KIC 7211759: A Rapidly Rotating δ Sct– γ Dor Hybrid Pulsator

KIC 7211759 is a rapidly rotating δ Sct– γ Dor hybrid pulsator. Based on high-precision photometric data from the Kepler and TESS missions, we conduct a systematic asteroseismic study of this star. We detect a pulsation spectrum spanning a broad frequency range from low-frequency gravity modes to high-frequency pressure modes (0.6–90 day −1 ). Long-term amplitude and phase modulations have been observed in the dominant pulsation modes, exhibiting features distinct from known systematic effects. Our analysis confirms that these modulations arise from beating between closely spaced frequency components. By combining the Fourier transform, autocorrelation function, and histogram of frequency differences methods, we identify the p -mode large separation to two candidate values and constrain two candidate period spacings for g -modes. In addition, we infer a likely rotation frequency of ν rot ≈ 2.2237 day −1 from the low-frequency signals. Further constraints from stellar evolution models, incorporating Δ ν , Δ P g , and fundamental atmospheric parameters, yield a mass of 1.70 ± 0.08 M ⊙ , a radius of 2.28 ± 0.27 R ⊙ , and and an age of 1.19 ± 0.04 dex, placing the star at the evolutionary stage just past the second turning point of the main sequence.