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We calculate nucleosynthesis in Population (Pop) III supernovae (SNe) andcompare the yields with various abundance patterns of extremely metal-poor(EMP) stars. We assume that the observed EMP stars are the second generationstars, which have the metal-abundance patterns of Pop III SNe. Previoustheoretical yields of Pop III SNe cannot explain the trends in the abundanceratios among iron-peak elements (Mn, Co, Ni, Zn)/Fe as well as the large C/Feratio observed in certain EMP stars with [Fe/H] <~ -2.5. In the present paper,we show that if we introduce higher explosion energies and mixing-fallback inthe core-collapse SN models of M ~ 20 - 130 Msun, the above abundance featuresof both typical and C-rich EMP stars can be much better explained. We suggestthat the abundance patterns of the [Fe/H] ~ -2.5 stars correspond to supernovayields with normal explosion energies, while those of the carbon un-enhanced([C/Fe] < 1) stars with [Fe/H] =~ -4 ~ - 3 correspond to high-energy supernovayields. The abundance patterns of the C-rich ([C/Fe]>~ 2) and low [Fe/H] (=~ -5\~ -3.5) stars can be explained with the yields of faint SNe that eject little56Ni as observed in SN1997D. In the supernova-induced star formation model, wecan qualitatively explain why the EMP stars formed by the faint or energeticsupernovae have lower [Fe/H] than the EMP stars formed by normal supernovae. Wealso examine how the abundance ratios among iron-peak elements depend on theelectron mole fraction Ye, and conclude that a large explosion energy is stillneeded to realize the large Co/Fe and Zn/Fe ratios observed in typical EMPstars with [Fe/H] <~ -3.5.Comment: 33 pages, 17 figures, 7 tables, To appear in the Astrophysical  Journal 2005, January 1

Variations in the Abundance Pattern of Extremely Metal‐Poor Stars and Nucleosynthesis in Population III Supernovae