Tidal dissipation within large icy satellites: Applications to Europa and Titan

Tobie, G.; Mocquet, A.; Sotin, C.

doi:10.1016/j.icarus.2005.04.006

Cited by 202 publications

(269 citation statements)

References 54 publications

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“…Mass and size of Saturn are shown in Table 1, which are consistent with Remus et al (2012Remus et al ( , 2015. Lainey et al (2017) assume more detailed models with layered structure and the calculation method by Tobie et al (2005), and mention that the viscosity range to generate the observed Q s is compatible between their complex model and the simple two layer model. In the structure models by Remus et al (2012Remus et al ( , 2015 and Lainey et al (2017), the fluid envelope is assumed to be non-dissipative.…”

Section: Introductionsupporting

confidence: 73%

Frequency-dependent tidal dissipation in a viscoelastic Saturnian core and expansion of Mimas’ semi-major axis

Dake¹,

Hußmann²

2017

A&A

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Context. Regarding tidal dissipation in Saturn, usually parameterized by Saturn's quality factor Q, there remains a discrepancy between conventional estimates and the latest determination that has been derived from astrometric observations of Saturn's inner satellites. If dissipation in Saturn is as large as the astrometric observations suggest, and is independent of time and tidal frequency, conventional models predict that Mimas' initial orbit should be located inside Saturn's synchronous orbit or even inside its Roche limit, in contradiction to formation models. Aims. Using simple structure models and assuming Saturn's core to be viscoelastic, we look for dissipation models which are consistent with both the latest astrometric observations and with Mimas' orbital migration. Methods. Firstly, using a two-layer model of Saturn's interior structure, we constrain the ranges of rigidity and viscosity of Saturn's core which are consistent with Saturn's dissipation derived from astrometric observations at the tidal frequencies of Enceladus, Tethys, and Dione. Next, within the constrained viscosity and rigidity ranges, we calculate Mimas' semi-major axis considering the frequency dependence of viscoelastic dissipation in Saturn's core. By the two calculations, we evaluate (1) Saturnian models which can explain the astrometrically determined Saturnian dissipation, and (2) whether Mimas' initial semi-major axis is larger than the synchronous orbit. Results. We show that if the core is assumed to be solid with a viscosity of 10 13 −10 14 Pa s (depending on its size), the lower boundary of the observed Saturnian dissipation at tidal frequencies of Enceladus, Tethys, and Dione (k 2s /Q s ∼ 4 × 10 −5 where k 2s is Saturn's second degree Love number and Q s its quality factor) can be explained by our model. In this viscosity range, Mimas can stay outside the synchronous orbit and the Roche limit for 4.5 billion years of evolution. Conclusions. In the case of a frequency dependent viscoelastic dissipative core, the lower boundary of the observed Saturnian dissipation can be consistent with the orbital expansion of Mimas. In this model, the assumption of a late formation of Mimas, discussed recently, is not required.

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Section: Introductionsupporting

confidence: 73%

Frequency-dependent tidal dissipation in a viscoelastic Saturnian core and expansion of Mimas’ semi-major axis

Dake¹,

Hußmann²

2017

A&A

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“…The same effort should also be undertaken for planetary interiors to have tidal models taking into account their structural and dynamical properties (e.g. Correia & Laskar, 2003;Ogilvie & Lin, 2004;Tobie et al, 2005;Henning et al, 2009;Efroimsky, 2012;Remus et al, 2012b;Correia et al, 2014;Guenel et al, 2014). The second important step, will be to take into account dependence of tidal dissipation/torques on tidal frequency.…”

Section: Discussionmentioning

confidence: 99%

Effect of the rotation and tidal dissipation history of stars on the evolution of close-in planets

Bolmont

Mathis

2016

Celest Mech Dyn Astr

130

194

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Since twenty years, a large population of close-in planets orbiting various classes of low-mass stars (from M-type to A-type stars) has been discovered. In such systems, the dissipation of the kinetic energy of tidal flows in the host star may modify its rotational evolution and shape the orbital architecture of the surrounding planetary system. In this context, recent observational and theoretical works demonstrated that the amplitude of this dissipation can vary over several orders of magnitude as a function of stellar mass, age and rotation. In addition, stellar spin-up occurring during the Pre-Main-Sequence (PMS) phase because of the contraction of stars and their spin-down because of the torque applied by magnetized stellar winds strongly impact angular momentum exchanges within star-planet systems. Therefore, it is now necessary to take into account the structural and rotational evolution of stars when studying the orbital evolution of close-in planets. At the same time, the presence of planets may modify the rotational dynamics of the host stars and as a consequence their evolution, magnetic activity and mixing. In this work, we present the first study of the dynamics of close-in planets of various masses orbiting low-mass stars (from 0.6 M to 1.2 M ) where we compute the simultaneous evolution of the star's structure, rotation and tidal dissipation in its external convective enveloppe. We demonstrate that tidal friction due to the stellar dynamical tide, i.e. tidal inertial waves excited in the convection zone, can be larger by several orders of magnitude than the one of the equilibrium tide currently used in celestial mechanics, especially during the PMS phase. Moreover, because of this stronger tidal friction in the star, the orbital migration of the planet is now more pronounced and depends more on the stellar mass, rotation and age. This would very weakly affect the planets in the habitable zone because they are located at orbital distances such that stellar tide-induced migration happens on very long timescales. We also demonstrate that the rotational evolution of host stars is only weakly affected by the presence of planets except for massive companions.

