Region of motion in the Sitnikov four-body problem when the fourth mass is finite

This article deals with the region of motion in the Sitnikov four-body problem where three bodies (called primaries) of equal masses fixed at the vertices of an equilateral triangle. Fourth mass which is finite confined to moves only along a line perpendicular to the instantaneous plane of the motions of the primaries. Contrary to the Sitnikov problem with one massless body the primaries are moving in non-Keplerian orbits about their centre of mass. It is investigated that for very small range of energy h the motion is possible only in small region of phase space. Condition of bounded motions has been derived. We have explored the structure of phase space with the help of properly chosen surfaces of section. Poincarè surfaces of section for the energy range ?0.480≤h≤?0.345 have been computed. We have chosen the plane (q ₁,p ₁) as surface of section, with q ₁ is the distance of a primary from the centre of mass. We plot the respective points when the fourth body crosses the plane q ₂=0. For low energy the central fixed point is stable but for higher value of energy splits in to an unstable and two stable fixed points. The central unstable fixed point once again splits for higher energy into a stable and three unstable fixed points. It is found that at h=?0.345 the whole phase space is filled with chaotic orbits.     

The origin of eucrites,diogenites, and olivine diogenites: Magma ocean crystallization and shallow magma chamber processes on Vesta

The asteroid 4 Vesta is one of the very few heavenly bodies to have been linked to samples on Earth: the howardite‐eucrite‐diogenite (HED) meteorite suite. This large and diverse suite of meteorites provides a detailed picture of Vesta's igneous and postigneous history. We have used the range of igneous rock types and compositions in the HED suite to test a series of chemical models for solidification processes following peak melting (magma ocean) conditions on Vesta. Fractional crystallization cannot have been a dominant early process in the magma ocean because it leads to excessive Fe‐enrichment in the melt. Models that are dominated by equilibrium crystallization cannot produce orthopyroxene cumulates (diogenites). Our best models invoke 60–70% equilibrium crystallization of a magma ocean followed by continuous extraction of the residual melt into shallow magma chambers. Fractional crystallization in these magma chambers combined with continuous or periodic addition of more melt from the slowly compacting crystal mush (magmatic recharge) can produce all of the igneous HED lithologies (noncumulate and cumulate eucrites, diogenites, dunites, harzburgites, and olivine diogenites). Magmatic recharge can also explain the narrow range in eucrite compositions and the variability of incompatible trace element concentrations in diogenites. We predict an internal structure for Vesta that permits excavation of the HEDs during the formation of the Rheasilvia basin, while remaining consistent with observations from the Dawn mission and most impact models.     

26Al‐26Mg isotope systematics of the first solids in the early solar system

High‐precision bulk aluminum‐magnesium isotope measurements of calcium‐aluminum‐rich inclusions (CAIs) from CV carbonaceous chondrites in several laboratories define a bulk ²⁶Al‐²⁶Mg isochron with an inferred initial ²⁶Al/²⁷Al ratio of approximately 5.25 × 10^?5, named the canonical ratio. Nonigneous CV CAIs yield well‐defined internal ²⁶Al‐²⁶Mg isochrons consistent with the canonical value. These observations indicate that the canonical ²⁶Al/²⁷Al ratio records initial Al/Mg fractionation by evaporation and condensation in the CV CAI‐forming region. The internal isochrons of igneous CV CAIs show a range of inferred initial ²⁶Al/²⁷Al ratios, (4.2–5.2) × 10^?5, indicating that CAI melting continued for at least 0.2 Ma after formation of their precursors. A similar range of initial ²⁶Al/²⁷Al ratios is also obtained from the internal isochrons of many CAIs (igneous and nonigneous) in other groups of carbonaceous chondrites. Some CAIs and refractory grains (corundum and hibonite) from unmetamorphosed or weakly metamorphosed chondrites, including CVs, are significantly depleted in ²⁶Al. At least some of these refractory objects may have formed prior to injection of ²⁶Al into the protosolar molecular cloud and its subsequent homogenization in the protoplanetary disk. Bulk aluminum and magnesium‐isotope measurements of various types of chondrites plot along the bulk CV CAI isochron, suggesting homogeneous distribution of ²⁶Al and magnesium isotopes in the protoplanetary disk after an epoch of CAI formation. The inferred initial ²⁶Al/²⁷Al ratios of chondrules indicate that most chondrules formed 1–3 Ma after CAIs with the canonical ²⁶Al/²⁷Al ratio.     

