Effects of low-viscous layers and a non-zero obliquity on surface stresses induced by diurnal tides and non-synchronous rotation: The case of Europa

In this study we present a semi-analytical Maxwell-viscoelastic model of the variable tidal stress field acting on Europa’s surface. In our analysis, we take into account surface stresses induced by the small eccentricity of Europa’s orbit, the non-zero obliquity of Europa’s spin axis - both acting on a diurnal 3.55-days timescale - and the reorientation of the ice shell as a result of non-synchronous rotation (NSR). We assume that Europa’s putative ocean is covered by an ice shell, which we subdivide in a low-viscous and warm lower ice layer (asthenosphere, viscosity 10¹²-10¹⁷ Pa s), and a high-viscous and cold upper ice layer (lithosphere, viscosity 10²¹ Pa s).Viscoelastic relaxation influences surface stresses in two ways: (1) through viscoelastic relaxation in the lithosphere and (2) through the viscoelastic tidal response of Europa’s interior. The amount of relaxation in the lithosphere is proportional to the ratio between the period of the forcing mechanism and the Maxwell time of the high-viscous lithosphere. As a result, this effect is only relevant to surface stresses caused by the slow NSR mechanism. On the other hand, the importance of the viscoelastic response on surface stresses is proportional to the ratio between the relaxation time (τ_j) of a given viscoelastic mode j and the period of the forcing function. On a diurnal timescale the fast relaxation of transient modes related to the low viscosity of the asthenosphere can alter the magnitude and phase shift of the diurnal stress field at Europa’s surface. The effects are largest, up to 20% in magnitude and 7° in phase for ice rigidities lower than 3.487 GPa, when the relaxation time of the aforementioned transient modes approaches the inverse of the average angular rate of Europa’s orbit. On timescales relevant for NSR (>10⁴ years) the magnitude and phase shift of NSR surface stresses can be affected by viscoelastic relaxation of the ocean-ice boundary. This effect, however, becomes only important when the behavior of the lithosphere w.r.t. NSR approaches the fluid limit, i.e. for strong relaxation in the lithosphere. The combination of NSR and diurnal stresses for different amounts of viscoelastic relaxation of NSR stresses in the lithosphere leads to a large variety of global stress fields that can explain the formation of the large diversity of lineament morphologies observed on Europa’s surface. Variation of the amount of relaxation in the lithosphere is likely due to changes in the spin rate of Europa and/or the rheological properties of the surface.In addition, we show that a small obliquity(<1°) can have a considerable effect on Europa’s diurnal stress field. A non-zero obliquity breaks the symmetric distribution of stress patterns with respect to the equator, thereby affecting the magnitude and orientation of the principal stresses at the surface. As expected, increasing the value of Europa’s obliquity leads to larger diurnal stresses at the surface, especially when Europa is located 90° away from the nodes formed by the intersection of its orbital and equatorial planes.     

Scaling of melt production in hypervelocity impacts from high-resolution numerical simulations

The volume of melt produced in hypervelocity planetary impacts and the size and shape of the melted region are key to understanding the impact histories of solid planetary bodies and the geological effects of impacts on their surfaces and interiors. Prior work of Pierazzo et al. (Pierazzo, E., Vickery, A.M., Melosh, H.J. [1997]. Icarus 127, 408-423) gave the first estimates of impact melt production in geological materials using a modern hydrocode and equation of state. However, computational limits at the time forced use of low resolution, which may have resulted in low melt volumes. Our simulations with 50 times higher resolution provide independent confirmation of the Pierazzo et al. (Pierazzo, E., Vickery, A.M., Melosh, H.J. [1997]. Icarus 127, 408-423) melt volumes in aluminum, iron, dunite, and granite impacts at velocities between 20 and 80 km/s. In ice/ice impacts, we find that melt volumes depend on target temperature and are lower than predicted by Pierazzo et al. (Pierazzo, E., Vickery, A.M., Melosh, H.J. [1997]. Icarus 127, 408-423). Our melt volumes are directly proportional to impact energy for all materials, over a wide range of impact velocity. We also report new data for melt volume scalings for ice/dunite and iron/dunite impacts and the size and shape of melted region, valuable for interpretation of cratering records and studies of impact-induced differentiation.     

