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.     

Dark matter accretion wakes of high-redshift black holes

Anisotropic emission of gravitational waves during the merger of black holes induces a recoil velocity on the centre of mass of the binary and the final merger product can then be ejected from its host galaxy. We consider ejected black holes which stay on bound orbits around their host haloes. A recoiled black hole which moves on an almost radial orbit outside the virial radius of its central galaxy, in the cold dark matter background, reaches its apapsis in a finite time. Due to small dark matter velocity dispersion at high redshifts and also the small black hole velocity near the apapsis passage a high-density wake forms around these black hole. Gamma-ray emission can result from the enhancement of dark matter annihilation in these wakes. The diffuse high-energy gamma-ray background from the ensemble of such black holes in the Hubble volume is also evaluated.     

New chitinozoans from the historical type area of the Hirnantian Stage and additional key sections in the Wye Valley,Wales, UK

The type locality for several core elements of the Hirnantia brachiopod fauna is a small disused quarry on the western slopes of Cwm Hirnant. There, the Hirnant Limestone Member of the Foel‐y‐Ddinas Mudstone Formation yields a new, well‐preserved chitinozoan assemblage, attributed to the Spinachitina taugourdeaui Biozone. This allows tight correlation with the Hirnantian of Baltica and Laurentia and neatly ties the chitinozoan zonation with the classical brachiopod fauna. Nearby, the chitinozoan assemblage from the Caradoc Cymerig Limestone Member at Gelli‐grîn belongs to the Spinachitina cervicornis Biozone?, and is identical to that recovered from the Burrellian in the Onny Valley, Welsh Borderland. A Silurian assemblage higher up section, discovered in the Cwm‐yr‐Aethnen Formation, is attributed to the globally recognized Eisenackitina dolioliformis Biozone. Attempts to integrate the chitinozoan and graptolite biozonation, in the central Welsh Rhayader area, were less successful. Copyright © 2008 John Wiley & Sons, Ltd.     

Normalisation des systèmes linéaires canoniques et application au problème restreint des trois corps

An algorithm is given for normalizing conservative linear Hamiltonian systems. This one generalizes Siegel's method to the cases where the eigenvalues are multiple. We obtain by a canonical transformation a normal form of two blocks, one of which is the upper Jordan form, and the other, the lower Jordan form. We select real solutions from the solutions of these equations, and we apply the result to the restricted three body problem in the vicinity of the triangular points for Routh's critical mass ratio.

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_n est la matrice unité d'ordren,O _n est la matrice nulle d'ordren.     

Experimental study of brucite dissolution and precipitation in aqueous solutions: surface speciation and chemical affinity control

Dissolution and precipitation rates of brucite (Mg(OH)₂) were measured at 25°C in a mixed-flow reactor as a function of pH (2.5 to 12), ionic strength (10⁻⁴ to 3 M), saturation index (−12 < log Ω < 0.4) and aqueous magnesium concentrations (10⁻⁶ to 5·10⁻⁴ M). Brucite surface charge and isoelectric point (pH_IEP) were determined by surface titrations in a limited residence time reactor and electrophoretic measurements, respectively. The pH of zero charge and pH_IEP were close to 11. A two-pK, one site surface speciation model which assumes a constant capacitance of the electric double layer (5 F/m²) and lack of dependence on ionic strength predicts the dominance of >MgOH₂⁺ species at pH < 8 and their progressive replacement by >MgOH° and >MgO⁻ as pH increases to 10-12. Rates are proportional to the square of >MgOH₂⁺ surface concentration at pH from 2.5 to 12. In accord with surface speciation predictions, dissolution rates do not depend on ionic strength at pH 6.5 to 11. Brucite dissolution and precipitation rates at close to equilibrium conditions obeyed TST-derived rate laws. At constant saturation indices, brucite precipitation rates were proportional to the square of >MgOH₂⁺ concentration. The following rate equation, consistent with transition state theory, describes brucite dissolution and precipitation kinetics over a wide range of solution composition and chemical affinity:

     

Heliocentric evolution of the degradation of polyoxymethylene: Application to the origin of the formaldehyde (H2CO) extended source in Comet C/1995 O1 (Hale-Bopp)

The H₂CO production rates measured in Comet C/1995 O1 (Hale-Bopp) from radio wavelength observations [Biver, N., and 22 colleagues, 2002a. Earth Moon Planets 90, 5-14] showed a steep increase with decreasing heliocentric distance. We studied the heliocentric evolution of the degradation of polyoxymethylene (formaldehyde polymers: (CH₂O)_n, also called POM) into gaseous H₂CO. POM decomposition can indeed explain the H₂CO density profile measured in situ by Giotto spacecraft in the coma of Comet 1P/Halley, which is not compatible with direct release from the nucleus [Cottin, H., Bénilan, Y., Gazeau, M.-C., Raulin, F., 2004. Icarus 167, 397-416]. We show that the H₂CO production curve measured in Comet C/1995 O1 (Hale-Bopp) can be accurately reproduced by this mechanism with a few percents by mass of solid POM in grains. The steep heliocentric evolution is explained by the thermal degradation of POM at distances less than 3.5 AU. This study demonstrates that refractory organics present in cometary dust can significantly contribute to the composition of the gaseous coma. POM, or POM-like polymers, might be present in cometary grains. Other molecules, like CO and HNC, might also be produced by a similar process.     

TNOs are Cool: A Survey of the Transneptunian Region

Over one thousand objects have so far been discovered orbiting beyond Neptune. These trans-Neptunian objects (TNOs) represent the primitive remnants of the planetesimal disk from which the planets formed and are perhaps analogous to the unseen dust parent-bodies in debris disks observed around other main-sequence stars. The dynamical and physical properties of these bodies provide unique and important constraints on formation and evolution models of the Solar System. While the dynamical architecture in this region (also known as the Kuiper Belt) is becoming relatively clear, the physical properties of the objects are still largely unexplored. In particular, fundamental parameters such as size, albedo, density and thermal properties are difficult to measure. Measurements of thermal emission, which peaks at far-IR wavelengths, offer the best means available to determine the physical properties. While Spitzer has provided some results, notably revealing a large albedo diversity in this population, the increased sensitivity of Herschel and its superior wavelength coverage should permit profound advances in the field. Within our accepted project we propose to perform radiometric measurements of 139 objects, including 25 known multiple systems. When combined with measurements of the dust population beyond Neptune (e.g. from the New Horizons mission to Pluto), our results will provide a benchmark for understanding the Solar debris disk, and extra-solar ones as well.     

Magnesite growth rates as a function of temperature and saturation state

Magnesite growth rates and step velocities have been measured systematically as a function of temperature from 80 to 105 °C and saturation state in 0.1 M NaCl solutions using hydrothermal atomic force microscopy (HAFM). The observations indicate that at these conditions magnesite precipitation is dominated by the coupling of step generation via spiral growth at screw dislocations and step advancement away from these dislocations. As these two processes occur in series the slowest of these dominates precipitation rates. At 100 °C magnesite growth rates (r) determined by HAFM are consistent with

r=k(Ω-1)²,