We investigate anew the distribution of absolute carbon abundance, © $=
\log,\epsilon $©, for carbon-enhanced metal-poor (CEMP) stars in the halo of
the Milky Way, based on high-resolution spectroscopic data for a total sample
of 305 CEMP stars. The sample includes 147 CEMP- (and CEMP-r/s) stars, 127
CEMP-no stars, and 31 CEMP stars that are unclassified, based on the currently
employed [Ba/Fe] criterion. We confirm previous claims that the distribution of
© for CEMP stars is (at least) bimodal, with newly determined peaks
centered on © (the high-C region) and © (the low-C
region). A very high fraction of CEMP- (and CEMP-r/s) stars belong to the
high-C region, while the great majority of CEMP-no stars reside in the low-C
region. However, there exists complexity in the morphology of the ©-[Fe/H]
space for the CEMP-no stars, a first indication that more than one class of
first-generation stellar progenitors may be required to account for their
observed abundances. The two groups of CEMP-no stars we identify exhibit
clearly different locations in the (Na)-© and (Mg)-© spaces,
also suggesting multiple progenitors. The clear distinction in © between
the CEMP- (and CEMP-) stars and the CEMP-no stars appears to be $as
successfullikely\ more\ astrophysically\ fundamental$, for the
separation of these sub-classes as the previously recommended criterion based
on [Ba/Fe] (and [Ba/Eu]) abundance ratios. This result opens the window for its
application to present and future large-scale low- and medium-resolution
spectroscopic surveys.

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