Stability of methane clathrate hydrates under pressure: Influence on outgassing processes of methane on Titan

We have conducted high-pressure experiments in the H₂O-CH₄ and H₂O-CH₄-NH₃ systems in order to investigate the stability of methane clathrate hydrates, with an optical sapphire-anvil cell coupled to a Raman spectrometer for sample characterization. The results obtained confirm that three factors determine the stability of methane clathrate hydrates: (1) the bulk methane content of the samples; (2) the presence of additional gas compounds such as nitrogen; (3) the concentration of ammonia in the aqueous solution. We show that ammonia has a strong effect on the stability of methane clathrates. For example, a 10 wt.% NH₃ solution decreases the dissociation temperature of methane clathrates by 14-25 K at pressures above 5 MPa. Then, we apply these new results to Titan’s conditions. Dissociation of methane clathrate hydrates and subsequent outgassing can only occur in Titan’s icy crust, in presence of locally large amounts of ammonia and in a warm context. We propose a model of cryomagma chamber within the crust that provides the required conditions for methane outgassing: emplacement of an ice plume triggers the melting (if solid) or heating (if liquid) of large ammonia-water pockets trapped at shallow depth, and the generated cryomagmas dissociate surrounding methane clathrate hydrates. We show that this model may allow for the outgassing of significant amounts of methane, which would be sufficient to maintain the presence of methane in Titan’s atmosphere for several tens of thousands of years after a large cryovolcanic event.     

The temperature of Europa's subsurface water ocean

A 100 km deep liquid water ocean probably underlies the icy exterior of Jupiter's satellite Europa. The long-term persistence of a liquid ocean beneath an ice shell presents a thermal conundrum: Is the temperature of the ocean equal to the freezing point of water at the bottom of the ice shell, or is it equal to the somewhat warmer temperature at which water attains its maximum density? We argue that most of the ocean is at the temperature of maximum density and that the bulk of the vigorously convecting ocean is separated from the bottom of the ice shell by a thin “stratosphere” of stably stratified water which is at the freezing point, and therefore buoyant. If Europa's subsurface water ocean is warm, it could explain the widespread geologic evidence for apparent melt-through events observed on its surface and may constrain the overall age of its surface.     

Morphology and origin of palimpsests on Ganymede based on Galileo observations

Palimpsests are large, circular, low-relief impact scars on Ganymede and Callisto. These structures were poorly understood based on Voyager-era analysis, but high-resolution Galileo images allow more detailed inspection. We analyze images of four Ganymedean palimpsests targeted by Galileo: Memphis and Buto Faculae, Epigeus, and Zakar. Ganymedean craters and Europan ring structures are used as tools to help better understand palimpsests, based on morphologic similarities. From analysis of Galileo images, palimpsests consist of four surface units: central plains, an unoriented massif facies, a concentric massif facies, and outer deposits. Using as a tie point the location in these structures where secondary craters begin to appear, outer deposits of palimpsests are analogous to the outer ejecta facies of craters; the concentric massif facies of palimpsests are analogous to the pedestal facies of craters; and the unoriented massif facies and central plains are analogous to crater interiors. These analogies are supported by the presence of buried preexisting structure beneath the outer two and absence of buried structure beneath the inner two units. Our observations indicate that palimpsest deposits represent fluidized impact ejecta, rather than cryovolcanic deposits or ancient crater interiors.     

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.     

