Tidal torque rotation effects

The lag in the tidal response to Jupiter creates a torque on Europa's rotation which, averaged over each orbit, tends to drive the rotation to a rate slightly different from synchronous. That rate depends on details of the tidal response, but according to theory is expected to be only slightly faster than synchronous (Greenberg and Weidenschilling, 1984).

Even given Europa's orbital e, the rotation might be synchronous if a non-spherically symmetric, frozen-in density distribution (like that of the Earth's Moon) were locked to the direction of Jupiter. Given that Europa is substantially heated by tidal friction (see below), it may not be able to support such a frozen-in asymmetry. It is also conceivable that the silicate interior is locked to the direction of Jupiter by a mass asymmetry, while the ice crust, uncoupled from the silicate by an intervening liquid water layer, rotates non-synchronously due to the tidal torque.

Even a completely solid Europa would rotate non-synchronously as long as mass asymmetries are small enough. Non-synchronous rotation would not in itself imply the existence of an ocean. However, both the existence of an ocean and non-synchronous rotation are made possible by the substantial tidal heating.

Observational evidence places some constraints on the actual rotation rate. A comparison of Europa's orientation during the Voyager 2 encounter with that observed 18 y later by Galileo showed no detectable deviation from synchroneity. Hoppa et al. (1999c) found that any deviation must be small (as predicted), with a period >12 000 y, relative to the direction of Jupiter.

In principle, further evidence could come from changes in the orientations of cracking over time, as terrain moved west-to-east through the theoretical tidal stress field. The possibility that the observed tectonic patterns might contain some record of such reorientation was noted by Helfenstein and Parmentier (1985) and McEwen (1986). Studies of cross-cutting sequences of lineaments from early Galileo spacecraft images suggested just such a variation in the azimuths over time (Geissler etal., 1998).

However, more recent studies using higher-resolution images and exploring several regions suggest that the systematic result was an artefact of an incomplete data set (Sarid et al., 2004, 2005). The sequence of azimuth formation is not continuous and can only be consistent with non-synchronous rotation if one or two cracks (at most) form during each cycle of rotation. That result is reasonable, because once one crack forms in a given region, it would relieve further tidal stress until it has rotated into a different stress regime. This change over time is important in the evolution of the hypothetical ecosystem discussed in Section 15.4.

Other lines of evidence do suggest non-synchronous rotation. As the tectonic effects of tidal stress began to be better understood, various features were found to have likely formed further west than their current positions, including strike-slip faults (Hoppa et al., 1999b, 2000) and cycloidal crack patterns. From the latter, Hoppa et al. (2001b) inferred a non-synchronous period of <250 000 y, but >12 000 y based on the Voyager-Galileo comparison discussed above. There is also similar evidence from strike-slip faults for substantial 'polar wander' within the past few million years, in which the ice shell, uncoupled from the interior, was reoriented relative to the spin axis (Sarid et al., 2002). Supporting evidence for polar wander comes from asymmetries in distributions of small pits, uplifts, and chaotic terrain (Greenberg, 2005).

15.3.2 Tidal stress: tectonic effects Crack patterns

Global-scale lineament patterns (e.g., those in Figure 15.1) correlate roughly with tidal stress patterns (i.e., major global- and regional-scale lineaments are generally orthogonal to directions of maximum tension), showing that the lineaments result from cracking (e.g., Greenberg et al. (1998)). Because the morphology of these lineaments involves large-scale ridge systems, we infer that ridges result from cracks.

A distinct and ubiquitous shape for cracks and ridges on Europa is a chain of arcs, known as cycloids, first discovered by Voyager (Figure 15.6) (Smith et al., 1979; Lucchitta and Soderblom, 1982). Many of these are marked by double ridges; cycloidal cracks that have not yet developed ridges are also common; many dilational bands appear to have initiated as arcuate cracks; even the major strike-slip fault Astypalaea appears to have begun as a chain of arcuate cracks. Typically these features have arcuate segments ~ 100 km long and the chains run for ~ 1000 km.

This distinctive style of cracking probably occurs as a result of the periodic changes in tidal stress due to the orbital eccentricity (Hoppa etal., 1999a). Suppose a given crack initiates at a time when the tidal tension exceeds the local strength of the ice. It will then propagate across the surface perpendicular to the local tidal tension. On a timescale of hours, as Europa moves in its orbit, the orientation of the stress varies. Hence the crack propagates in an arc until the stress falls below a critical value necessary to continue cracking. Crack propagation comes to a halt. A few hours later, the tension returns to a high enough value, now in a different direction, so crack propagation resumes at an angle to the direction at which it had stopped. Thus a series of arcs is created (each corresponding to one orbit's worth of propagation), with cusps between them.

