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Astronomy&AstrophysicsReview As expected, short-period systems present circular orbits while the longer-period binaries show a wide range of eccentricities: No eccentric orbit is found for periods below 1.5 days. It is also clear that systems with stars having convective envelopes circularise more easily, and up to longer periods, than those with radiative envelopes. Diagrams such as Fig. \ref{tidal} are often used because periods and eccentricities are easily obtained, even for non-eclipsing systems. However, our data also allow us to plot the orbital eccentricity as a function of relative radius (i.e., the radius of the star in units of the orbital semi-axis major). We do so in the right-hand panels of Fig. \ref{tidal}, which is more interesting from a physical point of view, given the dependence of tidal circularisation time scales on high powers of the relative radii.
Our sample clearly shows a decreasing dispersion in eccentricity with increasing relative radius, all orbits being circular for relative radii above \(\sim\)0.25. The long-period system \(\alpha\) Cen fits naturally into Fig. \ref{tidal} as an eccentric system with near-zero relative radii. Again, convective envelopes achieve circularisation for smaller relative radii than radiative ones: Highly eccentric orbits are observed only for quite small relative radii in stars with convective envelopes, while circular orbits are already rare among radiative stars below relative radius 0.1.