1. Introduction
1.1 Current empirical limit
2. Predictions in the homogeneous limit
3. Inhomogeneous limit: No mixing
3.1 The fraction of Population III stars
3.2 The low-metallicity threshold
4. Interstellar dispersal
4.1 Diffusion
4.2 Turbulent mixing
4.3 The dispersal of metals
5. Inhomogeneous limit: Dispersal by mixing
5.1 Mixed-dispersal, high-evolution SIM
5.2 Mixed-dispersal, low-evolution model
6. Discussion
6.1 The low-metallicity threshold
6.2 The fraction of Population III stars
6.3 Predicted and observed MDFs
6.4 Halo evolution
7. Conclusion
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