Model Estimates of Non-Hydrostatic Stresses in the Martian Crust and Mantle: 1—Two-Level Model

Regions of maximum shear and tension–compression stresses in the Martian interior have been revealed using two types of models: the elastic model and the model with an elastic lithosphere of varied thickness (150–500 km) positioned on a weak layer that has partially lost its elastic properties. The weakening is simulated by a ten-fold lower value of the shear modulus down to the core boundary. The numerical simulation applies Green’s functions (load number method) with the step of 1 × 1 grade along latitude and longitude down to a depth of 1000 km. The boundary condition is the expansion of the latest data on Martian topography and the gravitational field (model MRO120D) in spherical harmonics up to the degree and order of 90 in relation to the reference surface that is assumed an equilibrium spheroid. The considered two-level compensation model assumes nonequilibrium relief and density anomalies at the crust–mantle boundary to be the sources of the anomalous gravitational field. Calculations are performed for two test models of Martian internal structure with the crust mean thicknesses of 50 to 100 km and mean density of 2900 kg/m³. Considerable tangential and simultaneously compressive stresses occur under the Tharsis region. The main regions of high shear and simultaneously extentional stresses are located in the Hellas region crust and in the lithosphere of the following regions: Argyre Planitia, Mare Acidalium, Arcadia Planitia and Valles Marineris. The zone of high maximum shear and extentional stresses has been found at the base of the lithosphere under the Olympus volcano and that under the Elysium rise.     

Rayleigh-Taylor instability as a mechanism for corona formation on Venus

In this study we explore the idea that coronae have formed on Venus as a result of gravitational (Rayleigh-Taylor) instability of the lithosphere. The lithosphere is represented by a system of stratified homogeneous viscous layers (low-density crust over high density mantle, over lower density layer beneath the lithosphere). A small harmonic perturbation imposed on the base of the lithosphere is observed to result in gravitational instability under the constraint of assumed axisymmetry. Topography develops with time under the influence of dynamic stress associated with downwelling or upwelling, and spatially variable crustal thickening or thinning. Topography may therefore be elevated or depressed above a mantle downwelling, but the computed gravity anomaly is always negative above a mantle downwelling in a homogeneous asthenosphere. The ratio of peak gravity to topography anomaly depends primarily on the ratio of crust to lithospheric viscosity. Average observed ratios are well resolved for two groups of coronae (∼40 mgal km⁻¹), consistent with models in which the crust is perhaps 5 times stronger than the lithosphere. Group 3a (rim surrounding elevated central region) coronae are inferred to arise from a central upwelling model, whereas Group 8 (depression) coronae are inferred to arise from central downwelling. Observed average coronae radii are consistent with a lithospheric thickness of only 50 km. An upper low-density crustal layer is 10-20 km thick, as inferred from the amplitude of gravity and topography anomalies.     

Dynamic topography of the East European craton: Shedding light upon lithospheric structure, composition and mantle dynamics

Most of the East European Craton lacks surface relief; however, the amplitude of topography at the top of the basement exceeds 20 km, the amplitude of topography undulations at the crustal base reaches almost 30 km with an amazing amplitude of ca. 50 km in variation in the thickness of the crystalline crust, and the amplitude of topography variations at the lithosphere–asthenosphere boundary exceeds 200 km. This paper examines the relative contributions of the crust, the subcrustal lithosphere, and the dynamic support of the sublithospheric mantle to maintain surface topography, using regional seismic data on the structure of the crystalline crust and the sedimentary cover, and thermal and large-scale P- and S-wave seismic tomography data on the structure of the lithospheric mantle. For the Precambrian lithosphere, an analysis of Vp/Vs ratio at 100, 150, 200, and 250 km depths does not show any age-dependence, suggesting that while Vp/Vs ratio can be effectively used to outline the cratonic margins, it is not sensitive to compositional variations within the cratonic lithosphere.Statistical analysis of age-dependence of velocity, density, and thermal structure of the continental crust and subcrustal lithosphere in the study area (0–62E, 45–72N) allows to link lithospheric structure with the tectonic evolution of the region since the Archean. Crustal thickness decreases systematically with age from 42–44 km in regions older than 1.6 Ga to 37–40 km in the Paleozoic–Mesoproterozoic structures, and to ca. 31 km in the Meso-Cenozoic regions. However, the isostatic contribution of the crust to the surface topography of the East European Craton is almost independent of age (ca. 4.5 km) due to an interplay of age-dependent crustal and sedimentary thicknesses and lithospheric temperatures.On the contrary, the contribution of the subcrustal lithosphere to the surface topography strongly depends on the age, being slightly positive (+ 0.3 + 0.7 km) for the regions older than 1.6 Ga and negative (− 0.5–1 km) for younger structures. This leads to age-dependent variations in the residual topography, i.e. the topography which cannot be explained by the assumed thermal and density structure of the lithosphere, and which can (at least partly) originate from the dynamic component caused by the mantle flow. Positive dynamic topography at the cratonic margins, which exceeds 2 km in the Norwegian Caledonides and in the Urals, clearly links their on-going uplift with deep mantle processes. Negative residual topography beneath the Archean-Paleoproterozoic cratons (− 1–2 km) indicates either a smaller density deficit (ca. 0.9%) in their subcrustal lithosphere than predicted by global petrologic data on mantle-derived xenoliths or the presence of a strong convective downwelling in the mantle. Such mantle downflows can effectively divert heat from the lithospheric base, leading to a long-term survival of the Archean-Paleoproterozoic lithosphere.     

