We present an analytical and phenomcnological model for metal enrichment in halos based on hierarchical structure formation. This model assumes that astration of normal stellar populations along with Type Ⅱ super-novae (SNe Ⅱ) already occurs at very high redshift. It focuses on the regime of [Fe/H] < -1, in which SNe Ia are not major contributors. The regime of [Fe/H] > - 1, in which SNe Ia are major contributors, is also discussed in general. For halos that are not disrupted by SN Ⅱ explosions, the chemical evolution of the gas and stars is explicitly determined by the rate of gas infall as compared with the astration rate and the corresponding rate of metal production by SNe Ⅱ per H atom in the gas. This model provides a good description of the data on [Fe/H] for damped Lyα systems over a wide range of redshift, 0.5 < z < 5. For all halos not disrupted by SN Ⅱ explosions, if there is a cessation of gas infall, the metallicities of the stars follow a bimodal distribution. This distribution is characterized by a sharp peak at the value of [Fe/H] corresponding to the time of infall cessation and by a broad peak at a higher value of [Fe/H] corresponding to the subsequent period of astration during which the bulk of the remaining gas forms stars. Such a distribution can be compared with that observed for the Galactic halo stars. If the gas in a halo is rapidly lost on cessation of infall, then an assemblage of stars with a very sharply defined [Fe/H] value will be left behind. This assemblage of stars may be accreted by a larger system and become a globular cluster of the larger system. We discuss the masses and metallicities of the globular clusters in this model considering the criterion for the onset of astration and possible disruption of low-mass halos by SN Ⅱ explosions. The implications of possible globular clusters with very low metallicities of [Fe/H] approx < 3 are also discussed.
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