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Dwarf carbon (dC) stars, main sequence stars showing carbon molecular bands, were initially thought to be a mystery class since only AGB stars are sufficiently evolved enough to have dredged carbon into their atmospheres. However, a few types of giants are known to show anomalous abundances --- notably, the CH and Ba stars and, more recently, the CEMP-s stars --- and were also found to have a high binary frequency. This discovery led to suspicions that these systems were all in post mass transfer binary systems, where a former AGB companion has since faded to a white dwarf. The dC stars may be the enhanced-abundance progenitors of most, if not all, of these systems, but this mechanism requires the existence of a high binary frequency for dCs. Here, we examine a large sample of dC stars targeted for repeat spectroscopy by the Sloan Digital Sky Survey's Time Domain Spectroscopic Survey to constrain the binary frequency and orbital properties. We analyze radial velocity variability between spectral epochs for a sample of 240 dC stars with a total of 540 spectra. A handful of dC systems show large velocity shifts (> 100 km s$^{-1}$) between repeat spectra. We compare the dCs to a control sample with a similar distribution of magnitude, color, proper motion, and parallax. Using MCMC methods, we use the measured $\Delta$RV distribution to estimate the separation distribution assuming both a unimodal and bimodal distribution. These models result in mean separations of less than 1 AU, corresponding to periods on the order of 1 year for varying dC masses. These results support the conclusion that dC stars form from close binary systems via mass transfer.

The Time-Domain Spectroscopic Survey: Radial Velocity Variability in Dwarf Carbon Stars