Measurements of the elastic thickness under ancient lunar terrain

The part of a planet's gravity that is coherent with its topography provides information about the deflection of its crust after loading, and hence the resistance of its lithosphere to bending at the time the load was emplaced. We used observed line of sight accelerations from Lunar Prospector, together with the accelerations we would have expected if anomalies in the gravity field were only caused by topography, to estimate the admittance and coherence between topography and gravity over several regions of the lunar nearside. We then compared our estimates to what we would expect if the lithosphere behaved as a floating elastic plate or shell, assuming a linear relationship between topography and gravity. We found in the region surrounding the southern highland crater Clavius that the data can be modeled using a thin plate with Te=12±5 km and uncorrelated loads at the surface and base of the upper crust. A spherical shell model with surface loading is less satisfactory: to fit the admittance adequately requires topography with wavelengths over 400 km to be formed when Te≈ 1 km and the remainder when Te≈7.5 km. By contrast, the apparent lack of compensation around the youngest giant impact basins requires a plate with Te>80 km or a shell with Te>25 km. Our results indicate the thickness of the lunar lithosphere increased from ≈12 km in the pre-Nectarian to >25 km in the Nectarian.     

Geophysical implications of the Martian Gravity Field

The undulations of the Martian gravitational potential indicate lateral density variations in the Mars interior. A gravitating and solid Martian model deforms under the influence of these variations, producing stress differences of about 125 bars at a depth of about 200 km. Introduction of a partially molten core of 1300 km radius does not affect the stress distribution in the mantle significantly, whereas the assumption of a partially molten asthenosphere umderlying a solid lithosphere of about 300 km increases the stress differences appreciably. A strong linear correlation of the gravitational potential and the surface topography indicates that the extensive volcanism at the Tharsis region is a recent phenomenon. The high stresses associated with this region imply that there has been no extensive molten region within the upper 300 km since the volcanism.     

Strength of Faults on Mars from MOLA Topography

The stresses which must be maintained on faults bounding the rift topography at Tempe Fossae—the “North Tempe Rift” (NTR)—and Valles Marineris (VM) on Mars are estimated, using a simple elastic model and topographic data from the Mars Orbiter Laser Altimeter (MOLA). The absence of rift-flank uplift at the NTR is consistent with an elastic thickness, T_e, of 20 km or greater at the time of rift formation. The maximum resolved shear stresses on bounding faults due to this topography do not therefore exceed 20 MPa, similar to the inferred strength of terrestrial faults. Elastic thickness estimates at VM are mostly around 50 km or greater. Therefore, for canyon widths of ∼400 km, the bounding faults of VM, if present, must be able to withstand stresses of up to approximately 100 MPa. However, if the fault-controlled sections of the canyons do not exceed 150 km in width, as suggested by geomorphological analysis, the fault strength required is only 20 MPa. Although the maximum resolved shear stresses required to support the topography at VM may need to be greater than the stresses which terrestrial faults can support, at least some faults on Mars are no stronger than similar features on Earth. This observation is consistent with the existence of liquid water in the shallow subsurface of Mars at the time the faults were active. On Venus, plate tectonics is probably prevented by the frictional resistance to motion across strong faults. On Mars, it is more likely that the large thickness of the elastic layer of the lithosphere and the possible positive buoyancy of the crust are responsible for the observed lack of plate tectonics.     

