Influence of periodic orbits on the formation of giant planetary systems

The late-stage formation of giant planetary systems is rich in interesting dynamical mechanisms. Previous simulations of three giant planets initially on quasi-circular and quasi-coplanar orbits in the gas disc have shown that highly mutually inclined configurations can be formed, despite the strong eccentricity and inclination damping exerted by the disc. Much attention has been directed to inclination-type resonance, asking for large eccentricities to be acquired during the migration of the planets. Here we show that inclination excitation is also present at small to moderate eccentricities in two-planet systems that have previously experienced an ejection or a merging and are close to resonant commensurabilities at the end of the gas phase. We perform a dynamical analysis of these planetary systems, guided by the computation of planar families of periodic orbits and the bifurcation of families of spatial periodic orbits. We show that inclination excitation at small to moderate eccentricities can be produced by (temporary) capture in inclination-type resonance and the possible proximity of the non-coplanar systems to spatial periodic orbits contributes to maintaining their mutual inclination over long periods of time.     

Impact of nitrogenous fertilizers on carbonate dissolution in small agricultural catchments: Implications for weathering CO2 uptake at regional and global scales

The goal of this study was to highlight the occurrence of an additional proton-promoted weathering pathway of carbonate rocks in agricultural areas where N-fertilizers are extensively spread, and to estimate its consequences on riverine alkalinity and uptake of CO₂ by weathering. We surveyed 25 small streams in the calcareous molassic Gascogne area located in the Garonne river basin (south-western France) that drain cultivated or forested catchments for their major element compositions during different hydrologic periods. Among these catchments, the Hay and the Montoussé, two experimental catchments, were monitored on a weekly basis. Studies in the literature from other small carbonate catchments in Europe were dissected in the same way. In areas of intensive agriculture, the molar ratio (Ca + Mg)/HCO₃ in surface waters is significantly higher (0.7 on average) than in areas of low anthropogenic pressure (0.5). This corresponds to a decrease in riverine alkalinity, which can reach 80% during storm events. This relative loss of alkalinity correlates well with the content in surface waters. In cultivated areas, the contribution of atmospheric/soil CO₂ to the total riverine alkalinity (CO_{2 ATM-SOIL}/HCO₃) is less than 50% (expected value for carbonate basins), and it decreases when the nitrate concentration increases. This loss of alkalinity can be attributed to the substitution of carbonic acid (natural weathering pathway) by protons produced by nitrification of N-fertilizers (anthropogenic weathering pathway) occurring in soils during carbonate dissolution. As a consequence of these processes, the alkalinity over the last 30 years shows a decreasing trend in the Save river (one of the main Garonne river tributaries, draining an agricultural catchment), while the nitrate and calcium plus magnesium contents are increasing.We estimated that the contribution of atmospheric/soil CO₂ to riverine alkalinity decreased by about 7-17% on average for all the studied catchments. Using these values, the deficit of CO₂ uptake can be estimated as up to 0.22-0.53 and 12-29 Tg¹ yr⁻¹ CO₂ on a country scale (France) and a global scale, respectively. These losses represent up to 5.7-13.4% and only 1.6-3.8% of the total CO₂ flux naturally consumed by carbonate dissolution, for France and on a global scale, respectively. Nevertheless, this loss of alkalinity relative to the Ca + Mg content relates to carbonate weathering by protons from N-fertilizers nitrification, which is a net source of CO₂ for the atmosphere. This anthropogenic CO₂ source is not negligible since it could reach 6-15% of CO₂ uptake by natural silicate weathering and could consequently partly counterbalance this natural CO₂ sink.     

Secular frequencies of 3-D exoplanetary systems

Using a 12th order expansion of the perturbative potential in powers of the eccentricities and the inclinations, we study the secular effects of two non-coplanar planets which are not in mean–motion resonance. By means of Lie transformations (which introduce an action–angle formulation of the Hamiltonian), we find the four fundamental frequencies of the 3-D secular three-body problem and compute the long-term time evolutions of the Keplerian elements. To find the relations between these elements, the main combinations of the fundamental frequencies common to these evolutions are identified by frequency analysis. This study is performed for two different reference frames: a general one and the Laplace plane. We underline the known limitations of the linear Laplace–Lagrange theory and point out the great sensitivity of the 3-D secular three-body problem to its initial values. This analytical approach is applied to the exoplanetary system Andromedae in order to search whether the eccentricities evolutions and the apsidal configuration (libration of ) observed in the coplanar case are maintained for increasing initial values of the mutual inclination of the two orbital planes. Anne-Sophie Libert is FNRS Research Fellow.     

