The librations, shape, and icy shell of Europa

Europa, the smallest of the Galilean satellites, has a young icy surface and most likely contains an internal ocean. The primary objective of possible future missions to Europa is the unambiguous detection and characterization of a subsurface ocean. The thickness of the overlying icy shell provides important information on the thermal evolution of the satellite and on the interaction between the ocean and the surface, the latter being fundamental for astrobiology. However, the thickness is not well known, and estimates range from several hundred of meters to some ten of kilometers. Here, we investigate the use of libration (rotation variation) observations to study the interior structure of Europa and in particular its icy shell. A dynamical libration model is developed, which includes gravitational coupling between the icy shell and the heavy solid interior. The amplitude of the main libration signal at 3.55 days (the orbital period) is shown to depend on Europa's shape and structure. Models of the interior structure of Europa are constructed and the equatorial flattening of the internal layers, which are key parameters for the libration, are calculated by assuming that Europa is in hydrostatic equilibrium. Europa's flattened shape is assumed to be due to rotation and permanent tides, and we extend the classical Radau equation for rotationally flattened bodies to include also tidal deformation. We show that the presence of an ocean increases the amplitude of libration by about 10%, depending mainly on the thickness of the icy shell. Therefore, libration observations offer possibility of detection of a subsurface ocean in Europa and estimation of the thickness of its overlying icy shell.     

A model for the temperature-dependence of tidal dissipation in convective plumes on icy satellites: Implications for Europa and Enceladus

To explain the formation of surface features on Europa, Enceladus, and other satellites, many authors have postulated the spatial localization of tidal heating within convective plumes. However, the concept that enhanced tidal heating can occur within a convective plume has not been rigorously tested. Most models of this phenomenon adopt a tidal heating with a temperature-dependence derived for an incompressible, homogeneous (zero-dimensional) Maxwell material, but it is unclear whether this formulation is relevant to the heterogeneous situation of a warm plume surrounded by cold ice. To determine whether concentrated dissipation can occur in convective plumes, we develop a two-dimensional model to compute the volumetric dissipation rate for an idealized, vertically oriented, isolated convective plume obeying a Maxwellian viscoelastic compressible rheology. We apply the model to the Europa and Enceladus ice shells, and we investigate the consequences for partial melting and resurfacing processes on these bodies. We find that the tidal heating is strongly temperature dependent in a convective ice plume and could produce elevated temperatures and local partial melting in the ice shells of Europa and Enceladus. Our calculation provides the first quantitative verification of the hypothesis by Sotin et al. [Sotin, C., Head, J.W., Tobie, G., 2002. Geophys. Res. Lett. 29. 74-1] and others that the tidal dissipation rate is a strong function of temperature inside a convective plume. On Europa, such localized heating could help allow the formation of domes and chaos terrains by convection. On Enceladus, localized tidal heating in a thermal plume could explain the concentrated activity at the south pole and its associated heat transport of 2-7 GW.     

Effects of plasticity on convection in an ice shell: Implications for Europa

Europa's surface exhibits numerous pits, uplifts, and disrupted chaos terrains that have been suggested to result from convection in the ice shell. To test this hypothesis, we present numerical simulations of convection in an ice shell including the effects of plasticity, which provides a simple continuum representation for brittle or semibrittle deformation along discrete fractures. Plastic deformation occurs when stresses reach a specified yield stress; at lower stresses, the fluid flow follows a Newtonian, temperature-dependent viscosity. Four distinct modes of behavior can occur. For yield stresses exceeding ∼1 bar, plastic effects are negligible and stagnant-lid convection, with no surface motion and minimal topography, results. At intermediate yield stresses, a stagnant lid forms but deforms plastically, leading to surface velocities up to several millimeters per year. Slightly smaller yield stresses allow episodic, catastrophic overturns of the upper conductive lid, with (transient) stagnant lids forming in between overturn events. The smallest yield stresses allow continual recycling of the upper lid, with simultaneous, gradual ascent of warm ice to the surface and descent of cold, near-surface ice into the interior. The exact yield stresses over which each regime occurs depend on the ice-shell thickness, melting-temperature viscosity, and activation energy for viscous creep. To form hummocky matrix and translate chaos plates by several kilometers, substantial surface strain must accompany chaos formation, and the three plasticity-dominated convection modes described here can provide such deformation. Our simulations suggest that, if yield stresses of ∼0.2-1 bar are relevant to Europa, then convection in Europa's ice shell can produce chaos-like structures at the surface. However, our simulations have difficulty explaining Europa's numerous pits and uplifts. When plasticity forces the upper lid to participate in the convection, dynamic topography of ∼50-100-m amplitude results, but the topographic structures generally have diameters of 30-100 km, an order of magnitude wider than typical pits and uplifts. None of our simulations produced isolated pits or uplifts of any diameter.     

