2023MNRAS.525..876M

In this project, we determined the constraints on the modified tidal quality factor, $Q_{\rm pl}^{\prime }$, of gas-giant planets orbiting close to their host stars. We allowed $Q_{\rm pl}^{\prime }$ 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 $Q_{\rm pl}^{\prime }$ for each system separately and combined them to find general constraints on $Q_{\rm pl}^{\prime }$ 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 $Q_{\rm pl}^{\prime }$. 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 $\log _{10}Q_{\rm pl}^{\prime }$ for HJs is 5.0 ± 0.5 for the range of tidal period from 0.8 to 7 d. We did not see any clear sign of frequency dependence of $Q_{\rm pl}^{\prime }$.