Comment on “Mechanics of tidally driven fractures in Europa's ice shell” by S. Lee, R.T. Pappalardo, and N.C. Makris [2005. Icarus 177, 367-379]

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.     

New estimates for the sublimation rate for ice on the Moon

The strong hydrogen signal that the Lunar Prospector saw at the Moon's poles suggests that water ice may be present near the surface of the lunar regolith. A robotic mission to obtain in situ samples and to quantify the amount of this valuable resource must be designed carefully to avoid dissipating too much heat in the regolith during coring or drilling and, thus, causing the ice to sublimate before it is processed. Here I use new results for the saturation vapor pressure of water ice to extend previous estimates of its sublimation rate down to a temperature of 40 K, typical of the permanently shaded craters near the lunar poles where the water ice is presumed to be trapped. I find that, for temperatures below 70 K, the sublimation rate of an exposed ice surface is much less than one molecule of water vapor lost per square centimeter of surface per hour. But even if a small ice sample (∼4 ng) were heated to 150 K, it could exist for over two hours without sublimating a significant fraction of its mass. Hence, carefully designed sampling and sample handling should be able to preserve water ice obtained near the lunar poles for an accurate measurement of its in situ concentration.     

Fracture penetration in planetary ice shells

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.     

Preliminary studies concerning subsurface probes for the exploration of icy planetary bodies

It is well-known that the permanent terrestrial ice sheets (glaciers and polar caps) contain a lot of information about the recent geological history and in particular about climatic changes. Extrapolating this fact to other ice sheets in the solar system (e.g. the Mars polar regions, the icy moons of the outer planets, etc.), we may expect a similar wealth of information. To obtain this information it is possible to drill holes or melt the ice by a heated probe, which in this way is able to penetrate the surface and investigate the deeper layers in situ. In the latter case the driving agent is the heating power and the weight of the probe. In this paper we consider the application of such “melting probes” for exploring the structure of ice sheets in extraterrestrial environments. We describe several laboratory experiments with simple melting probes performed under cryo-vacuum conditions and compare the results with tests in a terrestrial environment. The experiments revealed that under space conditions the downward motion of a heated probe in an ice sheet is characterized by intermittent periods of sublimation and melting of the surrounding ice, sometimes interrupted by periods where a part of the probe's outer surface is frozen to the surrounding ice. This leads to a temporary blocking of the probe's downward motion. A similar situation can occur when the trailing tether is frozen in behind the probe. During the periods of ice sublimation the penetration process is significantly more power consuming, due to the large difference between the latent heat of sublimation and the latent heat of melting for water ice.     

Reply to “Comment on ‘Mechanics of tidally driven fractures in Europa's ice shell’ ”

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.     

Heat flow, lenticulae spacing, and possibility of convection in the ice shell of europa

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.     

Model of explosive eruptions of water vapor and dust on icy satellites

The possibility of generating water vapor and other gaseous products during nonvolcanic explosive eruptions in lithospheres of icy satellites is discussed. Explosive eruptions of ice, with its fragmentation into micro-and nanofragments, can occur in the extensive deep layers of such icy satellites as Europa, Ganymede, Enceladus, etc., if giant cracks are episodically formed in the lithospheres of these satellites. Such cracks can be produced by tidal forces, synchronous resonances of satellites, or especially powerful impacts. The model is based on the recently obtained experimental evidence that explosive ice instability (Bridgman effect) is formed at a strong nonuniform compression in the regions of high pressures and low temperatures. Water films, the thicknesses of which reach several microns, can be formed during the process of the mutual friction of ice fragments during their quasi-liquid flow at the instant of an explosive eruption. About 1–10 dm³ of a water film can be produced in 1 m³ of erupted ice fragments. Water vapor can be formed from a water film when this water boils up after a rapid pressure drop as a result of an ice-water mixture eruption from cracks. A certain amount of gaseous products in the form of hydrogen, oxygen, and ammonia molecules and radicals on their basis can be generated during the sputtering induced by electrons and ions and the dissociation of nanofragments of ice during the process of ice explosive fragmentation as a result of fracto-, tribo-, and secondary emission. The estimates indicate that the volume of water vapor erupted on satellites can be larger than that of discharged ionized gases by a factor of not less than 10⁵–10⁷. Water vapor and microscopic ice fragments can be erupted from cracks in the lithospheres of small Enceladus-type satellites at velocities higher than the second cosmic velocity. Gaseous products generated in such episodic processes can, most probably, substantially contribute to the density of the atmosphere that exists on small icy satellites, but can only insignificantly contribute to this density on large satellites. The stick-slip motions of the most condensed plumes of water vapor and dust, normal to the satellite surface, along the mouths of gigantic cracks may indicate that the proposed model is realistic. Such wanderings of water vapor plumes can result in the synchronous motions of thermal patches on the satellite surface along crack mouths at velocities of about 10 km/h.     

