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 < $[Z/H]$<-2.15$. Finally, we create an
interpretable regression model to predict the radius of metal-rich influence of
\piii star systems within the first 7-18 Myr after the first light. The model
predicts the radius with $R_2 \gtrsim 0.4$ and mean squared error $\leq 0.06$.
The probability distribution function of predicted radii compares well to that
of observed radii with Jensen-Shannon distance $\lesssim 0.2$ for all modelled
times.
