Tides on Europa, and the thickness of Europa's icy shell

Wahr, John; Zuber, M. T.; Smith, David E.; Lunine, Jonathan I.

doi:10.1029/2006je002729

Cited by 92 publications

(128 citation statements)

References 37 publications

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“…This term is more than a factor 1000 smaller than the main term Cθ in Eq. (1), even with the large value of k 2 = 0.26 for a model with a subsurface ocean (e.g., Wahr et al, 2006), and will therefore be neglected in this study. We here also neglect the effect of zonal tides on rotation.…”

Section: Rigid Librationsmentioning

confidence: 99%

“…Measurements of the time-variable tidal gravity variations through the dynamic effect of Europa's gravity field on the trajectory of an orbiter (Wu et al, 2001), preferably combined with altimetry measurements of the tidal surface displacements (Wahr et al, 2006;Castillo et al, 2000), as well as extensive characterization of the magnetic field in the neighborhood of Europa by a magnetometer on board of a low-flying orbiter (Khurana et al, 1998;Kivelson et al, 1999Kivelson et al, , 2000 can provide conclusive information for the detection of an ocean. However, tidal measurements may not be sufficient to determine accurately the depth and thickness mainly because of the poorly known composition and rheological characteristics of the icy shell (Wahr et al, 2006), and in interpretations of magnetic data the depth of the ocean may be difficult to separate from the ocean conductivity. A clear picture of Europa's interior could be obtained from seismic sounding (Kovach and Chyba, 2001; Lee et al, 2003), but that would require a lander.…”

Section: Introductionmentioning

confidence: 99%

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The librations, shape, and icy shell of Europa

Hoolst

Rambaux

Karatekin

et al. 2008

Icarus

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Europa, the smallest of the Galilean satellites, has a young icy surface and most likely contains an internal ocean. The primary objective of possible future missions to Europa is the unambiguous detection and characterization of a subsurface ocean. The thickness of the overlying icy shell provides important information on the thermal evolution of the satellite and on the interaction between the ocean and the surface, the latter being fundamental for astrobiology. However, the thickness is not well known, and estimates range from several hundred of meters to some ten of kilometers. Here, we investigate the use of libration (rotation variation) observations to study the interior structure of Europa and in particular its icy shell. A dynamical libration model is developed, which includes gravitational coupling between the icy shell and the heavy solid interior. The amplitude of the main libration signal at 3.55 days (the orbital period) is shown to depend on Europa's shape and structure. Models of the interior structure of Europa are constructed and the equatorial flattening of the internal layers, which are key parameters for the libration, are calculated by assuming that Europa is in hydrostatic equilibrium. Europa's flattened shape is assumed to be due to rotation and permanent tides, and we extend the classical Radau equation for rotationally flattened bodies to include also tidal deformation. We show that the presence of an ocean increases the amplitude of libration by about 10%, depending mainly on the thickness of the icy shell. Therefore, libration observations offer possibility of detection of a subsurface ocean in Europa and estimation of the thickness of its overlying icy shell.

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Section: Rigid Librationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The librations, shape, and icy shell of Europa

Hoolst

Rambaux

Karatekin

et al. 2008

Icarus

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“…The measurements of these tides, together with altimetry observations, have been proposed as elements capable of constraining to some extent the depth of the subsurface ocean and thickness of the ice-I layers (e.g., Wahr et al 2006), and are planned to be implemented in the two orbiters of the Europa Jupiter System Mission (2009), hence the interest in discussing the main features of these possible forced internal translational oscillations. If the amplitudes of the induced variations were large enough to be detected with the equipment included in the Jovian mission, they might provide another way to constrain the internal structure of the observed icy bodies.…”

Section: Discussionmentioning

confidence: 99%

“…Apart from the aforementioned monitoring of the induced magnetic fields in the neighborhood of the body (e.g., Kivelson et al 2000), other observation programs have been proposed. For example, one is to measure the variation of the gravity field and surface displacements of the body caused by the tides exerted by the primary, whose amplitude would be considerably increased by the presence of a liquid layer (e.g., Moore & Schubert 2000;Wahr et al 2006;Hussmann et al 2007). Another potential way of characterizing a subsurface ocean is to consider the rotational state of the body (e.g., Stiles et al 2008;Van Hoolst et al 2009).…”