Study of a thermal drill head for the exploration of subsurface planetary ice layers

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.     

OMEGA/Mars Express: South Pole Region, water vapor daily variability

Polar regions on Mars are the most suitable places to observe water vapor daily variability because in any observation crossing the Pole we can observe very different local time and because the poles are considered to be the main permanent and seasonal water reservoir of the planet. We report on a daily variability of water vapor in the South Pole Region (SPR), observed by OMEGA/Mars Express during the south spring-summer period (Ls∼250°-270°) outside the CO₂ ice cap, that has never been observed before by other instruments. We have been able to estimate an increase of few precipitable microns during the day. A possible scenario includes the presence of regolith, or another component that could gather water from the atmosphere, adsorbing the water into the surface during the night time and desorbing it as soon as the Sun reaches sufficient height to heat the ground. This hypothesis is even more plausible considering the presence of observed local enhancements in the morning sections associated with the illumination of the Sun and the total absence in the data for water ice.     

Thermal convection in ice-I shells of Titan and Enceladus

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.     

On convection in ice I shells of outer Solar System bodies, with detailed application to Callisto

It has been argued that the dominant non-Newtonian creep mechanisms of water ice make the ice shell above Callisto's ocean, and by inference all radiogenically heated ice I shells in the outer Solar System, stable against solid-state convective overturn. Conductive heat transport and internal melting (oceans) are therefore predicted to be, or have been, widespread among midsize and larger icy satellites and Kuiper Belt objects. Alternatively, at low stresses (where non-Newtonian viscosities can be arbitrarily large), convective instabilities may arise in the diffusional creep regime for arbitrarily small temperature perturbations. For Callisto, ice viscosities are low enough that convection is expected over most of geologic time above the internal liquid layer for plausible ice grain sizes (?a few mm); the alternative for early Callisto, a conducting shell over a very deep ocean (>450 km), is not compatible with Callisto's present partially differentiated state. Moreover, if convection is occurring today, the stagnant lid would be quite thick (∼100 km) and compatible with the lack of active geology. Nevertheless, Callisto's steady-state heat flow may have fallen below the convective minimum for its ice I shell late in Solar System history. In this case convection ends, the ice shell melts back at its base, and the internal ocean widens considerably. The presence of such an ocean, of order 200 km thick, is compatible with Callisto's moment-of-inertia, but its formation would have caused an ∼0.25% radial expansion. The tectonic effects of such a late, slow expansion are not observed, so convection likely persists in Callisto, possibly subcritically. Ganymede, due to its greater size, rock fraction and full differentiation, has a substantially higher heat flow than Callisto and has not reached this tectonic end state. Titan, if differentiated, and Triton should be more similar to Ganymede in this regard. Pluto, like Callisto, may be near the tipping point for convective shutdown, but uncertainties in its size and rock fraction prevent a more definitive assessment.     

Aram Chaos and its constraints on the surface heat flux of Mars

The surface heat flux of a planet is an important parameter to characterize its internal activity and to determine its thermal evolution. Here we report on a new method to constrain the surface heat flux of Mars during the Hesperian. For this, we explore the consequences for the martian surface heat flux from a recently presented new hypothesis for the formation of Aram Chaos (Zegers, T.E., Oosthoek, J.H.P., Rossi, A.P., Blom, J.K., Schumacher, S. [2010]. Earth Planet. Sci. Lett. 297, 496-504. doi:10.1016/j.epsl.2010.06.049.). In this hypothesis the chaotic terrain is thought to have formed by melting of a buried ice sheet. The slow sedimentation and burial of the ice sheet led to an increased thermal insulation of the ice and subsequently to a temperature increase high enough to trigger melting and the formation of the subsurface lake. As these processes highly depend on the thermal properties of the subsurface and especially on the surface heat flux, it is possible to constrain the latter by using numerical simulations. Based on the hypothesis for the formation of Aram Chaos, we conducted an extensive parameter study to determine the parameter settings leading to sufficient melting of the buried ice sheet. We find that the surface heat flux in the Aram Chaos region during the Hesperian was most likely between 20 and 45 mW m⁻² with a possible maximum value of up to 60 mW m⁻².     

