Constraining tidal quality factor using spin period in eclipsing binaries

Evolution of binary objects under the influence of tides drastically affects the expected observational properties of the system. With the discovery of a large number of close-in hot Jupiter systems and eclipsing binaries from missions such as Kepler and Transiting Exoplanet Survey Satellite, it has become imperative to understand the extent of tidal influence on their formation and observed properties. In the case of binary systems, an efficient tidal dissipation can lead to either spin-up or spin-down of the stars and/or spin-orbit synchronization, depending upon the exchange of angular momentum between the star and the orbit. We combine the eclipsing binary systems from the Kepler mission with stellar and orbital parameters available in the literature to create a catalogue of 41 eclipsing binaries suitable for analysis of tidal dissipation. Empirically, the efficiency of tidal dissipation is parametrized using a modified tidal quality factor ($Q_{\star }^{\prime }$). We find constraints on $Q_{\star }^{\prime }$ using the observed rotation period of the primary star in the eclipsing binary systems. We calculate detailed evolutions of binary systems under the combined influence of tides, stellar evolution, and loss of stellar angular momentum to magnetic winds, and perform Markov chain Monte Carlo simulations to account for the uncertainties in the observed data. Our analysis shows that $\log _{10}{Q^{\prime }_{\star }}=7.818\pm 0.035$ can reproduce the observed primary star spin in almost all systems in our sample.