We show that SDSS J170733.93+585059.7 (hereafter SDSS J1707+58), previously identified by Aoki and collaborators as a carbon-enhanced metal-poor star (with s-process-element enhancements; CEMP-s), on the assumption that it is a main-sequence turn-off
star, is the RR Lyrae star VIII-14 identified by the Lick Astrograph Survey. Revised abundances for SDSS J1707+58 are [Fe/H] = -2.92, [C/Fe] = +2.79, and [Ba/Fe] = +2.83. It is thus one of the most metal-poor RR Lyrae stars known, and has more extreme [C/Fe] and [Ba/Fe] than the only other RR Lyrae star known to have a CEMP-s spectrum (TY Gru). Both stars are Oosterhoff II stars with prograde kinematics, in contrast to stars with [C/Fe] < +0.7, such as KP Cyg and UY CrB, which are disk stars. Twelve other RR Lyrae stars with [C/Fe] >= +0.7 are presented as CEMP candidates for further study.
(Abridged) Carbon-enhanced metal-poor (CEMP) stars in the halo components of the Milky Way are explored, based on accurate determinations of the carbon-to-iron ([C/Fe]) abundance ratios and kinematic quantities for over 30000 calibration stars from t
he Sloan Digital Sky Survey (SDSS). Using our present criterion that low-metallicity stars exhibiting [C/Fe] ratios (carbonicity) in excess of [C/Fe]$ = +0.7$ are considered CEMP stars, the global frequency of CEMP stars in the halo system for feh $< -1.5$ is 8%; for feh $< -2.0$ it is 12%; for feh $<-2.5$ it is 20%. We also confirm a significant increase in the level of carbon enrichment with declining metallicity, growing from $<$[C/Fe]$>$ $sim +1.0$ at feh $= -1.5$ to $<$[C/Fe]$>$ $sim +1.7$ at feh $= -2.7$. The nature of the carbonicity distribution function (CarDF) changes dramatically with increasing distance above the Galactic plane, $|$Z$|$. For $|$Z$|$ $< 5$ kpc, relatively few CEMP stars are identified. For distances $|$Z$|$ $> 5$ kpc, the CarDF exhibits a strong tail towards high values, up to [C/Fe] $>$ +3.0. We also find a clear increase in the CEMP frequency with $|$Z$|$. For stars with $-2.0 <$ [Fe/H] $< -$1.5, the frequency grows from 5% at $|$Z$|$ $sim 2$ kpc to 10% at $|$Z$|$ $sim 10$ kpc. For stars with [Fe/H] $< -$2.0, the frequency grows from 8% at $|$Z$|$ $sim 2$ kpc to 25% at $|$Z$|$ $sim 10$ kpc. For stars with $-2.0 <$ [Fe/H] $< -$1.5, the mean carbonicity is $<$[C/Fe]$>$ $sim +1.0$ for 0 kpc $<$ $|$Z$|$ $<$ 10 kpc, with little dependence on $|$Z$|$; for [Fe/H] $< -$2.0, $<$[C/Fe]$>$ $sim +1.5$, again roughly independent of $|$Z$|$.
Recent observations of r-process-enriched metal-poor star abundances reveal a non-uniform abundance pattern for elements $Zleq47$. Based on non-correlation trends between elemental abundances as a function of Eu-richness in a large sample of metal-po
or stars, it is shown that the mixing of a consistent and robust light element primary process (LEPP) and the r-process pattern found in r-II metal-poor stars explains such apparent non-uniformity. Furthermore, we derive the abundance pattern of the LEPP from observation and show that it is consistent with a missing component in the solar abundances when using a recent s-process model. As the astrophysical site of the LEPP is not known, we explore the possibility of a neutron capture process within a site-independent approach. It is suggested that scenarios with neutron densities $n_{n}leq10^{13}$ $cm^{-3}$ or in the range $n_{n}geq10^{24}$ $cm^{-3}$ best explain the observations.
