E. S. Phinney
Theoretical Astrophysics, 130-33 California Institute of Technology, Pasadena, California 91125
We show that the predicted amount of tidal circularization in a detached binary containing a giant is, according to Zahn's (1966, 1989) theory, determined only by observable properties of its orbit, and a single integral along the giant's stellar evolutionary sequence. We perform these integrals, display them graphically, and provide fitting formulae.
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 calculations to 28 binaries in 12 open clusters. We show that the orbital parameters of all can be understood within the circularization theory, and that the mixing length parameter in Zahn's theory is well constrained: 1 < alpha < 3. We show that the orbital period alone does not separate circular and eccentric orbits, and point out that the eccentricity of the orbit can sometimes distinguish between giant stars and core helium burning `clump' stars even in circumstances where this is difficult spectroscopically.
In some special types of binary systems, the circularization is sensitive to aspects of stellar evolution theory that are not well understood: the maximum depth of penetration of the outer convective zone, the radius 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 studying stellar evolution.