Connecting atmospheric science and atmospheric models for aerocapture at Titan and the outer planets

Many atmospheric measurement systems, such as the sounding instruments on Voyager, gather atmospheric information in the form of temperature versus pressure level. In these terms, there is considerable consistency among the mean atmospheric profiles of the outer planets Jupiter through Neptune, including Titan. On a given planet or on Titan, the range of variability of temperature versus pressure level due to seasonal, latitudinal, and diurnal variations is also not large. However, many engineering needs for atmospheric models relate not to temperature versus pressure level but atmospheric density versus geometric altitude. This need is especially true for design and analysis of aerocapture systems. Drag force available for aerocapture is directly proportional to atmospheric density. Available aerocapture “corridor width” (allowable range of atmospheric entry angle) also depends on height rate of change of atmospheric density, as characterized by density scale height. Characteristics of hydrostatics and the gas law equation mean that relatively small systematic differences in temperature versus pressure profiles can integrate at high altitudes to very large differences in density versus altitude profiles. Thus, a given periapsis density required to accomplish successful aerocapture can occur at substantially different altitudes (∼150-300 km) on the various outer planets, and significantly different density scale heights (∼20-50 km) can occur at these periapsis altitudes. This paper will illustrate these effects and discuss implications for improvements in atmospheric measurements to yield significant impact on design of aerocapture systems for future missions to Titan and the outer planets. Relatively small-scale atmospheric perturbations, such as gravity waves, tides, and other atmospheric variations can also have significant effect on design details for aerocapture guidance and control systems. This paper will discuss benefits that would result from improved understanding of Titan and outer planetary atmospheric perturbation characteristics. Details of recent engineering-level atmospheric models for Titan and Neptune will be presented, and effects of present and future levels of atmospheric uncertainty and variability characteristics will be examined.     

The dust environment at Titan

To explain the observed abundances of CO₂ in Titan's atmosphere, a relatively high water deposition into the atmosphere needs to be invoked due to the importance of H₂O photolysis in CO₂ production. A likely source of H₂O is icy dust particles from space. This paper considers the direct dust input to Titan's atmosphere from the interplanetary environment, and also ejecta particles from micrometeoroid impacts with the icy satellites Hyperion, Iapetus and Phoebe. It is found that the likely mass influx to Titan is 10^–16 to 10^–15 kg m^–2 s^–1. This mass influx is an order of magnitude too low to explain the observed levels of CO₂ in Titan's atmosphere in the context of a recent photochemical model. This leads one to speculate as to the likelihood of one large impact to Titan in the recent past;i.e., that the atmosphere is not in equilibrium but is cnrrently losing CO₂.     

Long-term atmospheric variability on Uranus and Neptune

Long-term photometric measurements of Uranus and Neptune through 2005 show variations in brightness. For Uranus, much of the variation can be interpreted as seasonal, i.e., caused by viewing angle changes of an oblate planet. The photometry suggests that if seasonal variations on Uranus are north-south symmetric, then the northern pole should begin to brighten in 2006. However, seasonal “aspect” changes cannot explain all the variation; the Uranus observations require intrinsic atmospheric change. Furthermore, Uranus observations spanning many scale heights in the atmosphere may show similar change. For Neptune, variations in sub-solar latitude may explain the general shape of the long-term light curve, but significant deviations occur that have no explanation at present. Observations are needed over a longer temporal baseline than currently exists to fully characterize both atmospheres.     

The haze and methane distributions on Neptune from HST-STIS spectroscopy

We analyzed a data cube of Neptune acquired with the Hubble STIS spectrograph on August 3, 2003. The data covered the full afternoon hemisphere at 0.1 arcsec spatial resolution between 300 and 1000 nm wavelength at 1 nm resolution. Navigation was accurate to 0.004 arcsec and 0.05 nm. We constrained the vertical aerosol structure with radiative transfer calculations. Ultraviolet data confirmed the presence of a stratospheric haze of optical depth 0.04 at 370 nm wavelength. Bright, discrete clouds, most abundant near latitudes −40° and 30°, had their top near the tropopause. They covered 1.7% of the observed disk if they were optically thick. The methane abundance above the cloud tops was 0.0026 and 0.0017 km-am for southern and northern clouds, respectively, identical to earlier observations by Sromovsky et al. (Sromovsky, L.A., Fry, P.M., Dowling, T.E., Baines, K.H., Limaye, S.S., [2001b]. Icarus 149, 459-488). Aside from these clouds, the upper troposphere was essentially clear. Below the 1.4-bar layer, a vertically uniform haze extended at least down to 10 bars with optical depth of 0.10-0.16/bar, depending on the latitude. Haze particles were bright at wavelengths above 600 nm, but darkened toward the ultraviolet, at the equator more so than at mid and high latitudes. A dark band near −60° latitude was caused by a 0.01 decrease of the single scattering albedo in the visible, which was close to unity. A comparison of methane and hydrogen absorptions contradicted the current view that methane is uniformly mixed in latitude and altitude below the ∼1.5-bar layer. The 0.04 ± 0.01 methane mixing ratio is only uniform at low latitudes. At high southern latitudes, it is depressed roughly between the 1.2 and 3.3-bar layers compared to low-latitude values. The maximum depression factor is ∼2.7 at 1.8 bars. We present models with 2° latitude sampling across the full sunlit globe that fit the observed reflectivities to 2.8% rms.     

