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Mixing and fallback models in faint supernova models are supposed toreproduce the abundance patterns of observed carbon-enhanced metal-poor (CEMP)stars in the Galactic halo. A fine tuning of the model parameters forindividual stars is required to reproduce the observed ratios of carbon toiron. We focus on extremely metal-poor stars formed out of the ejecta from themixing and fallback models using a chemical evolution model. Our chemicalevolution models take into account the contribution of individual stars tochemical enrichment in host halos together with their evolution in the contextof the hierarchical clustering. Parametrized models of mixing and fallbackmodels for Pop. III faint supernovae are implemented in the chemical evolutionmodels with merger trees to reproduce the observed CEMP stars. A variety ofchoices for model parameters on star formation and metal-pollution by faintsupernovae is unable to reproduce the observed stars with [Fe/H] < -4 and [C/H]> -2, which are the majority of CEMP stars among the lowest metallicity stars.Only possible solution is to form stars from small ejecta mass, which producesan inconsistent metallicity distribution function. We conclude that not all theCEMP stars are explicable by the mixing and fallback models. We also tested thecontribution of binary mass transfers from AGB stars that are also supposed toreproduce the abundances of known CEMP stars. This model reasonably reproducesthe distribution of carbon and iron abundances simultaneously only if we assumethat long-period binaries are favored at [Fe/H] < -3.5.

Are Faint Supernovae Responsible for Carbon-Enhanced Metal-Poor Stars?