Metal enrichment by the first-generation ( Pop III ) stars is the very first step of the matter cycle in the structure formation and it is followed by the formation of extremely metal-poor ( EMP ) stars .
To investigate the enrichment process by the Pop III stars , we carry out a series of numerical simulations including the feedback effects of photoionization and supernovae ( SNe ) of Pop III stars with a range of masses of minihaloes ( MHs ) , M _ { halo } , and Pop III stars , M _ { PopIII } .
We find that the metal-rich ejecta reaches neighbouring haloes and external enrichment ( EE ) occurs when the halo binding energy is sufficiently below the SN explosion energy , E _ { { SN } } .
The neighbouring haloes are only superficially enriched , and the metallicity of the clouds is { [ Fe / H ] } < -5 .
Otherwise , the SN ejecta falls back and recollapses to form enriched cloud , i.e .
internal enrichment ( IE ) process takes place .
In case that a Pop III star explodes as a core-collapse SNe ( CCSNe ) , MHs undergo IE , and the metallicity in the recollapsing region is -5 \lesssim { [ Fe / H ] } \lesssim - 3 in most cases .
We conclude that IE from a single CCSN can explain the formation of EMP stars .
For pair-instability SNe ( PISNe ) , EE takes place for all relevant mass range of MHs , consistent with no observational sign of PISNe among EMP stars .