The characteristics of observed arcuate features can be reproduced theoretically, using strength values plausible for bulk ice (~105 Pa) and a speed of propagation of a few kilometres per hour. Because each arc segment represents propagation during one Europan orbit, a typical cycloidal crack must have formed in about one (terrestrial) month. In general, the orientation and curvature of the cycloidal chain as a whole is determined by the location at which the crack formed. Thus one can determine the formation location by fitting the model to those characteristics; such modelling (Hoppa et al., 2001b; Hurford et al., 2007) constrains Europa's rotation (Section 15.3.1).

In all cases a subsurface ocean was required in order to have adequate tidal amplitude to form the observed cycloidal geometries. If there were no ocean, and the tidal amplitude were correspondingly small, cracking would require the ice to be even weaker. In that case, the shapes of cycloids would be distinctly different from what is seen on Europa. Thus the presence of cycloidal lineaments, and their correlation with theoretical characteristics, provided the first widely convincing evidence for the hypothesized liquid water ocean (Hoppa et al., 1999a). Because many cycloids formed during the past few million years, they suggest that the ocean still exists. More recently, studies of Europa's effect on the Jovian magnetosphere provided corroborating evidence for a current liquid ocean (Khurana et al., 1998; Zimmer et al., 2000). Tidally active cracks Once a crack forms, it relieves the tidal stress in its vicinity. Further cracking is unlikely as long as the crack remains 'active', that is until it anneals so that it can support transverse tension again. During the time that the crack is active and unannealed, the periodic tidal distortion of the satellite's icy shell results in a working of the crack. That is, depending on time, location, and crack orientation, there may be a regular opening and closing of the crack and/or a periodic shearing along the crack. The repeated opening and closing would pump ice and slush from the ocean to the surface, creating the ubiquitous double ridges and their modified forms. Moreover, such working appears to have also driven strike-slip displacement along many cracks on Europa, which in turn indicates that cracks penetrate all the way down to the liquid ocean, a strong constraint on ice thickness. The next two subsections describe how the working of active cracks may build double ridges and drive strike-slip displacement.

Ridge formation The regular opening and closing of a crack can build a ridge by a process of tidal extrusion (Greenberg et al., 1998), which operates as illustrated in Figure 15.9: as the tides open cracks (Figure 15.9A), water flows to the float line, where it boils in the vacuum and freezes owing to the cold. As the walls of the crack close a few hours later (Figure 15.9B), a slurry of crushed ice, slush, and water is squeezed to the surface and deposited on both sides of the crack (Figure 15.9C, D).

— Thin 'lead' ice


Ice crust


Fig. 15.9. A schematic of the diurnal steps of ridge-building as described in the text.

Given the frequency of the process, ridges of typical size (100 m high and 1 km wide) can grow quickly, in as little as 20 000 y. Identification of a mechanism for ridge formation that is so fast is important, because many generations of Europan ridges have formed over the past 108 y (the maximum age of the surface on the basis of the paucity of craters); also, each ridge probably had to form well within one rotational period.

Thus ridges appear to form by a process in which active cracks are bathed in liquid water (including whatever impurities the ocean contains) on a daily basis. Any localized heating due to friction at these cracks would further maintain this process. Fagents et al. (2000) have proposed that the darkening that flanks major ridge systems may be related to heat along the lineament, allowing impurities in the ice to be concentrated at the surface. Given the exposure of liquid water during the ridge-formation process described above, the dark material flanking major ridge systems is plausibly associated with oceanic substances. This material might have been emplaced at the margins of ridges as oceanic fluid spread through porous ridges (Greenberg et al., 1998), or geyser-like plumes might have sprayed the surface during the daily exposure of liquid water to the vacuum (Kadel et al., 1998).

Another model of ridge formation assumes that long linear diapirs (low-density blobs in the viscous crust) have risen from below the surface, tilting it upward along the sides of cracks (Head et al., 1999). That model was predicated on hypothetical solid-state diapirism in a tens-of-kilometres thick layer of ice, and assumes uniform upwelling over hundreds of kilometres for each major ridge pair, which seems implausible. Moreover, the linear diapir model is inconsistent with the observed properties of ridges in a variety of ways (e.g., Greenberg (2005)).

