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More than 340 non-eclipsing binaries of A-F stars as primaries at intermediate periods (100-1000 d) were newly found by uninterrupted photometry with ultra high-precision taken over 4 yr by Kepler space mission via the phase modulation of pulsating stars, and their orbital parameters, which were difficult to measure with conventional methods and were very incomplete, were then determined. This asteroseismic finding of binaries tripled the number of intermediate-mass binaries with full orbital solutions, and opened a new window to statistics of binaries. We outline the methods of finding non-eclipsing binaries by photometry and of deriving the orbital parameters, and demonstrate their validation. Statistical study of the newly discovered binaries along with the known spectroscopic binaries near A-F main-sequence are then presented, converting distribution in the mass-function into the mass-ratio distribution with the help of Abel-type integral equation.

Asteroseismology as a new window to statistics of binaries