Article révisé par les pairs
Résumé : Context. Over the last few decades it has become more evident that binarity is a prevalent phenomenon amongst RV Tauri stars with a disc. This study is a contribution to comprehend the role of binarity upon late stages of stellar evolution. Aims. In this paper we determine the binary status of six Galactic RV Tauri stars, namely DY Ori, EP Lyr, HP Lyr, IRAS 17038-4815, IRAS 09144-4933, and TW Cam, which are surrounded by a dusty disc. The radial velocities are contaminated by high-amplitude pulsations. We disentangle the pulsations from the orbital signal in order to determine accurate orbital parameters. We also place them on the HR diagram, thereby establishing their evolutionary nature. Methods. We used high-resolution spectroscopic time series obtained from the HERMES and CORALIE spectrographs mounted on the Flemish Mercator and Swiss Leonhard Euler Telescopes, respectively. An updated ASAS/AAVSO photometric time series is analysed to complement the spectroscopic pulsation search and to clean the radial velocities from the pulsations. The pulsation-cleaned orbits are fitted with a Keplerian model to determine the spectroscopic orbital parameters. We also calibrated a PLC relationship using type II cepheids in the LMC and apply the relation to our Galactic sample to obtain accurate distances and hence luminosities. Results. All six of the Galactic RV Tauri stars included in this study are binaries with orbital periods ranging between ∼650 and 1700 days and with eccentricities between 0.2 and 0.6. The mass functions range between 0.08 to 0.55 M⊙ which points to an unevolved low-mass companion. In the photometric time series we detect a long-term variation on the timescale of the orbital period for IRAS 17038-4815, IRAS 09144-4933, and TW Cam. Our derived stellar luminosities indicate that all except DY Ori and EP Lyr are post-AGB stars. DY Ori and EP Lyr are likely examples of the recently discovered dusty post-RGB stars. Conclusions. The orbital parameters strongly suggest that the evolution of these stars was interrupted by a strong phase of binary interaction during or even prior to the AGB. The observed eccentricities and long orbital periods among these stars provide a challenge to the standard theory of binary evolution.