Orbital solutions derived from radial velocities and time delays for four Kepler systems with A/F-type (candidate) hybrid pulsators

Context. The presence of A/F-type Kepler hybrid stars extending across the entirety of the delta Scuti - gamma Doradus instability strips and beyond remains largely unexplained. In order to better understand these particular stars, we performed a multi-epoch spectroscopic study of a sample of 49 candidate A/F-type hybrid stars and one cool(er) hybrid object detected by the Kepler mission. We determined a lower limit of 27% for the multiplicity fraction. For six spectroscopic systems, we also reported long-term variations in the time delays (TDs). For four systems, the TD variations are fully coherent with those of the radial velocities (RVs ) and can be attributed to orbital motion.Aims. We aim to improve the orbital solutions for those spectroscopic systems with long orbital periods (order of 4-6 years) among the Kepler hybrid stars that we continued to observe.Methods. The orbits are computed based on a simultaneous modelling of the RVs obtained with high-resolution spectrographs and the photometric TDs derived from time-dependent frequency analyses of the Kepler light curves.Results. We refined the orbital solutions of four spectroscopic systems with A/F-type Kepler hybrid component stars: KIC 4480321, 5219533, 8975515, and KIC 9775454. Simultaneous modelling of both data types analysed together enabled us to improve the orbital solutions (all), obtain more robust and accurate information on the mass ratio (some for the first time), and identify the component with the short-period delta Sct-type pulsations (all). The information gained is maximized when one of the components, generally the one exhibiting the delta Sct-type pulsations, is a fast rotator. In several cases, we were also able to derive new constraints for the minimum component masses. From a search for regular frequency patterns in the high-frequency regime of the Fourier transforms of each system, we found no evidence of tidal splitting among the triple systems with close (inner) companions. However, some systems exhibit frequency spacings that can be explained by the mechanism of rotational splitting.