Hydrocarbon lakes on Titan

The Huygens Probe detected dendritic drainage-like features, methane clouds and a high surface relative humidity (∼50%) on Titan in the vicinity of its landing site [Tomasko, M.G., and 39 colleagues, 2005. Nature 438, 765-778; Niemann, H.B., and 17 colleagues, 2005. Nature 438, 779-784], suggesting sources of methane that replenish this gas against photo- and charged-particle chemical loss on short (10-100) million year timescales [Atreya, S.K., Adams, E.Y., Niemann, H.B., Demick-Montelara, J.E., Owen, T.C., Fulchignoni, M., Ferri, F., Wilson, E.H., 2006. Planet. Space Sci. In press]. On the other hand, Cassini Orbiter remote sensing shows dry and even desert-like landscapes with dunes [Lorenz, R.D., and 39 colleagues, 2006a. Science 312, 724-727], some areas worked by fluvial erosion, but no large-scale bodies of liquid [Elachi, C., and 34 colleagues, 2005. Science 308, 970-974]. Either the atmospheric methane relative humidity is declining in a steady fashion over time, or the sources that maintain the relative humidity are geographically restricted, small, or hidden within the crust itself. In this paper we explore the hypothesis that the present-day methane relative humidity is maintained entirely by lakes that cover a small part of the surface area of Titan. We calculate the required minimum surface area coverage of such lakes, assess the stabilizing influence of ethane, and the implications for moist convection in the atmosphere. We show that, under Titan's surface conditions, methane evaporates rapidly enough that shorelines of any existing lakes could potentially migrate by several hundred m to tens of km per year, rates that could be detected by the Cassini orbiter. We furthermore show that the high relative humidity of methane in Titan's lower atmosphere could be maintained by evaporation from lakes covering only 0.002-0.02 of the whole surface.     

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

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

Titan's diverse landscapes as evidenced by Cassini RADAR's third and fourth looks at Titan

Cassini's third and fourth radar flybys, T7 and T8, covered diverse terrains in the high southern and equatorial latitudes, respectively. The T7 synthetic aperture radar (SAR) swath is somewhat more straightforward to understand in terms of a progressive poleward descent from a high, dissected, and partly hilly terrain down to a low flat plain with embayments and deposits suggestive of the past or even current presence of hydrocarbon liquids. The T8 swath is dominated by dunes likely made of organic solids, but also contain somewhat enigmatic, probably tectonic, features that may be partly buried or degraded by erosion or relaxation in a thin crust. The dark areas in T7 show no dune morphology, unlike the dark areas in T8, but are radiometrically warm like the dunes. The Huygens landing site lies on the edge of the T8 swath; correlation of the radar and Huygens DISR images allows accurate determination of its coordinates, and indicates that to the north of the landing site sit two large longitudinal dunes. Indeed, had the Huygens probe trajectory been just 10 km north of where it actually was, images of large sand dunes would have been returned in place of the fluvially dissected terrain actually seen—illustrating the strong diversity of Titan's landscapes even at local scales.     

