The equatorial shape and gravity field of Mercury from MESSENGER flybys 1 and 2

On 14 January and 6 October 2008 the MESSENGER spacecraft passed within 200 km of the surface of Mercury. These flybys by MESSENGER provided the first observations of Mercury from a spacecraft since the Mariner 10 flybys in 1974 and 1975. Data from the Mercury Laser Altimeter (MLA) provided new information on the equatorial shape of Mercury, and Doppler tracking of the spacecraft through the flybys provided new data on the planet’s gravity field. The MLA passes were on opposite hemispheres of the planet and span collectively ∼40% of the equatorial circumference. The mean elevation of topography observed during flyby 1, in the longitude range 0-90°E, is greater than that seen during flyby 2 in the longitude range 180-270°E, indicating an offset between centers of mass and figure having a magnitude and phase in general agreement with topography determined by Earth-based radar. Both MLA profiles are characterized by slopes of ∼0.015° downward to the east, which is consistent with a long-wavelength equatorial shape defined by a best-fitting ellipse. The Doppler tracking data show sensitivity to the gravitational structure of Mercury. The equatorial ellipticity of the gravitational field, C_2,2, is well determined and correlates with the equatorial shape. The S_2,2 coefficient is ∼0, as would be expected if Mercury’s coordinate system, defined by its rotational state, is aligned along its principal axes of inertia. The recovered value of the polar flattening of the gravitational potential, J₂, is considerably lower in magnitude than the value obtained from Mariner 10 tracking, a result that is problematic for internal structure models. This parameter is not as well constrained as the equatorial ellipticity because the flyby trajectories were nearly in the planet’s equatorial plane. The residuals from the Doppler tracking data suggest the possibility of mascons on Mercury, but flyby observations are of insufficient resolution for confident recovery. For a range of assumptions on degree of compensation and crustal and mantle densities, the allowable crustal thickness is consistent with the upper limit of about 100 km estimated from the inferred depth of faulting beneath a prominent lobate scarp, an assumed ductile flow law for crustal material, and the condition that temperature at the base of the crust does not exceed the solidus temperature. The MESSENGER value of C_2,2 has allowed an improved estimate of the ratio of the polar moment of inertia of the mantle and crust to the full polar moment (C_m/C), a refinement that strengthens the conclusion that Mercury has at present a fluid outer core.     

Iapetus' geophysics: Rotation rate, shape, and equatorial ridge

Iapetus has preserved evidence that constrains the modeling of its geophysical history from the time of its accretion until now. The evidence is (a) its present 79.33-day rotation or spin rate, (b) its shape that corresponds to the equilibrium figure for a hydrostatic body rotating with a period of ∼16 h, and (c) its high, equatorial ridge, which is unique in the Solar System. This paper reports the results of an investigation into the coupling between Iapetus' thermal and orbital evolution for a wide range of conditions including the spatial distributions with time of composition, porosity, short-lived radioactive isotopes (SLRI), and temperature. The thermal model uses conductive heat transfer with temperature-dependent conductivity. Only models with a thick lithosphere and an interior viscosity in the range of about the water ice melting point can explain the observed shape. Short-lived radioactive isotopes provide the heat needed to decrease porosity in Iapetus' early history. This increases thermal conductivity and allows the development of the strong lithosphere that is required to preserve the 16-h rotational shape and the high vertical relief of the topography. Long-lived radioactive isotopes and SLRI raise internal temperatures high enough that significant tidal dissipation can start, and despin Iapetus to synchronous rotation. This occurred several hundred million years after Iapetus formed. The models also constrain the time when Iapetus formed because the successful models are critically dependent upon having just the right amount of heat added by SLRI decay in this early period. The amount of heat available from short-lived radioactivity is not a free parameter but is fixed by the time when Iapetus accreted, by the canonical concentration of ²⁶Al, and, to a lesser extent, by the concentration of ⁶⁰Fe. The needed amount of heat is available only if Iapetus accreted between 2.5 and 5.0 Myr after the formation of the calcium aluminum inclusions as found in meteorites. Models with these features allow us to explain Iapetus' present synchronous rotation, its fossil 16-h shape, and the context within which the equatorial ridge arose.     

