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The fraction of binary stars (fb) is one of most valuable tool to probe thestar formation and evolution of multiple systems in the Galaxy. We focus on therelationship between fb and stellar metallicity ([Fe/H]) by employing thedifferential radial velocity (DRV) method and the large sample observed by theLarge Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST).Main-sequence stars from A- to K-types in the third data release (DR3) ofLAMOST are selected to estimate fb. Contributions to a profile of DRV fromradial velocity (RV) error of single stars (\sigma) and orbital motion ofbinary stars are evaluated from the profile of DRV. Finally, we employ 365,911stars with randomly repeating spectral observations to present a detailedanalysis of fb and \sigma in the two-dimensional (2D) space of Teff and [Fe/H].The A-type stars are more likely to be companions in binary star systems thanother stars. Furthermore, the reverse correlation between fb and [Fe/H] can beshown statistically, which suggests that fb is a joint function of Teff and[Fe/H]. At the same time, \sigma of the sample for different Teff and [Fe/H]are fitted. Metal-rich cold stars in our sample have the best RV measurement.

The binarity of Galactic dwarf stars along with effective temperature and metallicity