Comparison of velocimeter and coherent lidar measurements for building frequency assessment

Over recent years there has been a growing interest in the building frequency analysis for earthquake and structural engineering fields using ambient vibrations. Simultaneously, velocity measurements with LASER remote sensing techniques have gained more interest for several applications. This paper details the comparison of the frequency analysis obtained using sensitive velocimeter sensor and coherent LIDAR (Light Detection and Ranging) sensor, and applied to one RC existing building. Ambient vibrations recordings were processed using the Frequency Domain Decomposition method for defining the frequencies and mode shapes of the building target, while LASER remote sensing approach used coherent LIDAR method for velocity and frequency measurement. The results of the two systems are discussed. A good agreement is observed, which let us conclude on the ability of the coherent LIDAR to assess the frequency of existing buildings for structural and earthquake engineering fields at long range and without any retroreflector on the structure.     

阿尔金断裂带对青藏高原北部生长、隆升的制约

大量的同位素年代学证据表明(古)阿尔金断裂带可能形成于三叠纪,后又经历了侏罗纪、白垩纪的强烈左旋走滑活动,自印度板块与欧亚大陆碰撞后阿尔金断裂再次活动。主要的走滑活动发生在:(1)245~220Ma;(2)180~140Ma;(3)120~100Ma;(4)90~80Ma;(5)60~45Ma;(6)渐新世至中新世;(7)上新世至更新世以及(8)全新世。沿阿尔金断裂带,伴随左旋走滑活动形成一系列的逆冲断裂和正断裂,反映走滑过程中伴随隆升作用的存在,并且形成自北向南包括祁连山、大雪山、党河南山、柴北缘山、祁漫塔格山和昆仑山,表明阿尔金断裂带制约着青藏高原北部的生长和隆升。阿尔金断裂带东、西两端的白垩纪和新生代火山活动是断裂走滑活动的响应。     

Origin and continuation of 3/2, 5/2, 3/1, 4/1 and 5/1 resonant periodic orbits in the circular and elliptic restricted three-body problem

We consider a planetary system consisting of two primaries, namely a star and a giant planet, and a massless secondary, say a terrestrial planet or an asteroid, which moves under their gravitational attraction. We study the dynamics of this system in the framework of the circular and elliptic restricted three-body problem, when the motion of the giant planet describes circular and elliptic orbits, respectively. Originating from the circular family, families of symmetric periodic orbits in the 3/2, 5/2, 3/1, 4/1 and 5/1 mean-motion resonances are continued in the circular and the elliptic problems. New bifurcation points from the circular to the elliptic problem are found for each of the above resonances, and thus, new families continued from these points are herein presented. Stable segments of periodic orbits were found at high eccentricity values of the already known families considered as whole unstable previously. Moreover, new isolated (not continued from bifurcation points) families are computed in the elliptic restricted problem. The majority of the new families mainly consists of stable periodic orbits at high eccentricities. The families of the 5/1 resonance are investigated for the first time in the restricted three-body problems. We highlight the effect of stable periodic orbits on the formation of stable regions in their vicinity and unveil the boundaries of such domains in phase space by computing maps of dynamical stability. The long-term stable evolution of the terrestrial planets or asteroids is dependent on the existence of regular domains in their dynamical neighbourhood in phase space, which could host them for long-time spans. This study, besides other celestial architectures that can be efficiently modelled by the circular and elliptic restricted problems, is particularly appropriate for the discovery of terrestrial companions among the single-giant planet systems discovered so far.     

Eocene migmatite formation and diachronous burial revealed by petrochronology in NW Himalaya,Zanskar