The geology of Hotei Regio, Titan: Correlation of Cassini VIMS and RADAR

Joint Cassini VIMS and RADAR SAR data of ∼700-km-wide Hotei Regio reveal a rich collection of geological features that correlate between the two sets of images. The degree of correlation is greater than anywhere else seen on Titan. Central to Hotei Regio is a basin filled with cryovolcanic flows that are anomalously bright in VIMS data (in particular at 5 μm) and quite variable in roughness in SAR. The edges of the flows are dark in SAR data and appear to overrun a VIMS-bright substrate. SAR-stereo topography shows the flows to be viscous, 100-200 m thick. On its southern edge the basin is ringed by higher (∼1 km) mountainous terrain. The mountains show mixed texture in SAR data: some regions are extremely rough, exhibit low and spectrally neutral albedo in VIMS data and may be partly coated with darker hydrocarbons. Around the southern margin of Hotei Regio, the SAR image shows several large, dendritic, radar-bright channels that flow down from the mountainous terrain and terminate in dark blue patches, seen in VIMS images, whose infrared color is consistent with enrichment in water ice. The patches are in depressions that we interpret to be filled with fluvial deposits eroded and transported by liquid methane in the channels. In the VIMS images the dark blue patches are encased in a latticework of lighter bands that we suggest to demark a set of circumferential and radial fault systems bounding structural depressions. Conceivably the circular features are tectonic structures that are remnant from an ancient impact structure. We suggest that impact-generated structures may have simply served as zones of weakness; no direct causal connection, such as impact-induced volcanism, is implied. We also speculate that two large dark features lying on the northern margin of Hotei Regio could be calderas. In summary the preservation of such a broad suite of VIMS infrared color variations and the detailed correlation with features in the SAR image and SAR topography evidence a complex set of geological processes (pluvial, fluvial, tectonic, cryovolcanic, impact) that have likely remained active up to very recent geological time (<10⁴ year). That the cryovolcanic flows are excessively bright in the infrared, particularly at 5 μm, might signal ongoing geological activity. One study [Nelson, R.M., and 28 colleagues, 2009. Icarus 199, 429-441] reported significant 2-μm albedo changes in VIMS data for Hotei Arcus acquired between 2004 and 2006, that were interpreted as evidence for such activity. However in our review of that work, we do not agree that such evidence has yet been found.     

Impact craters on Titan

Five certain impact craters and 44 additional nearly certain and probable ones have been identified on the 22% of Titan’s surface imaged by Cassini’s high-resolution radar through December 2007. The certain craters have morphologies similar to impact craters on rocky planets, as well as two with radar bright, jagged rims. The less certain craters often appear to be eroded versions of the certain ones. Titan’s craters are modified by a variety of processes including fluvial erosion, mass wasting, burial by dunes and submergence in seas, but there is no compelling evidence of isostatic adjustments as on other icy moons, nor draping by thick atmospheric deposits. The paucity of craters implies that Titan’s surface is quite young, but the modeled age depends on which published crater production rate is assumed. Using the model of Artemieva and Lunine (2005) suggests that craters with diameters smaller than about 35 km are younger than 200 million years old, and larger craters are older. Craters are not distributed uniformly; Xanadu has a crater density 2-9 times greater than the rest of Titan, and the density on equatorial dune areas is much lower than average. There is a small excess of craters on the leading hemisphere, and craters are deficient in the north polar region compared to the rest of the world. The youthful age of Titan overall, and the various erosional states of its likely impact craters, demonstrate that dynamic processes have destroyed most of the early history of the moon, and that multiple processes continue to strongly modify its surface. The existence of 24 possible impact craters with diameters less than 20 km appears consistent with the Ivanov, Basilevsky and Neukum (1997) model of the effectiveness of Titan’s atmosphere in destroying most but not all small projectiles.     

Mapping of Titan: Results from the first Titan radar passes

The first two swaths collected by Cassini's Titan Radar Mapper were obtained in October of 2004 (Ta) and February of 2005 (T3). The Ta swath provides evidence for cryovolcanic processes, the possible occurrence of fluvial channels and lakes, and some tectonic activity. The T3 swath has extensive areas of dunes and two large impact craters. We interpret the brightness variations in much of the swaths to result from roughness variations caused by fracturing and erosion of Titan's icy surface, with additional contributions from a combination of volume scattering and compositional variations. Despite the small amount of Titan mapped to date, the significant differences between the terrains of the two swaths suggest that Titan is geologically complex. The overall scarcity of impact craters provides evidence that the surface imaged to date is relatively young, with resurfacing by cryovolcanism, fluvial erosion, aeolian erosion, and likely atmospheric deposition of materials. Future radar swaths will help to further define the nature of and extent to which internal and external processes have shaped Titan's surface.     