Lineament Analysis and Geophysical Modelling of the Alba Patera Region on Mars

Global data sets of images, topography and gravity are available for Mars from several orbiter missions. At the eve of new global data from Mars Global Surveyor (MGS), the capabilities of 3D geophysical modelling based on areal topography and gravity data combined with geologic-tectonic image interpretation is demonstrated here. A unique structure is chosen for the model calculations: the Alba Patera volcanic complex at the northern border of the Tharsis rise. Five groups of graben are discriminated: Ceraunius Fossae, Catenae, Tantalus Fossae (radial group) radial to the Tharsis rise, mainly associated to the formation of Tharsis, and Alba and Tantalus Fossae (circular group), younger than the other graben and circular around Alba Patera. Combining 3D elastic flexure of the lithosphere due to a 3D topographic surface load with 3D gravity models results in a rather thick lithosphere (150–200 km) and thick crust (60–100 km). In another model estimate it has been assumed that the circular grabens are induced by the stresses from the surface load of Alba Patera. In a first order calculation the surface stresses under a point load have been determined resulting in a good correlation of the stress maximum with the location of the circular grabens for a 50-km thick lithosphere. This is in accordance with earlier results from this method, but in contradiction with the thick lithosphere derived from flexure-gravity models. One possibility for this contradiction may be that the different models represent two evolutionary points of Alba Patera. (1) The correlation of stresses with the circular grabens may represent an older stage of evolution with a thinner lithosphere. (2) The flexure-gravity models represent a younger to present stage with a thick lithosphere. The results of the lithosphere thicknesses are compared with an admittance calculation and different thermal evolution models which determine comparable thicknesses (150 km). More detailed models including 3D stress models should wait for new data sets from MGS. The results from the lineament analysis and geophysical modelling are summarized in an evolution model for Alba Patera.     

Density and stress distribution in the moon

A model is presented for the lateral variations of density within the Moon. The model gives rise to a gravitational potential which is equal to the observed potential at the lunar surface, moreover, it minimizes the total shear-strain energy of the Moon. The model exhibits lateral variations of about ±0.25 g cc^–1 within 50 km depth. The variations, however, reduce to ±0.06 and ±0.008 g cc^–1 within layers at 50–135 and 135–235 km respectively, and they become negligible below this region. The associated stress differences are found to be about 50 bar within 600 km depth, having their maximum values of about 90 bars at a depth of about 250 km. On the basis of these stress differences a strength of about 100 bar is concluded for the upper 400 km of the lunar interior for the last 3.3 b.y.Paper dedicated to Professor Harold C. Urey on the occasion of his 80th birthday on 29 April, 1973.The Lunar Science Institute is operated by the Universities Space Research Association under Contract No. NSR 09-051-001 with the National Aeronautics and Space Administration. This paper is Lunar Science Institute Contribution No. 117.     

Strength of the lithosphere of the Galilean satellites

Several approaches have been used to estimate the ice shell thickness on Callisto, Ganymede, and Europa. Here we develop a method for placing a strict lower bound on the thickness of the strong part of the shell (lithosphere) using measurements of topography. The minimal assumptions are that the strength of faults in the brittle lithosphere is controlled by lithostatic pressure according to Byerlee's law and the shell has relatively uniform density and thickness. Under these conditions, the topography of the ice provides a direct measure of the bending moment in the lithosphere. This topographic bending moment must be less than the saturation bending moment of the yield strength envelope derived from Byerlee's law. The model predicts that the topographic amplitude spectrum decreases as the square of the topographic wavelength. This explains why Europa is rugged at shorter wavelengths (∼10 km) but extremely smooth, and perhaps conforming to an equipotential surface, at longer wavelengths (>100 km). Previously compiled data on impact crater depth and diameter [Schenk, P.M., 2002. Nature 417, 419-421] on Europa show good agreement with the spectral decrease predicted by the model and require a lithosphere thicker than 2.5 km. A more realistic model, including a ductile lower lithosphere, requires a thickness greater than 3.5 km. Future measurements of topography in the 10-100 km wavelength band will provide tight constraints on lithospheric strength.     