Convective-conductive transitions and sensitivity of a convecting ice shell to perturbations in heat flux and tidal-heating rate: Implications for Europa

We investigate the response of conductive and convective ice shells on Europa to variations of heat flux and interior tidal-heating rate. We present numerical simulations of convection in Europa's ice shell with Newtonian, temperature-dependent viscosity and tidal heating. Modest variations in the heat flux supplied to the base of a convective ice shell, ΔF, can cause large variations of the ice-shell thickness Δδ. In contrast, for a conductive ice shell, large ΔF involves relatively small Δδ. We demonstrate that, for a fluid with temperature-dependent viscosity, the heat flux undergoes a finite-amplitude jump at the critical Rayleigh number Racr. This jump implies that, for a range of heat fluxes relevant to Europa, two equilibrium states—corresponding to a thin, conductive shell and a thick, convective shell—exist for a given heat flux. We show that, as a result, modest variations in heat flux near the critical Rayleigh number can force the ice shell to switch between the thin, conductive and thick, convective configurations over a ∼10⁷-year interval, with thickness changes of up to ∼10-30 km. Depending on the orbital and thermal history, such switches might occur repeatedly. However, existing evolution models based on parameterized-convection schemes have to date not allowed these transitions to occur. Rapid thickening of the ice shell would cause radial expansion of Europa, which could produce extensional tectonic features such as fractures or bands. Furthermore, based on interpretations for how features such as chaos and ridges are formed, several authors have suggested that Europa's ice shell has recently undergone changes in thickness. Our model provides a mechanism for such changes to occur.     

Model constraints on the opening rates of bands on Europa

A mid-ocean-ridge spreading analog is used to constrain the opening rates and brittle-ductile transition depths for two axisymmetric ridged bands on Europa. Estimates of brittle-ductile transition depth based on the morphologies of Yelland and Ino Lineae are combined with a conductive cooling model based on a mid-ocean ridge analog to estimate the opening rates and active lifetimes of the bands. This model limits local strain rates to ∼¹⁰⁻¹⁵-¹⁰⁻¹² s⁻¹, opening rates to 0.2-40 mm yr⁻¹, and active lifetimes of the bands to 0.1-30 Myr. If the observed structures in the outer portions of ridged bands are indeed normal faults, the estimated range for the tensile strength of ice on Europa is 0.4-2 MPa, consistent with nonsynchronous rotation as the dominant driving mechanism for band opening.     

Geophysical consequences of planetary-scale impacts into a Mars-like planet

All planetary bodies with old surfaces exhibit planetary-scale impact craters: vast scars caused by the large impacts at the end of Solar System accretion or the late heavy bombardment. Here we investigate the geophysical consequences of planetary-scale impacts into a Mars-like planet, by simulating the events using a smoothed particle hydrodynamics (SPH) model. Our simulations probe impact energies over two orders of magnitude (2 × 10²⁷-6 × 10²⁹ J), impact velocities from the planet’s escape velocity to twice Mars’ orbital velocity (6-50 km/s), and impact angles from head-on to highly oblique (0-75°). The simulation results confirm that for planetary-scale impacts, surface curvature, radial gravity, the large relative size of the impactor to the planet, and the greater penetration of the impactor, contribute to significant differences in the geophysical expression compared to small craters, which can effectively be treated as acting in a half-space. The results show that the excavated crustal cavity size and the total melt production scale similarly for both small and planetary-scale impacts as a function of impact energy. However, in planetary-scale impacts a significant fraction of the melt is sequestered at depth and thus does not contribute to resetting the planetary surface; complete surface resetting is likely only in the most energetic (6 × 10²⁹ J), slow, and head-on impacts simulated. A crater rim is not present for planetary-scale impacts with energies >10²⁹ J and angles ?45°, but rather the ejecta is more uniformly distributed over the planetary surface. Antipodal crustal removal and melting is present for energetic (>10²⁹ J), fast (>6 km/s), and low angle (?45°) impacts. The most massive impactors (with both high impact energy and low velocity) contribute sufficient angular momentum to increase the rotation period of the Mars-sized target to about a day. Impact velocities of >20 km/s result in net mass erosion from the target, for all simulated energies and angles. The hypothesized impact origin of planetary structures may be tested by the presence and distribution of the geochemically-distinct impactor material.     

