Binary Star Fractions from the LAMOST DR4
  Stellar systems composed of single, double, triple or high-order systems are
rightfully regarded as the fundamental building blocks of the Milky Way. Binary
stars play an important role in formation and evolution of the Galaxy. Through
comparing the radial velocity variations from multi-epoch observations, we
analyze the binary fraction of dwarf stars observed with the LAMOST. Effects of
different model assumptions such as orbital period distributions on the
estimate of binary fractions, are investigated. The results based on log-normal
distribution of orbital periods reproduce the previous complete analyses better
than the power-law distribution. We find that the binary fraction increases
with $T_{\rm eff}$ and decreases with [Fe/H]. We first investigate the relation
between $\alpha$-elements and binary fraction in such a large sample as the
LAMOST. The old stars with high [$\alpha$/Fe] dominate higher binary fraction
than young stars with low [$\alpha$/Fe]. At the same mass, former forming stars
possess a higher binary fraction than newly forming ones, which may be related
with the evolution of the Galaxy.
