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. Model MDFs are calculated for a fiducial Galaxy formation scenario and a range of assumptions about the astrophysics of star formation and chemical enrichment at early times. The observed MDF and the apparent absence of true Population III stars from the halo strongly imply that there is some critical metallicity, Z(cr) less than or similar to 10(-4) Z(circle dot), below which low-mass star formation is inhibited and perhaps impossible. The observed constraints from the halo MDF, relative metal abundances from extremely metal-poor Galactic halo stars, and the ionizing photon budget needed to reionize the IGM together imply a stellar IMF below Zcr that is peaked in the range of massive stars that experience core-collapse supernovae, with mean mass < M > 8-42 M circle dot. This mass range is similar to the masses predicted by models of primordial star formation that account for formation feedback. A set of five plausible IMF cases is presented, ranging from broadly peaked with mean mass similar to 15 M-circle dot to narrowly peaked at mean mass similar to 70 M-circle dot. These IMF cases cannot be distinguished formally by the available constraints, but the models with lower characteristic mass produce overall better fits to the available data. The model also implies that metal-poor halo stars below [Fe/H] less than or similar to - 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.