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1.
The proposed past eruption of liquid water on Europa and ongoing eruption of water vapor and ice on Enceladus have led to discussion about the feasibility of cracking a planetary ice shell. We use a boundary element method to model crack penetration in an ice shell subjected to tension and hydrostatic compression. We consider the presence of a region at the base of the ice shell in which the far-field extensional stresses vanish due to viscoelastic relaxation, impeding the penetration of fractures towards a subsurface ocean. The maximum extent of fracture penetration can be limited by hydrostatic pressure or by the presence of the unstressed basal layer, depending on its thickness. Our results indicate that Europa's ice shell is likely to be cracked under 1-3 MPa tension only if it is ?2.5 km thick. Enceladus' ice shell may be completely cracked if it is capable of supporting ∼1-3 MPa tension and is less than 25 km thick. 相似文献
2.
Both Lee et al. and Qin et al. consider propagation of a surface initiated tensile crack oriented vertically in an ice sheet of finite thickness with gravitational overburden. Lee et al. assume the crack walls are always in contact and bear normal stress from overburden. In this closed crack scenario, overburden stress increases linearly with depth just as in an ice half-space. Crack walls cannot sustain tension, so the effect of far field tension is concentrated in the material below the crack walls. This leads to the deep crack penetrations of Lee et al. Qin et al., however, assume an open crack scenario. They inappropriately apply normal stress to open crack walls which are exposed to vacuum and so physically cannot sustain a normal stress [Timoshenko, S.P., Goodier, J.N., 1970. Theory of Elasticity, third ed. McGraw-Hill, New York, p. 191]. Since this inappropriate normal stress is horizontally oriented it has the effect of artificially concentrating compressive stress in the material below the open crack. The severely limited crack propagation depths of Qin et al. result from this inappropriate boundary condition on an open crack wall. 相似文献
3.
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. 相似文献
4.
Ice-shell thickness and ocean depth are calculated for steady state models of tidal dissipation in Europa's ice shell using the present-day values of the orbital elements. The tidal dissipation rate is obtained using a viscoelastic Maxwell rheology for the ice, the viscosity of which has been varied over a wide range, and is found to strongly increase if an (inviscid) internal ocean is present. To determine steady state values, the tidal dissipation rate is equated to the heat-transfer rate through the ice shell calculated from a parameterized model of convective heat transfer or from a thermal conduction model, if the ice layer is found to be stable against convection. Although high dissipation rates and heat fluxes of up to 300 mWm−2 are, in principle, possible for Europa, these values are unrealistic because the states for which they are obtained are thermodynamically unstable. Equilibrium models have surface heat flows around 20 mWm−2 and ice-layer thicknesses around 30 km, which is significantly less than the total thickness of the H2O-layer. These results support models of Europa with ice shells a few tens of kilometers thick and around 100-km-thick subsurface oceans. 相似文献
5.
Coupled thermal-orbital evolution models of Europa and Io are presented. It is assumed that Io, Europa, and Ganymede evolve in the Laplace resonance and that tidal dissipation of orbital energy is an internal heat source for both Io and Europa. While dissipation in Io occurs in the mantle as in the mantle dissipation model of Segatz et al. (1988, Icarus 75, 187), two models for Europa are considered. In the first model dissipation occurs in the silicate mantle while in the second model dissipation occurs in the ice shell. In the latter model, ice shell melting and variations of the shell thickness above an ocean are explicitly included. The rheology of both the ice and the rock is cast in terms of a viscoelastic Maxwell rheology with viscosity and shear modulus depending on the average temperature of the dissipating layer. Heat transfer by convection is calculated using a parameterization for strongly temperature-dependent viscosity convection. Both models are consistent with the present orbital elements of Io, Europa, and Ganymede. It is shown that there may be phases of quasi-steady evolution with large or small dissipation rates (in comparison with radiogenic heating), phases with runaway heating or cooling and oscillatory phases during which the eccentricity and the tidal heating rate will oscillate. Europa's ice thickness varies between roughly 3 and 70 km (dissipation in the silicate layer) or 10 and 60 km (dissipation in the ice layer), suggesting that Europa's ocean existed for geological timescales. The variation in ice thickness, including both convective and purely conductive phases, may be reflected in the formation of different geological surface features on Europa. Both models suggest that at present Europa's ice thickness is several tens of km thick and is increasing, while the eccentricity decreases, implying that the satellites evolve out of resonance. Including lithospheric growth in the models makes it impossible to match the high heat flux constraint for Io. Other heat transfer processes than conduction through the lithosphere must be important for the present Io. 相似文献
6.
