Geometric Derivation of the Delaunay Variables and Geometric Phases

We derive the classical Delaunay variables by finding a suitable symmetry action of the three torus T³ on the phase space of the Kepler problem, computing its associated momentum map and using the geometry associated with this structure. A central feature in this derivation is the identification of the mean anomaly as the angle variable for a symplectic S ¹ action on the union of the non-degenerate elliptic Kepler orbits. This approach is geometrically more natural than traditional ones such as directly solving Hamilton–Jacobi equations, or employing the Lagrange bracket. As an application of the new derivation, we give a singularity free treatment of the averaged J ₂-dynamics (the effect of the bulge of the Earth) in the Cartesian coordinates by making use of the fact that the averaged J ₂-Hamiltonian is a collective Hamiltonian of the T³ momentum map. We also use this geometric structure to identify the drifts in satellite orbits due to the J ₂ effect as geometric phases.     

Cosmic structure growth and dark energy

Dark energy has a dramatic effect on the dynamics of the Universe, causing the recently discovered acceleration of the expansion. The dynamics are also central to the behaviour of the growth of large-scale structure, offering the possibility that observations of structure formation provide a sensitive probe of the cosmology and dark energy characteristics. In particular, dark energy with a time-varying equation of state can have an influence on structure formation stretching back well into the matter-dominated epoch. We analyse this impact, first calculating the linear perturbation results, including those for weak gravitational lensing. These dynamical models possess definite observable differences from constant equation of state models. Then we present a large-scale numerical simulation of structure formation, including the largest volume to date involving a time-varying equation of state. We find the halo mass function is well described by the Jenkins et al. mass function formula. We also show how to interpret modifications of the Friedmann equation in terms of a time-variable equation of state. The results presented here provide steps toward realistic computation of the effect of dark energy in cosmological probes involving large-scale structure, such as cluster counts, the Sunyaev–Zel'dovich effect or weak gravitational lensing.     

Robust Scalings in Compressible Flux Pile-Up Reconnection

Flux pile-up magnetic reconnection is traditionally considered only for incompressible plasmas. The question addressed in this paper is whether the pile-up scalings with resistivity are robust when plasma compressibility is taken into account. A simple analytical argument makes it possible to understand why the transition from a highly compressible limit to the incompressible one is difficult to discern in typical simulations spanning a few decades in resistivity. From a practical standpoint, however, flux pile-up reconnection in a compressible plasma can lead to anomalous electric resistivity in the current sheet and flare-like energy release of magnetic energy in the solar corona.     

Pan-African eclogite facies metamorphism of ultramafic rocks in the Shackleton Range, Antarctica

In the Shackleton Range of East Antarctica, garnet-bearing ultramafic rocks occur as lenses in supracrustal high-grade gneisses. In the presence of olivine, garnet is an unmistakable indicator of eclogite facies metamorphic conditions. The eclogite facies assemblages are only present in ultramafic rocks, particularly in pyroxenites, whereas other lithologies – including metabasites – lack such assemblages. We conclude that under high-temperature conditions, pyroxenites preserve high-pressure assemblages better than isofacial metabasites, provided the pressure is high enough to stabilize garnet–olivine assemblages (i.e. ≥18–20 kbar). The Shackleton Range ultramafic rocks experienced a clockwise P–T path and peak conditions of 800–850 °C and 23–25 kbar. These conditions correspond to ∼70 km depth of burial and a metamorphic gradient of 11–12 °C km⁻¹ that is typical of a convergent plate-margin setting. The age of metamorphism is defined by two garnet–whole-rock Sm–Nd isochrons that give ages of 525 ± 5 and 520 ± 14 Ma corresponding to the time of the Pan-African orogeny. These results are evidence of a Pan-African suture zone within the northern Shackleton Range. This suture marks the site of a palaeo-subduction zone that likely continues to the Herbert Mountains, where ophiolitic rocks of Neoproterozoic age testify to an ocean basin that was closed during Pan-African collision. The garnet-bearing ultramafic rocks in the Shackleton Range are the first known example of eclogite facies metamorphism in Antarctica that is related to the collision of East and West Gondwana and the first example of Pan-African eclogite facies ultramafic rocks worldwide. Eclogites in the Lanterman Range of the Transantarctic Mountains formed during subduction of the palaeo-Pacific beneath the East Antarctic craton.     

Estimation of snow water equivalent using microwave radiometry over Arctic first‐year sea ice

The magnitude and spatial distribution of snow on sea ice are both integral components of the ocean–sea‐ice–atmosphere system. Although there exists a number of algorithms to estimate the snow water equivalent (SWE) on terrestrial surfaces, to date there is no precise method to estimate SWE on sea ice. Physical snow properties and in situ microwave radiometry at 19, 37 and 85 GHz, V and H polarization were collected for a 10‐day period over 20 first‐year sea ice sites. We present and compare the in situ physical, electrical and microwave emission properties of snow over smooth Arctic first‐year sea ice for 19 of the 20 sites sampled. Physical processes creating the observed vertical patterns in the physical and electrical properties are discussed. An algorithm is then developed from the relationship between the SWE and the brightness temperature measured at 37 GHz (55°) H polarization and the air temperature. The multiple regression between these variables is able to account for over 90% of the variability in the measured SWE. This algorithm is validated with a small in situ data set collected during the 1999 field experiment. We then compare our data against the NASA snow thickness algorithm, designed as part of the NASA Earth Enterprise Program. The results indicated a lack of agreement between the NASA algorithm and the algorithm developed here. This lack of agreement is attributed to differences in scale between the Special Sensor Microwave/Imager and surface radiometers and to differences in the Antarctic versus Arctic snow physical and electrical properties. Copyright © 2003 John Wiley & Sons, Ltd.     

F stars, metallicity and the ages of red galaxies at z > 1

We explore whether the rest-frame near-ultraviolet spectral region, observable in high-redshift galaxies via optical spectroscopy, contains sufficient information to allow the degeneracy between age and metallicity to be lifted. We do this by first testing the ability of evolutionary synthesis models to reclaim the correct metallicity when fitted to the near-ultraviolet spectra of F stars of known (subsolar and supersolar) metallicity. F stars are of particular interest because the rest-frame near-ultraviolet spectra of the oldest known elliptical galaxies at   z > 1  appear to be dominated by F stars near to the main-sequence turn-off.
We find that, in the case of the F stars, where the Hubble Space Telescope ultraviolet spectra have a high signal-to-noise ratio, fitting models in which the metallicity is allowed to vary as a free parameter is rather successful at deriving the correct metallicity. As a result, the estimated turn-off ages of these stars yielded by model-fitting are well constrained. Encouraged by this we have fitted these same variable-metallicity models to the deep, optical spectra of the   z ≃ 1.5 mJy  radio galaxies 53W091 and 53W069 obtained with the Keck telescope. While the age and metallicity are not so easily constrained for these galaxies, we find that even when metallicity is allowed as a free parameter, the best estimates of their ages are still ≥3 Gyr, with ages younger than 2 Gyr now strongly excluded. Furthermore, we find that a search of the entire parameter space of metallicity and star formation history using MOPED leads to the same conclusion. Our results therefore continue to argue strongly against an Einstein–de Sitter universe, and favour a Λ-dominated universe in which star formation in at least these particular elliptical galaxies was completed somewhere in the redshift range   z = 3–5  .