Tidal Dissipation in Rotating Giant Planets

By Gordon I. Ogilvie, D. Lin. 2003

329 citations recorded by the source corpus.

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 parameterized 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 solid cores. With some modifications, our approach can also be applied to low-mass stars with extended convective envelopes. 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. We argue that inertial waves provide a natural avenue for efficient tidal dissipation in most cases of interest. In the presence of a solid core, the excited disturbance tends to be localized on a web of rays rather than resembling a smooth eigenfunction. The resulting value of Q depends, in principle, in a highly erratic way on the forcing frequency, but we provide analytical and numerical evidence that the frequency-averaged dissipation rate may be asymptotically independent of the viscosity in the limit of small Ekman number. For a smaller viscosity, the tidal disturbance has a finer spatial structure and individual resonances are more pronounced. In short-period extrasolar planets, tidal dissipation via inertial waves becomes somewhat less efficient once they are spun down to a synchronous state. However, if the stellar irradiation of the planet leads to the formation of a radiative outer layer that supports generalized Hough modes, the tidal dissipation rate can be enhanced, albeit with significant uncertainty, through the excitation and damping of these waves. The dissipative mechanisms that we describe offer a promising explanation of the historical evolution and current state of the Galilean satellites, as well as the observed circularization of the orbits of short-period extrasolar planets.

Subfields: Astronomy and Astrophysics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/9839f36eca32ed7c9770c84e28c9f84f0180526a

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Citations in the corpus

Tidal Dissipation in Stars and Giant Planets (2014, background): “Ogilvie & Lin (2004) considered a polytrope with a solid core, and found that the tidal dissipation rate has a strong dependence on frequency in this range.”
Hot Jupiters in Binary Star Systems (2007, background): “Ogilvie & Lin (2004) find that tidally dissipated energy is deposited throughout the bulk of the planet, raising 5 the possibility that the planet will expand catastrophically.”
STRONG TIDAL DISSIPATION IN SATURN AND CONSTRAINTS ON ENCELADUS' THERMAL STATE FROM ASTROMETRY (2012, background): “Although both of these fluid tides are damped through turbulent friction, they yield a relatively low value of the dissipation parameter: k2/Q ~ 10 -6 at most (Ogilvie & Lin 2004).”
Young Massive Star Clusters (2010, background): “It has fallen somewhat out of favor since the late 1980s, but it may be entering a revival of sorts Ogilvie & Lin (2004).”
Tidal dissipation in planet-hosting stars: damping of spin-orbit misalignment and survival of hot Jupiters (2011, background): “…(as in the convection zone outside the solid core of a giant planet or in the convective envelope of a solar-type star), tidal disturbances are concentrated in very narrow regions (called “wave attractors”) where dissipation takes place (Ogilvie & Lin 2004; Ogilvie 2009; Goodman & Lackner 2009).”
Spin-Orbit Evolution of Short-Period Planets (2004, background): “…a dispersion in the rate of eccentricity dissipation, the spin of a planet changes as it undergoes Kelvin-Helmholtz contraction such that the relevant frequency-averaged Q value ( 106) may be asymptotically independent of the viscosity in the limit of small Ekman number (Ogilvie & Lin 2004).”
Tidal obliquity evolution of potentially habitable planets (2011, background): “For gaseous planets and for stars, numerical simulations and analytical studies find a complex response spectrum, which is extremely sensitive to the size and depth of the convective and radiative layers (Ogilvie & Lin 2004; Goodman & Lackner 2009).”
Tidal heating in icy satellite oceans (2014, unknown): “Nature 456, 770-772; Tyler, R.H. [2009].”
Observational Evidence for Tidal Interaction in Close Binary Systems (2007, background): “At the same time, it was taken for granted that tidal dissipation inside the short-period planets has synchronized their own rotation with their orbital frequency (e.g., Rasio et al. 1996; Ogilvie & Lin 2004).”
On the tidal evolution of Hot Jupiters on inclined orbits (2009, background): “…calculations of the excitation and dissipation of internal waves have indicated that Q′ varies in a complicated way with the tidal frequency (see Savonije et al. 1995; Savonije & Papaloizou 1997; Papaloizou & Savonije 1997; Ogilvie & Lin 2004, hereafter OL04; Ogilvie & Lin 2007, hereafter OL07).”
Long-term tidal evolution of short-period planets with companions (2007, background): “More recent work by Ogilvie & Lin (2004) and Wu (2005) who consider tidal forcing in slowly rotating planets (appropriate to synchronously rotating short-period planets) find that Q-values for such planets tend to be similar to that of Jupiter.”
Tidal Heating of Extrasolar Planets (2008, background): “Considerable progress is being made in this area (Ogilvie & Lin 2004, 2007).”
New constraints on Saturn’s interior from Cassini astrometric data (2015, background): “∂ ∂cl d 2! ri dt(2) ⎛ ⎝⎜ ⎞ ⎠⎟ = 1 mi ∂ ! Fi ∂ rj ∂ rj ∂cl + ∂ ! Fi ∂" rj ∂" rj ∂cl ⎛ ⎝⎜ ⎞ ⎠⎟ + ∂ ! Fi ∂cl j ∑ ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ , (5)”
TIDAL EVOLUTION OF CLOSE-IN PLANETS (2010, background): “This is because tidal quality factors depend sensitively on the detailed interior structure of the body (either star or planet), as well as the tidal forcing frequency and amplitude, and are unlikely to be expressed as a simple constant value (e.g., Ogilvie & Lin 2004, 2007; Wu 2005).”
Tidal Evolution of Close-in Extrasolar Planets (2007, methodology): “First, the tidal dissipation 187 parameter Qp for the planet is usually based on model-dependent estimates based on the tidal evolution of the Jovian satellite system (Yoder & Peale 1981) or on physical theories of tidal dissipation (Goldreich & Nicholson 1977; Ogilvie & Lin 2004).”
Tidal Dissipation in Rotating Solar-Type Stars (2007, background): “In a previous paper (Ogilvie & Lin 2004, hereafter Paper I) we studied the excitation and dissipation of tidal disturbances in rotating giant planets, which are mostly or fully convective.”