Lithospheric structure and tectonics at Isidis Planitia, Mars

We characterize the lithospheric structure of Isidis Planitia on Mars by analyzing Mars Global Surveyor and Mars Odyssey gravity and topography data using a flexural model of a thin elastic shell including bending and membrane stresses. Isidis Planitia is a circular, relatively flat plain formed near the end of the Early Noachian, at the edge of the highlands-lowlands boundary and the site of a large free-air gravity anomaly, features consistent with modification and filling of an impact basin. Our results suggest that the bulk density of the fill material inside Isidis must be more than 2600 kg m⁻³ and higher densities are probable. A comparison of the faulting observed at Nili Fossae to the predicted zone of extensional strain northwest of Isidis constrains the thickness of the elastic lithosphere to be 100-180 km thick beneath the basin at the time of loading. We also find that loads outside of the basin play a significant role in the interpretation of the tectonics; simplified models tend to overestimate the lithospheric thickness. We place relatively narrow bounds on the thermal gradient (3.4-6.5 K km⁻¹) and heat flux (13.6-26 mW m⁻²) at Isidis at the time of loading.     

Ionospheric models of Saturn,Uranus, and Neptune

Model ionospheres are calculated for Saturn, Uranus, and Neptune. Protons are the major ions above 150 km altitude measured from a reference level where the hydrogen density is 1 × 10¹⁶ molecules cm^?3, while below 150 km quick conversion of protons to H₃⁺ ions by a three-body association mechanism leads to a rapid removal of ionization in dissociative recombination of H₃⁺. Electron density maxima are found at about 260 km for Saturn and Uranus and 200 km for Neptune. Present knowledge of the physical and chemical processes in the atmospheres of these planets suggests that their ionospheres probably will not be Jupiter-like.     

The topography of Iapetus' leading side

We have used Cassini stereo images to study the topography of Iapetus' leading side. A terrain model derived at resolutions of 4-8 km reveals that Iapetus has substantial topography with heights in the range of −10 km to +13 km, much more than observed on the other middle-sized satellites of Saturn so far. Most of the topography is older than 4 Ga [Neukum, G., Wagner, R., Denk, T., Porco, C.C., 2005. Lunar Planet. Sci. XXXVI. Abstract 2034] which implies that Iapetus must have had a thick lithosphere early in its history to support this topography. Models of lithospheric deflection by topographic loads provide an estimate of the required elastic thickness in the range of 50-100 km. Iapetus' prominent equatorial ridge [Porco, C.C., and 34 colleagues, 2005. Science 307, 1237-1242] reaches widths of 70 km and heights of up to 13 km from their base within the modeled area. The morphology of the ridge suggests an endogenous origin rather than a formation by collisional accretion of a ring remnant [Ip, W.-H., 2006. Geophys. Res. Lett. 33, doi:10.1029/2005GL025386. L16203]. The transition from simple to complex central peak craters on Iapetus occurs at diameters of 11±3 km. The central peaks have pronounced conical shapes with flanking slopes of typically 11° and heights that can rise above the surrounding plains. Crater depths seem to be systematically lower on Iapetus than on similarly sized Rhea, which if true, may be related to more pronounced crater-wall slumping (which widens the craters) on Iapetus than on Rhea. There are seven large impact basins with complex morphologies including central peak massifs and terraced walls, the largest one reaches 800 km in diameter and has rim topography of up to 10 km. Generally, no rings are observed with the basins consistent with a thick lithosphere but still thin enough to allow for viscous relaxation of the basin floors, which is inferred from crater depth-to-diameter measurements. In particular, a 400-km basin shows up-domed floor topography which is suggestive of viscous relaxation. A model of complex crater formation with a viscoplastic (Bingham) rheology [Melosh, H.J., 1989. Impact Cratering. Oxford Univ. Press, New York] of the impact-shocked icy material provides an estimate of the effective cohesion/viscosity at . The local distribution of bright and dark material on the surface of Iapetus is largely controlled by topography and consistent with the dark material being a sublimation lag deposit originating from a bright icy substrate mixed with the dark components, but frost deposits are possible as well.     

On the origins of band topography, Europa

We use stereo-derived topography of extensional bands on Europa to show that these features can be elevated by 100-150 m with respect to the surroundings, and that the positive topography sometimes extends beyond the band margins. Lateral variations in shell thickness cannot maintain the observed topography for timescales greater than ∼0.1 Myr. Lateral density variations can maintain the observed topography indefinitely; mean density contrasts of 5 and 50 kg m⁻³ are required for shell thicknesses of 20 and 2 km, respectively. Density variations caused by temperature contrasts require either present-day heating or that bands are young features (<1 Myr old). Stratigraphic analyses suggest that these mechanisms are unlikely. The observation that bands form from ridges may be explained by an episode of shear-heating on ridges weakening the ridge area, and leading to strain localization during extension. Fracture porosity is likely to persist over Myr timescales in the top one-third to one-quarter of the conductive part of the ice shell. Lateral variations in this porosity (of order 20%) are the most likely mechanism for producing band topography if the ice shell is thin (≈2 km); porosity variations of 2% or less are required if the shell is thicker (≈20 km). If the ice shell is thick, lateral variations in salt content are a more likely mechanism. Warm ice will tend to lose dense, low-melting temperature phases and be buoyant relative to colder, salt-rich ice. Thus, lateral density variations will arise naturally if bands have been the sites of either localized heating or upwelling of warm ice during extension.     