Comparison of heat balance characteristics at five glaciers in the Southern Hemisphere

Ablation characteristics of five glaciers in Patagonia and New Zealand were compared. Investigated glaciers were Tyndall and Moreno in southern Patagonia, Soler and San Rafael in northern Patagonia, and Franz Josef in New Zealand. Micro-meteorological observations were carried out at the glaciers and the heat balance components were estimated. At Franz Josef and Soler glaciers, the sensible heat flux is the largest and the latent heat flux is the second, and they are larger than the net radiation. At San Rafael Glacier, the net radiation is the largest and the latent heat flux is the smallest component, which is similar to Moreno and Tyndall glaciers. Though the latent heat flux is the smallest component at San Rafael Glacier, it is more than twice as large as that at Tyndall Glacier and contributes substantially to ice melting. The ratios of heat balance components were very different among glaciers, but the total heat flux ranged from about 240 to 300 W m⁻² showing little difference among glaciers.     

Early Mars climate near the Noachian–Hesperian boundary: Independent evidence for cold conditions from basal melting of the south polar ice sheet (Dorsa Argentea Formation) and implications for valley network formation

Currently, and throughout much of the Amazonian, the mean annual surface temperatures of Mars are so cold that basal melting does not occur in ice sheets and glaciers and they are cold-based. The documented evidence for extensive and well-developed eskers (sediment-filled former sub-glacial meltwater channels) in the south circumpolar Dorsa Argentea Formation is an indication that basal melting and wet-based glaciation occurred at the South Pole near the Noachian–Hesperian boundary. We employ glacial accumulation and ice-flow models to distinguish between basal melting from bottom-up heat sources (elevated geothermal fluxes) and top-down induced basal melting (elevated atmospheric temperatures warming the ice). We show that under mean annual south polar atmospheric temperatures (?100 °C) simulated in typical Amazonian climate experiments and typical Noachian–Hesperian geothermal heat fluxes (45–65 mW/m²), south polar ice accumulations remain cold-based. In order to produce significant basal melting with these typical geothermal heat fluxes, the mean annual south polar atmospheric temperatures must be raised from today’s temperature at the surface (?100 °C) to the range of ?50 to ?75 °C. This mean annual polar surface atmospheric temperature range implies lower latitude mean annual temperatures that are likely to be below the melting point of water, and thus does not favor a “warm and wet” early Mars. Seasonal temperatures at lower latitudes, however, could range above the melting point of water, perhaps explaining the concurrent development of valley networks and open basin lakes in these areas. This treatment provides an independent estimate of the polar (and non-polar) surface temperatures near the Noachian–Hesperian boundary of Mars history and implies a cold and relatively dry Mars climate, similar to the Antarctic Dry Valleys, where seasonal melting forms transient streams and permanent ice-covered lakes in an otherwise hyperarid, hypothermal climate.     

Evaporation of ice in planetary atmospheres: Ice-covered rivers on mars

The evaporation rate of water ice on the surface of a planet with an atmosphere involves an equilibrium between solar heating and radiative and evaporative cooling of the ice layer. The thickness of the ice is governed principally by the solar flux which penetrates the ice layer and then is conducted back to the surface. These calculations differ from those of Lingenfelter et al. [(1968) Science161, 266–269] for putative lunar channels in including the effect of the atmosphere. Evaporation from the surface is governed by two physical phenomena: wind and free convection. In the former case, water vapor diffuses from the surface of the ice through a lamonar boundary layer and then is carried away by eddy diffusion above, provided by the wind. The latter case, in the absence of wind, is similar, except that the eddy diffusion is caused by the lower density of water vapor than the Martian atmosphere. For mean Martian insolations the evaporation rate above the ice is ～ 10^?8 g cm^?2 sec^?1. Thus, even under present Martian conditions a flowing channel of liquid water will be covered with ice which evaporates sufficiently slowly that the water below can flow for hundreds of kilometers even with quite modest discharges. Evaporation rates are calculated for a wide range of frictional velocities, atmospheric pressures, and insolations and it seems clear that at least some subset of observed Martian channels may have formed as ice-choked rivers. Typical equilibrium thicknesses of such ice covers are ～ 10 to 30 m; typical surface temperatures are 210 to 235°K. Ice-covered channels or lakes on Mars today may be of substantial biological interest. Ice is a sufficiently poor conductor of heat that sunlight which penetrates it can cause melting to a depth of several meters or more. Because the obliquity of Mars can vary up to some 35°, the increased polar heating at such times seems able to cause subsurface melting of the ice caps to a depth which corresponds to the observed lamina thickness and may be responsible for the morphology of these polar features.     

The electrical conductivity of Io

If Io has a thin crust of ice [this possibility has recently been suggested by Lewis (1971)] then the electrical resistance of the satellite is determined by an outer layer of thickness ∼8 km and is higher by a factor ∼10¹⁵ than that needed to account for the modulation of Jupiter's decametric radio emission in the unipolar inductor model of Goldreich and Lynden-Bell. The modulation, however, could possibly be accounted for if the surface composition of Io is chondritic or if it has an ionosphere.     