Accurate and approximate calculations of Raman scattering in the atmosphere of Neptune

Raman scattering by H₂ in Neptune's atmosphere has significant effects on its reflectivity for λ<0.5 μm, producing baseline decreases of ∼20% in a clear atmosphere and ∼10% in a hazy atmosphere. However, few accurate Raman calculations are carried out because of their complexity and computational costs. Here we present the first radiation transfer algorithm that includes both polarization and Raman scattering and facilitates computation of spatially resolved spectra. New calculations show that Cochran and Trafton's (1978, Astrophys. J. 219, 756-762) suggestion that light reflected in the deep CH₄ bands is mainly Raman scattered is not valid for current estimates of the CH₄ vertical distribution, which implies only a 4% Raman contribution. Comparisons with IUE, HST, and groundbased observations confirm that high altitude haze absorption is reducing Neptune's geometric albedo by ∼6% in the 0.22-0.26 μm range and by ∼13% in the 0.35-0.45 μm range. A sample haze model with 0.2 optical depths of 0.2-μm radius particles between 0.1 and 0.8 bars fits reasonably well, but is not a unique solution. We used accurate calculations to evaluate several approximations of Raman scattering. The Karkoschka (1994, Icarus 111, 174-192) method of applying Raman corrections to calculated spectra and removing Raman effects from observed spectra is shown to have limited applicability and to undercorrect the depths of weak CH₄ absorption bands. The relatively large Q-branch contribution observed by Karkoschka is shown to be consistent with current estimates of Raman cross-sections. The Wallace (1972, Astrophys. J. 176, 249-257) approximation, produces geometric albedo ∼5% low as originally proposed, but can be made much more accurate by including a scattering contribution from the vibrational transition. The original Pollack et al. (1986, Icarus 65, 442-466) approximation is inaccurate and unstable, but can be greatly improved by several simple modifications. A new approximation based on spectral tuning of the effective molecular single scattering albedo provides low errors for zenith angles below 70° in a clear atmosphere, although intermediate clouds present problems at longer wavelengths.     

Uranus and Neptune interior models

This paper is concerned with the interior structure of Uranus and Neptune. Our approach is three-fold. First, a set of three-layer models for both Uranus and Neptune are constructed using a method similar to that used in the study of the terrestrial planets. The variations of the mass density (s) and flattening e(s) with fractional mean radius s for two representative models of Uranus and Neptune are calculated. The results are tabulated. A comparison of these models shows that these two planets are probably very similar to each other in their basic dynamical features. Such similarity is very seldom seen in our solar system. Secondly, we check the conformance between the theoretical results and observational data for the two planets. And thirdly, the 6th degree Stokes zonal parameters for Uranus and for Neptune are predicted, based on the interior models put forward in this paper.     

