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We measure the rotation periods of 19 stars in the {\it Kepler} transitingplanetary systems, $P_{\rm rot, astero}$ from asteroseismology and $P_{\rm rot,phot}$ from photometric variation of their lightcurve. Two stars exhibit twoclear peaks in the Lomb-Scargle periodogram, neither of which agrees with theseismic rotation period. Other four systems do not show any clear peak, whosestellar rotation period is impossible to estimate reliably from the photometricvariation; their stellar equators may be significantly inclined with respect tothe planetary orbital plane. For the remaining 13 systems, $P_{\rm rot,astero}$ and $P_{\rm rot, phot}$ agree within 30\%. Interestingly, three out ofthe 13 systems are in the spin-orbit resonant state in which $P_{\rm orb,b}/P_{\rm rot, astero} \approx 1$ with $P_{\rm orb, b}$ being the orbitalperiod of the inner-most planet of each system. The corresponding chanceprobability is ($0.2$-$4.7$) \% based on the photometric rotation period datafor 464 {\it Kepler} transiting planetary systems. While further analysis ofstars with reliable rotation periods is required to examine the statisticalsignificance, the spin-orbit resonance between the star and planets, ifconfirmed, have important implications for the star-planet tidal interaction,in addition to the origin of the spin-orbit (mis-)alignment of transitingplanetary systems.

the astronomical journal

Asteroseismic determination of the stellar rotation period of the Kepler  transiting planetary systems and its implications for the spin-orbit  architecture