Distribution and interplay of geologic processes on Titan from Cassini radar data

The Cassini Titan Radar Mapper is providing an unprecedented view of Titan’s surface geology. Here we use Synthetic Aperture Radar (SAR) image swaths (Ta-T30) obtained from October 2004 to December 2007 to infer the geologic processes that have shaped Titan’s surface. These SAR swaths cover about 20% of the surface, at a spatial resolution ranging from ∼350 m to ∼2 km. The SAR data are distributed over a wide latitudinal and longitudinal range, enabling some conclusions to be drawn about the global distribution of processes. They reveal a geologically complex surface that has been modified by all the major geologic processes seen on Earth - volcanism, tectonism, impact cratering, and erosion and deposition by fluvial and aeolian activity. In this paper, we map geomorphological units from SAR data and analyze their areal distribution and relative ages of modification in order to infer the geologic evolution of Titan’s surface. We find that dunes and hummocky and mountainous terrains are more widespread than lakes, putative cryovolcanic features, mottled plains, and craters and crateriform structures that may be due to impact. Undifferentiated plains are the largest areal unit; their origin is uncertain. In terms of latitudinal distribution, dunes and hummocky and mountainous terrains are located mostly at low latitudes (less than 30°), with no dunes being present above 60°. Channels formed by fluvial activity are present at all latitudes, but lakes are at high latitudes only. Crateriform structures that may have been formed by impact appear to be uniformly distributed with latitude, but the well-preserved impact craters are all located at low latitudes, possibly indicating that more resurfacing has occurred at higher latitudes. Cryovolcanic features are not ubiquitous, and are mostly located between 30° and 60° north. We examine temporal relationships between units wherever possible, and conclude that aeolian and fluvial/pluvial/lacustrine processes are the most recent, while tectonic processes that led to the formation of mountains and Xanadu are likely the most ancient.     

Modelling of possible mud volcanism on Titan

Possible sedimentary basins on Titan are potential sites for the formation of mud volcanoes. In order to constrain the appearance of such features in remotely sensed imagery being acquired by the Cassini spacecraft, we have modelled the formation of mud volcanoes on Titan for a series of plausible mud compositions, climatic conditions and geological settings, as well as addressing the full range of eruption variables; mud viscosity, conduit diameter and eruption duration. We find that for an acetylene mud source containing 20 wt% liquid methane in pore spaces, overlain by a sheet of water ice 500-m thick, a mud volcano can grow as high as 140 m. Assuming reasonable eruption parameters, such an edifice may develop into a pancake-like dome several kilometres in diameter. If observed and properly characterised, mud volcanoes would provide an important window on the subsurface distribution and dynamics of solids and liquids in sedimentary basins on Titan.     

A 3 km atmospheric boundary layer on Titan indicated by dune spacing and Huygens data

Some 20% of Titan’s surface is covered in large linear dunes that resemble in morphology, size and spacing (1-3 km) those seen on Earth. Although gravity, atmospheric density and sand composition are very different on these two worlds, this coincident size scale suggests that the controlling parameter limiting the growth of giant dunes, namely the boundary layer thickness (Andreotti et al., 2009). Nature, 457, 1120-1123], is similar. We show that a ∼3 km boundary layer thickness is supported by Huygens descent data and is consistent with results from Global Circulation Models taking the distinctive thermal inertia and albedo of the dune sands into account. While the boundary layer thickness on Earth controlling dunes can vary by an order of magnitude depending on the proximity of oceans, which have very different thermal properties from dry land, the relative invariance of dune spacing on Titan is consistent with relatively uniform thermal properties near the dunes and no prominent variation with latitude is seen.     

Radar-bright channels on Titan

During Cassini’s T44 flyby of Titan (May 28, 2008), the Cassini SAR (synthetic aperture radar) revealed sinuous channels in the Southwest of Xanadu. These channels feature very large radar cross-sections, up to 5 dB, whereas the angle of incidence was relatively high, ∼20°. This backscatter is larger than allowed by the coherent backscatter model considered to explain the unusual reflective and polarization properties of the icy satellites and only a few radar scattering mechanisms can be responsible for such high radar returns. The presence of rounded (icy) pebbles with size larger than the radar wavelength (2.18 cm) is proposed to explain the large radar cross-sections measured in these units. The radar-bright channels are thus interpreted as riverbeds, where debris, likely shaped and transported by fluvial activity, have been deposited. Similar debris were observed in the landing site of the Huygens probe. This work may point the way to an explanation for the enhanced brightness of other fluvial regions of Titan.     

