A robust measure of tidal circularization in coeval binary populations: The solar-type spectroscopic binary population in the open cluster M35

We present a new homogeneous sample of 32 spectroscopic binary orbits in the young ( similar to 150 Myr) main-sequence open cluster M35. The distribution of orbital eccentricity versus orbital period ( e log P) displays a distinct transition from eccentric to circular orbits at an orbital period of similar to 10 days. The transition is due to tidal circularization of the closest binaries. The population of binary orbits in M35 provide a significantly improved constraint on the rate of tidal circularization at an age of 150 Myr. We propose a new and more robust diagnostic of the degree of tidal circularization in a binary population based on a functional fit to the e log P distribution. We call this new measure the "tidal circularization period.'' The tidal circularization period of a binary population represents the orbital period at which a binary orbit with the most frequent initial orbital eccentricity circularizes ( defined as e = 0.01) at the age of the population. We determine the tidal circularization period for M35, as well as for seven additional binary populations spanning ages from the pre - main sequence ( similar to 3 Myr) to the late main sequence ( similar to 10 Gyr), and use Monte Carlo error analysis to determine the uncertainties on the derived circularization periods. We conclude that current theories of tidal circularization cannot account for the distribution of tidal circularization periods with population age.