The evolution of the martian elastic lithosphere and implications for crustal and mantle rheology

Estimates of the martian elastic lithosphere thickness Te imply that Te increased from around 20 km in the Noachian to about 70 km in the Amazonian period. A phase of rapid lithospheric growth is observed during the Hesperian and we propose that this elastic thickness history is a consequence of the martian crustal rheology and its thermal evolution. A wet crustal rheology is found to generate a mechanically incompetent layer in the lower crust during the early evolution and the rapid growth of Te during the Hesperian results from the disappearance of this layer due to planetary cooling. The incompetent layer and the related rapid lithospheric growth are absent for a dry basaltic crustal rheology, which is therefore incompatible with the observations. Furthermore, we find that the observed elastic thickness evolution is best compatible with a wet mantle rheology, although a dry mantle cannot be ruled out. It therefore seems likely that rheologically significant amounts of water were retained in the Martian crust and mantle after planetary accretion.     

Implications of large elastic thicknesses for the composition and current thermal state of Mars

The martian elastic lithosphere thickness Te has recently been constrained by modeling the geodynamical response to loading at the martian polar caps and Te was found to exceed 300 km at the north pole today. Geological evidence suggests that Mars has been volcanically active in the recent past and we have reinvestigated the martian thermal evolution, identifying models which are consistent with Te>300 km and the observed recent magmatic activity. We find that although models satisfying both constraints can be constructed, special assumptions regarding the concentration and distribution of radioactive elements, the style of mantle convection and/or the mantle's volatile content need to be made. If a dry mantle rheology is assumed, strong plumes caused by, e.g., a strongly pressure dependent mantle viscosity or endothermic phase transitions near the core-mantle boundary are required to allow for decompression melting in the heads of mantle plumes. For a wet mantle, large mantle water contents of the order of 1000 ppm are required to allow for partial mantle melting. Also, for a moderate crustal enrichment of heat producing, elements the planet's bulk composition needs to be 25 and 50% sub-chondritic for dry and wet mantle rheologies, respectively. Even then, models resulting in a globally averaged elastic thicknesses of Te>300 km are difficult to reconcile with most elastic thickness estimates available for the Hesperian and Amazonian periods. It therefore seems likely that large elastic thicknesses in excess of 300 km are not representative for the bulk of the planet and that Te possibly shows a large degree of spatial heterogeneity.     

The thermal evolution of Mars as constrained by paleo-heat flows

Lithospheric strength can be used to estimate the heat flow at the time when a given region was deformed, allowing us to constrain the thermal evolution of a planetary body. In this sense, the high (>300 km) effective elastic thickness of the lithosphere deduced from the very limited deflection caused by the north polar cap of Mars indicates a low surface heat flow for this region at the present time, a finding difficult to reconcile with thermal history models. This has started a debate on the current heat flow of Mars and the implications for the thermal evolution of the planet. Here we perform refined estimates of paleo-heat flow for 22 martian regions of different periods and geological context, derived from the effective elastic thickness of the lithosphere or from faulting depth beneath large thrust faults, by considering regional radioactive element abundances and realistic thermal conductivities for the crust and mantle lithosphere. For the calculations based on the effective elastic thickness of the lithosphere we also consider the respective contributions of crust and mantle lithosphere to the total lithospheric strength. The obtained surface heat flows are in general lower than the equivalent radioactive heat production of Mars at the corresponding times, suggesting a limited contribution from secular cooling to the heat flow during the majority of the history of Mars. This is contrary to the predictions from the majority of thermal history models, but is consistent with evidence suggesting a currently fluid core, limited secular contraction for Mars, and recent extensive volcanism. Moreover, the interior of Mars could even have been heating up during part of the thermal history of the planet.     

Crustal recycling, mantle dehydration, and the thermal evolution of Mars

We have reinvestigated the coupled thermal and crustal evolution of Mars taking new laboratory data concerning the flow behavior of iron-rich olivine into account. The low mantle viscosities associated with the relatively higher iron content of the martian mantle as well as the observed high concentrations of heat producing elements in a crust with a reduced thermal conductivity were found to promote phases of crustal recycling in many models. As crustal recycling is incompatible with an early separation of geochemical reservoirs, models were required to show no episodes of crustal recycling. Furthermore, admissible models were required to reproduce the martian crust formation history, to allow for the formation of partial melt under present day mantle conditions and to reproduce the measured concentrations of potassium and thorium on the martian surface. Taking dehydration stiffening of the mantle viscosity by the extraction of water from the mantle into account, we found that admissible models have low initial upper mantle temperatures around 1650 K, preferably a primordial crustal thickness of 30 km, and an initially wet mantle rheology. The crust formation process on Mars would then be driven by the extraction of a primordial crust after core formation, cooling the mantle to temperatures close to the peridotite solidus. According to this scenario, the second stage of global crust formation took place over a more extended period of time, waning at around 3500 Myr b.p., and was driven by heat produced by the decay of radioactive elements. Present-day volcanism would then be driven by mantle plumes originating at the core-mantle boundary under regions of locally thickened, thermally insulating crust. Water extraction from the mantle was found to be relatively efficient and close to 40% of the total inventory was lost from the mantle in most models. Assuming an initial mantle water content of 100 ppm and that 10% of the extracted water is supplied to the surface, this amount is equivalent to a 14 m thick global surface layer, suggesting that volcanic outgassing of H₂O could have significantly influenced the early martian climate and increased the planet’s habitability.     

