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We utilize the hydrodynamic and N-body code 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 10^-3\ M_ yr^{-1 Mpc^-1} near z10, 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 ₂ₑ₈ₓ=10^-4\ Z_, required for the Pop~III to Pop~II transition in star formation mode until z7. 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 Z10^-2\ Z_, whereas the minimum found in externally enriched haloes is Z10^-7\ Z_. 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.
Jaacks et al. (Mon,) studied this question.