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1.
Recent observations of the south pole of Saturn's moon Enceladus by the Cassini spacecraft have revealed an active world, powered by internal heat. In this paper, we propose that localized subsurface melting on Enceladus has produced an internal south polar sea. Evidence for this localized sea comes from the shape of Enceladus, which does not match a differentiated body at its current orbital position. We show that melting induced by the observed heat flow at the south pole produces a large enough pit to match the shape of Enceladus with a differentiated rock and ice interior. Numerical modeling of melting and ice flow shows that the sea produced beneath the south pole is stable against inflow of ductile ice from its surroundings for the duration of the heating. The shape modification due to melting also produces a negative degree-two gravity anomaly, which can reorient the spin axis of Enceladus in order to place the sea at the pole. 相似文献
2.
The intense activity at the south pole of Enceladus hints at an internal water reservoir. However, there is no direct evidence of liquid water at present and its long-term stability in the interior remains problematic. By modeling heat production and transfer in the ice shell in a spherical geometry, we show that tidal heating naturally leads to a concentration of convective hot upwellings in the south polar region, favoring the preservation of liquid water at depth. We show that large volumes of water are produced within the ice shell at the south pole during periods of elevated orbital eccentricity (3–5 times the present-day value). Strong lateral variations in the melt production and crystallization rates result in stress concentration in the south polar region, thus providing an explanation for the tectonic activity observed today. We predict that an internal ocean may be sustained over the long term as the consequence of repeated periods with elevated orbital eccentricity, leading to episodic melting and resurfacing events. 相似文献
3.
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. 相似文献
4.
Tidal dissipation has been suggested as the heat source for the south polar thermal anomaly on Enceladus. We find that under present-day conditions and assuming Maxwellian behavior, tidal dissipation is negligible in the silicate core. Dissipation may be significant in the ice shell if the shell is decoupled from the silicate core by a subsurface ocean. We have run a series of self-consistent convection and conduction models in 2D axisymmetric and 3D spherical geometry in which we include the spatially-variable tidal heat production. We find that in all cases, the shell removes more heat from the interior than can be produced in the core by radioactive decay, resulting in cooling of the interior and the freezing of any ocean. Under likely conditions, a 40-km thick ocean made of pure water would freeze solid on a ∼30 Ma timescale. An ocean containing other chemical components will have a lower freezing point, but even a water-ammonia eutectic composition will only prolong the freezing, not prevent it. If the eccentricity of Enceladus were higher (e?0.015) in the past, the increased dissipation in the ice shell may have been sufficient to maintain a liquid layer. We cannot therefore rule out the presence of a transient ocean, as a relic of an earlier era of greater heating. If the eccentricity is periodically pumped up, the ocean may have thickened and thinned on a similar timescale as the orbital evolution, provided the ocean never froze completely. We conclude that the current heat flux of Enceladus and any possible subsurface ocean is not in steady-state, and is the remnant of an epoch of higher eccentricity and tidal dissipation. 相似文献
5.
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
6.
Aspects of two qualitative models of Enceladus’ dust plume—the so-called “Cold Faithful” [Porco, C.C., et al., 2006. Cassini observes the active south pole of Enceladus. Science 311, 1393-1401; Ingersoll, A.P., et al., 2006. Models of the Enceladus plumes. In: Bulletin of the American Astronomical Society, vol. 38, p. 508] and “Frigid Faithful” [Kieffer, S.W., et al., 2006. A clathrate reservoir hypothesis for Enceladus’ south polar plume. Science 314, 1764; Gioia, G., et al., 2007. Unified model of tectonics and heat transport in a Frigid Enceladus. Proc. Natl. Acad. Sci. 104, 13578-13591] models—are analyzed quantitatively. The former model assumes an explosive boiling of subsurface liquid water, when pressure exerted by the ice crust is suddenly released due to an opening crack. In the latter model the existence of a deep shell of clathrates below Enceladus’ south pole is conjectured; clathrates can decompose explosively when exposed to vacuum through a fracture in the outer icy shell. For the Cold Faithful model we estimate the maximal velocity of ice grains, originating from water splashing in explosive boiling. We find that for water near the triple point this velocity is far too small to explain the observed plume properties. For the Frigid Faithful model we consider the problem of momentum transfer from gas to ice particles. It arises since any change in the direction of the gas flow in the cracks of the shell requires re-acceleration of the entrained grains. While this effect may explain the observed speed difference of gas and grains if the gas evaporates from triple point temperature (273.15 K) [Schmidt, J., et al., 2008. Formation of Enceladus dust plume. Nature 451, 685], the low temperatures of the Frigid Faithful model imply a too dilute vapor to support the observed high particle fluxes in Enceladus’ plume. 相似文献
7.