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“…We now apply these general expressions to a specific rheology that depends on the physical properties of the material. Given our lack of knowledge of the internal structure of giant planets, we implement the simplest model, namely the Maxwell model, which has the advantage of involving only two parameters and is thus easy to use (Tobie 2003;Tobie et al 2005). A critical overview of the four main rheological models was done by Henning et al (2009), thus we refer the reader to the three aforementioned papers for a detailed comparison.…”

Section: Implementation Of An Anelastic Modelmentioning

confidence: 99%

“…however, no experiments are available at the very-high pressures and temperatures we may expect in Jupiter's and Saturn's cores (Guillot 2005). Nevertheless, geophysical and experimental data allow to constrain the rheology of the icy satellites of Jupiter, since their ranges of pressure and temperature are similar to those of the outer mantle of the Earth (Tobie 2003). Then, keeping in mind that these values may differ by several orders of magnitude in our case, we adopt reference values based on these data, assuming that Jupiter's and Saturn's cores are made of ice and rock.…”

Section: Rheological Parameters Of the Corementioning

confidence: 99%

“…Peale & Cassen (1978) evaluated the tidal dissipation in the Moon by considering various models of internal structure. Tobie et al (2005) applied the Maxwell rheological model to evaluate the dissipation in Titan and Europa; Ross & Schubert (1986) compared three different linear models of viscoelasticity (KelvinVoigt, Maxwell, and standard anelastic solid), to which Henning et al (2009) added the Burgers body. All these studies have inspired our interest in the tidal dissipation resulting from the anelastic deformation of the solid parts of a planet when perturbed by a companion.…”

Section: Introduction and General Contextmentioning

confidence: 99%

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Anelastic tidal dissipation in multi-layer planets

Remus

Mathis

Zahn

et al. 2012

A&A

112

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Context. Earth-like planets have viscoelastic mantles, whereas giant planets may have viscoelastic cores. The tidal dissipation of these solid regions, which are gravitationally perturbed by a companion body, strongly depends on their rheology and the tidal frequency. Therefore, modeling tidal interactions provides constraints on planets' properties and helps us to understand their history and evolution, in either our solar system or exoplanetary systems. Aims. We examine the equilibrium tide in the anelastic parts of a planet for every rheology, and by taking into account the presence of a fluid envelope of constant density. We show how to obtain the different Love numbers describing its tidal deformation, and discuss how the tidal dissipation in the solid parts depends on the planet's internal structure and rheology. Finally, we show how our results may be implemented to describe the dynamical evolution of planetary systems. Methods. We expand in Fourier series the tidal potential exerted by a point mass companion, and express the dynamical equations in the orbital reference frame. The results are cast in the form of a complex disturbing function, which may be implemented directly in the equations governing the dynamical evolution of the system. Results. The first manifestation of the tide is to distort the shape of the planet adiabatically along the line of centers. The response potential of the body to the tidal potential then defines the complex Love numbers, whose real part corresponds to the purely adiabatic elastic deformation and the imaginary part accounts for dissipation. The tidal kinetic energy is dissipated into heat by means of anelastic friction, which is modeled here by the imaginary part of the complex shear modulus. This dissipation is responsible for the imaginary part of the disturbing function, which is implemented in the dynamical evolution equations, from which we derive the characteristic evolution times. Conclusions. The rate at which the system evolves depends on the physical properties of the tidal dissipation, and specifically on (1) how the shear modulus varies with tidal frequency, (2) the radius, and (3) the rheological properties of the solid core. The quantification of the tidal dissipation in the solid core of giant planets reveals a possible high dissipation that may compete with dissipation in fluid layers.

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Tidal dissipation within large icy satellites: Applications to Europa and Titan

Cited by 202 publications

References 54 publications

Frequency-dependent tidal dissipation in a viscoelastic Saturnian core and expansion of Mimas’ semi-major axis

Frequency-dependent tidal dissipation in a viscoelastic Saturnian core and expansion of Mimas’ semi-major axis

Effect of the rotation and tidal dissipation history of stars on the evolution of close-in planets

Anelastic tidal dissipation in multi-layer planets

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