The fraction of binary systems in various stellar populations of the Galaxy and the distribution of their orbital parameters are important but not well-determined factors in studies of star formation, stellar evolution, and Galactic chemical evolution. While observational studies have been carried out for a large sample of nearby stars, including some metal-poor, Population II stars, almost no constraints on the binary nature for extremely metal-poor (EMP; [Fe/H] < -3.0) stars have yet been obtained. Here we investigate the fraction of double-lined spectroscopic binaries and carbon-enhanced metal-poor (CEMP) stars, many of which could have formed as pairs of low-mass and intermediate-mass stars, to estimate the lower limit of the fraction of binary systems having short periods. The estimate is based on a sample of very metal-poor stars selected from the Sloan Digital Sky Survey, and observed at high spectral resolution in a previous study by Aoki et al. That survey reported three double-lined spectroscopic binaries and 11 CEMP stars, which we consider along with a sample of EMP stars from the literature compiled in the SAGA database. We have conducted measurements of the velocity components for stacked absorption features of different spectral lines for each double-lined spectroscopic binary. Our estimate indicates that the fraction of binary stars having orbital periods shorter than 1000 days is at least 10 %, and possibly as high as 20 %, if the majority of CEMP stars are formed in such short-period binaries. This result suggests that the period distribution of EMP binary systems is biased toward short periods, unless the binary fraction of low-mass EMP stars is significantly higher than that of other nearby stars.
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