2020MNRAS.498.1871M

The PHOEBE code was used to analyse the Kepler light-curve and to estimate the physical and geometrical parameters of a rare pulsating binary system, KIC 3858884. The analysis indicated that the system is composed of two detached and very similar main-sequence A-type stars, in a highly eccentric orbit with e = 0.47. After disentangling the binarity effect, the residual data were subjected to Fourier frequency decomposition using PERIOD04 software. The resulting frequency spectrum consists of two moderately high-amplitude nearby frequencies, F1 = 7.232199 d^–1 and F2=7.472889 d^–1, which were attributed to δ Scuti-type pulsations. In addition, 18 frequencies were identified that were exact harmonics of the orbital frequency f_ orb_= 0.038533 d^–1, and also 53 anharmonics. However, it was found that many of these anharmonic frequencies coupled together non-linearly to give harmonic modes of pulsation. Furthermore, some existing theoretical models of the tidal oscillations were numerically verified in general binary systems through estimations of various modal characteristics, for example mode quantum numbers n, l, m, energies E_i, threshold energies E_i,th, damping rates γ_i, growth rates Γ_i and stability criteria, etc. The evolution of the stars in the binary system was compared with some similar single pulsating stars on the Hertzsprung-Russell diagram and it was concluded that the evolution of a single star is more rapid. Finally, the observed rate of apsidal line displacement was estimated through eclipse timing variation analysis as U_obs = 74745.2 ± 2566 yr. This was compared with the theoretically calculated rate of the line of apsides motion, U_Theo = 73588 ± 2298 yr, and found to be in good agreement within errors, hence verifying general relativity theory once again.