Lifetime of short-period binaries measured from their Galactic
  kinematics
  As a significant fraction of stars are in multiple systems, binaries play a
crucial role in stellar evolution. Among short-period (<1 day) binary
characteristics, age remains one of the most difficult to measure. In this
paper, we constrain the lifetime of short-period binaries through their
kinematics. With the kinematic information from Gaia Data Release 2 and light
curves from {\it Wide-field Infrared Survey Explorer} (WISE), we investigate
the eclipsing binary fraction as a function of kinematics for a volume-limited
main-sequence sample. We find that the eclipsing binary fraction peaks at a
tangential velocity of $10^{1.3-1.6}$ km/s, and decreases towards both low and
high velocity end. This implies that thick disk and halo stars have eclipsing
binary fraction $\gtrsim 10$ times smaller than the thin-disk stars. This is
further supported by the dependence of eclipsing binary fraction on the
Galactic latitude. Using Galactic models, we show that our results are
inconsistent with any known dependence of binary fraction on metallicity.
Instead, our best-fit models suggest that the formation of these short-period
binaries is delayed by 0.6-3 Gyr, and the disappearing time is less than the
age of the thick disk. The delayed formation time of $\gtrsim0.6$ Gyr implies
that these short-period main-sequence binaries cannot be formed by pre-main
sequence interaction and the Kozai-Lidov mechanism alone, and suggests that
magnetic braking plays a key role in their formation. Because the main-sequence
lifetime of our sample is longer than 14 Gyr, if the disappearance of
short-period binaries in the old population is due to their finite lifetime,
our results imply that most ($\gtrsim90$%) short-period binaries in our sample
merge during their main-sequence stage.