Enceladus: Present internal structure and differentiation by early and long-term radiogenic heating 总被引：1，自引：0，他引：1
Pre-Cassini images of Saturn's small icy moon Enceladus provided the first indication that this satellite has undergone extensive resurfacing and tectonism. Data returned by the Cassini spacecraft have proven Enceladus to be one of the most geologically dynamic bodies in the Solar System. Given that the diameter of Enceladus is only about 500 km, this is a surprising discovery and has made Enceladus an object of much interest. Determining Enceladus' interior structure is key to understanding its current activity. Here we use the mean density of Enceladus (as determined by the Cassini mission to Saturn), Cassini observations of endogenic activity on Enceladus, and numerical simulations of Enceladus' thermal evolution to infer that this satellite is most likely a differentiated body with a large rock-metal core of radius about 150 to 170 km surrounded by a liquid water-ice shell. With a silicate mass fraction of 50% or more, long-term radiogenic heating alone might melt most of the ice in a homogeneous Enceladus after about 500 Myr assuming an initial accretion temperature of about 200 K, no subsolidus convection of the ice, and either a surface temperature higher than at present or a porous, insulating surface. Short-lived radioactivity, e.g., the decay of 26Al, would melt all of the ice and differentiate Enceladus within a few million years of accretion assuming formation of Enceladus at a propitious time prior to the decay of 26Al. Long-lived radioactivity facilitates tidal heating as a source of energy for differentiation by warming the ice in Enceladus so that tidal deformation can become effective. This could explain the difference between Enceladus and Mimas. Mimas, with only a small rock fraction, has experienced relatively little long-term radiogenic heating; it has remained cold and stiff and less susceptible to tidal heating despite its proximity to Saturn and larger eccentricity than Enceladus. It is shown that the shape of Enceladus is not that of a body in hydrostatic equilibrium at its present orbital location and rotation rate. The present shape could be an equilibrium shape corresponding to a time when Enceladus was closer to Saturn and spinning more rapidly, or more likely, to a time when Enceladus was spinning more rapidly at its present orbital location. A liquid water layer on Enceladus is a possible source for the plume in the south polar region assuming the survivability of such a layer to the present. These results could place Enceladus in a category similar to the large satellites of Jupiter, with the core having a rock-metal composition similar to Io, and with a deep overlying ice shell similar to Europa and Ganymede. Indeed, the moment of inertia factor of a differentiated Enceladus, C/MR2, could be as small as that of Ganymede, about 0.31. 相似文献
8.
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
9.
Recently, the Cassini spacecraft has detected ongoing geologic activity near the south pole of Saturn's moon Enceladus. In contrast, the satellite's north-polar region is heavily cratered and appears to have been geologically inactive for a long time. We propose that this hemispheric dichotomy is caused by interior dynamics with degree-one convection driving the south-polar activity. We investigate a number of core sizes and internal heating rates for which degree-one convection occurs. The numerical simulations imply that a core radius of less than 100±20 km and an energy input at a rate of 3.0 to 5.5 GW would be required for degree-one convection to prevail. This is within the range of the observed thermal power release near Enceladus' south pole. Provided that Enceladus is not fully differentiated, degree-one convection is found to be a viable mechanism to explain Enceladus' hemispheric dichotomy. 相似文献
10.
Th. Roatsch M. Wählisch A. Hoffmeister F. Scholten R. Wagner P. Helfenstein 《Planetary and Space Science》2008,56(1):109-116
The Cassini Imaging Science Subsystem (ISS) acquired 377 high-resolution images (<1 km/pixel) during three close flybys of Enceladus in 2005 [Porco, C.C., et al., 2006. Cassini observes the active south pole of Enceladus. Science 311, 1393-1401.]. We combined these images with lower resolution Cassini images and four others taken by Voyager cameras to produce a high-resolution global controlled mosaic of Enceladus. This global mosaic is the baseline for a high-resolution Enceladus atlas that consists of 15 tiles mapped at a scale of 1:500,000. The nomenclature used in this atlas was proposed by the Cassini imaging team and was approved by the International Astronomical Union (IAU). The whole atlas is available to the public through the Imaging Team's website (http://ciclops.org/maps). 相似文献
11.