Geochemical studies of the SUBO 18 (Enkingen) drill core and other impact breccias from the Ries crater,Germany

Suevite and melt breccia compositions in the boreholes Enkingen and Polsingen are compared with compositions of suevites from other Ries boreholes and surface locations and discussed in terms of implications for impact breccia genesis. No significant differences in average chemical compositions for the various drill cores or surface samples are noted. Compositions of suevite and melt breccia from southern and northeastern sectors of the Ries crater do not significantly differ. This is in stark contrast to the published variations between within‐crater and out‐of‐crater suevites from northern and southern sectors of the Bosumtwi impact structure, Ghana. Locally occurring alteration overprint on drill cores—especially strong on the carbonate‐impregnated suevite specimens of the Enkingen borehole—does affect the average compositions. Overall, the composition of the analyzed impact breccias from Ries are characterized by very little macroscopically or microscopically recognized sediment‐clast component; the clast populations of suevite and impact melt breccia are dominated consistently by granitic and intermediate granitoid components. The Polsingen breccia is significantly enriched in a dioritic clast component. Overall, chemical compositions are of intermediate composition as well, with dioritic‐granodioritic silica contents, and relatively small contributions from mafic target components. Selected suevite samples from the Enkingen core have elevated Ni, Co, Cr, and Ir contents compared with previously analyzed suevites from the Ries crater, which suggest a small meteoritic component. Platinum‐group element (PGE) concentrations for some of the enriched samples indicate somewhat elevated concentrations and near‐chondritic ratios of the most immobile PGE, consistent with an extraterrestrial contribution of 0.1–0.2% chondrite‐equivalent.     

Trace element geochemistry of CR chondrite metal

We report trace element analyses by laser ablation inductively coupled plasma mass spectrometry (LA‐ICP‐MS) of metal grains from nine different CR chondrites, distinguishing grains from chondrule interior (“interior grains”), chondrule surficial shells (“margin grains”), and the matrix (“isolated grains”). Save for a few anomalous grains, Ni‐normalized trace element patterns are similar for all three petrographic settings, with largely unfractionated refractory siderophile elements and depleted volatile Au, Cu, Ag, S. All three types of grains are interpreted to derive from a common precursor approximated by the least‐melted, fine‐grained objects in CR chondrites. This also excludes recondensation of metal vapor as the origin of the bulk of margin grains. The metal precursors were presumably formed by incomplete condensation, with evidence for high‐temperature isolation of refractory platinum‐group‐element (PGE)‐rich condensates before mixing with lower temperature PGE‐depleted condensates. The rounded shape of the Ni‐rich, interior grains shows that they were molten and that they equilibrated with silicates upon slow cooling (1–100 K h^?1), largely by oxidation/evaporation of Fe, hence their high Pd content, for example. We propose that Ni‐poorer, amoeboid margin grains, often included in the pyroxene‐rich periphery common to type I chondrules, result from less intense processing of a rim accreted onto the chondrule subsequent to the melting event recorded by the interior grains. This means either that there were two separate heating events, which formed olivine/interior grains and pyroxene/margin grains, respectively, between which dust was accreted around the chondrule, or that there was a single high‐temperature event, of which the chondrule margin records a late “quenching phase,” in which case dust accreted onto chondrules while they were molten. In the latter case, high dust concentrations in the chondrule‐forming region (at least three orders of magnitude above minimum mass solar nebula models) are indicated.     

3‐D hydrodynamic simulations of the solar chromosphere

We present first results of three‐dimensional numerical simulations of the non‐magnetic solar chromosphere, computed with the radiation hydrodynamics code CO⁵BOLD. Acoustic waves which are excited at the top of the convection zone propagate upwards into the chromosphere where the waves steepen into shocks. The interaction of the waves leads to the formation of complex structures which evolve on short time scales. Consequently, the model chromosphere is highly dynamical, inhomogeneous, and thermally bifurcated.     

