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 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 ^ { -1 } , 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 .
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 \gtrsim 0.6 Gyr is too long for any pre-main sequence interaction alone and is more consistent with the three-body interaction through the Kozai-Lidov mechanism and magnetic winds .
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 ( \gtrsim 90 % ) short-period binaries in our sample are destroyed during their main-sequence stage .