Transfer of mass from Io to Europa and beyond due to cometary impacts

We simulate the production and orbital evolution of escaping ejecta due to cometary impacts on Io. The model includes the four Galilean satellites, Amalthea, Thebe, Jupiter's gravitational moments, Saturn and the Sun. Five scenarios are examined: an impact at the apex, the sub-jovian point, the anti-jovian point, the antapex, and at the south pole of Io. We estimate that on average a cometary impact injects thrice its mass (in the form of Io surface material) into jovicentric orbit. The majority of the escaping debris comes back to Io, but a sizeable fraction (between 5.0 and 8.7%) manages to reach Europa, and a smaller fraction Ganymede (between 1.5 and 4.6%). Smaller fractions reached Amalthea Thebe, Callisto, and Jupiter itself. For million year time scales, the mass transfer to Europa is estimated as 1.8-3.1×¹⁰¹⁴ g/Myr. The median time for transfer of ejecta from Io to Europa is ∼56 years.     

Modeling global impact effects on middle-sized icy bodies: applications to Saturn's moons

Disrupted terrains that form as a consequence of giant impacts may help constrain the internal structures of planets, asteroids, comets and satellites. As shock waves and powerful seismic stress waves propagate through a body, they interact with the internal structure in ways that may leave a characteristic impression upon the surface. Variations in peak surface velocity and tensile stress, related to landform degradation and surface rupture, may be controlled by variations in core size, shape and density. Caloris Basin on Mercury and Imbrium Basin on the Moon have disturbed terrain at their antipodes, where focusing is most intense for an approximately symmetric spheroid. Although, the icy saturnian satellites Tethys, Mimas, and Rhea possess giant impact structures, it is not clear whether these structures have correlated disrupted terrains, antipodal or elsewhere. In anticipation of high-resolution imagery from Cassini, we investigate antipodal focusing during giant impacts using a 3D SPH impact model. We first investigate giant impacts into a fiducial 1000 km diameter icy satellite with a variety of core radii and compositions. We find that antipodal disruption depends more on core radius than on core density, suggesting that core geometry may express a surface signature in global impacts on partially differentiated targets. We model Tethys, Mimas, and Rhea according to their image-derived shapes (triaxial for Tethys and Mimas and spherical for Rhea), varying core radii and densities to give the proper bulk densities. Tethys shows greater antipodal values of peak surface velocity and peak surface tensile stress, indicating more surface damage, than either Mimas or Rhea. Results for antipodal and global fragmentation and terrain rupture are inconclusive, with the hydrocode itself producing global disruption at the limits of model resolution but with peak fracture stresses never exceeding the strength of laboratory ice.     

Possible ancient giant basin and related water enrichment in the Arabia Terra province, Mars

A circular albedo feature in the Arabia Terra province was first hypothesized as an ancient impact basin using Viking-era information. To test this unpublished hypothesis, we have analyzed the Viking era-information together with layers of new data derived from the Mars Global Surveyor (MGS) and Mars Odyssey (MO) missions. Our analysis indicates that Arabia Terra is an ancient geologic province of Mars with many distinct characteristics, including predominantly Noachian materials, a unique part of the highland-lowland boundary, a prominent paleotectonic history, the largest region of fretted terrain on the planet, outflow channels with no obvious origins, extensive exposures of eroded layered sedimentary deposits, and notable structural, albedo, thermal inertia, gravity, magnetic, and elemental signatures. The province also is marked by special impact crater morphologies, which suggest a persistent volatile-rich substrate. No one characteristic provides definitive answers to the dominant event(s) that shaped this unique province. Collectively the characteristics reported here support the following hypothesized sequence of events in Arabia Terra: (1) an enormous basin, possibly of impact origin, formed early in martian history when the magnetic dynamo was active and the lithosphere was relatively thin, (2) sediments and other materials were deposited in the basin during high erosion rates while maintaining isostatic equilibrium, (3) sediments became water enriched during the Noachian Period, and (4) basin materials were uplifted in response to the growth of the Tharsis Bulge, resulting in differential erosion exposing ancient stratigraphic sequences. Parts of the ancient basin remain water-enriched to the present day.     