Pliocene–Quaternary fluvial and aeolian records in the Souss Basin, southwest Morocco: A geomorphological model

The Souss Basin in SW Morocco is filled by Pliocene–Quaternary fluvial, fluvio-lacustrine and aeolian sediments, representing an excellent archive of palaeohydrology, palaeoclimate and the effects of crustal deformation. In general these sediments indicate stream-dominated alluvial systems, influenced by fluctuations in climate (humidity/aridity). Lakes developed within the basin around the Pliocene–Pleistocene transition and persisted into the Early Pleistocene. During this early period, relatively humid conditions are indicated by the dominance of coarse-grained sedimentation in the upper reaches of fluvial systems, the existence of large lakes and the considerable sediment thicknesses in the centre of the basin. Uplift of the surrounding mountain ranges contributed to piedmont formation by providing large amounts of coarse-grained material that accumulated at the lowland margin. Climatic deterioration in the Middle Pleistocene was accompanied by progressively more irregular and disrupted fluvial regimes. These trends were evident in the Late Pleistocene and became clearer after the mid-Holocene, with aeolian activity becoming the dominant sedimentary agent. Differences between upstream and downstream depositional regimes became marked: while coarse-grained sedimentation has characterized the upper reaches of wadi catchments, fine-grained sedimentation has prevailed downstream. Hiatuses in sedimentation throughout the Pliocene and Quaternary are marked by palaeosol horizons interbedded within the sedimentary sequences, indicating alternate vegetated (stable) and unvegetated (unstable/active) phases (biostasy and ‘rhexistasy’).     

Cladocora caespitosa bioconstructions in the Columbretes Islands Marine Reserve (Spain,NW Mediterranean): distribution,size structure and growth

Today, living banks of the coral Cladocora caespitosa appear to be restricted to a few Mediterranean locations and are threatened by the escalating impacts affecting coastal areas. In this study the exceptional occurrence of the Mediterranean coral C. caespitosa in the Columbretes Islands Marine Reserve (NW Mediterranean, Spain) is characterised in terms of spatial distribution, cover area, colony size and growth rates. The coral colonies form beds and banks in rocky bottoms within a semi‐enclosed bay that offers both hydrodynamic protection and high water exchange. The spatial distribution of the C. caespitosa colonies, from 5 to 27 m depth, is highly aggregated, depending on sea‐floor morphology and showing up to 80% of substrate coverage. The annual corallite growth rates obtained through the alizarin red staining method and x‐ray image analysis are similar, and range between 2.55 ± 0.79 mm and 2.54 ± 0.81 mm, respectively. The exceptional nature of these bioconstructions is due to their cumulative cover area, which is comparable in size to the largest C. caespitosa bioconstructions described to date in Mljet National Park (Croatia, Adriatic Sea).     

Trophic ecology of Pomatoschistus microps within an intertidal bay (Roscoff,France), investigated through gut content and stable isotope analyses

The diet of Pomatoschistus microps has been studied using both gut content and stable isotope analyses. In the Roscoff Aber Bay (Brittany, France), this fish is commonly found on sandy muddy intertidal flats. Gut content analyses were also interpreted using trophic indices. Owing to the large diversity of prey consumed, these indices emphasised the opportunistic feeding behaviour of P. microps. Here, this species fed mainly on endofauna with meiofauna being of high relative importance. The main biotic components of its trophic habitat, characterized by δ¹³C and δ¹⁵N, provided evidence of a major trophic pathway based on drift Enteromorpha sp. Trophic positions estimated by both diet analyses and isotopic analyses led to similar results. In this bay, P. microps is a first‐order predator with a low degree of omnivory. Despite a preferential consumption of the amphipod Corophium arenarium, we assumed that this goby behaves as a generalist feeding on a uniform variety of endofauna taxa.     

Diversity and temporal fluctuations of epiphytes and sessile invertebrates on the rhizomes Posidonia oceanica in a seagrass meadow off Tunisia

The aim of this work is to study the temporal dynamics of rhizome epiphytes and sessile animals living on the rhizomes of the seagrass Posidonia oceanica in the east of Tunisia. Surveys were conducted in October 2009, and in January, April and August 2010 on a fringing reef located in Chebba. Rhizomes were sampled by SCUBA diving at three stations. Samples were examined with a microscope to estimate the cover of macroinvertebrate and macroalgal organisms on the top 10 cm of each rhizome. Results revealed a high diversity of epiphytes on P. oceanica rhizomes with a dominance of red and brown algae, ascidians, and bryozoans. Distinct temporal changes were observed in Oued Lafrann, with a high January cover (winter period) for all groups. These winter increases can be attributed to: (i) the low phenological parameters of P. oceanica in winter that reduce the effects of shading, (ii) life cycles of the epiphytes and invertebrates, (iii) water motion and (iv) grazing.