Structural evolution in elliptical galaxies: the age–shape relation

We test the hypothesis that the apparent axial ratio of an elliptical galaxy is correlated with the age of its stellar population. We find that old ellipticals (with estimated ages t >7.5 Gyr) are rounder on average than younger ellipticals. The statistical significance of this shape difference is greatest at small radii; a Kolmogorov–Smirnov test comparing the axial ratios of the two populations at R = R _e/16 yields a statistical significance greater than 99.96 per cent. The relation between age and apparent shape is linked to the core/power-law surface brightness profile dichotomy. Core ellipticals have older stellar populations, on average, than power-law ellipticals and are rounder in their inner regions. Our findings are consistent with a scenario in which power-law ellipticals are formed in gas-rich mergers, while core ellipticals form in dissipationless mergers, with cores formed and maintained by the influence of a binary black hole.     

The shape distribution of asteroid families: Evidence for evolution driven by small impacts

A statistical analysis of brightness variability of asteroids reveals how their shapes evolve from elongated to rough spheroidal forms, presumably driven by impact-related phenomena. Based on the Sloan Digital Sky Survey Moving Object Catalog, we determined the shape distribution of 11,735 asteroids, with special emphasis on eight prominent asteroid families. In young families, asteroids have a wide range of shape elongations, implying fragmentation-formation. In older families we see an increasing number of rough spheroids, in agreement with the predictions of an impact-driven evolution. Old families also contain a group of moderately elongated members, which we suggest correspond to higher-density, more impact-resistant cores of former fragmented asteroids that have undergone slow shape erosion. A few percent of asteroids have very elongated shapes, and can either be young fragments or tidally reshaped bodies. Our results confirm that the majority of asteroids are gravitationally bound “rubble piles.”     

Chaplygin gas of Tachyon Nature Imposed by Noether Symmetry and constrained via H(z) data

An action of general form is proposed for a Universe containing matter, radiation and dark energy. The latter is interpreted as a tachyon field non-minimally coupled to the scalar curvature. The Palatini approach is used when varying the action so the connection is given by a more generic form. Both the self-interaction potential and the non-minimally coupling function are obtained by constraining the system to present invariability under global point transformation of the fields(Noether Symmetry). The only possible solution is shown to be that of minimal coupling and constant potential(Chaplygin gas). The behavior of the dynamical properties of the system is compared to recent observational data, which infers that the tachyon field must indeed be dynamical.     

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.     

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.     

Denudation and uplift history of the Jameson Land basin, East Greenland—constrained from maturity and apatite fission track data

The Jameson Land basin in East Greenland comprises a well exposed succession of Upper Paleozoic–Mesozoic sediments. During Middle Devonian–Early Permian rifting, 13 km of continental clastics were deposited. In latest Paleozoic to Mesozoic times, 4 km of sediments accumulated during regional subsidence. In the Early Paleocene, during North Atlantic break-up, the basin was covered by a thick volcanic pile. Subsequently, uplift and erosion took place over the whole region. The volcanic cover was completely removed from Jameson Land and erosion cut deeply into the underlying sediments. To assess the exploration potential of Jameson Land, a basin modelling study with 21 1D pseudo-wells was carried out based on all seismic and surface data available. In addition to the calculation of hydrocarbon generation in space and time, the basin modelling provided an opportunity to study the magnitude and timing of uplift and erosion. Basin modelling constrained by apatite fission track data has made it possible to determine a consistent uplift and erosion history of the area. Tectonic backstripping based on a simple Airy type isostatic model has been used to separate the tectonic uplift from the actual uplift. The combined basin modelling and backstripping study has led to the following conclusions: (1) the thickness of the Cretaceous succession varied from 1.3 km in the south to 0.3 km in the north; (2) the volcanic rocks formed a wedge with a thickness of >2 km in the south thinning to <0.1 km in the north; (3) the subsequent erosion of 2–3 km is in response to tectonic uplift with a magnitude of 1 km, and the calculated tectonic uplift shows increasing values to the north. The erosion rate generally accelerated from Late Paleocene up to the present time.     

