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1.
Cassini radar observations show that Titan's spin is slightly faster than synchronous spin. Angular momentum exchange between Titan's surface and the atmosphere over seasonal time scales corresponding to Saturn's orbital period of 29.5 year is the most likely cause of the observed non-synchronous rotation. We study the effect of Saturn's gravitational torque and torques between internal layers on the length-of-day (LOD) variations driven by the atmosphere. Because static tides deform Titan into an ellipsoid with the long axis approximately in the direction to Saturn, non-zero gravitational and pressure torques exist that can change the rotation rate of Titan. For the torque calculation, we estimate the flattening of Titan and its interior layers under the assumption of hydrostatic equilibrium. The gravitational forcing by Saturn, due to misalignment of the long axis of Titan with the line joining the mass centers of Titan and Saturn, reduces the LOD variations with respect to those for a spherical Titan by an order of magnitude. Internal gravitational and pressure coupling between the ice shell and the interior beneath a putative ocean tends to reduce any differential rotation between shell and interior and reduces further the LOD variations by a few times. For the current estimate of the atmospheric torque, we obtain LOD variations of a hydrostatic Titan that are more than 100 times smaller than the observations indicate when Titan has no ocean as well as when a subsurface ocean exists. Moreover, Saturn's torque causes the rotation to be slower than synchronous in contrast to the Cassini observations. The calculated LOD variations could be increased if the atmospheric torque is larger than predicted and or if fast viscous relaxation of the ice shell could reduce the gravitational coupling, but it remains to be studied if a two order of magnitude increase is possible and if these effects can explain the phase difference of the predicted rotation variations. Alternatively, the large differences with the observations may suggest that non-hydrostatic effects in Titan are important. In particular, we show that the amplitude and phase of the calculated rotation variations are similar to the observed values if non-hydrostatic effects could strongly reduce the equatorial flattening of the ice shell above an internal ocean.  相似文献   

2.
The origin of Titan’s atmospheric methane is a key issue for understanding the origin of the saturnian satellite system. It has been proposed that serpentinization reactions in Titan’s interior could lead to the formation of the observed methane. Meanwhile, alternative scenarios suggest that methane was incorporated in Titan’s planetesimals before its formation. Here, we point out that serpentinization reactions in Titan’s interior are not able to reproduce the deuterium over hydrogen (D/H) ratio observed at present in methane in its atmosphere, and would require a maximum D/H ratio in Titan’s water ice 30% lower than the value likely acquired by the satellite during its formation, based on Cassini observations at Enceladus. Alternatively, production of methane in Titan’s interior via radiolytic reactions with water can be envisaged but the associated production rates remain uncertain. On the other hand, a mechanism that easily explains the presence of large amounts of methane trapped in Titan in a way consistent with its measured atmospheric D/H ratio is its direct capture in the satellite’s planetesimals at the time of their formation in the solar nebula. In this case, the mass of methane trapped in Titan’s interior can be up to ∼1300 times the current mass of atmospheric methane.  相似文献   

3.
F. Nimmo  B.G. Bills 《Icarus》2010,208(2):896-904
The long-wavelength topography of Titan has an amplitude larger than that expected from tidal and rotational distortions at its current distance from Saturn. This topography is associated with small gravity anomalies, indicating a high degree of compensation. Both observations can be explained if Titan has a floating, isostatically-compensated ice shell with a spatially-varying thickness. The spatial variations arise because of laterally-variable tidal heating within the ice shell. Models incorporating shell thickness variations result in an improved fit to the observations and a degree-two tidal Love number h2t consistent with expectations, without requiring Titan to have moved away from Saturn. Our preferred models have a mean shell thickness of ≈100 km in agreement with the observed gravity anomalies, and a heat flux appropriate to a chondritic Titan. Shell thickness variations are eliminated by convection; we therefore conclude that Titan’s ice shell is not convecting at the present day.  相似文献   

