Constraints on Tidal Quality Factor in Kepler Eclipsing Binaries using Tidal Synchronization: A Frequency-Dependent Approach

TL;DR

This study investigates how the tidal quality factor in Sun-like stars varies with frequency, using Kepler binary data and Bayesian analysis, revealing constraints for different tidal periods and implications for tidal dissipation efficiency.

Contribution

It introduces a frequency-dependent model of the tidal quality factor and constrains it using Kepler eclipsing binaries, highlighting its variation with tidal period.

Findings

Q' is well constrained for periods > 15 days, around 10^8.

Q' decreases slightly at shorter periods, indicating more efficient dissipation.

For periods < 15 days, Q' is broadly constrained, overlapping with circularization estimates.

Abstract

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 ($Q_\star'$). 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 $Q_\star'$ for Sun-like stars. We parameterize $Q_\star'$ 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 $Q_\star'$ is well constrained for tidal periods > 15 days, with a value of $Q_\star' \sim 10^8$ for periods > 30 days and a slight suggested decrease at shorter periods. For tidal periods < 15 days, $Q_\star'$ 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: $Q_\star' \sim 10^6$.