Binary fractions of G and K dwarf stars based on the Gaia EDR3 and
  LAMOST DR5: impacts of the chemical abundances
  Basing on the large volume \textit{Gaia} Early Data Release 3 and LAMOST Data
Release 5 data, we estimate the bias-corrected binary fractions of the field
late G and early K dwarfs. A stellar locus outlier method is used in this work,
which works well for binaries of various periods and inclination angles with
single epoch data. With a well-selected, distance-limited sample of about 90
thousand GK dwarfs covering wide stellar chemical abundances, it enables us to
explore the binary fraction variations with different stellar populations. The
average binary fraction is 0.42$\pm$0.01 for the whole sample. Thin disk stars
are found to have a binary fraction of 0.39$\pm$0.02, thick disk stars own a
higher one of 0.49$\pm$0.02, while inner halo stars possibly own the highest
binary fraction. For both the thin and thick disk stars, the binary fractions
decrease toward higher [Fe/H], [$\alpha$/H], and [M/H] abundances. However, the
suppressing impacts of the [Fe/H], [$\alpha$/H], and [M/H] are more significant
for the thin disk stars than those for the thick disk stars. For a given
[Fe/H], a positive correlation between [$\alpha$/Fe] and the binary fraction is
found for the thin disk stars. However, this tendency disappears for the thick
disk stars. We suspect that it is likely related to the different formation
histories of the thin and thick disks. Our results provide new clues for
theoretical works on binary formation.