The Cassini probe observed a young and smooth surface around the south pole of Enceladus, while around the north pole the surface was found to be relatively old and inactive (Porco, C.C. et al. [2006]. Science 311, 1393–1401). This heterogeneous surface implies that the ice thickness of Enceladus is not uniform between the north and south polar regions. Determining the thickness of the icy layer is important to confirm the existence of an internal ocean as well as to reveal the heating mechanism of Enceladus. We show that the measurement of radio waves induced by cosmic neutrinos can be an effective method to constrain the ice thickness of a localized area where conventional gravity or electromagnetic field measurements cannot be used. This method could be used to constrain the thickness of the icy layer on Enceladus even if the ice is a few tens of kilometers thick, measuring over a period of several years, which greatly exceeds the ability of radar sounding, and hence could be used in future orbiter missions. 相似文献
7.
Two opposing models to explain the geological features observed on Europa’s surface have been proposed. The thin-shell model states that the ice shell is only a few kilometers thick, transfers heat by conduction only, and can become locally thinner until it exposes an underlying ocean on the satellite’s surface. According to the thick-shell model, the ice shell may be several tens of kilometers thick and have a lower convective layer, above which there is a cold stagnant lid that dissipates heat by conduction. Whichever the case, from magnetic data there is strong support for the presence of a layer of salty liquid water under the ice. The present study was performed to examine whether the possibility of convection is theoretically consistent with surface heat flows of ∼100-200 mW m−2, deduced from a thin brittle lithosphere, and with the typical spacing of 15-23 km proposed for the features usually known as lenticulae. It was obtained that under Europa’s ice shell conditions convection could occur and also account for high heat flows due to tidal heating of the convective (nearly isothermal) interior, but only if the dominant water ice rheology is superplastic flow (with activation energy of 49 kJ mol−1; this is the rheology thought dominant in the warm interior of the ice shell). In this case the ice shell would be ∼15-50 km thick. Furthermore, in this scenario explaining the origin of the lenticulae related to convective processes requires ice grain size close to 1 mm and ice thickness around 15-20 km. 相似文献
8.
Richard Greenberg Gregory V. Hoppa Gwen Bart Terry Hurford 《Celestial Mechanics and Dynamical Astronomy》2003,87(1-2):171-188
The ice crust of Europa probably floats over a deep liquid-water ocean, and has been continually resurfaced by tectonic and thermal processes driven by tides. Tidal working causes rotational torque, surface stress, internal heating, and orbital evolution. The stress patterns expected on such a crust due to reorientation of the tidal bulge by non-synchronous rotation and due to orbital eccentricity, which introduces periodic ('diurnal') variations in the tide, are shown as global maps. By taking into account the finite rate of crack propagation, global maps are generated of cycloidal features and other distinctive patterns, including the crack shapes characteristic of the wedges region and its antipode on the sub-Jovian hemisphere. Theoretical maps of tidal stress and cracking can be compared with observed tectonics, with the possibility of reconstructing the rotational history of the satellite. 相似文献
9.
This paper describes a new approach based on variational principles to calculate the radial distribution of tidal energy dissipation in any satellite. The advantage of the model with respect to classical solutions, is that it relates in a straightforward way the radial distribution of the time-averaged dissipation rate to its sensitivity to the corresponding distribution of viscoelastic parameters. This method is applied to Io-, Europa-, and Titan-like interiors, and it is tested against the results obtained by two classical methods by determining global dissipation as well as radial and lateral distributions within satellite interiors. By exploring systematically the different parameters defining the interior models, we demonstrate that the presence of a deep ocean below an outer ice layer strongly influences the tidal dissipation distribution in both the outer ice layer and in the innermost part of the satellite. On the one hand, the ocean by imposing a large radial displacement at the base of the outer ice I layer, controls the distribution of tidal strain rate within the outer layer, making the tidal strain rate field very weakly sensitive to the viscosity variations. Conversely, in the high-pressure ice layer below the ocean, both tidal strain rate and dissipation are very sensitive to any variation of the ice viscosity. On the other hand, for identical structures of the mantle and of the core, the presence of a subsurface ocean reduces the strength of dissipation in the silicate mantle. The existence of a liquid layer within Europa makes models of the silicate mantle less dissipative than the predictions for Io. 相似文献
10.
The great thickness debate: Ice shell thickness models for Europa and comparisons with estimates based on flexure at ridges 总被引：1，自引：0，他引：1
Sandra E. Billings 《Icarus》2005,177(2):397-412
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. 相似文献
11.
