SIMBAD references

The detection of long-period binary stars containing a δ Scuti variable is helpful to study the formation and evolution of binaries in the intermediate-mass region. The phase modulation and the frequency modulation caused by the light travel effect make it possible to find such systems that are hard to be detected by other methods. In this paper, we combined Kepler and TESS data to extend the observation span to more than 12 yr. Time-frequency analysis was applied on some δ Scuti variables observed by both Kepler and TESS. After careful phase modulation analysis, we succeeded in detecting a binary system with an orbital period as long as 3924 days. The 525 s light travel time along the line of sight indicates that the hidden companion of KIC 3440495 is a stellar object. To date, it is the longest-period binary confirmed by the phase modulation method. The method described in this article can be applied to more Kepler and TESS pulsating variables in the future.