KIC 10855535: An elegant Delta Scuti pulsator with Amplitude and Phase Modulation

We investigated the pulsating behavior of KIC 10855535 using Kepler 4-year long cadence data. Two independent frequencies were detected: a pulsation frequency F0 = 17.733260(5)d-1 and a low frequency f8=0.412643(8)d-1 We identify F0 as the fundamental frequency, at which a equidistant quintuplet is centered, suggesting that the star orbits in a binary system. The fitted orbital parameters align well with those reported in previous literature. Long-term phase modulation caused by binarity has been confirmed by considering TESS light curve. Through adjusting light time via removing the light time effect, we measured a linear change in period of order $\dot{P}/P \simeq 1.44\times 10^{-7}yr^{-1}$, a value that could be indicative of stellar evolution. The star also exhibits a gradual and stable amplitude growth, thereby raising the possibility of structural changes during its evolution. We attributed f8 and its two harmonics to rotation and surface spots, with further analysis suggesting evolving characteristics over time. Based on the hypothesis, KIC 10855535 may rotate slowly for its type, with a speed of 37(2)km/s. Overall, KIC 10855535 presents an exceptionally clean spectrum and a relatively slow rotation as a {\delta} Sct pulsator, exhibiting a single pulsation mode that undergoes both amplitude and phase modulation.