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abstract: |
    We describe a method for the determination of stellar \[C/Fe\] abundance ratios using low-resolution ($R = 2000$) stellar spectra from the Sloan Digital Sky Survey (SDSS) and its Galactic sub-survey, the Sloan Extension for Galactic Understanding and Exploration (SEGUE). By means of a star-by-star comparison with a set of SDSS/SEGUE spectra with available estimates of [\[C/Fe\]]{} based on published high-resolution analyses, we demonstrate that we can measure \[C/Fe\] from SDSS/SEGUE spectra with S/N $\geq 15$ Å$^{-1}$ to a precision better than 0.35 dex for stars with atmospheric parameters in the range [$T_{\rm eff}$]{} = \[4400, 6700\] K, [$\log~g$]{} = \[1.0, 5.0\], [\[Fe/H\]]{} = \[$-$4.0, $+$0.5\], and [\[C/Fe\]]{} = \[$-0.25$, $+$3.5\]. Using the measured carbon-to-iron abundance ratios obtained by this technique, we derive the frequency of carbon-enhanced stars ([\[C/Fe\]]{} $\geq
    +0.7$) as a function of \[Fe/H\], for both the SDSS/SEGUE stars and other samples from the literature. We find that the differential frequency slowly rises from almost zero to about 14% at \[Fe/H\] $\sim$ –2.4, followed by a sudden increase, by about a factor of three, to 39% from \[Fe/H\] $\sim$ –2.4 to \[Fe/H\] $\sim$ –3.7. Although the number of stars known with \[Fe/H\] $< -4.0$ remains small, 