-body simulations, utilizing their individual merger histories and three-dimensional positions, and applies physically motivated prescriptions for star formation and feedback from Lyman-Werner (LW) radiation, hydrogen ionizing radiation, and external metal enrichment due to supernovae winds. This method is intended to complement analytic studies, which do not include clustering or individual merger histories, and hydrodynamical cosmological simulations, which include detailed physics, but are computationally expensive and have limited dynamic range. Utilizing this technique, we compute the cumulative Pop III and metal-enriched star formation rate density (SFRD) as a function of redshift at $z \geq 20$. We find that varying the model parameters leads to significant qualitative changes in the global star formation history. The Pop III star formation efficiency and the delay time between Pop III and subsequent metal-enriched star formation are found to have the largest impact. The effect of clustering (i.e. including the three-dimensional positions of individual halos) on various feedback mechanisms is also investigated. The impact of clustering on LW and ionization feedback is found to be relatively mild in our fiducial model, but can be larger if external metal enrichment can promote metal-enriched star formation over large distances.