4.
All landforms on Titan that are unambiguously identifiable can be explained by exogenic processes (aeolian, fluvial, impact cratering, and mass wasting). Previous suggestions of endogenically produced cryovolcanic constructs and flows have, without exception, lacked conclusive diagnostic evidence. The modification of sparse recognizable impact craters (themselves exogenic) can be explained by aeolian and fluvial erosion. Tectonic activity could be driven by global thermal evolution or external forcing, rather than by active interior processes. A lack of cryovolcanism would be consistent with geophysical inferences of a relatively quiescent interior: incomplete differentiation, only minor tidal heating, and possibly a lack of internal convection today. Titan might be most akin to Callisto with weather: an endogenically relatively inactive world with a cool interior. We do not aim to disprove the existence of any and all endogenic activity at Titan, nor to provide definitive alternative hypotheses for all landforms, but instead to inject a necessary level of caution into the discussion. The hypothesis of Titan as a predominantly exogenic world can be tested through additional Cassini observations and analyses of putative cryovolcanic features, geophysical and thermal modeling of Titan’s interior evolution, modeling of icy satellite landscape evolution that is shaped by exogenic processes alone, and consideration of possible means for supplying Titan’s atmospheric constituents that do not rely on cryovolcanism.  相似文献   

5.
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.  相似文献   

6.
We calculate the D/H ratio of CH4 from serpentinization on Titan to determine whether Titan’s atmospheric CH4 was originally produced inside the giant satellite. This is done by performing equilibrium isotopic fractionation calculations in the CH4-H2O-H2 system, with the assumption that the bulk D/H ratio of the system is equivalent to that of the H2O in the plume of Enceladus. These calculations show that the D/H ratio of hydrothermally produced CH4 would be markedly higher than that of atmospheric CH4 on Titan. The implication is that Titan’s CH4 is a primordial chemical species that was accreted by the moon during its formation. There are two evolutionary scenarios that are consistent with the apparent absence of endogenic CH4 in Titan’s atmosphere. The first is that hydrothermal systems capable of making CH4 never existed on Titan because Titan’s interior has always been too cold. The second is that hydrothermal systems on Titan were sufficiently oxidized so that C existed in them predominately in the form of CO2. The latter scenario naturally predicts the formation of endogenic N2, providing a new hypothesis for the origin of Titan’s atmospheric N2: the hydrothermal oxidation of 15N-enriched NH3. A primordial origin for CH4 and an endogenic origin for N2 are self-consistent, but both hypotheses need to be tested further by acquiring isotopic data, especially the D/H ratio of CH4 in comets, and the 15N/14N ratio of NH3 in comets and that of N2 in one of Enceladus’ plumes.  相似文献   

7.
Cycloids, arcuate features observed on Europa’s surface, have been interpreted as tensile cracks that form in response to diurnal tidal stress caused by Europa’s orbital eccentricity. Stress from non-synchronous rotation may also contribute to tidal stress, and its influence on cycloid shapes has been investigated as well. Obliquity, fast precession, and physical libration would contribute to tidal stress but have often been neglected because they were expected to be negligibly small. However, more sophisticated analyses that include the influence of Jupiter’s other large satellites and the state of Europa’s interior indicate that perhaps these rotational parameters are large enough to alter the tidal stress field and the formation of tidally-driven fractures. We test tidal models that include obliquity, fast precession, stress due to non-synchronous rotation, and physical libration by comparing how well each model reproduces observed cycloids. To do this, we have designed and implemented an automated parameter-searching algorithm that relies on a quantitative measure of fit quality, which we use to identify the best fits to observed cycloids. We then apply statistical techniques to determine the tidal model best supported by the data. By incorporating obliquity, fits to observed southern hemisphere cycloids improve, and we can reproduce equatorial and equator-crossing cycloids. Furthermore, we find that obliquity plus physical libration is the tidal model best supported by the data. With this model, the obliquities range from 0.32° to 1.35°. The libration amplitudes are 0.72–2.44°, and the libration phases are −6.04° to 17.72° with one outlier at 84.5°. The variability in obliquity is expected if Europa’s ice shell is mechanically decoupled from the interior, and the libration amplitudes are plausible in the presence of a subsurface ocean. Indeed, the presence of a decoupling ocean may result in feedbacks that cause all of these rotational parameters to become time-variable.  相似文献   