Geology of the Selk crater region on Titan from Cassini VIMS observations

Observations of Titan obtained by the Cassini Visual and Infrared Mapping Spectrometer (VIMS) have revealed Selk crater, a geologically young, bright-rimmed, impact crater located ∼800 km north-northwest of the Huygens landing site. The crater rim-crest diameter is ∼90 km; its floor diameter is ∼60 km. A central pit/peak, 20-30 km in diameter, is seen; the ratio of the size of this feature to the crater diameter is consistent with similarly sized craters on Ganymede and Callisto, all of which are dome craters. The VIMS data, unfortunately, are not of sufficient resolution to detect such a dome. The inner rim of Selk crater is fluted, probably by eolian erosion, while the outer flank and presumed ejecta blanket appear dissected by drainages (particularly to the east), likely the result of fluvial erosion. Terracing is observed on the northern and western walls of Selk crater within a 10-15 km wide terrace zone identified in VIMS data; the terrace zone is bright in SAR data, consistent with it being a rough surface. The terrace zone is slightly wider than those observed on Ganymede and Callisto and may reflect differences in thermal structure and/or composition of the lithosphere. The polygonal appearance of the crater likely results from two preexisting planes of weakness (oriented at azimuths of 21° and 122° east of north). A unit of generally bright terrain that exhibits similar infrared-color variation and contrast to Selk crater extends east-southeast from the crater several hundred kilometers. We informally refer to this terrain as the Selk “bench.” Both Selk and the bench are surrounded by the infrared-dark Belet dune field. Hypotheses for the genesis of the optically bright terrain of the bench include: wind shadowing in the lee of Selk crater preventing the encroachment of dunes, impact-induced cryovolcanism, flow of a fluidized-ejecta blanket (similar to the bright crater outflows observed on Venus), and erosion of a streamlined upland formed in the lee of Selk crater by fluid flow. Vestigial circular outlines in this feature just east of Selk’s ejecta blanket suggest that this might be a remnant of an ancient, cratered crust. Evidently the southern margin of the feature has sufficient relief to prevent the encroachment of dunes from the Belet dune field. We conclude that this feature either represents a relatively high-viscosity, fluidized-ejecta flow (a class intermediate to ejecta blankets and long venusian-style ejecta flows) or a streamlined upland remnant that formed downstream from the crater by erosive fluid flow from the west-northwest.     

Shell thickness variations and the long-wavelength topography of Titan

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 h_2t 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.     

Sea-surface wave growth under extraterrestrial atmospheres: Preliminary wind tunnel experiments with application to Mars and Titan

We describe for the first time the generation and measurement of capillary waves in a water surface in a wind tunnel running with air at pressures of 15-1000 mbar. These experiments suggest a stronger dependence of wave generation on atmospheric density than the simple proportionality that might be expected from energy transfer arguments. Additionally, airflow over a nonaqueous fluid (kerosene) was found to produce waves of higher amplitude than for water under the same conditions. These preliminary results may indicate different efficiencies of wave generation on other planets, for which empirical terrestrial relations therefore do not apply, and thus may have a bearing on the lack of strong shoreline features on Mars and the possibility of specular glints from hydrocarbon lakes on Titan.     

Fluvial erosion and post-erosional processes on Titan

The surface of Titan has been revealed by Cassini observations in the infrared and radar wavelength ranges as well as locally by the Huygens lander instruments. Sand seas, recently discovered lakes, distinct landscapes and dendritic erosion patterns indicate dynamic surface processes. This study focus on erosional and depositional features that can be used to constrain the amount of liquids involved in the erosional process as well as on the compositional characteristics of depositional areas. Fluvial erosion channels on Titan as identified at the Huygens landing site and in RADAR and Visible and Infrared Mapping Spectrometer (VIMS) observations have been compared to analogous channel widths on Earth yielding average discharges of up to 1600 m³/s for short recurrence intervals that are sufficient to move centimeter-sized sediment and significantly higher discharges for long intervals. With respect to the associated drainage areas, this roughly translates to 1-150 cm/day runoff production rates with 10 years recurrence intervals and by assuming precipitation this implies 0.6-60 mm/h rainfall rates. Thus the observed surface erosion fits with the methane convective storm models as well as with the rates needed to transport sediment. During Cassini's T20 fly-by, the VIMS observed an extremely eroded area at 30° W, 7° S with resolutions of up to 500 m/pixel that extends over thousands of square kilometers. The spectral characteristics of this area change systematically, reflecting continuous compositional and/or particle size variations indicative of transported sediment settling out while flow capacities cease. To account for the estimated runoff production and widespread alluvial deposits of fine-grained material, release of area-dependent large fluid volumes are required. Only frequent storms with heavy rainfall or cryovolcanic induced melting can explain these erosional features.     