Thermal and topographic tests of Europa chaos formation models from Galileo E15 observations

Stereo topography of an area near Tyre impact crater, Europa, reveals chaos regions characterised by marginal cliffs and domical topography, rising to 100-200 m above the background plains. The regions contain blocks which have both rotated and tilted. We tested two models of chaos formation: a hybrid diapir model, in which chaos topography is caused by thermal or compositional buoyancy, and block motion occurs due to the presence of near-surface (1-3 km) melt; and a melt-through model, in which chaos regions are caused by melting and refreezing of the ice shell. None of the hybrid diapir models tested generate any melt within 1-3 km of the surface, owing to the low surface temperature. A model of ocean refreezing following melt-through gives effective elastic thicknesses and ice shell thicknesses of 0.1-0.3 and 0.5-2 km, respectively. However, for such low shell thicknesses the refreezing model requires implausibly large lateral density contrasts (50-100 kg m⁻³) to explain the elevation of the centres of the chaos regions. Although a global equilibrium ice shell thickness of ≈2 km is possible if Europa's mantle resembles that of Io, it is unclear whether local melt-through events are energetically possible. Thus, neither of the models tested here gives a completely satisfactory explanation for the formation of chaos regions. We suggest that surface extrusion of warm ice may be an important component of chaos terrain formation, and demonstrate that such extrusion is possible for likely ice parameters.     

Deep versus shallow origin of gravity anomalies, topography and volcanism on Earth, Venus and Mars

The relation between gravity anomalies, topography and volcanism can yield important insights about the internal dynamics of planets. From the power spectra of gravity and topography on Earth, Venus and Mars we infer that gravity anomalies have likely predominantly sources below the lithosphere up to about spherical harmonic degree l=30 for Earth, 40 for Venus and 5 for Mars. To interpret the low-degree part of the gravity spectrum in terms of possible sublithospheric density anomalies we derive radial mantle viscosity profiles consistent with mineral physics. For these viscosity profiles we then compute gravity and topography kernels, which indicate how much gravity anomaly and how much topography is caused by a density anomaly at a given depth. With these kernels, we firstly compute an expected gravity-topography ratio. Good agreement with the observed ratio indicates that for Venus, in contrast to Earth and Mars, long-wavelength topography is largely dynamically supported from the sublithospheric mantle. Secondly, we combine an empirical power spectrum of density anomalies inferred from seismic tomography in Earth’s mantle with gravity kernels to model the gravity power spectrum. We find a good match between modeled and observed gravity power spectrum for all three planets, except for 2?l?4 on Venus. Density anomalies in the Venusian mantle for these low degrees thus appear to be very small. We combine gravity kernels and the gravity field to derive radially averaged density anomaly models for the Martian and Venusian mantles. Gravity kernels for l?5 are very small on Venus below ≈800 km depth. Thus our inferences on Venusian mantle density are basically restricted to the upper 800 km. On Mars, gravity anomalies for 2?l?5 may originate from density anomalies anywhere within its mantle. For Mars as for Earth, inferred density anomalies are dominated by l=2 structure, but we cannot infer whether there are features in the lowermost mantle of Mars that correspond to Earth’s Large Low Shear Velocity Provinces (LLSVPs). We find that volcanism on Mars tends to occur primarily in regions above inferred low mantle density, but our model cannot distinguish whether or not there is a Martian analog for the finding that Earth’s Large Igneous Provinces mainly originate above the margins of LLSVPs.     

