Binary modelling techniques and frequency analysis have been applied to the Kepler photometric observations of KIC 4544587 to determine information about the orbital characteristics, individual components and tidal interactions. The system contains an early A-type δ Scuti variable, which pulsates in both pressure and gravity modes, and a late F- to early G-type star, which is possibly a solar-like oscillator. The Wilson-Devinney code was used to model the Quarter 3.2 data and PHOEBE was used to model the Quarter 7 data; the results of these two methods were then compared. Using PHOEBE the rate of apsidal advance was determined to be 0.0001179(1) rad d-1, which gives 145.9(1) yr for a complete precession.
Subsequently the binary model light curve was subtracted from the original data and frequency analysis was performed on the residuals. Fifteen frequencies were identified that are harmonics of the orbital period, 9 of which are in the g mode regime and 6 in the p mode regime. It was concluded that these frequencies are not an artifact of the model fit and thus are a signature of tidal resonance. It was also determined that many of the frequencies in the p mode regime are separated from the two dominant p modes by a multiple of the orbital frequency; six of the identified modes demonstrate this separation to an accuracy of 3 σ. As they are not orbital harmonics, the origin of these frequencies remains unknown. Currently we know of no other star demonstrating these characteristics.