Channel morphometry, sediment transport, and implications for tectonic activity and surficial ages of Titan basins

Fluvial features on Titan and drainage basins on Earth are remarkably similar despite differences in gravity and surface composition. We determined network bifurcation (R_b) ratios for five Titan and three terrestrial analog basins. Tectonically-modified Earth basins have R_b values greater than the expected range (3.0-5.0) for dendritic networks; comparisons with R_b values determined for Titan basins, in conjunction with similarities in network patterns, suggest that portions of Titan’s north polar region are modified by tectonic forces. Sufficient elevation data existed to calculate bed slope and potential fluvial sediment transport rates in at least one Titan basin, indicating that 75 mm water ice grains (observed at the Huygens landing site) should be readily entrained given sufficient flow depths of liquid hydrocarbons. Volumetric sediment transport estimates suggest that ∼6700-10,000 Titan years (∼2.0-3.0 × 10⁵ Earth years) are required to erode this basin to its minimum relief (assuming constant 1 m and 1.5 m flows); these lowering rates increase to ∼27,000-41,000 Titan years (∼8.0-12.0 × 10⁵ Earth years) when flows in the north polar region are restricted to summer months.     

Physical properties of Titan's surface at the Huygens landing site from the Surface Science Package Acoustic Properties sensor (API-S)

We present the results from the first sonar to be deployed outside of Earth, and the first active acoustic instrument on Titan, onboard the Huygens probe, and the implications of its data for the geomorphology and characteristics of the Huygens landing site. Signals were recorded from 90 m downwards until impact, with a maximum sensor footprint diameter at the ground of 39.2 m. Probe impact speed was measured to be 4.67 m s⁻¹. Derivation of terrain topography in a transect beneath the probe may indicate a ridge-trough terrain with an amplitude of about 1 m and a wavelength of about 10 m, although a flat surface is also consistent with the results. Modelling of the returned signal indicates that the surface acoustic properties at the landing site must be specular in nature, which may have two possible (not incompatible) causes—the surface may consist of sorted interlocking grains, smooth on the centimetre scale, which would imply either fluvial sorting or the infill of small particles interstitial to the larger particles (similar to a terrestrial playa). Alternatively, specularity may indicate the presence of methane as an interstitial liquid or as very small pools. Due to mission constraints, tens of metres around the landing site were not well-imaged by Huygens' cameras except for the narrow azimuth observed after impact (the camera did not look straight down, and was not in imaging mode during the last few hundred metres of descent). Thus the data presented are among the few direct observations of the landing site surroundings.     

Titan impacts and escape

We report on hydrodynamic calculations of impacts of large (multi-kilometer) objects on Saturn’s moon Titan. We assess escape from Titan, and evaluate the hypothesis that escaping ejecta blackened the leading hemisphere of Iapetus and peppered the surface of Hyperion.We carried out two- and three-dimensional simulations of impactors ranging in size from 4 to 100 km diameter, impact velocities between 7 and 15 km s⁻¹, and impact angles from 0° to 75° from the vertical. We used the ZEUSMP2 hydrocode for the calculations. Simulations were made using three different geometries: three-dimensional Cartesian, two-dimensional axisymmetric spherical polar, and two-dimensional plane polar. Three-dimensional Cartesian geometry calculations were carried out over a limited domain (e.g. 240 km on a side for an impactor of size d_i = 10 km), and the results compared to ones with the same parameters done by Artemieva and Lunine (2005); in general the comparison was good. Being computationally less demanding, two-dimensional calculations were possible for much larger domains, covering global regions of the satellite (from 800 km below Titan’s surface to the exobase altitude 1700 km above the surface). Axisymmetric spherical polar calculations were carried out for vertical impacts. Two-dimensional plane-polar geometry calculations were made for both vertical and oblique impacts. In general, calculations among all three geometries gave consistent results.Our basic result is that the amount of escaping material is less than or approximately equal to the impactor mass even for the most favorable cases. Amounts of escaping material scaled most strongly as a function of velocity, with high-velocity impacts generating the largest amount, as expected. Dependence of the relative amount of escaping mass f_esc = m_esc/M_i on impactor diameter d_i was weak. Oblique impacts (impact angle θ_i > 45°) were more effective than vertical or near-vertical impacts; ratios of m_esc/M_i ∼ 1-2 were found in the simulations.     

