Tidal dissipation in rotating and evolving giant planets with application to exoplanet systems

Abstract

We study tidal dissipation in models of rotating giant planets with masses in the range $0.1 - 10 M_\mathrm{J}$ throughout their evolution. Our models incorporate a frequency-dependent turbulent effective viscosity acting on equilibrium tides (including its modification by rapid rotation consistent with hydrodynamical simulations) and inertial waves in convection zones, and internal gravity waves in the thin radiative atmospheres. We consider a range of planetary evolutionary models for various masses and strengths of stellar instellation. Dissipation of inertial waves is computed using a frequency-averaged formalism fully accounting for planetary structures. Dissipation of gravity waves in the radiation zone is computed assuming these waves are launched adiabatically and are subsequently fully damped (by wave breaking/radiative damping). We compute modified tidal quality factors $Q'$ and evolutionary timescales for these planets as a function of their ages. We find inertial waves to be the dominant mechanism of tidal dissipation in giant planets whenever they are excited. Their excitation requires the tidal period ($P_\mathrm{tide}$) to be longer than half the planetary rotation ($P_\mathrm{rot}/2$), and we predict inertial waves to provide a typical $Q'\sim 10^3 (P_\mathrm{rot}/1 \mathrm{d})^2$, with values between $10^5$ and $10^6$ for a 10-day period. We show correlations of observed exoplanet eccentricities with tidal circularisation timescale predictions, highlighting the key role of planetary tides. A major uncertainty in planetary models is the role of stably-stratified layers resulting from compositional gradients, which we do not account for here, but which could modify predictions for tidal dissipation rates.