Tidal Dissipation in Rotating Giant Planets

Abstract

Many extrasolar planets orbit sufficiently close to their host stars that significant tidal interactions can be expected, resulting in an evolution of the spin and orbital properties of the planets. The accompanying dissipation of energy can also be an important source of heat, leading to the inflation of short-period planets and even mass loss through Roche-lobe overflow. Tides may therefore play an important role in determining the observed distributions of mass, orbital period, and eccentricity of the extrasolar planets. In addition, tidal interactions between gaseous giant planets in the solar system and their moons are thought to be responsible for the orbital migration of the satellites, leading to their capture into resonant configurations.Traditionally, the efficiency of tidal dissipation is simply parametrized by a quality factor Q, which depends, in principle, in an unknown way on the frequency and amplitude of the tidal forcing. In this paper, we treat the underlying fluid dynamical problem with the aim of determining the efficiency of tidal dissipation in gaseous giant planets such as Jupiter, Saturn, or the short-period extrasolar planets. Efficient convection enforces a nearly adiabatic stratification in these bodies, which may or may not contain rocky cores. With some modifications, our approach can also be applied to fully convective low-mass stars.In cases of interest, the tidal forcing frequencies are typically comparable to the spin frequency of the planet but are small compared to its dynamical frequency. We therefore study the linearized response of a slowly and possibly differentially rotating planet to low-frequency tidal forcing. Convective regions of the planet support inertial waves, which possess a dense or continuous frequency spectrum in the absence of viscosity, while any radiative regions support generalized Hough waves. We formulate the relevant equations for studying the excitation of these disturbances and present a set of illustrative numerical calculations of the tidal dissipation rate.

Transiting exoplanets from the CoRoT space mission

“…Lainey et al 2009) which was transformed into the planets Q p , taking into account that: (i) Q p scales with the tide forcing period (see Ferraz-Mello et al 2008); (ii) Q p scales with R −5 (cf. Eggleton et al 1998;Ogilvie & Lin 2004). We thus obtain, for CoRoT-16b the factor Q p = 9 × 10 5 .…”

Deformation and tidal evolution of close-in planets and satellites using a Maxwell viscoelastic rheology

“…The "convective time" can also be considered for gaseous planets (that is, adopting τ = τ c ), since they can admit regions of turbulent convection (e.g., Guillot 1999; Ogilvie & Lin 2004). For planets, the effective viscosity of turbulent convection falls rapidly as the oscillation frequency is increased, and in the limit of high tidal frequencies, there is a viscoelastic response to deformation (Ogilvie & Lesur 2012).…”

Non-linear tides in a homogeneous rotating planet or star: global modes and elliptical instability

“…Rasio et al 1996;Winn & Fabrycky 2015). The mechanisms responsible for tidal dissipation are not fully understood, though much progress has been made over the past decade (Ogilvie & Lin 2004;Wu 2005;Ivanov & Papaloizou 2007;Ogilvie & Lin 2007;Goodman & Lackner 2009;Remus et al 2012;Favier et al 2014;Ogilvie 2014).…”

“…This is unfortunate, because previous work has primarily focused on studying tides in the linear regime (e.g. Ogilvie & Lin 2004;Wu 2005;Ivanov & Papaloizou 2007;Ogilvie 2013). While these calculations are a necessary first step, and are likely to provide important information to help us to understand the tidal response in real bodies, they do not probe any nonlinear fluid effects which could significantly modify the outcome of tidal forcing.…”