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.     

Cycloidal cracks on Europa: Improved modeling and non-synchronous rotation implications

Cycloidal crack patterns on Europa are influenced by tides induced by orbital eccentricity, which in turn is driven by the Laplace orbital resonance. Their shapes potentially record the location of their formation (relative to the direction of Jupiter), as well as the parameters of crack formation. Hoppa et al. [Hoppa, G., Tufts, B.R., Greenberg, R., Geissler, P., 1999a. Icarus 141, 287-298] modeled several cycloid chains using a fixed set of material parameters, but some details did not fit. We now allow material parameters to vary for each arc of an observed cycloid. In general, with minimal variation of model parameters between the arcs, fits are greatly improved. Furthermore, accounting for tidal stress accumulated during non-synchronous rotation, in addition to diurnal stress, allows even better fits. Even with the added freedom in the model our fits allow us to better constrain the location where each cycloid may have formed. Our results support Hoppa et al.'s finding that only a few cracks form ridges per cycle of non-synchronous rotation in the region examined, probably because cracking relieves built up stress until further substantial rotation occurs.     

Plate motion on Europa and nonrigid behavior of the Icy lithosphere: The Castalia Macula region

We have developed a generalized quantitative technique for determining the finite pole of rotation between two rigid plates and use it to critically examine differing reconstructions of a region surrounding a prominent dark spot on Europa, Castalia Macula. This region is located near the equator of Europa's trailing hemisphere and has been suggested as a site where crustal convergence may have occurred. Previous reconstructions of the region have indicated that a ridge set and/or a band-like complex that define a collection of tectonic plates in the region accommodated surface contraction. However, a critical examination of the differences between these reconstructions has been complicated by the lack of a finite pole of rotation for the plates involved in either reconstruction. We have applied our modeling technique, coupled with a detailed examination of the morphology and cross-cutting relationships involving this ridge set and band-like complex, to determine if a unique reconstruction exists for several tectonic plates in this region. The cross-cutting relationships involving the ridge set also allow us to test the general assumption that plates behave rigidly on Europa. Assuming rigid behavior, our results suggest that a unique reconstruction does exist, indicating the ridge set accommodated surface contraction. However, analysis performed to test the assumption of plate rigidity indicates that one or more of the plates in the region did not behave rigidly. This does not rule out surface contraction along the ridge set but does indicate that a component of nonrigid behavior must be considered.     

X-ray probes of magnetospheric interactions with Jupiter's auroral zones, the Galilean satellites, and the Io plasma torus

Remote observations with the Chandra X-ray Observatory and the XMM-Newton Observatory have shown that the jovian system is a source of X-rays with a rich and complicated structure. The planet's polar auroral zones and its disk are both powerful sources of X-ray emission. Chandra observations revealed X-ray emission from the Io plasma torus and from the Galilean moons Io, Europa, and possibly Ganymede. The emission from the moons is due to bombardment of their surfaces by highly energetic magnetospheric protons, and oxygen and sulfur ions. These ions excite atoms in their surfaces leading to fluorescent X-ray emission lines. These lines are produced against an intense background continuum, including bremsstrahlung radiation from surface interactions of primary magnetospheric and secondary electrons. Although the X-ray emission from the Galilean moons is faint when observed from Earth orbit, an imaging X-ray spectrometer in orbit around one or more of these moons, operating from 200 eV to 8 keV with 150 eV energy resolution, would provide a detailed mapping of the elemental composition in their surfaces. Surface resolution of 40 m for small features could be achieved in a 100-km orbit around one moon while also remotely imaging surfaces of other moons and Jupiter's upper atmosphere at maximum regional resolutions of hundreds of kilometers. Due to its relatively more benign magnetospheric radiation environment, its intrinsic interest as the largest moon in the Solar System, and its mini-magnetosphere, Ganymede would be the ideal orbital location for long-term observational studies of the jovian system. Here we describe the physical processes leading to X-ray emission from the surfaces of Jupiter's moons and the properties required for the technique of imaging X-ray spectroscopy to map the elemental composition of their surfaces, as well as studies of the X-ray emission from the planet's aurora and disk and from the Io plasma torus.     

Mechanics of tidally driven fractures in Europa's ice shell

A fracture mechanics model is developed for the initiation and propagation of a crack through a porous ice layer of finite thickness under gravitational overburden. It is found that surface cracks generated in response to a tidally induced stress field may penetrate through the entire outer brittle layer if a subsurface ocean is present on Europa. Such penetration is found to be very unlikely in the absence of an ocean. A cycloidal crack would then form as a sequence of near instantaneous discrete failures, each extending roughly the brittle layer thickness in range, linked with a much lower apparent propagation speed set by the moving tidal stress field. The implications of this porous ice fracture model for ice-penetrating radar scattering loss and seismic activity are quantified.     

