We calculate nucleosynthesis in Population ( Pop ) III supernovae ( SNe ) and compare the yields with various abundance patterns of extremely metal-poor ( EMP ) stars .
We assume that the observed EMP stars are the second generation stars , which have the metal-abundance patterns of Pop III SNe .
Previous theoretical yields of Pop III SNe can not explain the trends in the abundance ratios among iron-peak elements ( Mn , Co , Ni , Zn ) /Fe as well as the large C/Fe ratio observed in certain EMP stars with [ Fe/H ] \mathrel { \hbox to 0.0 pt { \lower 4.0 pt \hbox { $ \sim$ } } \raise 1.0 pt \hbox { $ < $ } } -2.5 .
In the present paper , we show that if we introduce higher explosion energies and mixing-fallback in the core-collapse SN models of M \sim 20 - 130 M _ { \odot } , the above abundance features of both typical and C-rich EMP stars can be much better explained .
We suggest that the abundance patterns of the [ Fe/H ] \sim - 2.5 stars correspond to supernova yields with normal explosion energies , while those of the carbon un-enhanced ( [ C/Fe ] < 1 ) stars with [ Fe/H ] \simeq - 4 \sim - 3 correspond to high-energy supernova yields .
The abundance patterns of the C-rich ( [ C/Fe ] \mathrel { \hbox to 0.0 pt { \lower 4.0 pt \hbox { $ \sim$ } } \raise 1.0 pt \hbox { $ > $ } } 2 ) and low [ Fe/H ] ( \simeq - 5 \sim - 3.5 ) stars can be explained with the yields of faint SNe that eject little ^ { 56 } Ni as observed in SN1997D .
In the supernova-induced star formation model , we can qualitatively explain why the EMP stars formed by the faint or energetic supernovae have lower [ Fe/H ] than the EMP stars formed by normal supernovae .
We also examine how the abundance ratios among iron-peak elements depend on the electron mole fraction Y _ { e } , and conclude that a large explosion energy is still needed to realize the large Co/Fe and Zn/Fe ratios observed in typical EMP stars with [ Fe/H ] \mathrel { \hbox to 0.0 pt { \lower 4.0 pt \hbox { $ \sim$ } } \raise 1.0 pt \hbox { $ < $ } } -3.5 .