Simulations of a comet impact on the Moon and associated ice deposition in polar cold traps

Modeling results of the water vapor plume produced by a comet impact on the Moon and of the resulting water ice deposits in the lunar cold traps are presented. The water vapor plume is simulated near the point of impact by the SOVA hydrocode and in the far field by the Direct Simulation Monte Carlo (DSMC) method using as input the SOVA hydrocode solution at a fixed hemispherical interface. The SOVA hydrocode models the physics of the impact event such as the surface deformation and material phase changes during the impact. The further transport and retention processes, including gravity, photodestruction processes, and variable surface temperature with local polar cold traps, are modeled by the DSMC method for months after impact. In order to follow the water from the near field of the impact to the full planetary induced atmosphere, the 3D parallel DSMC code used a collision limiting scheme and an unsteady multi-domain approach. 3D results for the 45° oblique impact of a 2 km in diameter comet on the surface of the Moon at 30 km/s are presented. Most of the cometary water is lost due to escape just after impact and only ∼3% of the cometary water is initially retained on the Moon. Early downrange focusing of the water vapor plume is observed but the later material that is moving more slowly takes on a more symmetric shape with time. Several locations for the point of impact were investigated and final retention rates of ∼0.1% of the comet mass were observed. Based on the surface area of the cold traps used in the present simulations, ∼1 mm of ice would have accumulated in the cold traps after such an impact. Estimates for the total mass of water accumulated in the polar cold traps over 1 byr are consistent with recent observations.     

Organics-glued dust aggregates in Halley's coma and some implications of the snow line inward motion for the formation of comets

In view of the solar nebula models, organics-glued dust aggregates (whose disintegration resulted in the two phenomena found in Halley's coma, the dust boundary and small-scale dust structures) originated due to coagulation of iceless dust particles somewhere within the snow line, and then were incorporated into Halley's nucleus as a consequence of the snow line inward motion. This implies that two types of comets exist: outer comets, formed entirely beyond the snow line, and inner comets, similar to Halley, which are bodies intermediate between outer comets and primitive asteroids. The presence of large iceless dust aggregates in nuclei of inner comets constrains the inward drift velocity of meter-sized dust bodies, which in turn implies that the radial transport of water in the solar nebula was predominantly outward. It is shown that in nuclei of inner comets: both the upper mass limit of iceless dust aggregates and the ice mantle thickness increase with decreasing formation heliocentric distance, while the cumulative mass distribution index decreases; the lower limit of the mass index is ∼0.8, and the upper limit of the ice mantle thickness is ∼10⁻³ cm (∼200 times the interstellar value); the lower limit of the latent heat of organics in organic mantles of submicron particles increases toward small heliocentric distances; the recondensation of organics combined with the growth of dust bodies leads to a fractionation of organics within iceless dust aggregates; last accreted sub-units of an aggregate are always glued by organics with the lowest value of the latent heat, which somewhat exceeds 60 kJ/mol. Based on in situ observations at Halley, the parameters characterizing iceless dust aggregates in that comet are calculated. Finally, feasible observational tests of the conclusions drawn are discussed.     

A Shock-Wave Heating Model for Chondrule Formation: Effects of Evaporation and Gas Flows on Silicate Particles

A shock-wave heating model is one of the possible models for chondrule formation. We examine, within the framework of a shock-wave heating model, the effects of evaporation on the heating of chondrule precursor particles and the stability of their molten state in the postshock flow. We numerically simulate the heating process in the flow taking into account evaporation. We find that the melting criterion and the minimum radius criterion do not change significantly. However, if the latent heat cooling due to the evaporation dominates the radiative cooling from the precursor particle, the peak temperature of the precursor particle is suppressed by a few hundred Kelvins. We also find that the total gas pressure (ram plus static) acting on the precursor particle exceeds the vapor pressure of the molten precursor particle. Therefore, it is possible to form chondrules in the shock-wave heating model if the precursor temperature increases up to the melting point.     

Heat flow and depth to a possible internal ocean on Triton

The Raz Fossae, a pair of ≈15-km wide trough en echelon interpreted as grabens, can be used to propose an estimation of the depth to the brittle-ductile transition on Triton. This estimation may in turn give an idea of the thermal state of Triton's icy lithosphere when these features formed. Given the young age of its surface, the conclusions obtained could be roughly applicable to the present state of this satellite of Neptune. Considering water or ammonia dihydrate as possible components of the lithosphere and a feasible range of strain rates, it was estimated that surface heat flow is greater than that inferred from radiogenic heating, especially for a lithosphere dominated by water. Also, an internal ocean could lie at a depth of only ∼20 km beneath the surface. The presence over the surface of an insulating layer of ice of low thermal conductivity (e.g., nitrogen) or of regolith would only substantially alter these estimates if the effective surface temperature were considerably higher than the observed value of 38 K.