It is known that the carbon-enhanced , extremely metal-poor ( CEMP ) stars constitute a substantial proportion in the extremely metal-poor ( EMP ) stars of the Galactic Halo , by far larger than CH stars in Population II stars .
We investigate their origin with taking into account an additional evolutionary path to the surface carbon-enrichment , triggered by hydrogen engulfment by the helium flash convection , in EMP stars of [ { Fe } / { H } ] \lesssim - 2.5 .
This process is distinct from the third dredge-up operating in more metal-rich stars and also in EMP stars .
In binary systems of EMP stars , the secondary stars become CEMP stars through mass transfer from the primary stars of low and intermediate masses , which have developed the surface carbon-enhancement .
Our binary scenario can predict the variations in the abundances not only for carbon but also for nitrogen and s-process elements and reasonably explain the observed properties such as the stellar distributions with respect to the carbon abundances , the binary periods , and the evolutionary stages .
Furthermore , from the observed frequencies of CEMP stars with and without s-process element enhancement , we demonstrate that the initial mass function of EMP stars need to give the mean mass \sim 10 M _ { \odot } under the reasonable assumptions on the distributions of orbital separations and mass ratio of binary components .
This also indicates that the currently observed EMP stars were exclusively born as the secondary members of binaries , making up \sim 10 \% remnants of EMP binary systems of mass \sim 10 ^ { 8 } M _ { \odot } in total ; in addition to CEMP stars with white dwarf companions , a significant fraction of them have experienced supernova explosions of their companions .
We discuss the implications of the present results in relation to the formation of Galactic halo .