Self-consistent Semi-analytic Modeling of Feedback During Primordial Star Formation and Reionization

We present a new semi-analytic model of the formation of the first stars. Our method takes dark matter halo merger trees (including 3-dimensional spatial information) from cosmological N-body simulations as input and applies analytic prescriptions to compute both the Population III (Pop III) and metal-enriched star formation histories. We have developed a novel method to accurately compute the major feedback processes affecting Pop III star formation: H$_2$ photodissociation from Lyman-Werner (LW) radiation, suppression of star formation due to inhomogeneous reionization, and metal enrichment via supernovae winds. Our method utilizes a grid-based approach relying on fast Fourier transforms (FFTs) to rapidly track the LW intensity, ionization fraction, and metallicity in 3-dimensions throughout the simulation box. We present simulations for a wide range of astrophysical model parameters from $z\approx 30-6$. Initially long-range LW feedback and local metal enrichment and reionization feedback dominate. However, for $z \lesssim 15$ we find that the star formation rate density (SFRD) of Pop III stars is impacted by the combination of external metal enrichment (metals from one halo polluting other pristine halos) and inhomogeneous reionization. We find that the interplay of these processes is particularly important for the Pop III SFRD at $z \lesssim 10$. Reionization feedback delays star formation long enough for metal bubbles to reach halos that would otherwise form Pop III stars. Including these effects can lead to more than an order of magnitude decrease in the Pop III SFRD at $z=6$ compared to LW feedback alone.