Resurfacing of Titan by ammonia-water cryomagma

The Cassini Titan Radar Mapper observed on Titan several large features interpreted as cryovolcanic during the October 26, 2004 pass at high northern latitudes [Lopes, R.M.C., and 43 colleagues, 2007. Icarus 186, 395-412]. To date, models of ammonia-water resurfacing have not been tied to specific events or evolutionary stages of Titan. We propose a model of cryovolcanism that involves cracking at the base of the ice shell and formation of ammonia-water pockets in the ice. As these ammonia-water pockets undergo partial freezing in the cold ice shell, the ammonia concentration in the pockets increases, decreasing the negative buoyancy of the ammonia-water mixture. If the ice shell is contaminated by silicates delivered in impacts, the liquid-solid density difference would be even less. While the liquid cannot easily become buoyant relative to the surrounding ice, these concentrated ammonia-water pockets are sufficiently close to the neutral buoyancy point that large-scale tectonic stress patterns (tides, non-synchronous rotation, satellite volume changes, solid state convection, or subsurface pressure gradients associated with topography) would enable the ammonia to erupt effusively onto the surface. Rather than suggesting steady-state volcanism over the history of the Solar System, we favor a scenario where the cryovolcanic features could have been associated with episodic (potentially late) geological activity.     

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.     

Modeling crater populations on Venus and Titan

We describe a model for crater populations on planets and satellites with dense atmospheres, like those of Venus and Titan. The model takes into account ablation (or mass shedding), pancaking, and fragmentation. Fragmentation is assumed to occur due to the hydrodynamic instabilities promoted by the impactors’ deceleration in the atmosphere. Fragments that survive to hit the ground make craters or groups thereof. Crater sizes are estimated using standard laws in the gravity regime, modified to take into account impactor disruption. We use Monte Carlo methods to pick parameters from appropriate distributions of impactor mass, zenith angle, and velocity. Good fits to the Venus crater populations (including multiple crater fields) can be found with reasonable values of model parameters. An important aspect of the model is that it reproduces the dearth of small craters on Venus: this is due to a cutoff on crater formation we impose, when the expected crater would be smaller than the (dispersed) object that would make it. Hydrodynamic effects alone (ablation, pancaking, fragmentation) due to the passage of impactors through the atmosphere are insufficient to explain the lack of small craters. In our favored model, the observed number of craters (940) is produced by ∼5500 impactors with masses , yielding an age of (1-σ uncertainty) for the venusian surface. This figure does not take into account any uncertainties in crater scaling and impactor population characteristics, which probably increase the uncertainty to a factor of two in age.We apply the model with the same parameter values to Titan to predict crater populations under differing assumptions of impactor populations that reflect present conditions. We assume that the impactors (comets) are made of 50% porous ice. Predicted crater production rates are ≈190 craters . The smallest craters on Titan are predicted to be in diameter, and ≈5 crater fields are expected. If the impactors are composed of solid ice (density ), crater production rates increase by ≈70% and the smallest crater is predicted to be in diameter. We give cratering rates for denser comets and atmospheres 0.1 and 10 times as thick as Titan's current atmosphere. We also explicitly address leading-trailing hemisphere asymmetries that might be seen if Titan's rotation rate were strictly synchronous over astronomical timescales: if that is the case, the ratio of crater production on the leading hemisphere to that on the trailing hemisphere is ≈4:1.