The recently discovered water vapor plumes on Saturn's moon Enceladus, the polar caps of planet Mars and the possible ice volcanism on the Jovian satellites call for suitable techniques to explore deep ice layers of the solar system bodies. This paper presents a novel approach to deliver scientific probes into deeper layers of planetary ice. Several existing locomotion concepts and techniques for such probes are presented. After studying the mathematical framework of the melting locomotion process, melting tests with different head forms were done to evaluate the influence of the head's geometry on the melting process. This work led to a novel concept of a thermal drill head, using heat and mechanical drill in combination to penetrate the ice. We compare the performance of such a hybrid concept versus the melting penetration alone by a mathematical model and tests in ice with a prototype of the melting drill head. 相似文献
12.
The discovery of plumes of H2O vapor and ice particles erupting from the south pole of Enceladus, the tiny frigid satellite of Saturn, sparked controversy over whether these plumes are produced by boiling, or by sublimation with subsequent recondensation of the sublimated vapor [Porco, C.C., Helfenstein, P., Thomas, P.C., Ingersoll, A.P., Wisdom, J., West, R., Neukum, G., Denk, T., Wagner, R., Roatsch, T., Kieffer, S., Turtle, E., McEwen, A., Johnson, T.V., Rathbun, J., Veverka, J., Wilson, D., Perry, J., Spitale, J., Brahic, A., Burns, J.A., DelGenio, A.D., Dones, L., Murray, C.D., Squyres, S., 2006. Science 311, 1393-1401]. Porco et al.’s analysis that the masses of ice (I) and vapor (V) in the plume were comparable was taken to argue against the occurrence of sublimation and recondensation, leading to the hypothesis that the reservoir was boiling water, possibly as close as 7 m to the surface. Thus, it has been advocated that Enceladus should be a target for astrobiology exploration. Here we show, with recalculations using the original data and methodologies, as well as with new sensitivity studies, that the mass of ice in the column is significantly less than the mass of water vapor, and that by considering three additional effects, I/V is likely to be <0.2-0.1. This means that the plume is dominated by vapor that the thermodynamics permits to be easily produced by sublimation with recondensation. The low I/V ratio provides no compelling criterion for consideration of a liquid water reservoir. The uncertainties on the I/V ratio have not previously been discussed in the literature. Although the I/V ratio is sensitive to particle sizes and size distributions, the masses of ice (I) and vapor (V) are not comparable in any scenario constrained by available observations. We thus discuss the implications of sublimation from a thermodynamic point of view in a context that has not been presented previously. Constraints on I/V ratio from future spacecraft measurements of the plume, in conjunction with consideration of the total plume composition and multicomponent analysis, can help constrain source conditions for the plume. 相似文献
13.
Thermal histories of the small icy Saturnian satellites Mimas, Tethys, Dione, Rhea, and Iapetus are constructed by assuming that they formed as homogeneous ice-silicate mixtures. The models include effects of radiogenic and accretional heating, conductive and subsolidus convective heat transfer, and lithospheric growth. Accretional heating is unlikely to have melted the water ice in the interiors of these bodies and solid state creep of the predominately ice material precludes melting by radiogenic heating. Mimas is so small that its thermal evolution is essentially purely conductive; at present it is a cold, nearly isothermal body. Any subsolidus convection or thermal activity in Mimas would have been confined to a brief period in its early history and would have been due to a warm formation. The four largest satellites are big enough and contain sufficient heat-producing silicates that solid state convection beneath a rigid lithosphere is inevitable independent of initial conditions. Dione and Rhea have convective interiors for most of their thermal histories, while Tethys and Iapetus have mainly conductive thermal histories with early periods of convective 0activity. The thermal histories of the five satellites for the last 4 by are independent of initial conditions; at present they have cold, conductive interiors. The model thermal histories are qualitatively consistent with the appearances of these satellites: Mimas has an ancient heavily cratered surface, Tethys and probably Iapetus have both heavily cratered and more lightly cratered areas, and Dione and Rhea have extensively modified surfaces. Because of their similar sizes and densities, Mimas and Enceladus are expected to have similar surfaces and thermal histories, but instead Enceladus has the most modified surface of all the small icy Saturnian satellites. Our results suggest a heat source for Enceladus, in addition to radiogenic and accretional heating; tidal dissipation is a possibility. Because the water ice in these bodies does not melt, resurfacing must be accomplished by the melting of a low-melting-temperature minor component such as ammonia hydrate. 相似文献
14.