The heat flow of Europa

The heat flow from Europa has profound implications for ice shell thickness and structure, as well as for the existence of an internal ocean, which is strongly suggested by magnetic data. The brittle-ductile transition depth and the effective elastic thickness of the lithosphere are here used to perform heat flow estimations for Europa. Results give preferred heat flow values (for a typical geological strain rate of ¹⁰⁻¹⁵ s⁻¹) of 70-110 mW m⁻² for a brittle-ductile transition 2 km deep (the usually accepted upper limit for the brittle-ductile transition depth in the ice shell of Europa), 24-35 mW m⁻² for an effective elastic thickness of 2.9 km supporting a plateau near the Cilix impact crater, and >130 mW m⁻² for effective elastic thicknesses of ?0.4 km proposed for the lithosphere loaded by ridges and domes. These values are clearly higher than those produced by radiogenic heating, thus implying an important role for tidal heating. The ?19-25 km thick ice shell proposed from the analysis of size and depth of impact structures suggests a heat flow of ?30-45 mW m⁻² reaching the ice shell base, which in turn would imply an important contribution to the heat flow from tidal heating within the ice shell. Tidally heated convection in the ice shell could be capable to supply ∼100 mW m⁻² for superplastic flow, and, at the Cilix crater region, ∼35-50 mW m⁻² for dislocation creep, which suggests local variations in the dominant flow mechanism for convection. The very high heat flows maybe related to ridges and domes could be originated by preferential heating at special settings.     

The geothermal gradient of Io: Consequences for lithosphere structure and volcanic eruptive activity

We solve numerically the equations describing the transfer of heat through the lithosphere of Io by a mixture of conduction and volcanic advection as proposed by O’Reilly and Davies (O’Reilly, T.C., Davies, G.F. [1981]. Geophys. Res. Lett. 8, 313-316), removing the requirement that average material properties must be used. As expected, the dominance of advective heat transfer by volcanic eruptions means that Io’s geothermal gradient well away from volcanic centres is very small, of order 1 K km⁻¹. This result is independent of any reasonable assumptions about the radiogenic heating rate in the lithosphere. The lithosphere temperature does not increase greatly above the surface temperature until the base of the lithosphere is approached, except in limited areas around shallow magma bodies. As a consequence, solid volatile sulphur compounds mobilized by volcanic processes and re-deposited on the surface of Io commonly remain solid until they reach great depths as they are progressively buried by ongoing activity. For current estimates of the volcanic heat transfer rate, melting of SO₂ does not begin until a depth of ∼20 km and sulphur remains solid to a depth of ∼26 km in a 30 km thick lithosphere. Rising magmas can incorporate fluids from these deep sulphur compound aquifers, and we quantify the major influence that this can have on the bulk density of the magma and hence the resulting possible intrusion and eruption styles.     

The topography of Janus

A topographic model of Saturn's larger co-orbital satellite Janus was derived from the shapes of limbs and terminators in Voyager images, modified locally to accommodate large craters and ridges. The model is presented here in tabular and graphic form, including the first detailed shaded relief maps of the satellite. The shape is approximated by a triaxial ellipsoid with axes of 196, 192 and 150 km. The volume is estimated to be 3.0 ± 0.5 × 10⁶ km³, leading to a density estimate of 0.67 ± 0.10 g/cm³. The surface is heavily cratered. Several possible crater chains of uncertain significance are observed, but few prominent linear ridges and no narrow grooves.     

A model and map of Amalthea

A topographic model of Amalthea (JV) was derived from the shapes of limbs and terminators in Voyager images, modified locally to accommodate large craters and ridges. The model is presented in tabular and graphic form, including the first detailed shaded relief maps of the satellite. The shape is very irregular, with radii varying between about 53 and 151 ± 5 km. The minimum value occurs in a deep crater at the south pole. The volume is estimated to be 2.5 ± 0.5 × 10⁶km³. A prominent groove or valley extends some 150 km across the trailing side. High albedo, spectrally distinct markings are mapped and found to have a less obvious relationship with relief than previously suggested.     

New determination of the size and bulk density of the binary Asteroid 22 Kalliope from observations of mutual eclipses

In 2007, the M-type binary Asteroid 22 Kalliope reached one of its annual equinoxes. As a consequence, the orbit plane of its small moon, Linus, was aligned closely to the Sun's line of sight, giving rise to a mutual eclipse season. A dedicated international campaign of photometric observations, based on amateur-professional collaboration, was organized and coordinated by the IMCCE in order to catch several of these events. The set of the compiled observations is released in this work. We developed a relevant model of these events, including a topographic shape model of Kalliope refined in the present work, the orbit solution of Linus as well as the photometric effect of the shadow of one component falling on the other. By fitting this model to the only two full recorded events, we derived a new estimation of the equivalent diameter of Kalliope of 166.2±2.8 km, 8% smaller than its IRAS diameter. As to the diameter of Linus, considered as purely spherical, it is estimated to 28±2 km. This substantial “shortening” of Kalliope, gives a bulk density of 3.35±0.33 g/cm³, significantly higher than past determinations but more consistent with its taxonomic type. Some constraints can be inferred on the composition.