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It is known that the carbon-enhanced, extremely metal-poor (CEMP) starsconstitute a substantial proportion in the extremely metal-poor (EMP) stars ofthe Galactic Halo, by far larger than CH stars in Population II stars. Weinvestigate their origin with taking into account an additional evolutionarypath to the surface carbon-enrichment, triggered by hydrogen engulfment by thehelium flash convection, in EMP stars of $[Fe/H] \lesssim -2.5$. This processis distinct from the third dredge-up operating in more metal-rich stars andalso in EMP stars. In binary systems of EMP stars, the secondary stars becomeCEMP stars through mass transfer from the primary stars of low and intermediatemasses, which have developed the surface carbon-enhancement. Our binaryscenario can predict the variations in the abundances not only for carbon butalso for nitrogen and s-process elements and reasonably explain the observedproperties such as the stellar distributions with respect to the carbonabundances, the binary periods, and the evolutionary stages. Furthermore, fromthe observed frequencies of CEMP stars with and without s-process elementenhancement, we demonstrate that the initial mass function of EMP stars need togive the mean mass $~10\msun$ under the reasonable assumptions on thedistributions of orbital separations and mass ratio of binary components. Thisalso indicates that the currently observed EMP stars were exclusively born asthe secondary members of binaries, making up $\sim 10%$ remnants of EMP binarysystems of mass $~10^8\msun$ in total; in addition to CEMP stars with whitedwarf companions, a significant fraction of them have experienced supernovaexplosions of their companions. We discuss the implications of the presentresults in relation to the formation of Galactic halo.Comment: 66 pages, 12 figures, 2 tables Accepted for publication in Ap

The Origin of Carbon Enhancement and the Initial Mass Function of Extremely Metal‐poor Stars in the Galactic Halo