Detecting non-uniform period spacings in the Kepler photometry of gamma Doradus stars: methodology and case studies

Context. The analysis of stellar oscillations is one of the most reliable ways to probe stellar interiors. Recent space missions such as Kepler have provided us with an opportunity to study these oscillations with unprecedented detail. For many multi-periodic pulsators such as {\gamma} Doradus stars, this led to the detection of dozens to hundreds of oscillation frequencies that could not be found from ground-based observations. Aims. We aim to detect non-uniform period spacings in the Fourier spectra of a sample of {\gamma} Doradus stars observed by Kepler. Such detection is complicated by both the large number of significant frequencies in the space photometry and by overlapping non-equidistant rotationally split multiplets. Methods. Guided by theoretical properties of gravity-mode oscillation of {\gamma} Doradus stars, we developed a period-spacing detection method and applied it to Kepler observations of a few stars, after having tested the performance from simulations. Results. The application of the technique resulted in the clear detection of non-uniform period spacing series for three out of the five treated Kepler targets. Disadvantages of the technique are also discussed, and include the disability to distinguish between different values of the spherical degree and azimuthal order of the oscillation modes without additional theoretical modelling. Conclusions. Despite the shortcomings, the method is shown to allow solid detections of period spacings for {\gamma} Doradus stars, which will allow future asteroseismic analyses of these stars.