Section: Motivationmentioning

confidence: 99%

Free Translational Oscillations of Icy Bodies With a Subsurface Ocean Using a Variational Approach

Escapa

Fukushima

2011

The Astronomical Journal

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We analyze the influence of the interior structure of an icy body with an internal ocean on the relative translational motions of its solid constituents. We consider an isolated body differentiated into three homogeneous layers with spherical symmetry: an external ice-I layer, a subsurface ammonia-water ocean, and a rocky inner core. This composition represents icy bodies such as Europa, Titania, Oberon, and Triton, as well as Pluto, Eris, Sedna, and 2004 DW. We construct the equations of motion by assuming that the solid constituents are rigid and that the ocean is an ideal fluid, the internal motion being characterized by the relative translations of the solids and the induced flow in the fluid. Then we determine the dynamics of the icy body using the methods of analytical mechanics, that is, we compute the kinetic energy and the gravitational potential energy, and obtain the Lagrangian function. The resulting solution of the Lagrange equations shows that the solid layers perform translational oscillations of different amplitudes with respect to the barycenter of the body. We derive the dependence of the frequency of the free oscillations of the system on the characteristics of each layer, expressing the period of the oscillations as a function of the densities and masses of the ocean and the rocky inner core, and the mass of the icy body. We apply these results to previously developed subsurface models and obtain numerical values for the period and the ratio between the amplitudes of the translational oscillations of the solid components. The features obtained are quite different from the cases of Earth and Mercury. Our analytical formulas satisfactorily explain the source of these differences. When models of the same icy body, compatible with the existence of an internal ocean, differ in the thickness of the ice-I layer, their associated periods experience a relative variation of at least 10%. In particular, the different models for Titania and Oberon exhibit a larger variation of about 37% and 30%. This indicates an absolute difference of the order of three and two hours, respectively. This suggests that the free period of the internal oscillations might provide a new procedure to constrain the internal structure of icy bodies with a subsurface ocean.

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“…Equations (50)(51)(52) show that Jupiter's torque forces librations at orbital frequency n. We therefore seek solution of the form γ s = g s sin M , γ m = g m sin M…”

Section: Libration Solutionsmentioning

confidence: 99%

Librations of the Galilean satellites: The influence of global internal liquid layers

Baland

Hoolst

2010

Icarus

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The four Galilean satellites are thought to harbour one or even two global internal liquid layers beneath their surface layer. The iron core of Io and Ganymede is most likely (partially) liquid and also the core of Europa may be liquid. Furthermore, there are strong indications for the existence of a subsurface ocean in Europa, Ganymede, and Callisto. Here, we investigate whether libration observations can be used to prove the existence of these liquid layers and to constrain the thickness of the overlying solid layers. For Io, the presence of a small liquid core increases the libration of the mantle by a few percent with respect to an entirely solid Io and mantle libration observations could be used to determine the mantle thickness with a precision of several tens of kilometers given that the libration amplitude can be measured with a precision of one meter. For Europa, Ganymede, and Callisto, the presence of a water ocean close to the surface increases by at least an order of magnitude the ice shell libration amplitude with respect to an entirely solid satellite.The shell libration depends essentially on the shell thickness and to a minor extent on the density difference between the ocean and the ice shell. The possible presence of a liquid core inside Europa and Ganymede has no noticeable influence on their shell libration. For a precision of several meters on the libration measurements, in agreement with the expected accuracy with the NASA/ESA EJSM orbiter mission to Europa and Ganymede, an error on the shell thickness of a few tens kilometers is expected. Therefore, libration measurements can be used to detect liquid layers such as Io's core or water subsurface oceans in Europa, Ganymede, and Callisto and to constrain the thickness of the overlying solid surface layers.

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Tides on Europa, and the thickness of Europa's icy shell

Cited by 92 publications

References 37 publications

The librations, shape, and icy shell of Europa

The librations, shape, and icy shell of Europa

Free Translational Oscillations of Icy Bodies With a Subsurface Ocean Using a Variational Approach

Librations of the Galilean satellites: The influence of global internal liquid layers

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