The great thickness debate: Ice shell thickness models for Europa and comparisons with estimates based on flexure at ridges

Estimates of the thickness of the ice shell of Europa range from <1 to >30 km. The higher values are generally assumed to be estimates of the entire ice shell thickness, which may include a lower ductile layer of ice, whereas many of the smaller thickness estimates are based on analyses that only consider that portion of the ice layer that behaves elastically at a particular strain rate. One example of the latter is flexure analysis, in which the elastic ice layer is modeled as a plate or sphere that is flexed under the weight of a surface load. We present calculations based on flexure analysis in which we model the elastic ice layer as flexing under a line-load caused by ridges. We use precisely located, parallel flanking cracks as indicators of the location of greatest tensile stress induced by flexure. Our elastic thickness results are spatially variable: ∼500-2200 m (two sites) and ∼200-1000 m (one site). Thorough analysis of Europan flexure studies performed by various researchers shows that the type of model selected causes the greatest variability in the thickness results, followed by the choice of Young's modulus, which is poorly constrained for the Europan ice shell. Comparing our results to those of previously published flexure analyses for Europa, we infer spatial variability in the elastic ice thickness (at the time of load emplacement), with smooth bands having the thinnest elastic ice thickness of all areas studied. Because analysis of flexure-induced fracturing can only reveal the elastic thickness at the time of load emplacement, calculated thickness variability between features having different ages may also reflect a temporal variability in the thickness of Europa's ice shell.     

The evil twin of Agenor: tectonic convergence on Europa

The dilemma of the surface-area budget on Europa is resolved by identification of sites of crustal convergence, which have balanced the continual and common creation of new surface along dilational bands and pull-aparts. Convergence bands are characterized by a distinctive, albeit subdued, morphology. The prominent, unusual lineament Agenor is one of several examples. We also find diametrically opposite Agenor a similar bright linear feature surrounded by markings that allow reconstruction, which shows it to be a convergence feature. Until recently, identification of convergence sites was difficult because these features are subtle and do not exhibit structures (like the Himalayas or plate subduction) familiar from convergence of thick solid crusts on terrestrial planets.     

Segmented lineaments on Europa: Implications for the formation of ridge complexes and bright bands

We describe several segmented lineaments on Europa’s surface. These lineaments are extensive, stretching for 100s-1000s of km, and have ridge complex or bright band morphologies. The geometries of the segmented portions of these features are diagnostic of the remote normal and shear stress environment in which they formed and, therefore, constrain ridge complex and bright band formation mechanisms. Analysis of four ridge complexes indicates that they formed in a remote normal stress environment that was tensile and isotropic (or nearly so) and that these lineaments may have formed in a manner more analogous to bands on Europa than to ridges. The stress environment associated with these ridge complexes may also explain the anastomosing nature of their interior morphology. Analysis of two bright bands indicate that one formed in a remote normal stress environment that was tensile and the other was reactivated under a combination of remote tensile normal stress and remote sinistral shear stress. Aspects of the morphologies of these features also indicate that bright bands likely have complex deformation histories that can include multiple episodes of reactivation.     

Effects of low-viscous layers and a non-zero obliquity on surface stresses induced by diurnal tides and non-synchronous rotation: The case of Europa