Comment on “Mechanics of tidally driven fractures in Europa's ice shell” by S. Lee, R.T. Pappalardo, and N.C. Makris [2005. Icarus 177, 367-379]

We show Lee, Pappalardo, and Makris' [2005. Icarus 177, 367-379] argument that surface cracks in Europa's icy shell penetrate 3-10 times deeper in the presence of subsurface ocean is not correct. We use numerical calculations to demonstrate that there is at most 50% increase in penetration depth for a crack opening in a shell of finite thickness compared to a half-space. We also propose a simple equation based on force balances to estimate the maximum thickness of an ice shell that can be opened under tensile stress. Our calculations show that a crack can only penetrate 330-m-thick ice shell under 200 kPa far-field tensile stress and half of that if the stress is 100 kPa. But the presence of water would allow crack penetrate ∼4.0 km into the ice shell with zero porosity.     

Europa's opposition surge in the near-infrared: interpreting disk-integrated observations by Cassini VIMS

Near-infrared observations of Europa's disk-integrated opposition surge by Cassini VIMS, first published in Fig. 4 of Brown et al. (2003, Icarus, 164, 461), have now been modeled with the commonly used Hapke photometric function. The VIMS data set emphasizes observations at 16 solar phase angles from 0.4° to 0.6°—the first time the <1° phase “heart” of Europa's opposition surge has been observed this well in the near-IR. This data set also provides a unique opportunity to examine how the surge is affected by changes in wavelength and albedo: at VIMS wavelengths of 0.91, 1.73, and 2.25 μm, the geometric albedo of Europa is 0.81, 0.33, and 0.18, respectively. Despite this factor-of-four albedo range, however, the slope of Europa's phase curve at <1° phase is similar at all three wavelengths (to within the error bars) and this common slope is similar to the phase coefficient seen in visible-light observations of Europa. The two components of the opposition surge—involving different models of the physical cause of the surge—are the Shadow Hiding Opposition Effect (SHOE) and the Coherent Backscatter Opposition Effect (CBOE). Because of sparse VIMS phase coverage, it is not possible to constrain all the surge parameters at once in a Hapke function that has both SHOE and CBOE; accordingly, we performed separate Hapke fits for SHOE-only and CBOE-only surges. At 2.25 μm, where VIMS data are somewhat noisy, both types of surges can mimic the slope of the VIMS phase curve at <1° phase. At 0.91 and 1.73 μm, however—where VIMS data are “cleaner”—CBOE does a noticeably poorer job than SHOE of matching the VIMS phase coefficient at <1° phase; in particular, the best CBOE fit insists on having a steeper phase-curve slope than the data. This discrepancy suggests that Europa's near-IR opposition surge cannot be explained by CBOE alone and must have a significant SHOE component, even at wavelengths where Europa is bright.     

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.     

Cometary Delivery of Biogenic Elements to Europa

Jupiter's moon Europa may harbor an ocean beneath its ice cover, but the composition of that ocean and the overlying ice is nearly entirely unknown. Regardless of uncertainties in models for Europa's formation, we estimate lower limits for Europa's inventory of biogenic elements (such as C, N, O, and P) by investigating the contribution to the inventory of impact events over Europa's geologic history. A series of high-resolution hydrocode simulations were carried out over a range of comet densities (1.1, 0.8, and 0.6 g/cm³, corresponding to porosities between 0 and 45%) and impact velocities (16, 21.5, 26.5, and 30.5 km/s). We found that at typical impact velocities on Europa most impactor material reaches escape velocity, and it is assumed to be lost from Europa. For a nonporous comet, some fraction (20% or higher) of the projectile is retained by Europa even at the highest impact velocity modeled, 30.5 km/s. For porous comets, however, a significant fraction of the projectile (above 25%) is retained only for the lowest impact velocity modeled, 16 km/s. Integrated over solar system history, this suggests that 1 to 10 Gt of carbon could have been successfully delivered to Europa's surface by impacts of large comets (around 1 km in diameter). This is a few times more carbon than is contained in the procaryotic biomass of the upper 200 meters of the Earth's oceans, but about 2 orders of magnitude less if the whole depth of the oceans is considered. Therefore, regardless of its initial formation conditions, Europa should have a substantial inventory of “biogenic” elements, with implications for the chemistry of its oceans, ice cover, and the possibility of life.