Ultrafaint dwarf galaxies (UFDs) are typically assumed to have simple, stellar populations with star formation ending at reionization. Yet as the observations of these galaxies continue to improve, their star formation histories (SFHs) are revealed to be more complicated than previously thought. In this paper, we study how star formation, chemical enrichment, and mixing proceed in small, dark matter halos at early times using a high-resolution, cosmological, hydrodynamical simulation. The goals are to inform the future use of analytic models and to explore observable properties of the simulated halos in the context of UFD data. Specifically, we look at analytic approaches that might inform metal enrichment within and beyond small galaxies in the early Universe. We find that simple assumptions for modeling the extent of supernova-driven winds agree with the simulation on average whereas inhomogeneous mixing and gas flows have a large effect on the spread in simulated stellar metallicities. In the context of the UFDs, this work demonstrates that simulations can form halos with a complex SFH and a large spread in the metallicity distribution function within a few hundred Myr in the early Universe. In particular, bursty and continuous star formation are seen in the simulation and both scenarios have been argued from the data. Spreads in the simulated metallicities, however remain too narrow and too metal-rich when compared to the UFDs. Future work is needed to help reduce these discrepancies and advance our interpretation of the data.
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