In this study we present a semi-analytical Maxwell-viscoelastic model of the variable tidal stress field acting on Europa’s surface. In our analysis, we take into account surface stresses induced by the small eccentricity of Europa’s orbit, the non-zero obliquity of Europa’s spin axis - both acting on a diurnal 3.55-days timescale - and the reorientation of the ice shell as a result of non-synchronous rotation (NSR). We assume that Europa’s putative ocean is covered by an ice shell, which we subdivide in a low-viscous and warm lower ice layer (asthenosphere, viscosity 10¹²-10¹⁷ Pa s), and a high-viscous and cold upper ice layer (lithosphere, viscosity 10²¹ Pa s).Viscoelastic relaxation influences surface stresses in two ways: (1) through viscoelastic relaxation in the lithosphere and (2) through the viscoelastic tidal response of Europa’s interior. The amount of relaxation in the lithosphere is proportional to the ratio between the period of the forcing mechanism and the Maxwell time of the high-viscous lithosphere. As a result, this effect is only relevant to surface stresses caused by the slow NSR mechanism. On the other hand, the importance of the viscoelastic response on surface stresses is proportional to the ratio between the relaxation time (τ_j) of a given viscoelastic mode j and the period of the forcing function. On a diurnal timescale the fast relaxation of transient modes related to the low viscosity of the asthenosphere can alter the magnitude and phase shift of the diurnal stress field at Europa’s surface. The effects are largest, up to 20% in magnitude and 7° in phase for ice rigidities lower than 3.487 GPa, when the relaxation time of the aforementioned transient modes approaches the inverse of the average angular rate of Europa’s orbit. On timescales relevant for NSR (>10⁴ years) the magnitude and phase shift of NSR surface stresses can be affected by viscoelastic relaxation of the ocean-ice boundary. This effect, however, becomes only important when the behavior of the lithosphere w.r.t. NSR approaches the fluid limit, i.e. for strong relaxation in the lithosphere. The combination of NSR and diurnal stresses for different amounts of viscoelastic relaxation of NSR stresses in the lithosphere leads to a large variety of global stress fields that can explain the formation of the large diversity of lineament morphologies observed on Europa’s surface. Variation of the amount of relaxation in the lithosphere is likely due to changes in the spin rate of Europa and/or the rheological properties of the surface.In addition, we show that a small obliquity(<1°) can have a considerable effect on Europa’s diurnal stress field. A non-zero obliquity breaks the symmetric distribution of stress patterns with respect to the equator, thereby affecting the magnitude and orientation of the principal stresses at the surface. As expected, increasing the value of Europa’s obliquity leads to larger diurnal stresses at the surface, especially when Europa is located 90° away from the nodes formed by the intersection of its orbital and equatorial planes.     

The global shape of Europa: Constraints on lateral shell thickness variations

The global shape of Europa is controlled by tidal and rotational potentials and possibly by lateral variations in ice shell thickness. We use limb profiles from four Galileo images to determine the best-fit hydrostatic shape, yielding a mean radius of 1560.8±0.3 km and a radius difference a−c of 3.0±0.9 km, consistent with previous determinations and inferences from gravity observations. Adding long-wavelength topography due to proposed lateral variations in shell thickness results in poorer fits to the limb profiles. We conclude that lateral shell thickness variations and long-wavelength isostatically supported topographic variations do not exceed 7 and 0.7 km, respectively. For the range of rheologies investigated (basal viscosities from 10¹⁴ to ) the maximum permissible (conductive) shell thickness is 35 km. The relative uniformity of Europa's shell thickness is due to either a heat flux from the silicate interior, lateral ice flow at the base of the shell, or convection within the shell.     

The nature of Europa's dark non-ice surface material: Spatially-resolved high spectral resolution spectroscopy from the Keck telescope

We present new 1.45-1.75 μm spectra of Europa's dark non-ice material with a spectral resolution (λ/δλ) of 1200, obtained by using adaptive optics on the Keck telescope to spatially separate the spectrum of the non-ice material from that of the surrounding ice-rich regions. Despite the great increase in spectral resolution over the previous best spectra of the non-ice material, taken with Galileo's near-infrared mapping spectrometer (NIMS) with λ/δλ=66, no new fine-scale spectral structure is revealed. The smoothness of the spectra is inconsistent with available laboratory spectra of crystalline hydrated salts at Europa temperatures, but is more consistent with various combinations of non-crystalline hydrated salts and/or hydrated sulfuric acid, as have been matched to the lower-resolution NIMS spectra.     

Meteorological assessment of the surface temperatures on Titan: constraints on the surface type