Uranus and Neptune: Shape and rotation

Both Uranus and Neptune are thought to have strong zonal winds with velocities of several 100 m s⁻¹. These wind velocities, however, assume solid-body rotation periods based on Voyager 2 measurements of periodic variations in the planets’ radio signals and of fits to the planets’ magnetic fields; 17.24 h and 16.11 h for Uranus and Neptune, respectively. The realization that the radio period of Saturn does not represent the planet’s deep interior rotation and the complexity of the magnetic fields of Uranus and Neptune raise the possibility that the Voyager 2 radio and magnetic periods might not represent the deep interior rotation periods of the ice giants. Moreover, if there is deep differential rotation within Uranus and Neptune no single solid-body rotation period could characterize the bulk rotation of the planets. We use wind and shape data to investigate the rotation of Uranus and Neptune. The shapes (flattening) of the ice giants are not measured, but only inferred from atmospheric wind speeds and radio occultation measurements at a single latitude. The inferred oblateness values of Uranus and Neptune do not correspond to bodies rotating with the Voyager rotation periods. Minimization of wind velocities or dynamic heights of the 1 bar isosurfaces, constrained by the single occultation radii and gravitational coefficients of the planets, leads to solid-body rotation periods of ∼16.58 h for Uranus and ∼17.46 h for Neptune. Uranus might be rotating faster and Neptune slower than Voyager rotation speeds. We derive shapes for the planets based on these rotation rates. Wind velocities with respect to these rotation periods are essentially identical on Uranus and Neptune and wind speeds are slower than previously thought. Alternatively, if we interpret wind measurements in terms of differential rotation on cylinders there are essentially no residual atmospheric winds.     

The altitude of Neptune cloud features from high-spatial-resolution near-infrared spectra

We report on observations of Neptune from the 10-meter W.M. Keck II Telescope on June 17-18 (UT) 2000 and August 2-3 (UT) 2002 using the adaptive optics (AO) system to obtain a spatial resolution of 0.06 arcseconds. With this spatial resolution we can obtain spectra of individual bright features on the disk of Neptune in a filter centered near 2 microns. The use of a gas-only, simple reflecting layer radiative transfer model allows us to estimate the best fit altitudes of 18 bright features seen on these 4 nights and to set a constraint on the fraction of hydrogen in ortho/para equilibrium. On these nights there were three main types of features observed: northern hemisphere features in the range from +30 to −45 degrees; southern hemisphere features in the range from −30 to −50 degrees; and small southern features at −70 degrees. We find that the altitudes of the northern features are in the range from 0.023-0.064 bar, which places them in Neptune's stratosphere. Southern features at −30 to −50 degrees are mainly at altitudes from 0.10 to 0.14 bars. The small features at −70 degrees are somewhat deeper in the upper troposphere, at 0.17 and 0.27 bars. This pattern of features located at higher altitudes in the northern hemisphere and lower altitudes in the south has also been noted by previous observers. The best fits for all the observed spectra give a value of 1.0 for the fraction of hydrogen in ortho/para equilibrium; the value of the helium fraction is less well constrained by the data at 0.24. We suggest that the southern mid-latitude features are methane haze circulated up from below, while the −70° features may be isolated areas of upwelling in a general area of subsidence. Northern bright features may be due to subsidence of stratospheric haze material rather than upwelling and condensation of methane gas. We suggest that convection efficiently transports methane ice clouds to the tropopause in the Southern mid latitudes and thus plays a key role in the stratospheric haze production cycle.     

Detecting the signatures of Uranus and Neptune

With more than 15 years since the first radial velocity discovery of a planet orbiting a Sun-like star, the time baseline for radial velocity surveys is now extending out beyond the orbit of Jupiter analogs. The sensitivity to exoplanet orbital periods beyond that of Saturn orbital radii however is still beyond our reach such that very few clues regarding the prevalence of ice giants orbiting solar analogs are available to us. Here we simulate the radial velocity, transit, and photometric phase amplitude signatures of the Solar System giant planets, in particular Uranus and Neptune, and assess their detectability. We scale these results for application to monitoring low-mass stars and compare the relative detection prospects with other potential methods, such as astrometry and imaging. These results quantitatively show how many of the existing techniques are suitable for the detection of ice giants beyond the snow line for late-type stars and the challenges that lie ahead for the detection true Uranus/Neptune analogs around solar-type stars.     

Titan haze distribution and optical properties retrieved from recent observations

