Search for exoplanets around pulsating stars of A--F type in Kepler Short Cadence data and the case of KIC 8197761

We searched for extrasolar planets around pulsating stars by examining $\textit{Kepler}$ data for transit-like events hidden in the intrinsic variability. All Short Cadence observations for targets with 6000 K $< T_{\rm eff} <$ 8500 K were visually inspected for transit-like events following the removal of pulsational signals by sinusoidal fits. Clear transit-like events were detected in KIC 5613330 and KIC 8197761. KIC 5613330 is a confirmed exoplanet host (Kepler-635b), where the transit period determined here is consistent with the literature value. KIC 8197761 is a $\gamma$ Doradus - $\delta$ Scuti star exhibiting eclipses/transits occurring every 9.8686667(27) d, having durations of 8.37 h, and causing brightness drops $\frac{\Delta F}{F} = 0.00629(29)$. The star's pulsation spectrum contains several mode doublets and triplets, identified as $l = 1$, with a mean spacing of 0.001659(15) c/d, implying an internal rotation period of $301\pm3$ d. Trials to calculate the size of the light travel time effect (LTTE) from the pulsations to constrain the companion's mass ended inconclusive. Finding planets around $\gamma$ Doradus stars from the pulsational LTTE, therefore, is concluded to be unrealistic. Spectroscopic monitoring of KIC 8197761 revealed sinusoidal radial velocity variations with a semi-amplitude of $19.75 \pm 0.32$ km/s, while individual spectra present rotational broadening consistent with $v \sin i = 9\pm1$ km/s. This suggests that the stellar surface rotation is synchronized with the orbit, whereas the stellar core rotates $\sim$30 times slower. Combining the observed radial velocity variability with the transit photometry, constrains the companion's mass to be $\approx 0.28$ M$_{\odot}$, ruling out an exoplanet hypothesis.