The latitudinal profile of near-surface air temperature on Titan retrieved by Voyager 1 has been difficult to understand and raised several speculations about possible exotic processes that might be occurring near Titan's surface, while the thermal properties of the surface itself are unknown. This study systematically investigates the seasonal and spatial variation of the surface temperature and air temperature in the lower troposphere by a 3-dimensional general circulation model for different putative surface types (porous icy regolith, rock-ice mixture, hydrocarbon lakes). For any viable surface type the surface temperature is unlikely to be constant through the year and should more or less vary seasonally and even diurnally, most likely by a few K. Recent observations of tropospheric clouds may be evidence of seasonal variation of the surface temperature and the model predicts in the case of solid surface the development of a convective layer with superadiabatic lapse rates near the surface exactly at those latitudes and seasons where clouds have been identified. The latitudinal profile of the surface temperature retrieved from Voyager 1 infrared spectra can be explained without invoking exotic effects, provided the thermal inertia of the surface is relatively small and/or the surface albedo is low. A dominance of water ice (high thermal inertia and high albedo) at the surface is unfavorable to reproduce the observation. The latitudinal gradient of the surface temperature is particularly large at the hydrocarbon lake surface due to low albedo and small surface drag. Local anomalies of the surface albedo or surface thermal inertia are likely to cause substantial inhomogeneities of the surface temperature. Quasi-permanent accumulation of stratospheric haze at both poles would create a perennial equator-to-pole contrast of the surface temperature, but also a substantially lower global-mean surface temperature due to an enhanced anti-greenhouse effect in summer. The air temperature in the lower troposphere exhibits a tiny latitudinal gradient and a pole-to-pole gradient due to the presence of a pole-to-pole Hadley circulation, indicating that the temperature within the planetary boundary layer may exhibit a vertical profile characteristic of season, location and scenario. There may be a shallow near-surface inversion layer in cold seasons and a shallow convective layer in warm seasons.     

The effect of the internal structure of Mars on its seasonal loading deformations

Mars is continuously subjected to surface loading induced by seasonal mass changes in the atmosphere and ice caps due to the CO₂ sublimation and condensation process. It results in surface deformations and in time variations of gravity. Large wavelength annual and semi-annual variations of gravity (particularly zonal coefficients ΔJn) have been determined using present day geodetic satellite measurements. However loading deformations have been poorly studied for a planet like Mars. In this paper, we compute these deformations and their effect on spacecraft orbiting around Mars. Loading deformations of terrestrial planet are typically investigated assuming a spherical planet, radially symmetric. The mean radial structure of Mars is not well known. In particular the radius of the liquid or solid core remains not precisely determined. One may then wonder what is the effect of these uncertainties on loading deformations. Moreover, Mars presents a strong topography and probably large lateral variations of crustal thickness (relative to the Earth). The paper answer the questions of what is the effect of such lateral heterogeneities on surface deformations, and is the classical way to calculate loading deformation well adapted for a planet like Mars. In order to answer these questions we have investigated theoretically loading deformations of Mars-like planets. We first investigated classical load Love numbers. We show that for degrees inferior to 10, the load Love numbers mainly depend on the radius of the core and on its state, and that for degree greater than 10, they depend on the mean radius of mantle-crust interface. Using a General Circulation Model (GCM) of atmosphere and ice caps dynamics we show that loading vertical displacements have a 4-5 cm magnitude and present a North-South pattern with periodic transitions. Finally we investigated the effect of lateral variations of the crustal thickness on these loading deformations. We show that thickness heterogeneities perturb the deformations and the time variation of gravity at about 0.5%. However this perturbation on ΔJn is only about 1‰ due to main direct attraction of surface fluid layers. We conclude that lateral variations of crustal thickness are today negligible. However, observation of load Love numbers would bring information on the radial internal structure of the planet, particularly on the core radius. ΔJn study would permit to infer the load Love number , particularly for degree 2 and 3, knowing surface fluid layer dynamics. However load Love numbers are quite small (about 0.05), and despite the present good agreement between GCM and ΔJn observations, will only be estimated in the near future when a slightly better precision in observation and modeling will make it possible to infer these numbers. The investigation of load Love number , which are larger than numbers, would be particularly interesting. It would permit to study degree 1 contribution of atmosphere and ice caps dynamics, which is the most important component of surface fluid dynamics on Mars. Surface displacement measurements would be necessary on a few places near the pole regions, which may be possible in the future, with a project involving precise positioning of a lander on the surface of Mars.     

The phase dependence of brightness and color of the lunar surface: a study based on integral photometric data

A procedure of an a posteriori correction of the available data on the integral photometry of the Moon is described. This procedure reduces the regular errors of the integral phase curves caused by variations of the libration parameters; the effect due to libration can reach 4%. A method allowing the integral measurements of the Moon to be compared correctly with the photometric measurements of the lunar areas or laboratory samples imitating the lunar soil has been developed. To approximate the phase curves of integral albedo in the phase-angle range from 6° to 120°, we proposed a simple empirical formula A _eq(α) = m _l e ^?ρα + m ₂ e ^?0.7α, where α is the phase angle, ρ is the factor of effective roughness, and m ₁ + m ₂ is the surface albedo at a zero phase angle. An empirical phase dependence of the slope of the lunar spectrum in the 360–1060 nm range has been obtained. The results may be used to test various theoretical models of the light scattering by the lunar surface and to calibrate the data of ground-based and space-borne spectrophotometric observations.     

