Additions to the Theory of the Rotation of Europa

In a previous paper (The Rotation of Europa, Henrard, Celest. Mech. Dyn. Astr., 91, 131–149, 2005) we have developed a semi-analytical theory of Europa, one of the Galilean satellites of Jupiter. It is based on a synthetic theory of the orbit of Europa and is developed in the framework of Hamiltonian formalism. It was assumed that Europa is a rigid body and Jupiter a point mass. Several additional effects should be investigated in order to complete the theory. The present contribution considers the effect of the shape of Jupiter and of the gravitational pull of Io. The sensitivity of the main theory to a change in the values of the moments of inertia of Europa is also considered.     

Effects of Io ejecta on Europa

We examine the effects of Io ejecta on the surface and environment of Europa. We find that the observed sulfur on the trailing side of Europa, when interpreted as a deposit in equilibrium between implanation of, and sputtering by, corotating Io ejecta, implies a slow loss of material from Europa by sputtering. From this we infer that the spectrum of particles sputtered from water ice is soft. The quantity of observed sulfur and its confinement to the trailing hemisphere appear to exclude significant implantation and sputtering by energetic heavy ions. We also conclude that the contribution from Europa to the magnetospheric plasma (even at Europa itself) is negligible compared to the matter ejected from Io.     

Polar Wander and Surface Convergence of Europa's Ice Shell: Evidence from a Survey of Strike-Slip Displacement

Two global issues regarding Europa are addressed by a survey of strike-slip faults. First, a common type of terrain that appears to represent convergent sites of surface removal, which may help compensate for substantial widespread dilation along tectonic bands elsewhere, thus helping resolve the problem of conserving global surface area, is identified. Second, evidence for polar wander may provide the first confirmation of that theoretically predicted phenomenon. These results, among others, come from an extensive survey of strike-slip faults over the portion of the surface where Galileo images at 200-m/pixel resolution were obtained for regional mapping purposes. The images cover two broad swaths that run from the far north to the far south, one in the leading hemisphere and the other in the trailing hemisphere. Among the faults that have been mapped are a fault 170 km long with a strike-slip offset of 83 km, the greatest yet identified on Europa, and a quasi-circular strike-slip fault that surrounds a 500-km-wide plate, which has undergone rotation as a rigid unit. Reconstruction of specific examples of strike slip reveals sites of lateral convergence. Because Europa is unique in many ways, these sites are not similar to compression features on other bodies, which may explain why they had previously been difficult to identify. The distribution of strike slip in both hemispheres, when compared with predictions of the theory of tidal walking, provides evidence for polar wander: The crust of Europa appears to have slid as a single unit relative to the spin axis, such that the site on the crust that was previously at the north rotational pole has wandered, probably during the last few million years, to a location currently in the leading hemisphere, about 30° away from the spin axis. Such polar wander probably also explains symmetry patterns in the distribution of chaotic terrain, pits, and uplift features.     

The librations, shape, and icy shell of Europa

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.     

The influence of obliquity on europan cycloid formation

Tectonic patterns on Europa are influenced by tidal stress. An important well-recognized component is associated with the orbital eccentricity, which produces a diurnally varying stress as Jupiter's apparent position in Europa's sky oscillates in longitude. Cycloidal lineaments seem to have formed as cracks propagated in this diurnally varying stress field. Maps of theoretical cycloid patterns capture many of the characteristics of the observed distribution on Europa. However, a few details of the observed cycloid distribution have not been reproduced by previous models. Recently, it has been shown that Europa has a finite forced obliquity, so Jupiter's apparent position in Europa's sky will also oscillate in latitude. We explore this new type of diurnal effect on cycloid formation. We find that stress from obliquity may be the key to explaining several characteristics of observed cycloids such as the shape of equator-crossing cycloids and the shift in the crack patterns in the Argadnel Regio region. All of these improvements of the fit between observation and theory seem to require Jupiter crossing Europa's equatorial plane 45° to 180° after perijove passage, suggestive of complex orbital dynamics that locks the direction of Europa's pericenter with the direction of the ascending node at the time these cycloids were formed.     

Onset of Convection,Heat Flow and Thickness of the Europa‘s ice Shell

The observational evidence given by Galileo spacecraft about Europa supports an icy rigid layer of several kilometers over another ductile layer of ice in convection, which floats over an internal ocean of liquid water. Before the onset of convection, heat is transmitted into the crust by conduction. The heat flow analysis in the potentially convective layer gives values higher than those obtained previously by tidal dissipation models, and suggests that the ice may be limited to a thin layer of ∼4 km total thickness. This revised version was published online in July 2006 with corrections to the Cover Date.     