8.
Cassini RADAR topography data are used to evaluate Titan’s hypsometric profile, and to make comparisons with other planetary bodies. Titan’s hypsogram is unimodal and strikingly narrow compared with the terrestrial planets. To investigate topographic extremes, a novel variant on the classic hypsogram is introduced, with a logarithmic abscissa to highlight mountainous terrain. In such a plot, the top of the terrestrial hypsogram is quite distinct from those of Mars and Venus due to the ‘glacial buzz-saw’ that clips terrestrial topography above the snowline. In contrast to the positive skew seen in other hypsograms, with a long tail of positive relief due to mountains, there is an indication (weak, given the limited data for Titan so far) that the Titan hypsogram appears slightly negatively skewed, suggesting a significant population of unfilled depressions. Limited data permit only a simplistic comparison of Titan topography with other icy satellites but we find that the standard deviation of terrain height (albeit at different scales) is similar to those of Ganymede and Europa.  相似文献   

9.
Jere H. Lipps  Sarah Rieboldt 《Icarus》2005,177(2):515-527
Jupiter's moon Europa possesses an icy shell kilometers thick that may overlie a briny ocean. The inferred presence of water, tidal and volcanic energy, and nutrients suggests that Europa is potentially inhabited by some kind of life; indeed Europa is a primary target in the search for life in the Solar System although no evidence yet exists for any kind of life. The thickness of the icy crust would impose limits on life, but at least 15 broad kinds of habitats seem possible for Europa. They include several on the sea floor, at least 3 in the water column, and many in the ice itself. All of these habitats are in, or could be transported to, the icy shell where they could be exposed by geologic activity or impacts so they might be explored from the surface or orbit by future planetary missions. Taphonomic processes that transport, preserve, and expose habitats include buoyant ice removing bottom habitats and sediment to the underside of the ice, water currents depositing components of water column habitats on the ice bottom, cryovolcanoes depositing water on the surface, tidal pumping bringing water column and ice habitats to the near-surface ice, and subice freezing and diapiric action incorporating water column and bottom ice habitats into the lower parts of the icy shell. The preserved habitats could be exposed at or near the surface of Europa chiefly in newly-formed ice, tilted or rotated ice blocks, ridge debris, surface deposits, fault scarps, the sides of domes and pits, and impact craters and ejecta. Future exploration of Europa for life must consider careful targeting of sites where habitats are most likely preserved or exist close to the surface.  相似文献   

10.
Javier Ruiz  Rosa Tejero 《Icarus》2003,162(2):362-373
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   

11.
Javier Ruiz 《Icarus》2005,177(2):438-446
The heat flow from Europa has profound implications for ice shell thickness and structure, as well as for the existence of an internal ocean, which is strongly suggested by magnetic data. The brittle-ductile transition depth and the effective elastic thickness of the lithosphere are here used to perform heat flow estimations for Europa. Results give preferred heat flow values (for a typical geological strain rate of 10−15 s−1) of 70-110 mW m−2 for a brittle-ductile transition 2 km deep (the usually accepted upper limit for the brittle-ductile transition depth in the ice shell of Europa), 24-35 mW m−2 for an effective elastic thickness of 2.9 km supporting a plateau near the Cilix impact crater, and >130 mW m−2 for effective elastic thicknesses of ?0.4 km proposed for the lithosphere loaded by ridges and domes. These values are clearly higher than those produced by radiogenic heating, thus implying an important role for tidal heating. The ?19-25 km thick ice shell proposed from the analysis of size and depth of impact structures suggests a heat flow of ?30-45 mW m−2 reaching the ice shell base, which in turn would imply an important contribution to the heat flow from tidal heating within the ice shell. Tidally heated convection in the ice shell could be capable to supply ∼100 mW m−2 for superplastic flow, and, at the Cilix crater region, ∼35-50 mW m−2 for dislocation creep, which suggests local variations in the dominant flow mechanism for convection. The very high heat flows maybe related to ridges and domes could be originated by preferential heating at special settings.  相似文献   

