F. Verbunt et Es. Phinney, TIDAL CIRCULARIZATION AND THE ECCENTRICITY OF BINARIES CONTAINING GIANT STARS, Astronomy and astrophysics, 296(3), 1995, pp. 709-721
We show that the predicted amount of tidal circularization in a detach
ed binary containing a giant is, according to Zahn's (1966, 1989) theo
ry, determined only by observable properties of its orbit, and a singl
e integral along the giant's stellar evolutionary sequence. We perform
these integrals, display them graphically, and provide fitting formul
ae. Spectroscopic binaries in open clusters are ideal for testing the
theory of tidal circularization, since the stars' mass, luminosity and
temperature can all be determined with precision. We apply our calcul
ations to 28 binaries in 12 open clusters. We show that the orbital pa
rameters of all can be understood within the circularization theory, a
nd that the mixing length parameter in Zahn's theory is well constrain
ed: 1 less than or similar to alpha less than or similar to 3. We show
that the orbital period alone does not separate circular and eccentri
c orbits, and point out that the eccentricity of the orbit can sometim
es distinguish between giant stars and core helium burning 'clump' sta
rs even in circumstances where this is difficult spectroscopically. In
some special types of binary systems, the circularization is sensitiv
e to aspects of stellar evolution theory that are not well understood:
the maximum depth of penetration of the outer convective zone, the ra
dius at first dredge-up, the maximum radii of stars at the tips of the
giant and asymptotic giant branches. It thus appears that the orbits
of binaries containing giants may prove to be a useful tool for studyi
ng stellar evolution.