The plasma plumes of Europa and Callisto

We investigate the proposition that Europa and Callisto emit plasma plumes, i.e., a contiguous body of ionospheric plasma, extended in the direction of the corotation flow, analogous to the plume of smoke emitted in the downwind direction from a smokestack. Such plumes were seen by Voyager 1 to be emitted by Titan. We find support for this proposition in published data from Galileo Plasma Science and Plasma Wave observations taken in the corotation wakes of both moons and from magnetometer measurements reported from near the orbit of, but away from, Europa itself. This lends credence to the hypothesis that the plumes escaping from the ionospheres of Europa and Callisto are wrapped around Jupiter by corotation, survive against dispersion for a fairly long time and are convected radially by magnetospheric motions. We present simple models of plume acceleration and compare the plumes of the Europa and Callisto to the known plumes of Titan.     

Secondary and sesquinary craters on Europa

We address impact cratering on Io and Europa, with the emphasis on the origin of small craters on Europa as secondary to the primary impacts of comets on Io, Europa, and Ganymede. In passing we also address the origin of secondary craters generated by Zunil, a well-studied impact crater on Mars that is a plausible analog to impact craters on Io. At nominal impact rates, and taking volcanic resurfacing into account, we find that there should be 1.3 impact craters on Io, equally likely to be of any diameter between 100 m and 20 km. The corresponding model age of Europa's surface is between 60 and 100 Ma. This range of ages does not include a factor three uncertainty stemming from the uncertain sizes and numbers of comets. The mass of basaltic impact ejecta from Io to reach Europa is found to meet or exceed the micrometeoroid flux as a source of rock-forming elements to Europa's ice crust. To describe impact ejecta in more detail we adapt models for impact-generated spalls and Grady-Kipp fragments originally developed by Melosh. Our model successfully reproduces the observed size-number distributions of small craters on both Mars and Europa. However, the model predicts that a significant fraction of the 200-500 m diameter craters on Europa are not traditional secondary craters but are instead sesquinary craters caused by impact ejecta from Io that had gone into orbit about Jupiter. This prediction is not supported by observation, which implies that high speed spalls usually break up into smaller fragments that make smaller sesquinary craters. Iogenic basalts are also interesting because they provide stratigraphic horizons on Europa that in principle could be used to track historic motions of the ice, and they provide materials suitable to radiometric dating of Europa's surface.     

Analytical lunar libration tables

We have developed a theory of the rotation of the Moon, for the purpose of obtaining libration series explicitly dependent upon lunar gravitational field model parameters. A nonlinear model is used in which the rigid Moon, whose motion in space is that of the main problem of lunar theory, and whose gravity potential is represented through its third degree harmonics, is torqued by the Earth and Sun. The analytical series are then obtained as Poisson series. Numerical comparisons with Eckhardt's solution are briefly exposed.     

Long-periodic and secular perturbations to the orbit of a spherical satellite due to direct solar radiation pressure

A theory is developed for the perturbations to the orbit of a spherically symmetric satellite which accounts for the changes in the perigee and nodal positions and the variations of the Sun-Earth distance and direction over an orbital revolution. The theory is semi-analytical, the equations of motion being integrated with respect to time over the sunlit period of each orbital revolution. Long-periodic and short-periodic perturbations may be treated separately, and this is important for long-term analyses in terms of mean elements where short-period terms are averaged or omitted.     

Can redistribution of material by sputtering explain the hemispheric dichotomy of europa?

Sputtering and redeposition make up a significant geologic process on Europa and may contribute to the observed color differences between the leading and trailing hemispheres. Sputtering is particularly efficient on Europa as an erosive process, due to the high rate of ion bombardment from the Io plasma torus, together with Europa’s easily sputtered icy surface. We estimate the global average sputtering erosion rate on Europa at 14.7 mm Myr⁻¹. However, 42% to 86% of sputtered water molecules survive to redeposit onto the surface again. Due to gravitational escape and removal by electron-impact ionization, the number of redepositing particles cannot overcome sputtering erosion, and the global average result of sputtering is net erosion. However, neither sputtering nor redeposition is globally uniform, and differences in the global distributions of the two processes can result locally in net deposition.We propose that Europa’s hemispheric color dichotomy might be explained by net deposition on the leading hemisphere, which may obscure the non-ice signature by covering it with a thin water frost. To test this hypothesis, we have created a simulated model of the sputtering erosion/redeposition process on Europa. Our objectives are to determine the conditions under which net deposition occurs on the leading hemisphere and to evaluate the effects on this process of Jupiter’s gravity, of Europa’s rotation, and of the loss of water molecules to the jovian magnetosphere. We have followed the trajectories of hundreds of thousands of simulated sputtered water molecules in a Monte Carlo process, evolving their orbits under the gravity of both Europa and Jupiter. We have performed this model multiple times, in order to explore the effects of different assumptions of the global distribution of impacting ions, as well as of the sputtered particle ejection velocity. Based upon our results, we conclude that net deposition occurs under a wide range of conditions, making sputtering erosion and redeposition a plausible explanation for the hemispheric color dichotomy of Europa.     

