Early phases of the chemical evolution and formation history of extremely metal poor ( EMP ) stars are investigated using hierarchical galaxy formation models .
We build a merger tree of the Galaxy according to the extended Press-Schechter theory .
We follow the chemical evolution along the tree , and compare the model results to the metallicity distribution function ( MDF ) and abundance ratio distribution of the Milky Way halo .
We adopt three different initial mass functions ( IMFs ) .
In a previous studies , we argue that typical mass of EMP stars should be high-mass ( \sim 10 M _ { \odot } ) based on studies of binary origin carbon-rich EMP stars .
In this study , we show that only the high-mass IMF can explain a observed small number of EMP stars .
For relative element abundances , the high-mass IMF and the Salpeter IMF predict similar distributions .
We also investigate dependence on nucleosynthetic yields of supernovae ( SNe ) .
The theoretical SN yields by Kobayashi et al .
( 2006 ) and Chieffi & Limonge ( 2004 ) show reasonable agreement with observations for \alpha -elements .
Our model predicts significant scatter of element abundances at [ { Fe } / { H } ] < -3 .
Best fit yields for one zone chemical evolution model by Francois et al .
( 2004 ) well reproduces the trend of the typical abundances of EMP stars but our model with their yield predicts much larger scatter of abundances than the observations .
The model with hypernovae predicts Zn abundance in agreement with observations but other models predict lower [ { Zn } / { Fe } ] .
Ejecta from the hypernovae with large explosion energy is mixed in large mass and decreases scatter of the element abundances .