The VIMS instrument onboard Cassini observed the north polar region of Titan at 113° phase angle, 28 December 2006. On this spectral image, a vast polar cloud can be seen northward to 62°N, and elsewhere, the haze appears as the dominant source of scattering. Because the surface does not appear in the wavelength range between 0.3 and , this spectro-image is ideal to study airborn scatterers both in methane bands and windows. In this work, we study this image, along with another image taken at 13° phase angle. This image probe both the atmosphere and the surface from pole to pole. First, we characterise the spatial distribution of the haze layer above 100 km between 80°S and 70°N. We find a north south asymmetry with a haze opacity increasing by a factor 3 from the south pole to the equator, then a constant value up to about 30°N and a decrease of a factor 2 between 30°N and about 60°N. Beyond 60°N, we can see the influence of the north polar cloud, even in the band, but no polar haze accumulation. The fact that the north polar region is still in the polar night is a possible explanation. No haze accumulation is observed in the southern polar region. Secondly, we partly identify the origin of spectral features in the 2.8-μm methane window, which are found to be due to deuterated methane (CH₃D). This allows the analyse of this window and to retrieve the opacity of scatterers layer below 80 km (presumably made of aerosols and condensate droplets) between 35°N and 60°N. Finally, we constrained the values and the spectral behaviour of the imaginary part of the aerosol refractive index in the range between 0.3 and . To do so, we studied the 2.8-μm window with the image taken at 113° phase angle. To complete the analysis, we studied the transmission through the haze layer in the 3.4-μm band observed in solar occultation mode with VIMS, and we analysed the single scattering albedo retrieved with DISR instrument between 0.4 and . The imaginary part of the refractive index that we find for Titan aerosols follows Khare et al. (Khare, B.N. et al. [1984]. Icarus 60, 127-137) optical constant up to and becomes constant beyond this wavelength at least up to . It also has a prominent peak at and a secondary peak at , which indicates material rich in C-H bonds, with much less N-H bonds than in Khare et al. (1984) tholins.     

Sizes, shapes, and albedos of the inner satellites of Neptune

Based on 87 resolved Voyager images of the five innermost satellites of Neptune, their shapes were measured and fit by tri-axial ellipsoids with the semi-axes of 48 × 30 × 26 km for Naiad, 54 × 50 × 26 km for Thalassa, 90 × 74 × 64 km for Despina, 102 × 92 × 72 km for Galatea, and 108 × 102 × 84 km for Larissa. Thomas and Veverka published a similar shape for Larissa (104 × 89 km, J. Geophys. Res. 96, 19261-19268, 1991). The other satellites had no published shapes. Using Voyager photometry of the six inner satellites by the same authors and the revised sizes, including the published size of Proteus, the reflectivity within this inner system was found to vary by about 30%. Geometric albedos in the visible are estimated between 0.07 for Naiad and 0.10 for Proteus. The rotational lightcurves of these satellites seem to be due to satellite shapes.     

Determining Titan surface topography from Cassini SAR data

A technique, referred to as SARTopo, has been developed for obtaining surface height estimates with 10 km horizontal resolution and 75 m vertical resolution of the surface of Titan along each Cassini Synthetic Aperture Radar (SAR) swath. We describe the technique and present maps of the co-located data sets. A global map and regional maps of Xanadu and the northern hemisphere hydrocarbon lakes district are included in the results. A strength of the technique is that it provides topographic information co-located with SAR imagery. Having a topographic context vastly improves the interpretability of the SAR imagery and is essential for understanding Titan.SARTopo is capable of estimating surface heights for most of the SAR-imaged surface of Titan. Currently nearly 30% of the surface is within 100 km of a SARTopo height profile. Other competing techniques provide orders of magnitude less coverage.We validate the SARTopo technique through comparison with known geomorphological features such as mountain ranges and craters, and by comparison with co-located nadir altimetry, including a 3000 km strip that had been observed by SAR a month earlier. In this area, the SARTopo and nadir altimetry data sets are co-located tightly (within 5-10 km for one 500 km section), have similar resolution, and as expected agree closely in surface height. Furthermore the region contains prominent high spatial resolution topography, so it provides an excellent test of the resolution and precision of both techniques.     

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.     

Photometric variability of Uranus and Neptune, 1950-2004

Photoelectric intermediate-band b and y photometry of Uranus and Neptune obtained at each apparition since 1972, combined with broadband B and V photometry from 1950 to 1966, provide a record of planetary variability covering 2/3 of Uranus' 84-year orbital period and 1/3 of Neptune's 165-year orbital period. Almost all of the data were obtained with a dedicated 21-inch photometric telescope at Lowell Observatory. The data are quite homogeneous, with yearly uncertainties typically smaller than 0.01 mag (1%). The lightcurve of Uranus is sinusoidal with peaks at the solstices. The b amplitude slightly exceeds the expected 0.025 mag purely geometrical variation caused by oblateness as the planetary aspect changes, seen from Earth. The y amplitude is several times larger, indicating a strong equator-to-pole albedo gradient. The lightcurve is asymmetrical with respect to southern solstice, evidence of a temporal albedo variation. Neptune's post-1972 lightcurve exhibits a generally rising trend since 1972 interpreted by Sromovsky et al. [Sromovsky, L.A., Fry, P.M., Limaye, S.S., Baines, K.H., 2003. Icarus 163, 256-261] as a lagged sinusoidal seasonal variation. However, the 1950-1966 lightcurve segments are much fainter than expected, missing the proposed seasonal sinusoid by 0.1-0.2 mag. A major unknown component is therefore needed to explain Neptune's long-term variation. The apparent relationship between Neptune's brightness variation and the 11-year solar cycle seen in cycles 21-22 (1972-1996) has apparently now faded away. Further interpretation of the data in this paper will be found in a companion paper by Hammel and Lockwood [Hammel, H.B., Lockwood, G.W., 2005. Icarus. Submitted for publication].     