12.
Jupiter’s satellites are subject to strong tidal forces which result in variations of the gravitational potential and deformations of the satellites’ surfaces on the diurnal tidal cycle. Such variations are described by the Love numbers \(k_2\) and \(h_2\) for the tide-induced potential variation due to internal mass redistribution and the radial surface displacement, respectively. The phase-lags \( \phi _{k_2}\) and \( \phi _{h_2}\) of these complex numbers contain information about the rheological and dissipative states of the satellites. Starting from interior structure models and assuming a Maxwell rheology to compute the tidal deformation, we calculate the phase-lags in application to Ganymede and Europa. For both satellites we assume a decoupling of the outer ice-shell from the deep interior by a liquid subsurface water ocean. We show that, in this case, the phase-lag difference \(\varDelta \phi = \phi _{k_2}- \phi _{h_2}\) can provide information on the rheological and thermal state of the deep interiors if the viscosities of the deeper layers are small. In case of Ganymede, phase-lag differences can reach values of a few degrees for high-pressure ice viscosities \({<}10^{14}\) Pa s and would indicate a highly dissipative state of the deep interior. In this case \(\varDelta \phi \) is dominated by dissipation in the high-pressure ice layer rather than dissipation within the ice-I shell. These phase lags would be detectable from spacecraft in orbit around the satellite. For Europa \(\varDelta \phi \) could reach values exceeding \(20^\circ \) and phase-lag measurements could help distinguish between (1) a hot dissipative silicate mantle which would in thermal equilibrium correspond to a very thin outer ice-I shell and (2) a cold deep interior implying that dissipation would mainly occur in a thick (several tens of km) outer ice-I shell. These measurements are highly relevant for ESA’s Jupiter Icy Moons Explorer (JUICE) and NASA’s Europa Multiple Flyby Mission, both targeted for the Jupiter system.  相似文献   

13.
This study considers the global patterns of fracture that would result from nonsynchronous rotation of a tidally distorted planetary body. The incremental horizontal stresses in a thin elastic or viscous shell due to a small displacement of the axis of maximum tidal elongation are derived, and the resulting stress distributions are applied to interpret the observed pattern of fracture lineaments on Europa. The observed pattern of lineaments can be explained by nonsynchronous rotation if these features formed by tension fracturing and dike emplacement. Tension fracturing can occur for a small displacement of the tidal axis, so that the resulting lineaments may be consistent with other evidence suggesting a young age for the surface.  相似文献   

14.
The four Galilean satellites are thought to harbor one or even two global internal liquid layers beneath their surface layer. The iron core of Io and Ganymede is most likely (partially) liquid and also the core of Europa may be liquid. Furthermore, there are strong indications for the existence of a subsurface ocean in Europa, Ganymede, and Callisto. Here, we investigate whether libration observations can be used to prove the existence of these liquid layers and to constrain the thickness of the overlying solid layers. For Io, the presence of a small liquid core increases the libration of the mantle by a few percent with respect to an entirely solid Io and mantle libration observations could be used to determine the mantle thickness with a precision of several tens of kilometers given that the libration amplitude can be measured with a precision of 1 m. For Europa, Ganymede, and Callisto, the presence of a water ocean close to the surface increases by at least an order of magnitude the ice shell libration amplitude with respect to an entirely solid satellite. The shell libration depends essentially on the shell thickness and to a minor extent on the density difference between the ocean and the ice shell. The possible presence of a liquid core inside Europa and Ganymede has no noticeable influence on their shell libration. For a precision of several meters on the libration measurements, in agreement with the expected accuracy with the NASA/ESA EJSM orbiter mission to Europa and Ganymede, an error on the shell thickness of a few tens kilometers is expected. Therefore, libration measurements can be used to detect liquid layers such as Io’s core or water subsurface oceans in Europa, Ganymede, and Callisto and to constrain the thickness of the overlying solid surface layers.  相似文献   