The large crater on the small Asteroid (2867) Steins

The maximum size of impact craters on finite bodies marks the largest impact that can occur short of impact induced disruption of the body. Recently attention has started to focus on large craters on small bodies such as asteroids and rocky and icy satellites. Here the large crater on the recently imaged Asteroid (2867) Steins (with crater diameter to mean asteroid radius ratio of 0.79) is shown to follow a limit set by other similar sized bodies with moderate macroporosity (i.e. fractured asteroids). Thus whilst large, the crater size is not novel, nor does it require Steins to possess an extremely large porosity. In one of the components of the binary Asteroid (90) Antiope there is the recently reported presence of an extremely large depression, possibly a crater, with depression diameter to mean asteroid radius ratio of ∼(1.4–1.62). This is consistent with the maximum size of a crater expected from previous observations of very porous rocky bodies (i.e. rubble-pile asteroids). Finally, a relationship between crater diameter (normalised to body radius) is proposed as a function of body porosity which suggests that the doubling of porosity between fractured asteroids and rubble-pile asteroids, nearly doubles the size (D/R value) of the largest crater sustainable on a rocky body.     

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.     

How rapidly did Mars accrete? Uncertainties in the Hf-W timing of core formation

Estimates for the martian core formation timescale based on the hafnium-tungsten (Hf-W) isotopic system have varied by almost an order of magnitude, because of uncertainties in the martian mantle Hf/W ratio. Here we argue that the Hf/W ratio is ∼4 but is uncertain by ∼25%, resulting in (instantaneous) martian core formation timescales ranging from 0 to 10 Myr; accordingly, Hf-W isotope observations currently have limited utility in distinguishing between scenarios in which Mars formed as a stranded embryo and scenarios in which Mars suffered a prolonged accretion history.     

Segmented lineaments on Europa: Implications for the formation of ridge complexes and bright bands

We describe several segmented lineaments on Europa’s surface. These lineaments are extensive, stretching for 100s-1000s of km, and have ridge complex or bright band morphologies. The geometries of the segmented portions of these features are diagnostic of the remote normal and shear stress environment in which they formed and, therefore, constrain ridge complex and bright band formation mechanisms. Analysis of four ridge complexes indicates that they formed in a remote normal stress environment that was tensile and isotropic (or nearly so) and that these lineaments may have formed in a manner more analogous to bands on Europa than to ridges. The stress environment associated with these ridge complexes may also explain the anastomosing nature of their interior morphology. Analysis of two bright bands indicate that one formed in a remote normal stress environment that was tensile and the other was reactivated under a combination of remote tensile normal stress and remote sinistral shear stress. Aspects of the morphologies of these features also indicate that bright bands likely have complex deformation histories that can include multiple episodes of reactivation.     

The rayed crater Zunil and interpretations of small impact craters on Mars

A 10-km diameter crater named Zunil in the Cerberus Plains of Mars created ∼¹⁰⁷ secondary craters 10 to 200 m in diameter. Many of these secondary craters are concentrated in radial streaks that extend up to 1600 km from the primary crater, identical to lunar rays. Most of the larger Zunil secondaries are distinctive in both visible and thermal infrared imaging. MOC images of the secondary craters show sharp rims and bright ejecta and rays, but the craters are shallow and often noncircular, as expected for relatively low-velocity impacts. About 80% of the impact craters superimposed over the youngest surfaces in the Cerberus Plains, such as Athabasca Valles, have the distinctive characteristics of Zunil secondaries. We have not identified any other large (?10 km diameter) impact crater on Mars with such distinctive rays of young secondary craters, so the age of the crater may be less than a few Ma. Zunil formed in the apparently youngest (least cratered) large-scale lava plains on Mars, and may be an excellent example of how spallation of a competent surface layer can produce high-velocity ejecta (Melosh, 1984, Impact ejection, spallation, and the origin of meteorites, Icarus 59, 234-260). It could be the source crater for some of the basaltic shergottites, consistent with their crystallization and ejection ages, composition, and the fact that Zunil produced abundant high-velocity ejecta fragments. A 3D hydrodynamic simulation of the impact event produced 10¹⁰ rock fragments ?10 cm diameter, leading to up to 10⁹ secondary craters ?10 m diameter. Nearly all of the simulated secondary craters larger than 50 m are within 800 km of the impact site but the more abundant smaller (10-50 m) craters extend out to 3500 km. If Zunil is representative of large impact events on Mars, then secondaries should be more abundant than primaries at diameters a factor of ∼1000 smaller than that of the largest primary crater that contributed secondaries. As a result, most small craters on Mars could be secondaries. Depth/diameter ratios of 1300 small craters (10-500 m diameter) in Isidis Planitia and Gusev crater have a mean value of 0.08; the freshest of these craters give a ratio of 0.11, identical to that of fresh secondary craters on the Moon (Pike and Wilhelms, 1978, Secondary-impact craters on the Moon: topographic form and geologic process, Lunar Planet. Sci. IX, 907-909) and significantly less than the value of ∼0.2 or more expected for fresh primary craters of this size range. Several observations suggest that the production functions of Hartmann and Neukum (2001, Cratering chronology and the evolution of Mars, Space Sci. Rev. 96, 165-194) predict too many primary craters smaller than a few hundred meters in diameter. Fewer small, high-velocity impacts may explain why there appears to be little impact regolith over Amazonian terrains. Martian terrains dated by small craters could be older than reported in recent publications.     

