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We investigated the pulsating behavior of KIC 10855535 using Kepler 4 yr long-cadence data. Two independent frequencies were detected: a pulsation frequency F0 = 17.733260(5) day ^−1 and a low frequency f _8 = 0.412643(8) day ^−1 . We identify F0 as the fundamental frequency, at which an 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 the light curve from the Transiting Exoplanet Survey Satellite. By removing the light-time effect, we measured a linear change in period of order $\dot{P}/P\simeq 1.44\times {10}^{-7}\,{\mathrm{yr}}^{-1}$ , 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 f _8 and its two harmonics to rotation and surface spots, with further analysis suggesting characteristics evolving over time. Based on this hypothesis, KIC 10855535 may rotate slowly for its type, with a speed of 37(2) km s ^−1 . Overall, KIC 10855535 presents an exceptionally clean spectrum and a relatively slow rotation as a δ Sct pulsator, exhibiting a single pulsation mode that undergoes both amplitude and phase modulation.

We investigated the pulsating behavior of TIC 400562821 using high-precision observations from TESS. Fourier analysis of time-series data revealed three independent frequencies. The period ratios of F to F1 (0.774) and F to F2 (0.625), along with an amplitude change of approximately 0.1 mag, indicate that TIC 400562821 is a triple-mode High-Amplitude δ Scuti (HADS) star. Using the Best Parent Method and the Γ _O functions, we identified that the harmonics and sum combination frequencies of F and F1 are caused by the nonlinear response of the stellar medium to pulsation. We also analyzed the amplitude variations of F, F1, and F2. Observational data over 76 days show stable amplitudes for these modes. However, Radial Stellar Pulsations modeling suggests that, over 10,000 cycles, the amplitude of F remains constant, while F1 gradually decreases and F2 approaches zero. This implies that TIC 400562821 may eventually evolve into a single-mode HADS star. Furthermore, asteroseismic modeling was performed, and several effects, such as the mixing-length parameter α _MLT and nonadiabatic, were examined on this star. In view of the results by Daszyńska-Daszkiewicz et al. (i.e., α _MLT < ∼1 for δ Scuti stars), TIC 400562821 is suggested to be more likely in the post-main-sequence stage, with mass M = 1.34–1.38 M _⊙ and metallicity Z = 0.007–0.008, but still warrants further study to ascertain its nature.

In this paper, we analyze the light variation of KIC 8840638 using high-precision time-series data from the Kepler mission. The analysis reveals that this target is a new detached eclipsing binary system with a δ Scuti component, rather than a single δ Scuti star as previously known. The frequency analysis of short-cadence data reveals 95 significant frequencies, most of which lie in a frequency range of 23−32 day ^−1 . Among them, seven independent frequencies are detected in the typical frequency range of δ Scuti stars, and they are identified as pressure modes. In addition, a possible large separation value of Δ ν = 36.5 ± 0.1 μ Hz is also detected with the Fourier transform (FT) and autocorrelation function (AC) analysis. The orbital frequency f _orb (= 0.320008 day ^−1 ) and its harmonics are also detected directly in the frequency spectrum. The binary modelings derived from PHOEBE indicate that this binary system is in detached configurations with a mass ratio of $q={0.33}_{-0.04}^{+0.06}$ , an inclination angle of ${40.19}_{-2.84}^{+3.96}$ ​​​​​°. The derived parameters and binary evolutionary model suggest that the primary star is an object on the verge of leaving the main sequence with a temperature of ∼7600 K, while the secondary appears to be a cool component entering the giant branch with a temperature ∼3100 K lower than the primary. Moreover, this system may have undergone a mass ratio reversal, where the more massive star is the gainer component and the less massive one is the donor star.

In this paper, we present an analysis of the pulsating behavior of Kepler target KIC 9845907. Using the data from Kepler, we detected 85 significant frequencies, including the first overtone f _1 = 17.597 day ^−1 as the dominant frequency, the non-radial independent frequency f _3 = 31.428 day ^−1 ( ℓ = 1), as well as two modulation terms f _m _1 = 0.065 day ^−1 and f _m _2 = 1.693 day ^−1 . We found fourteen pairs of triplet structures with f _m _1 or f _m _2 , four pairs of which can further form quintuplet structures. We note these are the most intriguing features discovered in this study and they were recognized for the first time in δ Scuti stars. We discussed several possible explanations, i.e., beating, the Blazhko effect, combination mode hypothesis, nonlinear mode coupling, large separation, and stellar rotational splitting for these equidistant structures. Our asteroseismic models indicate this modulation with f _m _1 might be related to the rotational splitting. The study of more δ Scuti stars with triplet and/or quintuplet structures using high-precision space photometry would be helpful to further explore its origin.