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.

In this project, we determined the constraints on the modified tidal quality factor, $Q_{pl}^{\prime }$, of gas-giant planets orbiting close to their host stars. We allowed $Q_{pl}^{\prime }$ to depend on tidal frequency, accounting for the multiple tidal waves with time-dependent frequencies simultaneously present on the planet. We performed our analysis on 78 single-star and single-planet systems, with giant planets and host stars with radiative cores and convective outer shells. We extracted constraints on the frequency-dependent $Q_{pl}^{\prime }$ for each system separately and combined them to find general constraints on $Q_{pl}^{\prime }$ required to explain the observed eccentricity envelope while simultaneously allowing the observed eccentricities of all systems to survive to the present day. Individual systems do not place tight constraints on $Q_{pl}^{\prime }$. However, since similar planets must have similar tidal dissipation, we require that a consistent, possibly frequency-dependent, model must apply. Under that assumption, we find that the value of $\log _{10}Q_{pl}^{\prime }$ for HJs is 5.0 ± 0.5 for the range of tidal period from 0.8 to 7 days. We did not see any clear sign of frequency dependence of $Q_{pl}^{\prime }$.

Tidal dissipation in binary systems is the primary source for synchronization and circularization of the objects in the system. The efficiency of the dissipation of tidal energy inside stars or planets results in significant changes in observed properties of the binary system and is often studied empirically using a parameter, commonly known as the modified tidal quality factor (${Q_{\star }^{\prime }}$). Though often assumed constant, in general that parameter will depend on the particular tidal wave experiencing the dissipation and the properties of the tidally distorted object. In this work we study the frequency dependence of ${Q_{\star }^{\prime }}$ for Sun-like stars. We parameterize ${Q_{\star }^{\prime }}$ as a saturating power-law in tidal frequency and obtain constraints using the stellar rotation period of 70 eclipsing binaries observed by Kepler. We use Bayesian analysis to account for the uncertainties in the observational data required for tidal evolution. Our analysis shows that ${Q_{\star }^{\prime }}$ is well constrained for tidal periods >15 days, with a value of ${Q_{\star }^{\prime }}\sim 10^8$ for periods >30 days and a slight suggested decrease at shorter periods. For tidal periods <15 days, ${Q_{\star }^{\prime }}$ is no longer tightly constrained, allowing for a broad range of possible values that overlaps with the constraints obtained using tidal circularization in binaries, which point to much more efficient dissipation: ${Q_{\star }^{\prime }}\sim 10^6$.