KIC 7756853: two hybrid δ Sct - γ Dor stars with Rossby and gravito-inertial pulsation modes in a double-lined spectroscopic system

KIC 7756853 a bright Kepler target with a magnitude of (Kp = 8.96 mag), is a confirmed double-lined spectroscopic system following a comprehensive decade-long study of high-resolution spectra. This system has an orbital period of 99.32 days, a mass ratio of 0.91, and consists of two A-type stars. Their individual properties include Teff of 9700 and 7600 K, log g of 4.7 and 4.0 cgs and vsini = 31 and 51 km/s, for the primary and the secondary components, respectively. In search of pulsation frequencies of KIC 7756853, Fourier analysis was applied to the complete Kepler long-cadence data (Q0-Q17), Kepler short-cadence data (Q1), and the Transiting Exoplanet Survey Satellite TESS light curves (sectors 14-15, 40-41, 54-55). A total of 179 significant frequencies were detected, 31 of which are δ Sct-type modes with frequencies ranging from 18.24 to 28.28 1/d. The most prominent mode, f_1, exhibited a frequency of 21.1416 1/d. Two distinct regular frequency splittings were observed in both p-modes and low-frequency modes, linking these pulsation modes to two of the most significant low frequencies, i.e., f_3 =0.8914 1/d and f_9 = 2.5258 1/d. Significant low-frequency modes, indicative of r-modes and gravito-inertial modes, were observed in the inertial range (0.7 - 5.1 1/d) and the super-inertial range (5.1 - 7.8 1/d). The observed frequency splitting arises from the rotational effects of both primary and secondary components. It allows us to deduce a differential core-to-surface rotation rate of 1.062 for the secondary and 1.003 for the primary components. The coupling of rotation and pulsation in KIC 7756853 suggests the presence of a pair of (γ Dor - δ Sct) hybrid pulsators with intermediate to fast rotations. Based on the coupling of rotation and orbital motion, a detected variability slightly longer than Kepler's Earth-trailing orbital period (∼1.30 1/yr) hints at possible stellar spots on both components or a third body in the system with a rotation frequency of 0.71 1/d.