Tidal dissipation is investigated in a viscoelastic homogeneous sphere having the orbital and physical characteristics of the icy inner satellite of Saturn, Enceladus. The dissipated power is calculated for Kelvin-Voigt and Maxwell rheologies, whose dissipation function can be expressed in terms of viscosity. Expressions for the dissipated power as a function of viscosity is calculated in both cases and compared to the expression found for a lossy elastic body. A physical law relating viscosity of water ice to temperature and grain size is introduced and the feedback between dissipated power and temperature is investigated. It is found that tidal dissipation with current orbital eccentricity alone cannot account for the surface activity observed on Enceladus, if it is composed of water ice. 相似文献
15.
A Hovmöller diagram analysis of the dust optical depth measured by the Mars Global Surveyor Thermal Emission Spectrometer shows the occurrence of quasi-periodic westwardly-propagating disturbances with timescales of 10-20 sols during summer in the south polar region of Mars. Dust clouds emerge repeatedly around the region with a latitude of around 70-80°S and a longitude of 240-300°E, move westward at speeds of 3-6 m s−1, reach the region with a longitude of 60-120°E, and finally disappear. This longitude range coincides with elevated terrains in the south polar region, and in this region an increase of dust optical depth encircling the south pole is also observed. This implies that the quasi-periodic dust events will contribute to the enhancement of the atmospheric dust loading in this region. These dust events might be related to baroclinic instability caused by the thermal contrast across the CO2 cap edge, or the horizontal advection or vertical convection with radiative-dynamical feedback. The westward movement of the dust clouds suggests steady westward winds blowing in the near-surface layer, where the quasi-periodic dust lifting is expected to occur. Such a westward cap-edge flow will be created by the Coriolis force acting on the flow from the ice side to the regolith side. 相似文献
16.
We vapor deposit at 20 K a mixture of gases with the specific Enceladus plume composition measured in situ by the Cassini INMS [Waite, J.H., Combi, M.R., Ip, W.H., Cravens, T.E., McNutt, R.L., Kasprzak, W., Yelle, R., Luhmann, J., Niemann, H., Gell, D., Magee, B., Fletcher, G., Lunine, J., Tseng, W.L., 2006. Science 311, 1419-1422] to form a mixed molecular ice. As the sample is slowly warmed, we monitor the escaping gas quantity and composition with a mass spectrometer. Pioneering studies [Schmitt, B., Klinger, J., 1987. Different trapping mechanisms of gases by water ice and their relevance for comet nuclei. In: Rolfe, E.J., Battrick, B. (Eds.), Diversity and Similarity of Comets. SP-278. ESA, Noordwijk, The Netherlands, pp. 613-619; Bar-Nun, A., Kleinfeld, I., Kochavi, E., 1988. Phys. Rev. B 38, 7749-7754; Bar-Nun, A., Kleinfeld, I., 1989. Icarus 80, 243-253] have shown that significant quantities of volatile gases can be trapped in a water ice matrix well above the temperature at which the pure volatile ice would sublime. For our Enceladus ice mixture, a composition of escaping gases similar to that detected by Cassini in the Enceladus plume can be generated by the sublimation of the H2O:CO2:CH4:N2 mixture at temperatures between 135 and 155 K, comparable to the high temperatures inferred from the CIRS measurements [Spencer, J.R., Pearl, J.C., Segura, M., Flasar, F.M., Mamoutkine, A., Romani, P., Buratti, B.J., Hendrix, A.R., Spilker, L.J., Lopes, R.M.C., 2006. Science 311, 1401-1405] of the Enceladus “tiger stripes.” This suggests that the gas escape phenomena that we measure in our experiments are an important process contributing to the gases emitted from Enceladus. A similar experiment for ice deposited at 70 K shows that both the processes of volatile trapping and release are temperature dependent over the temperature range relevant to Enceladus. 相似文献
17.