The great thickness debate: Ice shell thickness models for Europa and comparisons with estimates based on flexure at ridges

Estimates of the thickness of the ice shell of Europa range from <1 to >30 km. The higher values are generally assumed to be estimates of the entire ice shell thickness, which may include a lower ductile layer of ice, whereas many of the smaller thickness estimates are based on analyses that only consider that portion of the ice layer that behaves elastically at a particular strain rate. One example of the latter is flexure analysis, in which the elastic ice layer is modeled as a plate or sphere that is flexed under the weight of a surface load. We present calculations based on flexure analysis in which we model the elastic ice layer as flexing under a line-load caused by ridges. We use precisely located, parallel flanking cracks as indicators of the location of greatest tensile stress induced by flexure. Our elastic thickness results are spatially variable: ∼500-2200 m (two sites) and ∼200-1000 m (one site). Thorough analysis of Europan flexure studies performed by various researchers shows that the type of model selected causes the greatest variability in the thickness results, followed by the choice of Young's modulus, which is poorly constrained for the Europan ice shell. Comparing our results to those of previously published flexure analyses for Europa, we infer spatial variability in the elastic ice thickness (at the time of load emplacement), with smooth bands having the thinnest elastic ice thickness of all areas studied. Because analysis of flexure-induced fracturing can only reveal the elastic thickness at the time of load emplacement, calculated thickness variability between features having different ages may also reflect a temporal variability in the thickness of Europa's ice shell.     

The evil twin of Agenor: tectonic convergence on Europa

The dilemma of the surface-area budget on Europa is resolved by identification of sites of crustal convergence, which have balanced the continual and common creation of new surface along dilational bands and pull-aparts. Convergence bands are characterized by a distinctive, albeit subdued, morphology. The prominent, unusual lineament Agenor is one of several examples. We also find diametrically opposite Agenor a similar bright linear feature surrounded by markings that allow reconstruction, which shows it to be a convergence feature. Until recently, identification of convergence sites was difficult because these features are subtle and do not exhibit structures (like the Himalayas or plate subduction) familiar from convergence of thick solid crusts on terrestrial planets.     

The shape distribution of asteroid families: Evidence for evolution driven by small impacts

A statistical analysis of brightness variability of asteroids reveals how their shapes evolve from elongated to rough spheroidal forms, presumably driven by impact-related phenomena. Based on the Sloan Digital Sky Survey Moving Object Catalog, we determined the shape distribution of 11,735 asteroids, with special emphasis on eight prominent asteroid families. In young families, asteroids have a wide range of shape elongations, implying fragmentation-formation. In older families we see an increasing number of rough spheroids, in agreement with the predictions of an impact-driven evolution. Old families also contain a group of moderately elongated members, which we suggest correspond to higher-density, more impact-resistant cores of former fragmented asteroids that have undergone slow shape erosion. A few percent of asteroids have very elongated shapes, and can either be young fragments or tidally reshaped bodies. Our results confirm that the majority of asteroids are gravitationally bound “rubble piles.”