Comprehensive bayesian modeling of tidal circularization in open cluster binaries part I: M 35, NGC 6819, NGC 188

Abstract

Tidal friction has long been recognized to circularize the orbits of binary stars over time. In this study, we use the observed distribution of orbital eccentricities in populations of binary stars to probe tidal dissipation. In contrast to previous studies, we incorporate a host of physical effects often neglected in other analyses, provide a much more general description of tides, model individual systems in detail (in lieu of population statistics), and account for all observational uncertainties. The goal is to provide a reliable measurement of the properties of tidal dissipation that is fully supported by the data, properly accounts for different dissipation affecting each tidal wave on each object separately, and evolves with the internal structure of the stars. We extract high precision measurements of tidal dissipation in short period binaries of Sun-like stars in three open clusters. We find that the tidal quality factor on the main sequence falls in the range $5.7 < \log _{10}Q_\star ^{\prime } < 6$ for tidal periods between 3 and 7.5 days. In contrast, the observed circularization in the 150 Myr old M 35 cluster requires that pre-main sequence stars are much more dissipative: $Q_\star ^{\prime } < 4\times 10^4$. We test for frequency dependence of the tidal dissipation, finding that for tidal periods between 3 and 7.5 days, if a dependence exists, it is sub-linear for main-sequence stars. Furthermore, by using a more complete physical model for the evolution, and by accounting for the particular properties of each system, we alleviate previously observed tensions in the circularization in the open clusters analyzed.