Cassini-Huygens observations have shown that Titan and Enceladus are geologically active icy satellites. Mitri and Showman [Mitri, G., Showman, A.P., 2005. Icarus 177, 447-460] and McKinnon [McKinnon, W.B., 2006. Icarus 183, 435-450] investigated the dynamics of an ice shell overlying a pure liquid-water ocean and showed that transitions from a conductive state to a convective state have major implications for the surface tectonics. We extend this analysis to the case of ice shells overlying ammonia-water oceans. We explore the thermal state of Titan and Enceladus ice-I shells, and also we investigate the consequences of the ice-I shell conductive-convective switch for the geology. We show that thermal convection can occur, under a range of conditions, in the ice-I shells of Titan and Enceladus. Because the Rayleigh number Ra scales with δ3/ηb, where δ is the thickness of the ice shell and ηb is the viscosity at the base of the ice-I shell, and because ammonia in the liquid layer (if any) strongly depresses the melting temperature of the water ice, Ra equals its critical value for two ice-I shell thicknesses: for relatively thin ice shell with warm, low-viscosity base (Onset I) and for thick ice shell with cold, high-viscosity base (Onset II). At Onset I, for a range of heat fluxes, two equilibrium states—corresponding to a thin, conductive shell and a thick, convective shell—exist for a given heat flux. Switches between these states can cause large, rapid changes in the ice-shell thickness. For Enceladus, we demonstrate that an Onset I transition can produce tectonic stress of ∼500 bars and fractures of several tens of km depth. At Onset II, in contrast, we demonstrate that zero equilibrium states exist for a range of heat fluxes. For a mean heat flux within this range, the satellite experiences oscillations in surface heat flux and satellite volume with periods of ∼50-800 Myr even when the interior heat production is constant or monotonically declining in time; these oscillations in the thermal state of the ice-I shell would cause repeated episodes of extensional and compressional tectonism. 相似文献
18.
Straddling the south polar region of Saturn's moon Enceladus, the four principal “tiger stripe” fractures are a likely source of tectonic activity and plume generation. Here we investigate tidally driven stress conditions at the tiger stripe fractures through a combined analysis of shear and normal diurnal tidal stresses and accounting for additional stress at depth due to the overburden pressure. We compute Coulomb failure conditions to assess failure location, timing, and direction (right- vs left-lateral slip) throughout the Enceladus orbital cycle and explore a suite of model parameters that inhibit or promote shear failure at the tiger stripes. We find that low coefficients of friction (μf=0.1-0.2) and shallow overburden depths (z=2-4 km) permit shear failure along the tiger stripe faults, and that right- and/or left-lateral slip responses are possible. We integrate these conditions into a 3D time-dependent fault dislocation model to evaluate tectonic displacements and stress variations at depth during a tiger stripe orbital cycle. Depending on the sequence of stress accumulation and subsequent fault slip, which varies as a function of fault location and orientation, frictional coefficient, and fault depth, we estimate resolved shear stress accumulation of ∼70 kPa prior to fault failure, which produces modeled strike-slip displacements on the order of ∼0.5 m in the horizontal direction and ∼5 mm in the vertical direction per slip event. Our models also indicate that net displacements on the order of 0.1 m per orbital cycle, in both right- and left-lateral directions, are possible for particular fault geometries and frictional parameters. Tectonic activity inferred from these analyses correlates with observed plume activity and temperature anomalies at Enceladus's south polar region. Moreover, these analyses provide important details of stress accumulation and the faulting cycle for icy satellites subjected to diurnal tidal stress. 相似文献
19.
A.D. Fortes 《Icarus》2007,191(2):743-748
The composition and abundance of volatile gases observed in the jets emanating from fissures near the south pole of Saturn's moon Enceladus are strongly indicative of outgassing from clathrate hydrates which formed as a result of hydrothermal activity rather than nebula condensation. I suggest that fluids must be able to permeate the ice shell, extensively metasomatising the mantle by emplacement of clathrates along fractures and grain boundaries, which subsequently are entrained in rising cryomagmas as xenoliths. These are carried upwards to the point where they dissociate, releasing their gas load into the magma and promoting the vigorous ice fountaining observed—a direct analogue of terrestrial basaltic fire fountains caused by volatile exsolution. This clathrate xenolith model can explain the measured volatile abundances, eruption velocities, the ice to vapour ratio in the plumes, and the vent temperatures. 相似文献
20.
Recently, Tyler [Tyler, R.H., 2009. Geophys. Res. Lett. 36, L15205; Tyler, R., 2011. Icarus, 211, 770-779] proposed that the tide due to an obliquity of greater than 0.1° might drive resonant flow in a liquid ocean at Enceladus, and that dissipation of the ocean’s kinetic energy may be an alternate source for the observed global heat flux. While there is currently no measurement of Enceladus’ obliquity, dissipation is expected to drive the spin pole to a Cassini state. Under this assumption, we find that Enceladus should occupy Cassini state 1 and that the obliquity of Enceladus should be less than 0.0015° for values of the degree-2 gravity coefficient C2,2 between 1.0 × 10−3 and 2.5 × 10−3. Unless there is a significant free obliquity or the gravity coefficient C2,2 has been significantly overestimated, it is unlikely that obliquity-driven flow in a subsurface ocean is the source of the extreme heat on Enceladus. 相似文献