Variations on the theme of double ridge formation are common (Greenberg et al., 1998; Greenberg, 2005). The multiple-ridge complexes that compose the centre stripes of many of the long triple bands probably formed as parallel, lateral cracks due to the weight of earlier ridges on the thin ice. These lateral cracks then become activated by tidal working and build their own ridges. Other ridges are wider and symmetrically lineated along their length, and are found where the adjacent terrain has separated somewhat. The dilation may have been due to incomplete extrusion of solid ice during daily crack closure (e.g., Figure 15.9C), which left jammed ice to gradually pry the cracks open.

Strike-slip displacement Strike-slip displacement (e.g., Figure 15.7) is common and widely distributed, often with long extent and large offset displacement (Schenk and McKinnon, 1989; Tufts, 1998; Tufts et al., 1999; Hoppa et al., 1999b, 2000; Sarid et al., 2002). Examples include a 170-km-long fault in the far north with > 80 km of shear offset, and a long, bent cycloidal crack whose shear offset indicates that a cohesive plate >400 km across rotated by about 1°. The 40 km shear offset fault along 800-km-long Astypalaea Linea near the south pole (Tufts et al., 1999; see Figures 15.6 and 15.7) was originally cycloid-shaped with double ridges. Under shear, ridges on opposite sides of the cracks moved in opposite directions, like trains passing on separate tracks. Those parts of the original crack that were oblique to the shear direction were pulled apart, yielding parallelograms of in-filled material, presumably slush from below. These sites show in detail the structure at a location where we know the crust was pulled apart, an important point of reference for interpretation of dilational bands (Section 15.2.2).

Tidal stress in the Astypalaea region drives the shear displacement by a mechanism analogous to walking (Tufts, 1998; Hoppa et al., 1999b). Over each orbital period, the tide goes through a sequence starting with tensile stress across the fault, followed 21 hours later by right-lateral shear, followed 21 hours later by compression across the fault, followed 21 hours later by left-lateral shear. Because the left-lateral shear stress occurs after the fault is compressed, friction at the crack may resist displacement, while right-lateral stress occurs immediately after the crack is opened by tension. Thus tides drive shear in the right-lateral sense in a ratcheting process. The mechanism is similar to walking, where an animal repeatedly separates a foot from the ground (analogous to a crack opening), moves it forward (analogous to shear displacement), presses it to the ground (analogous to compressive closing of a crack), and pushes it backward (analogous to the reverse shear phase), resulting in forward motion. On Europa this process moves plates of crust.

Surveys of strike-slip offsets over much of Europa show that they fit the predictions of the tidal-walking theory quite well (Hoppa et al., 2000; Sarid et al., 2002). Furthermore, the fit is even better if one takes into account some non-synchronous rotation and at least one polar wander event. Another result of the surveys of strike-slip was identification of large-plate displacements that showed where surface convergence had taken place (Sarid et al., 2002). The latter result is important because it shows how the surface-area budget may be balanced, even given the large amount of new surface created where cracks have dilated (Section 15.2.2).

The success of tidal walking in explaining the observed faulting argues strongly that the decoupling layer over which the surface plates slide is a fluid. Penetration to such a layer is required for the daily steps in the 'tidal-walking' model, because a fluid can deform as necessary on the short timescale of the orbit-driven tides. A thick, ductile, warm ice layer may, in principle, allow lateral displacement above it (Schenk and McKinnon, 1989; Golombek and Banerdt, 1990), but no studies have yet shown that tidal walking could be viable in that case.

Thus strike-slip requires that cracks penetrate through most of the crust, which in turn requires that the ice be quite thin, because the tidal tensile stress available for creation of the cracks is not high, only about 40 kPa. Such low tensile stresses are overwhelmed by the compressive hydrostatic overburden pressure at a depth of only ~100m. These cracks could be driven to greater depths by the insertion of liquid water or in-falling solid material. Cracks may also go to greater depth because additional stress is concentrated at the tip of the crack. It is unlikely that cracks could penetrate more than a few kilometres on Europa. Thus our model of strike-slip displacement implies that Europa's ice crust overlies liquid water, that cracks readily penetrate from the surface to the liquid ocean, and therefore the ice must be fairly thin.

Furthermore, Hoppa et al. (1999b) noted that strike-slip offsets are along ridge pairs, not simple cracks, implying that ridges form along cracks that penetrate all the way down to liquid water. This result is consistent with the evidence that ridges form as a result of the working of cracks that link the ocean to the surface (Section 15.3.2).

The observations and theory of strike-slip displacement have helped constrain the physical character of Europa in ways that are critical to the potential setting for life, including evidence for non-synchronous rotation, for polar wander, for penetration of cracks to the ocean, for significant crust displacement driven by the tidal walking process, and for zones of surface convergence.

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