Structure and evolution state of the principal component of V 380 Cyg

Crimean Laboratory, P. K. Shternberg State Astronomical Institute; Rostov State University. Translated from Astrofizika, Vol. 29, No. 2, pp. 300–309, September–October, 1988.     

Igneous cooling history of olivine‐phyric shergottite Yamato 980459 constrained by dynamic crystallization experiments

Dynamic crystallization experiments were performed on a liquid having the bulk composition of olivine‐phyric shergottite Yamato 980459, to constrain the igneous thermal history of this meteorite. Key characteristics of the meteorite's mineralogy and texture, including several morphologically distinct olivine and pyroxene crystal populations and a glassy mesostasis devoid of plagioclase, were replicated upon cooling from 1435 to 909 °C at 1 atmosphere under reducing conditions. Three sequential cooling ramps are required to produce synthetic samples with textures and compositions matching Yamato 980459. Olivine phenocrysts formed at <1 °C h^?1, presumably at depth in the Martian crust. Pyroxene phenocrysts formed mainly at ~10 °C h^?1, consistent with crystallization within a lava flow at depths of 25–45 cm. Increased cooling rate (~100 °C h^?1) in a third stage suppressed the formation of plagioclase and produced groundmass crystals, consistent with crystallization at lava flow depths of 5–7 cm. Although Y 980459 is unique among Martian meteorites (i.e., preserving a primary glassy mesostasis), its emplacement did not require unique physical conditions. Rather, the second and third cooling stages may reflect cooling within the core of a pāhoehoe‐like flow and subsequent breakout on the surface of Mars.     

Fundamental reference systems; Past,present, and future

The present fundamental reference system is defined by the FK5 Fundamental Reference Catalog and the associated IAU Resolutions of 1976 through 1982. The past is defined to be what preceded the present fundamental reference system and future is defined to be what ever will come after it. The resulting characteristics of the different fundamental reference systems are considered from the aspects of the observational data, the computational methods, and the underlying theories. Having developed an understanding of these operational fundamental reference systems, the desired properties of the ideal fundamental reference system are presented. Finally, some questions concerning the future fundamental reference system are presented.     

The symmetry energy and incompressibility constrained by the observations of glitching pulsars

We investigate the masses of glitching pulsars in order to constrain their equation of state(EOS). The observations of glitches(sudden jumps in rotational frequency) may provide information on the interior physics of neutron stars. With the assumption that glitches are triggered by superfluid neutrons, the masses of glitching neutron stars can be estimated using observations of maximum glitches.Together with the observations of thermal emission from glitching pulsars Vela and J1709–4429, the slope of symmetry energy and incompressibility of nuclear matter at saturation density can be constrained.The slope of symmetry energy L should be larger than 67 MeV while the lower limit of incompressibility for symmetric nuclear matter K_0 is 215 MeV. We also obtain a relationship between L and K_0:6.173 MeV + 0.283 K_0≤ L ≤ 7.729 MeV + 0.291 K_0. The restricted EOSs are consistent with the observations of 2-solar-mass neutron stars and gravitational waves from a binary neutron star inspiral.     

Saturn's rings: Particle composition and size distribution as constrained by microwave observations: I. Radar observations

We have calculated the radar backscattering characteristics of a variety of compositional and structural models of Saturn's rings and compared them with observations of the absolute value, wavelength dependence, and degree of depolarization of the rings' radar cross section (reflectivity). In the treatment of particles of size comparable to the wavelength of observation, allowance is made for the nonspherical shape of the particles by use of a new semiempirical theory based on laboratory experiments and simple physical principles to describe the particles' single scattering behavior. The doubling method is used to calculate reflectivities for systems that are many particles thick using optical depths derived from observations at visible wavelengths. If the rings are many particles thick, irregular centimeter- to meter-sized particles composed primarily of water ice attain sufficiently high albedos and scattering efficiencies to explain the radar observations. In that case, the wavelength independence of radar reflectivity implies the existence of a broad particle size distribution that is well characterized over the range 1 cm ? r ? m by n(r)dr = n₀r^?3dr. A narrower size distribution with $\text{a}\text{～ 6}\text{cm}$ is also a possibility. Particles of primarily silicate composition are ruled out by the radar observations. Purely metallic particles, either in the above size range and distributed within a many-particle-thick layer or very much larger in size and restricted to a monolayer, may not be ruled out on the basis of existing radar observations. A monolayer of very large ice “particle” that exhibit multiple internal scattering may not yet be ruled out. Observations of the variation of radar reflectivity with the opening angle of the rings will permit further discrimination between ring models that are many particles thick and ring models that are one “particle” thick.