The evolution of a comet nucleus is investigated, taking into account the crystallization process by which the gas trapped in the ice is released to flow through the porous ice matrix. The equations of conservation of the energy and of the masses of ice and gas are solved throughout the nucleus, to obtain the evolution of the temperature, gas pressure and density profiles. A spherical nucleus composed of cold, porous amorphous ice, with 10% of CO trapped in it, serves as initial model. Several values of density (porosity) and pore size are considered. For each combination of parameters the model is evolved for 20-30 revolutions in comet P/Halley's orbit. Two aspects of the release of gas upon crystallization are analyzed and discussed: (a) the resulting continuous outward flux with high peaks at the time of crystallization, which is a cyclic process in the low-density models and sporadic in the high-density ones; (b) the internal pressures obtained down to depths of a few tens to approximately 200 m (depending on parameters), that are found to exceed the compressional strength of cometary ice. As a result, both cracking and explosions of the overlying ice layer and ejection of gas and ice/dust grains are expected to follow crystallization. They should appear as outbursts or sudden brightening of the comet. The model of 0.2 g cm-3 density is found to reproduce quite well many of the light-curve and activity characteristics of comet P/Halley. 相似文献
12.
Europa's interior structure may be determined by relatively simple and robust seismo-acoustic echo sounding techniques. The strategy is to use ice cracking events or impacts that are hypothesized to occur regularly on Europa's surface as sources of opportunity. A single passive geophone on Europa's surface may then be used to estimate the thickness of its ice shell and the depth of its ocean by measuring the travel time of seismo-acoustic reflections from the corresponding internal strata. Quantitative analysis is presented with full-field seismo-acoustic modeling of the Europan environment. This includes models for Europan ambient noise and conditions on signal-to-noise ratio necessary for the proposed technique to be feasible. The possibility of determining Europa's ice layer thickness by surface wave and modal analysis with a single geophone is also investigated. 相似文献
13.
This study shows dependence of the surface diurnal tidal stress on the internal structure of Europa. Its purpose is to investigate possibility of cracking of the icy shell. The stress is evaluated under the plausible model of the internal structure constrained by the gravity field data. The possible effective stress at the sub-Jovian point decreases with thickening of the shell, while it does not depend on the core radius and the thickness of the H2O layer. The range of this value is from 0.095 to 0.161 MPa, which does not exceed the tensile strength of ice. The stress required for the surface cracking would be mainly due to longer period deformations, especially non-synchronous rotation. And/or the actual strength of the ice at the surface would be smaller because of the preexisting cracks than that at a laboratory of the same temperature. 相似文献
14.
Simon A. Kattenhorn 《Icarus》2002,157(2):490-506
A geologic map for the Bright Plains in the Conamara Chaos region of Europa is presented and is used to unravel a detailed fracture sequence using cross-cutting relationships and fracture mechanics principles. Fracture orientations in the Bright Plains region rotated with time, consistently in a clockwise sense. This conclusion agrees with the observations of other researchers' northern Europan hemisphere investigations and points strongly toward the fracture sequence being controlled by the effect of nonsynchronous rotation, whereby the outer ice crust of Europa rotates slightly faster than the satellite's interior. This is convincing evidence that Europa's crust has been decoupled from the interior, possibly due to the presence of a liquid ocean beneath the crust.Tidal stresses induced in the ice crust by the combined effects of nonsynchronous rotation and diurnal tidal flexing can be calculated using the assumption that the crust behaves elastically over relatively short time scales (i.e., no viscous relaxation of stresses). The fracture orientations in the Bright Plains area were compared to a global scale tidal stress field to determine the longitudes at which each fracture set developed. The fracture sequence points strongly to the Bright Plains region of the crust having rotated at least 720° (and perhaps up to 900°) with respect to the satellite's interior during the visible fracture history. This amount exceeds previously published estimates of nonsynchronous rotation. The orientations of the most recent surface fractures are incompatible with the current state of stress in the Bright Plains region, implying a period of a few thousand years since the most recent fracturing events based on existing nonsynchronous rotation rate estimates. 相似文献
15.
