2018MNRAS.476.4840B

In addition to rotation, a tidal force in a binary introduces another axis of symmetry joining the two centres of mass. If the stars are in circular orbit and synchronous rotation, a pulsation with spherical harmonic degree l is split into l + 1 frequencies. In the observer's frame of reference, these in turn are further split into equidistant frequencies spaced by multiples of the orbital frequency. In the periodogram of a pulsating star, tidal action can be seen as low-amplitude equidistant splitting of each oscillation mode which are not harmonics of the orbital frequency. This effect is illustrated using Kepler observations of the heartbeat variable, KIC 4142768, which is also a δ Scuti star. Even though the theory is only applicable to circular orbits, the expected equidistant splitting is clearly seen in all four of the highest amplitude modes. This results in amplitude variability of each pulsation mode with a period equal to the orbital period.