Stellar loci II. a model-free estimate of the binary fraction for field FGK stars

We propose a Stellar Locus OuTlier (SLOT) method to determine the binary fraction of main-sequence stars statistically. The method is sensitive to neither the period nor mass-ratio distributions of binaries, and able to provide model-free estimates of binary fraction for large numbers of stars of different populations in large survey volumes. We have applied the SLOT method to two samples of stars from the SDSS Stripe 82, constructed by combining the re-calibrated SDSS photometric data with respectively the spectroscopic information from the SDSS and LAMOST surveys. For the SDSS spectroscopic sample, we find an average binary fraction for field FGK stars of $41%\pm2%$. The fractions decrease toward late spectral types, and are respectively $44%\pm5%$, $43%\pm3%$, $35%\pm5%$, and $28%\pm6%$ for stars of $g-i$ colors between 0.3 -- 0.6, 0.6 -- 0.9, 0.9 -- 1.2, and 1.2 - 1.6\,mag. A modest metallicity dependence is also found. The fraction decreases with increasing metallicity. For stars of [Fe/H] between $-0.5$ - 0.0, $-1.0$ - $-0.5$, $-1.5$ - $-1.0$, and $-2.0$ - $-1.5$\,dex, the inferred binary fractions are $37%\pm3%$, $39%\pm3%$, $50%\pm9%$, and $53%\pm20%$, respectively. We have further divided the sample into stars from the thin disk, the thick disk, the transition zone between them, and the halo. The results suggest that the Galactic thin and thick disks have comparable binary fractions, whereas the Galactic halo contains a significantly larger fraction of binaries. Applying the method to the LAMOST spectroscopic sample yields consistent results. Finally, other potential applications and future work with the method are discussed.