The spectroscopic binaries RV Tauri and DF Cygni

Aim: The focus of this paper is on two famous but still poorly understood RV Tauri stars: RV Tau and DF Cyg. We aim at confirming their suspected binary nature and deriving their orbital elements to investigate the impact of their orbits on the evolution of these systems. This research is embedded into a wider endeavour to study binary evolution of low- and intermediate-mass stars. Method: The high amplitude pulsations were cleaned from the radial-velocity data to better constrain the orbital motion. We used Gaia DR2 parallaxes in combination with the SEDs to compute their luminosities which were complemented with the ones computed using a period-luminosity-colour relation. The ratio of the circumstellar infrared flux to the photospheric flux obtained from the SEDs was used to estimate the orbital inclination of each system. Results: DF Cyg and RV Tau are binaries with spectroscopic orbital periods of 784$\pm$16 days and 1198$\pm$17 days, respectively. These orbital periods are found to be similar to the long-term periodic variability in the photometric time series, indicating that binarity indeed explains the long-term photometric variability. Both systems are surrounded by a circumbinary disc which is grazed by our line-of-sight. As a result, the stellar photometric flux is extinct periodically with the orbital period. Our derived orbital inclinations enabled us to obtain accurate companion masses for DF Cyg and RV Tau. Analysis of the Kepler photometry of DF Cyg revealed a power spectrum with side lobes around the fundamental pulsation frequency. This modulation corresponds to the spectroscopic orbital period and hence to the long-term photometric period. Finally we report on the evidence of high velocity absorption features related to the H$_{\alpha}$ profile in both objects, indicating outflows launched from around the companion.