Baseline Metal Enrichment from Population III Star Formation in
  Cosmological Volume Simulations
  We utilize the hydrodynamic and N-body code {\small GIZMO} coupled with our
newly developed sub-grid Population~III (Pop~III) Legacy model, designed
specifically for cosmological volume simulations, to study the baseline metal
enrichment from Pop~III star formation at $z>7$. In this idealized numerical
experiment, we only consider Pop~III star formation. We find that our model
Pop~III star formation rate density (SFRD), which peaks at $\sim 10^{-3}\ {\rm
M_\odot yr^{-1} Mpc^{-1}}$ near $z\sim10$, agrees well with previous numerical
studies and is consistent with the observed estimates for Pop~II SFRDs. The
mean Pop~III metallicity rises smoothly from $z=25-7$, but does not reach the
critical metallicity value, $Z_{\rm crit}=10^{-4}\ Z_\odot$, required for the
Pop~III to Pop~II transition in star formation mode until $z\simeq7$. This
suggests that, while individual halos can suppress in-situ Pop~III star
formation, the external enrichment is insufficient to globally terminate
Pop~III star formation. The maximum enrichment from Pop~III star formation in
star forming dark matter halos is $Z\sim10^{-2}\ Z_\odot$, whereas the minimum
found in externally enriched haloes is $Z\gtrsim10^{-7}\ Z_\odot$. Finally,
mock observations of our simulated IGM enriched with Pop~III metals produce
equivalent widths similar to observations of an extremely metal poor damped
Lyman alpha (DLA) system at $z=7.04$, which is thought to be enriched by
Pop~III star formation only.
