KIC 11401845: An Eclipsing Binary with Multiperiodic Pulsations and Light Travel Time

We report the ${\it Kepler}$ photometry of KIC 11401845 displaying multiperiodic pulsations, superimposed on binary effects. Light-curve synthesis represents that the binary star is a short-period detached system with a very low mass ratio of $q$ = 0.070 and filling factors of $F_1$ = 45 % and $F_2$ = 99 %. Multiple frequency analyses were applied to the light residuals after subtracting the synthetic eclipsing curve from the observed data. We detected 23 frequencies with signal to noise amplitude ratios larger than 4.0, of which the orbital harmonics ($f_4$, $f_6$, $f_9$, $f_{15}$) in the low frequency domain may originate from tidally excited modes. For the high frequencies of 13.7$-$23.8 day$^{-1}$, the period ratios and pulsation constants are in the ranges of $P_{\rm pul}/P_{\rm orb}$ = 0.020$-$0.034 and $Q$ = 0.018$-$0.031 d, respectively. These values and the position on the Hertzsprung-Russell diagram demonstrate that the primary component is a $\delta$ Sct pulsating star. We examined the eclipse timing variation of KIC 11401845 from the pulsation-subtracted data and found a delay of 56$\pm$17 s in the arrival times of the secondary eclipses relative to the primary eclipses. A possible explanation of the time shift may be some combination of a light-travel-time delay of about 34 s and a very small eccentricity of $e \cos {\omega} <$ 0.0002. This result represents the first measurement of the R{\o}mer delay in non-compact binaries.