Hypervelocity impacts into ice‐topped layered targets: Investigating the effects of ice crust thickness and subsurface density on crater morphology 
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下载免费PDF全文 Many bodies in the outer solar system are theorized to have an ice shell with a different subsurface material below, be it chondritic, regolith, or a subsurface ocean. This layering can have a significant influence on the morphology of impact craters. Accordingly, we have undertaken laboratory hypervelocity impact experiments on a range of multilayered targets, with interiors of water, sand, and basalt. Impact experiments were undertaken using impact speeds in the range of 0.8–5.3 km s?1, a 1.5 mm Al ball bearing projectile, and an impact incidence of 45°. The surface ice crust had a thickness between 5 and 50 mm, i.e., some 3–30 times the projectile diameter. The thickness of the ice crust as well as the nature of the subsurface layer (liquid, well consolidated, etc.) have a marked effect on the morphology of the resulting impact crater, with thicker ice producing a larger crater diameter (at a given impact velocity), and the crater diameter scaling with impact speed to the power 0.72 for semi‐infinite ice, but with 0.37 for thin ice. The density of the subsurface material changes the structure of the crater, with flat crater floors if there is a dense, well‐consolidated subsurface layer (basalt) or steep, narrow craters if there is a less cohesive subsurface (sand). The associated faulting in the ice surface is also dependent on ice thickness and the substrate material. We find that the ice layer (in impacts at 5 km s?1) is effectively semi‐infinite if its thickness is more than 15.5 times the projectile diameter. Below this, the crater diameter is reduced by 4% for each reduction in ice layer thickness equal to the impactor diameter. Crater depth is also affected. In the ice thickness region, 7–15.5 times the projectile diameter, the crater shape in the ice is modified even when the subsurface layer is not penetrated. For ice thicknesses, <7 times the projectile diameter, the ice layer is breached, but the nature of the resulting crater depends heavily on the subsurface material. If the subsurface is noncohesive (loose) material, a crater forms in it. If it is dense, well‐consolidated basalt, no crater forms in the exposed subsurface layer. 相似文献
16.
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. 相似文献
17.
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. 相似文献
18.
A numerical study of gas flow through a porous cometary mantle is presented. A kinetic model based on the well-known Test Particle Monte Carlo Method for the solution of rarefied gas dynamics problems is proposed. The physical model consists of two spatial plane regions: the condensed ice phase and a porous dust mantle. The structure of the porous dust layer is described as a bundle of cylindrical inclined channels not crossing each other. A vertical temperature gradient may exist across the dust mantle. The aim is to investigate how the characteristics of molecular flow depend on the capillary length, inclination angle, and temperature gradient. Examples illustrating a significant deviation of some results from equilibrium values are shown. In particular, the gas velocity distribution at both ends of the pore is strongly non-Maxwellian if there is an important temperature contrast across the pore. The emergent gas flow rate is found to vary with the pore length/radius ratio in excellent agreement with Clausing's empirical formula. The degree of collimation of the flow is quantitatively studied as a function of the length/radius ratio, and consequences for the jet force of outgassing through a dust mantle or, indeed, a rough surface are estimated. 相似文献
19.
《Planetary and Space Science》2007,55(10):1225-1245
The process of tide-driven walking, proposed as a major mechanism for strike–slip displacement on Europa, is modeled using a finite-element numerical simulation of the behavior of viscoelastic material. For material parameters that are plausible for the water ice composing Europa's crust, the simulation confirms earlier analytic results for strike–slip displacement along a crack that penetrates down to the liquid water substrate. The finite element code permits testing other cases as well. Of considerable interest is whether tidal walking can operate if a crack penetrates not to liquid but only as far as warm, relatively viscous ice. In such a case, significant displacement can be driven, but only if the threshold value of the compressive force needed to lock the fault is near the value of the overburden stress at the bottom of the crack. Such special conditions are not needed for displacement if the crack penetrates to the underlying ocean. 相似文献
20.
We consider the scenario in which the presence of ammonia in the bulk composition of Enceladus plays a pivotal role in its thermochemical evolution. Because ammonia reduces the melting temperature of the ice shell by 100 K below that of pure water ice, small amounts of tidal dissipation can power an “ammonia feedback” mechanism that leads to secondary differentiation of Enceladus within the ice shell. This leads to compositionally distinct zones at the base of the ice shell arranged such that a layer of lower density (and compositionally buoyant) pure water ice underlies the undifferentiated ammonia-dihydrate ice layer above. We then consider a large scale instability arising from the pure water ice layer, and use a numerical model to explore the dynamics of compositional convection within the ice shell of Enceladus. The instability of the layer can easily account for a diapir that is hemispherical in scale. As it rises to the surface, it co-advects the warm internal temperatures towards the outer layers of the satellite. This advected heat facilitates the generation of a subsurface ocean within the ice shell of Enceladus. This scenario can simultaneously account for the origin of asymmetry in surface deformation observed on Enceladus as well as two global features inferred to exist: a large density anomaly within the interior and a subsurface ocean underneath the south polar region. 相似文献