Constraining tidal quality factor using spin period in eclipsing binaries

Abstract

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 TESS, 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 catalog of 41 eclipsing binaries suitable for analysis of tidal dissipation. Empirically, the efficiency of tidal dissipation is parameterized 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.

Examining the orbital decay targets KELT-9 b, KELT-16 b, and WASP-4b, and the transit-timing variations of HD 97658 b

“…With this, we can also give a 95% confidence lower limit on Q * of Q * > (9.0 ± 3.7) × 10 4 , with the best-fit parameter being Q * ,best = (1.7 ± 0.7) × 10 5 . This would place KELT-9 near the lower edge of the theoretical predictions, which range from 10 5 to 10 8.5 in the literature (Meibom & Mathieu 2005;Jackson et al 2008;Hansen 2010;Husnoo et al 2012;Penev et al 2012;Bonomo et al 2017;Penev et al 2018;Patel & Penev 2022), if the decay trend would be true. Some of these studies assumed Q * to be a universal constant, however.…”

Tidally Excited Inertial Waves in Stars and Planets: Exploring the Frequency-dependent and Averaged Dissipation with Nonlinear Simulations

“…We calculate ¢ Q for the asynchronous tide in these systems due to IW dissipation in their convective envelopes. We choose EBs satisfying P o > P 1 /2 (for IW excitation), where P 1 is the primary's rotation period (i.e., the more massive star, using P 1 min in Table 2 of Lurie et al 2017;Patel & Penev 2022). To compute ò and ò Ω , we also use data in Windemuth et al (2019;i.e., masses, radii, and ages).…”

Constraining stellar tidal quality factors from planet‐induced stellar spin‐up

“…Khaliullin & Khaliullina (2007) and Khaliullin & Khaliullina (2010) utilized the apsidal motion of the binary orbital axes as indicators of the internal axial rotation of early‐type (radiative) stars and tested the efficiency of radiative damping (Zahn 1975, 1977) on tidal synchronization and circularization rate. More recent work utilized POET, adopted for systems on eccentric orbits, to constrain the modified tidal quality factor of a sample of Sun‐like primary stars in eclipsing binaries by using their rotation periods and found a common value of $$$ \log {Q}^{\prime }=7.818\pm 0.035 $$$ (Patel & Penev 2022). A subsequent study explored the tidal frequency dependence of Q' in Sun‐like stars and parametrized Q' as a saturating power law in tidal frequency and obtained constraints using the rotation period of 70 eclipsing binaries observed by Kepler (Patel et al 2023).…”