冥族小天体与海王星特洛伊的近密交会

海王星外天体中的冥族小天体与海王星成2:3的平运动轨道共振,且具有较大的轨道偏心率,因此它们能与海王星特洛伊的轨道发生重叠,导致近密交会和碰撞,从而深刻地影响两者的动力学演化。利用数值模拟的方法,有效地获得了这两群小天体间近密交会的信息,讨论了可能影响两者近密交会频率的因素,包括小天体质量、轨道倾角和轨道偏心率等。在合理近似条件下,建立了估算两群小天体近密交会和碰撞次数的理论公式。结合已有的数值模拟结果,以及对冥族小天体观测数据的分析,对实际情况下冥族小天体群与典型特洛伊小天体之间的近密交会和碰撞次数进行了估算,证明近密交会较为频繁地发生,而碰撞则极其罕见,并且各尺寸范围的小天体对近密交会和碰撞次数的贡献各有不同。这一套分析和估算的方法可以直接应用在其他类似小天体间交会过程的估算上。     

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.     

Results from the Huygens probe on Titan

The Cassini–Huygens mission, comprising the NASA Saturn Orbiter and the ESA Huygens Probe, arrived at Saturn in late June 2004. The Huygens probe descended under parachute in Titan’s atmosphere on 14 January 2005, 3 weeks after separation from the Orbiter. We discuss here the breakthroughs that the Huygens probe, in conjunction with the Cassini spacecraft, brought to Titan science. We review the achievements ESA’s Huygens probe put forward and the context in which it operated. The findings include new localized information on several aspects of Titan science: the atmospheric structure and chemical composition; the aerosols distribution and content; the surface morphology and composition at the probe’s landing site; the winds, the electrical properties, and the implications on the origin and evolution of the satellite.     

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.     

The phase diagram of water and the magnetic fields of Uranus and Neptune

The interior of giant planets can give valuable information on formation and evolution processes of planetary systems. However, the interior and evolution of Uranus and Neptune is still largely unknown. In this paper, we compare water-rich three-layer structure models of these planets with predictions of shell structures derived from magnetic field models. Uranus and Neptune have unusual non-dipolar magnetic fields contrary to that of the Earth. Extensive three-dimensional simulations of Stanley and Bloxham (Stanley, S., Bloxham, J. [2004]. Nature 428, 151-153) have indicated that such a magnetic field is generated in a rather thin shell of at most 0.3 planetary radii located below the H/He rich outer envelope and a conducting core that is fluid but stably stratified. Interior models rely on equation of state data for the planetary materials which have usually considerable uncertainties in the high-pressure domain. We present interior models for Uranus and Neptune that are based on ab initio equation of state data for hydrogen, helium, and water as the representative of all heavier elements or ices. Based on a detailed high-pressure phase diagram of water we can specify the region where superionic water should occur in the inner envelope. This superionic region correlates well with the location of the stably-stratified region as found in the dynamo models. Hence we suggest a significant impact of the phase diagram of water on the generation of the magnetic fields in Uranus and Neptune.     

Forced obliquity and moments of inertia of Titan

The obliquity of Titan is small, but certainly non-zero, and may be used to place constraints on Titan's internal structure. The measured gravity coefficients of Titan imply that it is non-hydrostatic and thus the normal Darwin-Radau approach to determining internal structure cannot be applied. However, if the obliquity is assumed to be tidally damped (that is, in a Cassini state) then combining the obliquity with the measured gravity coefficients allows Titan's moment of inertia to be determined without invoking hydrostatic equilibrium. For polar moment values in the range (0.3<C/MR²<0.4), tidally-damped obliquity values of (0.115°<|ε|<0.177°) result. If the inferred moment value exceeds 0.4, this strongly suggests the presence of a near-surface ice shell decoupled from the interior, probably by a subsurface ocean.