Spectroscopic binaries among Hipparcos M giants III. The eccentricity-period diagram and mass-transfer signatures

Context. This paper is the third one in a series devoted to studying the properties of binaries involving M giants. Aims. We use a new set of orbits to construct the first (e − logP) diagram of an extensive sample of M giant binaries, to obtain their mass-function distribution, and to derive evolutionary constraints for this class of binaries and related systems. Methods. The orbital properties of binaries involving M giants were analysed and compared with those of related families of binaries (K giants, post-AGB stars, barium stars, Tc-poor S stars). Results. The orbital elements of post-AGB stars and M giants are not very different, which may indicate that, for the considered sample of post-AGB binaries, the post-AGB star left the AGB at quite an early stage (M4 or so). Neither are the orbital elements of post-mass-transfer binaries like barium stars very different from those of M giants, suggesting that the mass transfer did not alter the orbital elements much, contrary to current belief. Finally, we show that binary systems with e < 0. 4l ogP − 1 (with periods expressed in days) are predominantly post-mass-transfer systems, because (i) the vast majority of barium and S systems match this condition; and (ii) these systems have companion masses peaking around 0.6 M� , as expected for white dwarfs. The latter property has been shown to hold as well for open-cluster binaries involving K giants, for which a lower bound on the companion mass may easily be set.