On the habitability of the OGLE-2006-BLG-109L planetary system

We investigate the dynamics of putative Earth-mass planets in the habitable zone (HZ) of the extrasolar planetary system OGLE-2006-BLG-109L, a close analogue of the Solar system. Our work is inspired by the work of Malhotra & Minton. Using the linear Laplace–Lagrange theory, they identified a strong secular resonance that may excite large eccentricity of orbits in the HZ. However, due to uncertain or unconstrained orbital parameters, the subsystem of Jupiters may be found in a dynamically active region of the phase space spanned by low-order mean-motion resonances. To generalize this secular model, we construct a semi-analytical averaging method in terms of the restricted problem. The secular orbits of large planets are approximated by numerically averaged osculating elements. They are used to calculate the mean orbits of terrestrial planets by means of a high-order analytic secular theory developed in our previous works. We found regions in the parameter space of the problem in which stable, quasi-circular orbits in the HZ are permitted. The excitation of eccentricity in the HZ strongly depends on the apsidal angle of jovian orbits. For some combinations of that angle, eccentricities and semimajor axes consistent with the observations, a terrestrial planet may survive in low eccentric orbits. We also study the effect of post-Newtonian gravity correction on the innermost secular resonance.     

木卫二的内部结构模型和海洋层--伽利略探测的最新研究进展

伽利略探测获得了木卫二的最新探测资料，其更精确的重力探测数据使深入研究木卫二的内部结构成为可能，研究表明，木卫二有着比较复杂的内部结构，最外层是水冰层，中层是岩石幔，中心是金属核（Fe或Fe-FeS)。但重力探测数据并不能确定水冰层中水的物态。多方面的证据（如理论，地学，磁场等证据）都表明木卫二的表面冰层下存在液体的导电海洋层，其中磁场方面的证据可能最为有力，概述了对木卫地的内部结构模型和海洋层两方面的研究，并推断潮汐演化是木卫二海洋层存在重要原因。     

A model for the temperature-dependence of tidal dissipation in convective plumes on icy satellites: Implications for Europa and Enceladus

To explain the formation of surface features on Europa, Enceladus, and other satellites, many authors have postulated the spatial localization of tidal heating within convective plumes. However, the concept that enhanced tidal heating can occur within a convective plume has not been rigorously tested. Most models of this phenomenon adopt a tidal heating with a temperature-dependence derived for an incompressible, homogeneous (zero-dimensional) Maxwell material, but it is unclear whether this formulation is relevant to the heterogeneous situation of a warm plume surrounded by cold ice. To determine whether concentrated dissipation can occur in convective plumes, we develop a two-dimensional model to compute the volumetric dissipation rate for an idealized, vertically oriented, isolated convective plume obeying a Maxwellian viscoelastic compressible rheology. We apply the model to the Europa and Enceladus ice shells, and we investigate the consequences for partial melting and resurfacing processes on these bodies. We find that the tidal heating is strongly temperature dependent in a convective ice plume and could produce elevated temperatures and local partial melting in the ice shells of Europa and Enceladus. Our calculation provides the first quantitative verification of the hypothesis by Sotin et al. [Sotin, C., Head, J.W., Tobie, G., 2002. Geophys. Res. Lett. 29. 74-1] and others that the tidal dissipation rate is a strong function of temperature inside a convective plume. On Europa, such localized heating could help allow the formation of domes and chaos terrains by convection. On Enceladus, localized tidal heating in a thermal plume could explain the concentrated activity at the south pole and its associated heat transport of 2-7 GW.     

