Did Massive Primordial Stars Preenrich the Lyman Alpha Forest?

We examine the dynamical evolution and statistical properties of the supernova ejecta of massive primordial stars in a cosmological framework to determine whether this first population of stars could have enriched the universe to the levels and dispersions seen by the most recent observations of the Lyman-Alpha forest. We evolve a lambda CDM model in a 1 Mpc^3 volume to a redshift of z = 15 and add ``bubbles'' of metal corresponding to the supernova ejecta of the first generation of massive stars in all dark matter halos with masses greater than 5 times 10^5 solar masses. These initial conditions are then evolved to z = 3 and the distribution and levels of metals are compared to observations. In the absence of further star formation the primordial metal is initially contained in halos and filaments. Photoevaporation of metal-enriched gas due to the metagalactic ultraviolet background radiation at the epoch of reionization (z ~ 6) causes a sharp increase of the metal volume filling factor. At z = 3, ~ 2.5% of the simulation volume (approx. 20% of the total gas mass) is filled with gas enriched above a metallicity of 10^-4 Z_solar, and less than 0.6% of the volume is enriched above a metallicity of 10^-3 Z_solar. This suggests that, even with the most optimistic prescription for placement of primordial supernova and the amount of metals produced by each supernova, this population of stars cannot entirely be responsible for the enrichment of the Lyman-$\alpha$ forest to the levels and dispersions seen by current observations unless we have severely underestimated the duration of the Pop III epoch. However, comparison to observations show that Pop III supernovae can be significant contributors to the very low overdensity Lyman-Alpha forest.