Metal Dispersal and the Number of Population III Stars

Two fundamental constraints on the earliest star formation conditions in the Galaxy are an apparent empirical low-metallicity threshold of-4 ? Fe/H], an and upper limit to the fraction of Population III halo stars of F _III < 4 × 10^-4. How do these observed constraints compare with predictions of simple models? This is investigated within the framework of element dispersal from clustered core-collapse SNe. Simple arguments considering turbulent mixing within multi-phase ISM suggest that the observed low-metallicity threshold is consistent with rough expected values. However, the observed limit on F _III is two orders of magnitude larger than predictions from this simple, one-zone inhomogeneous chemical evolution.