The chemical nature of Europa surface material and the relation to a subsurface ocean

The surface composition of Europa is of special interest due to the information it might provide regarding the presence of a subsurface ocean. One source of this information is the infrared reflectance spectrum. Certain surface regions of Europa exhibit distorted H₂O vibrational overtone bands in the 1.5 and 2.0 μm region, as measured by the Galileo mission Near Infrared Mapping Spectrometer (NIMS). These bands are clearly the result of highly concentrated solvated contaminants. However, two interpretations of their identity have been presented. One emphasizes hydrated salt minerals and the other sulfuric acid, although each does not specifically rule out some of the other. It has been pointed out that accurate chemical identification of the surface composition must depend on integrating spectral data with geochemical models, and information on the tenuous atmosphere sputtered from the surface. It is also extremely important to apply detailed chemistry when interpreting the spectral data, including knowledge of mineral dissolution chemistry and the subsequent optical signatures of ion solvation in low-temperature ice. We present studies of flash frozen acid and salt mixtures as Europa surface analogs and demonstrate that solvated protons, metal cations and inorganic anions all influence the spectra and must all, collectively, be considered when assigning Europa spectral features. These laboratory data show best correlation with NIMS Europa spectra for multi-component mixtures of sodium and magnesium bearing sulfate salts mixed with sulfuric acid. The data provide a concentration upper bound of 50-mol% for MgSO₄ and 40-mol% for Na₂SO₄. This newly reported higher sodium and proton content is consistent with low-temperature aqueous differentiation and hydrothermal processing of carbonaceous chondrite-forming materials during the formation and early evolution of Europa.     

A revised model for cycloid growth mechanics on Europa: Evidence from surface morphologies and geometries

Although a single model currently exists to explain the development of curved Europan cycloids, there have been no systematic studies of the range of morphologies and quantifiable geometric parameters of cycloidal features. We address variations in geometry along individual cycloid segments, characterizing differences in cusp styles and angles, and addressing the morphologic aspects of cycloid segments and cusps. In so doing, we illustrate how geometric and morphologic evidence imply a formation mechanism that differs from the existing model in several aspects. The current model states that cycloids are initiated as tensile fractures that grow in a curved path in response to rotating diurnal tidal stresses on Europa. However, the geometry of a cycloid cusp necessitates that shear stress was resolved onto the existing cycloid segment by the rotating diurnal stresses at the instant of cusp formation. Furthermore, we observe that cycloid cusps have a strikingly similar geometry to tailcracks that developed at the tips of many ridge-like strike-slip faults on Europa in response to shearing at the fault tip. We suggest that this similarity in geometries can be attributed to an identical formation mechanism whereby cycloid cusps form by a tailcracking process. We therefore present a revised, mechanically-based model for cycloid formation that retains the basic premise that crack growth is governed by diurnal stresses, but describes the development of cycloid cusps in response to resolved shear stresses at the tips of existing cycloid segments. The ratio of normal to shear stress at the time of tailcrack formation dictates the cusp angle and, over longer time periods, influences the morphologic evolution of the cycloid segment as it is repeatedly reworked by tidal stresses.     

A whole-moon thermal history model of Europa: Impact of hydrothermal circulation and salt transport

A whole-moon numerical model of Europa is developed to simulate its thermal history. The thermal evolution covers three phases: (i) an initial, roughly 0.5 Gyr-long period of radiogenic heating and differentiation, (ii) a long period from 0.5 Gyr to 4 Gyr with continuing radiogenic heating but no tidal dissipative heating (TDH), and (iii) a final period covering the last 0.5 Gyr until the present, during which TDH is active. Hydrothermal plumes develop after the initial period of heating and differentiation and transport heat and salt from Europa’s silicate mantle to its ice shell. We find that, even without TDH, vigorous hydrothermal convection in the rocky mantle can sustain flow in an ocean layer throughout Europa’s history. When TDH becomes active, the ice shell melts quickly to a thickness of about 20 km, leaving an ocean 80 km or more deep. Parameterized convection in the ice shell is non-uniform spatially, changes over time, and is tied to the deeper ocean–mantle dynamics. We also find that the dynamics are affected by salt concentrations. An initially non-uniform salt distribution retards plume penetration, but is homogenized over time by turbulent diffusion and time-dependent flow driven by initial thermal gradients. After homogenization, the uniformly distributed salt concentrations are no longer a major factor in controlling plume transport. Salt transport leads to the formation of a heterogeneous brine layer and salt inclusions at the bottom of the ice shell; the presence of salt in the ice shell could strongly influence convection in that layer.     

Europa's neutral cloud: morphology and comparisons to Io

Ground based observations of sodium escaping from Europa suggest the presence of an extended cloud of neutrals orbiting Jupiter. Using a Monte Carlo model we show that the large scale morphology differs from the sodium cloud at Io. At Europa, the trailing cloud is brighter and more extended than the leading cloud. We then use our results to consider the morphology of Europa's oxygen cloud.