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.     

RXTE observations of the transient sources IGR J17091-3624 and IGR J18539+0727

We present the results of our analysis of the RXTE observations for two transient sources, IGR J17091-3624 and IGR J18539+0727, in April 2003. The derived energy spectra of the sources and the power-density spectra of their light curves make it possible to classify them as low/hard-state X-ray binaries. The parameters of the power spectrum for IGR J18539+0727 lead us to tentatively conclude that the compact object in this binary is a black hole.     

A Solution of Einstein's Field Equations fora Tachyonic Gas: Possible Astrophysical Applications

In this paper we show that a change in the signs of some of the metric components of the solution of the field equations for the classical cosmic string results in a solution which we interpret as a time-dependent wall composed of tachyons. We show that the walls have the property of focusing the paths of particles which pass through them. As an illustration of this focusing, we demonstrate the results of a simple simulation of the interaction between one such tachyon wall and a rotating disk of point masses. This interaction leads to the temporary formation of spiral structures. These spiral structures exist for a time on the order of one galactic rotation. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.