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

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 $~10\msun$ 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 $~10^8\msun$ 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.