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We present a comprehensive study of the eclipsing binary system KIC 10661783.The analysis of the whole Kepler light curve, corrected for the binary effects,reveals a rich oscillation spectrum with 590 significant frequency peaks, 207of which are independent. In addition to typical $\delta$ Sct frequencies, wefind small-amplitude signals in the low-frequency range that, most probably,are a manifestation of gravity-mode pulsations. We perform binary-evolutioncomputations for this system in order to find an acceptable model describingits current stage. Our models show that the binary KIC 10661783 was formed by arapid, almost conservative, mass transfer that heavily affected the evolutionof both components in the past. One of the most important effects of binaryevolution is the enormous enrichment of the outer layers of the main componentwith helium. This fact profoundly influences the pulsational properties of$\delta$ Scuti star models. For the first time, we demonstrate the effect ofbinary evolution on pulsational instability. We construct pulsational models ofthe main component in order to account for the mode instability of the observedfrequencies. Whereas the single-star evolution model is pulsational stable inthe whole frequency range, its binary-evolution counterpart has unstable modes,both, in high and low-frequency range. However, to obtain instability in almosta whole range of the observed frequencies, the modification of the mean opacityat the depth corresponding to temperatures log T = 4.69 K and log T = 5.06 Kwas necessary.

The eclipsing binary systems with $\delta$ Scuti component. I. KIC 10661783