The 2dF Galaxy Redshift Survey: the dependence of galaxy clustering on luminosity and spectral type

We investigate the dependence of galaxy clustering on luminosity and spectral type using the 2dF Galaxy Redshift Survey (2dFGRS). Spectral types are assigned using the principal-component analysis of Madgwick et al. We divide the sample into two broad spectral classes: galaxies with strong emission lines ('late types') and more quiescent galaxies ('early types'). We measure the clustering in real space, free from any distortion of the clustering pattern owing to peculiar velocities, for a series of volume-limited samples. The projected correlation functions of both spectral types are well described by a power law for transverse separations in the range  2<( σ / h ^-1 Mpc)<15  , with a marginally steeper slope for early types than late types. Both early and late types have approximately the same dependence of clustering strength on luminosity, with the clustering amplitude increasing by a factor of ∼2.5 between L * and 4 L *. At all luminosities, however, the correlation function amplitude for the early types is ∼50 per cent higher than that of the late types. These results support the view that luminosity, and not type, is the dominant factor in determining how the clustering strength of the whole galaxy population varies with luminosity.     

The 3D skeleton: tracing the filamentary structure of the Universe

The skeleton formalism, which aims at extracting and quantifying the filamentary structure of our Universe, is generalized to 3D density fields. A numerical method for computing a local approximation of the skeleton is presented and validated here on Gaussian random fields. It involves solving equation     , where  ∇ρ  and     are the gradient and Hessian matrix of the field. This method traces well the filamentary structure in 3D fields such as those produced by numerical simulations of the dark matter distribution on large scales, and is insensitive to monotonic biasing.
Two of its characteristics, namely its length and differential length, are analysed for Gaussian random fields. Its differential length per unit normalized density contrast scales like the probability distribution function of the underlying density contrast times the total length times a quadratic Edgeworth correction involving the square of the spectral parameter. The total length-scales like the inverse square smoothing length, with a scaling factor given by  0.21 (5.28 + n )  where n is the power index of the underlying field. This dependency implies that the total length can be used to constrain the shape of the underlying power spectrum, hence the cosmology.
Possible applications of the skeleton to galaxy formation and cosmology are discussed. As an illustration, the orientation of the spin of dark haloes and the orientation of the flow near the skeleton is computed for cosmological dark matter simulations. The flow is laminar along the filaments, while spins of dark haloes within 500 kpc of the skeleton are preferentially orthogonal to the direction of the flow at a level of 25 per cent.     

The structure of the Galactic halo: SDSS versus SuperCOSMOS

The halo structure at high Galactic latitudes near both the north and south poles is studied using Sloan Digital Sky Survey (SDSS) and SuperCOSMOS data. For the south cap halo, the archive of the SuperCOSMOS photographic photometry sky survey is used. The coincident source rate between SuperCOSMOS data in B _J band from 16.5 to 20.5 mag and SDSS data is about 92 per cent, in a common sky area in the south. While that in the R _F band is about 85 per cent from 16.5 to 19.5 mag. Transformed to the SuperCOSMOS system and downgraded to the limiting magnitudes of SuperCOSMOS, the star counts in the North Galactic Cap from SDSS show up to an  16.9 ± 6.3  per cent  asymmetric ratio (defined as relative fluctuations over the rotational symmetry structure) in the B _J band, and up to  13.5 ± 6.7  per cent  asymmetric ratio in the R _F band. From SuperCOSMOS B _J and R _F bands, the structure of the Southern Galactic hemisphere does not show the same obvious asymmetric structures as the northern sky does in both the original and downgraded SDSS star counts. An axisymmetric halo model with n = 2.8 and q = 0.7 can fit the projected number density from SuperCOSMOS fairly well, with an average error of about 9.17 per cent. By careful analysis of the difference of star counts between the downgraded SDSS northern halo data and SuperCOSMOS southern halo data, it is shown that no asymmetry can be detected in the South Galactic Cap at the accuracy of SuperCOSMOS, and the Virgo overdensity is likely a foreign component in the Galactic halo.