15.
B.J. Travis  J. Palguta  G. Schubert 《Icarus》2012,218(2):1006-1019
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   

16.
Tidal torque drives the rotational and orbital evolution of planet–satellite and star–exoplanet systems. This paper presents one analytical tidal theory for a viscoelastic multi-layered body with an arbitrary number of homogeneous layers. Starting with the static equilibrium figure, modified to include tide and differential rotation, and using the Newtonian creep approach, we find the dynamical equilibrium figure of the deformed body, which allows us to calculate the tidal potential and the forces acting on the tide generating body, as well as the rotation and orbital elements variations. In the particular case of the two-layer model, we study the tidal synchronization when the gravitational coupling and the friction in the interface between the layers is added. For high relaxation factors (low viscosity), the stationary solution of each layer is synchronous with the orbital mean motion (n) when the orbit is circular, but the rotational frequencies increase if the orbital eccentricity increases. This behavior is characteristic in the classical Darwinian theories and in the homogeneous case of the creep tide theory. For low relaxation factors (high viscosity), as in planetary satellites, if friction remains low, each layer can be trapped in different spin-orbit resonances with frequencies \(n/2,n,3n/2,2n,\ldots \). When the friction increases, attractors with differential rotations are destroyed, surviving only commensurabilities in which core and shell have the same velocity of rotation. We apply the theory to Titan. The main results are: (i) the rotational constraint does not allow us to confirm or reject the existence of a subsurface ocean in Titan; and (ii) the crust-atmosphere exchange of angular momentum can be neglected. Using the rotation estimate based on Cassini’s observation (Meriggiola et al. in Icarus 275:183–192, 2016), we limit the possible value of the shell relaxation factor, when a deep subsurface ocean is assumed, to \(\gamma _s\lesssim 10^{-9}\,\hbox {s}^{-1}\), which corresponds to a shell’s viscosity \(\eta _s\gtrsim 10^{18}\,\hbox {Pa}\,\hbox {s}\), depending on the ocean’s thickness and viscosity values. In the case in which a subsurface ocean does not exist, the maximum shell relaxation factor is one order of magnitude smaller and the corresponding minimum shell’s viscosity is one order higher.  相似文献   

17.
Lijie Han  Adam P. Showman 《Icarus》2011,212(1):262-267
We present self-consistent, fully coupled two-dimensional (2D) numerical models of thermal evolution and tidal heating to investigate how convection interacts with tidal dissipation under the influence of non-Newtonian grain-size-sensitive creep rheology (plausibly resulting from grain boundary sliding) in Europa’s ice shell. To determine the thermal evolution, we solved the convection equations (using finite-element code ConMan) with the tidal dissipation as a heat source. For a given heterogeneous temperature field at a given time, we determined the tidal dissipation rate throughout the ice shell by solving for the tidal stresses and strains subject to Maxwell viscoelastic rheology (using finite-element code Tekton). In this way, the convection and tidal heating are fully coupled and evolve together. Our simulations show that the tidal dissipation rate can have a strong impact on the onset of thermal convection in Europa’s ice shell under non-Newtonian GSS rheology. By varying the ice grain size (1-10 mm), ice-shell thickness (20-120 km), and tidal-strain amplitude (0-4 × 10−5), we study the interrelationship of convection and conduction regimes in Europa’s ice shell. Under non-Newtonian grain-size-sensitive creep rheology and ice grain size larger than 1 mm, no thermal convection can initiate in Europa’s ice shell (for thicknesses <100 km) without tidal dissipation. However, thermal convection can start in thinner ice shells under the influence of tidal dissipation. The required tidal-strain amplitude for convection to occur decreases as the ice-shell thickness increases. For grain sizes of 1-10 mm, convection can occur in ice shells as thin as 20-40 km with the estimated tidal-strain amplitude of 2 × 10−5 on Europa.  相似文献   

18.
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   

19.
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 (τj) 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.  相似文献   

20.
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   

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