Chemical Evolution in Hierarchical Models Of Cosmic Structure I: Constraints on the Early Stellar Initial Mass Function

I present a new Galactic chemical evolution model motivated by and grounded in the hierarchical theory of galaxy formation, as expressed by a halo merger history of the Galaxy. This model accurately reproduces the metallicity distribution function (MDF) for Population II stars residing today in the Galactic halo. The observed MDF and the apparent absence of true Population III stars from the halo strongly imply that there is some critical metallicity, Z_crit <~ 10^-4 Z_sun, below which low-mass star formation is inhibited, and perhaps impossible. The observed constraints from the halo MDF, relative metal abundances from Galactic halo stars, and the ionizing photon budget needed to reionize the IGM together imply a stellar IMF that is peaked in the range of massive stars that experience core-collapse supernovae, with mean mass <M> = 8 - 42 Msun. This mass range is similar to the masses predicted by models of primordial star formation that account for formation feedback. The model also implies that metal-poor halo stars below [Fe/H] <~ -3 had only 1 - 10 metal-free stars as their supernova precursors, such that the relative abundances in these halo stars exhibit IMF-weighted averages over the intrinsic yields of the first supernovae. This paper is the first part of a long term project to connect the high-redshift in situ indicators of early star formation with the low-z, old remnants of the first stars.