The number and metallicities of the most metal-poor stars
  Simple, one-zone models for inhomogeneous chemical evolution of the Galactic halo are used to predict the number fraction of zero-metallicity, Population III stars, which currently is empirically estimated at < 4e-4. These analytic models minimize the number of free parameters, highlighting the most fundamental constraints on halo evolution. There are disagreements of at least an order of magnitude between observations and predictions in limiting cases for both homogeneous Simple Model and Simple Inhomogeneous Model (SIM). Hence, this demonstrates a quantitative, unambiguous discrepancy in the observed and expected fraction of Population III stars. We explore how the metallicity distribution of the parent enrichment events f(z_0) drives the SIM and predictions for the Population III fraction. The SIM shows that the previously-identified "high halo" and "low halo" populations are consistent with a continuous evolutionary progression, and therefore may not necessarily be physically distinct populations. Possible evolutionary scenarios for halo evolution are discussed within the SIM's simplistic one-zone paradigm.   The values of z_0 depend strongly on metal dispersal processes, thus we investigate interstellar mixing and mass transport, for the first time explicitly incorporating this into a semi-analytic chemical evolution model. Diffusion is found to be inefficient for all phases, including the hot phase, of the interstellar medium (ISM): relevant diffusion lengths are 2 - 4 orders of magnitude smaller than corresponding length scales for turbulent mixing. Rough relations for dispersal processes are given for multiphase ISM. These suggest that the expected low-metallicity threshold above zero is consistent with the currently observed limit. 
M. S. Oey