Periodicities of the RV Tauri-type pulsating star DF Cygni: A combination of Kepler data with ground-based observations

Context. The RV Tauri stars constitute a small group of classical pulsating stars with some dozen known members in the Milky Way. The light variation is caused predominantly by pulsations, but these alone do not explain the full complexity of light curves. High-quality photometry of RV Tau-type stars is very rare. DF Cygni is the only member of this class of stars in the original Kepler field, hence allowing the most accurate photometric investigation of any RV Tauri star to date. Aims. The main goal is to analyse the periodicities of the RV Tauri-type star DF Cygni by combining four years of high-quality Kepler photometry with almost half a century of visual data collected by the American Association of Variable Star Observers (AAVSO). Methods. Kepler quarters of data were stitched together to minimize the systematic effects of space data. The mean levels have been matched with AAVSO visual data. Both datasets were submitted to Fourier and wavelet analyses, while the stability of the main pulsations was studied with the O–C method and analysis of time-dependent amplitudes. Results. DF Cygni shows very rich behaviour on all timescales. The slow variation has a period of 779.606 d and it has been remarkably coherent during the whole time span of the combined data. On top of the long-term cycles, the pulsations appear with a period of 24.925 d, or the double period of 49.85 d if we take the RV Tau-type alternation of the cycles into account. Both types of light variation significantly fluctuate in time, with a constantly changing interplay of amplitude and phase modulations. Long-period change (i.e. the RVb signature) somewhat resembles the long secondary period (LSP) phenomenon of pulsating red giants, whereas short-period pulsations are very similar to those of the Cepheid variables. Comparing the pulsation patterns with the latest models of Type-II Cepheids, we found evidence of strong non-linear effects that are directly observable in the Kepler light curve.