In this contribution, we highlight the importance of in-situ monazite geochronology linked to P−T modelling for identification of timescales of metamorphic processes. Barrovian-type micaschists, migmatites and augengneiss from the Gumburanjun dome in the southeastern extremity of the Gianbul dome, NW Himalaya, have been studied in order to correlate the early stages of Himalayan metamorphism at different crustal levels and infer the timing of anatexis. P−T−t paths are constrained through combined pseudosection modelling and in-situ and in-mount monazite and xenotime laser ablation–split-stream inductively coupled plasma-mass spectrometry. Petrography and garnet zoning combined with pseudosection modelling show that garnet-staurolite schists record burial from ~530 to 560°C and 5.5 kbar to ~630 to 660°C and 7 kbar; staurolite-kyanite schists from ~530 to 560°C and 5 kbar to ~670 to 680°C and 7−9 kbar; and garnet-kyanite migmatites from 540−570°C and 5 kbar to ~680 to 750°C and 7−10 kbar, probably also to >750°C and >9 kbar above the muscovite stability field. The decompression paths of garnet-staurolite schists indicate cooling on decompression, while garnet rim chemistry and local sillimanite growth point to a stage of re-equilibration at ~600 to 670°C and 4−6 kbar in some of the staurolite-kyanite schists, and at ~670 to 700°C and 6 kbar in garnet-kyanite migmatites. Some of the staurolite-kyanite schists and garnet-kyanite migmatites also contain andalusite or andalusite-cordierite. Monazite and xenotime were analysed in thin sections in garnet, staurolite and kyanite, and in the matrix; and in mounts. BSE images and compositional maps of monazite (xenotime was too small) show variable internal structures from homogeneous through patchy zoning with embayed to sharp boundaries. Two groups of samples can be identified on the basis of the presence or absence of c. 44 − 37 Ma ages. The first group of samples—two garnet-staurolite schists—recorded only c. 31 − 27 Ma ages in porphyroblasts and no c. 40 Ma ages. The second group (samples of staurolite-kyanite schist, garnet-kyanite migmatites, augengneiss) have both the older, c. 44 − 37 Ma monazite ages in porphyroblasts and younger ages down to c. 22 Ma. These significantly different ranges of ages from porphyroblasts of 44−37 Ma, and 31−27 Ma, are interpreted as the duration of prograde P−T paths in Eocene and Oligocene, and indicate diachronous two-stage burial of rocks. Early migmatization occurred at 38 Ma. The c. 29 Ma is interpreted as the time when rocks from the lower and middle crustal levels were partially exhumed and came in to contact with rocks that were downgoing at this time. Localized monazite recrystallization is as young as 26−24 Ma. The youngest ages of 23−22 Ma are related to leucogranite emplacement.     

Secular apsidal configuration of non-resonant exoplanetary systems

Using a high-order (order 12) expansion of the perturbative potential in powers of eccentricities [Libert, A.-S., Henrard, J., 2005. Celest. Mech. Dynam. Astron. 93, 187-200], we study the secular effects of two coplanar planets which are not in mean motion resonances. The main results concern eccentricity variations, oscillation amplitude of the angular difference of the apsidal lines (Δ?) and frequency of such an oscillation. We show that this analytical approach describes correctly the behaviour of most of the exosystems and underlines the known limitations of the linear Laplace-Lagrange theory. Apsidal configuration of υ Andromedae, HD 168443, HD 169830, HD 38529, HD 74156 and HD 12661 are examined. We also point out the great sensitivity of the υ Andromedae system to the initial values (e₁(0), e₂(0) or Δ?(0)).     

The dark side of zircon: textural,age, oxygen isotopic and trace element evidence of fluid saturation in the subvolcanic reservoir of the Island Park-Mount Jackson Rhyolite,Yellowstone (USA)

The Island Park-Mount Jackson series in the Yellowstone volcanic field, Wyoming (USA), is a suite of rhyolitic domes and lavas that erupted between the caldera-forming eruptions of the Mesa Fall Tuff (1.3 Ma) and the Lava Creek Tuff (0.6 Ma). Combined zircon U/Pb geochronology, Raman spectroscopy, oxygen isotopic and trace elemental compositions document storage conditions of these magmas between consecutive supereruptions. Based on comparison with co-erupted melt compositions and textural criteria, four zircon compositional groups are identified that record different stages along a continuous magmatic evolution from trace element-poor rhyolite at high temperatures to extremely fractionated rhyolite where zircon trace elements are highly enriched (e.g., >?1000 ppm U). These latter zircon domains are dark in cathodoluminescence images and show broadened Raman peaks relative to near-endmember zircon, indicating that substitution of non-stoichiometric trace elements into zircon leads to distortion of the crystal lattice. Some of these zircon domains contain inclusions of U-Th-REE-phases, likely originating from coupled dissolution–reprecipitation of metastable trace element-rich zircon in the presence of a fluid phase. Rhyolite-MELTS simulations indicate that at the conditions required to produce the observed enrichment in trace elements, a fluid phase is likely present. These findings illustrate that zircons can be assembled from a variety of co-existing magmatic environments in the same magma reservoir, including near-solidus volatile-rich melts close to the magmatic–hydrothermal transition.