Connecting Primordial Star Forming Regions and Second Generation Star Formation in the Phoenix Simulations

We introduce the {\em Phoenix Simulations}, a suite of highly resolved cosmological simulations featuring hydrodynamics, primordial gas chemistry, Population III and II star formation and feedback, UV radiative transfer, and saved outputs with \(\Delta t\)=200 kyr. The suite samples 73,523 distinct primordial star formation events within \npiii distinct regions, forming \ngii second-generation enriched star clusters by \(z \geq 12\) within a cumulative 156.25 Mpc\(^3\) volume. The regions that lead to enriched star formation contain up to \(167\) primordial stars, with 78.7 \% of regions having experienced multiple types of primordial supernovae. The extent of a primordial region, measured by its metal-rich surrounding cloud, is highly variable: the average region has radius \(\sim 3\) kpc, with 95 \% confidence limit on the distribution of measured radii is \(\sim 5-7\) kpc. For continuing star formation, we find that the metallicity distribution of second generation stars is similar to that of subsequent Population II star formation, with both distributions spanning hyper metal-deficient ([Z/H]\(\sim-7\)) to super-solar ([Z/H]\(\sim0.8\)). We find that the metallicity of second generation stars has no strong dependence on the configuration of progenitor supernovae, with the mean metallicity of second-generation stars having \(-1.73 < \)[Z/H]\(