Electric Discharges in the Protoplanetary Nebula as a Source of Impulse Magnetic Fields to Promote Dust Aggregation

Lightning discharge generated in the protoplanetary nebula is viewed as a temporally isolated surge in the flow of electrically charged particles, similar to that of terrestrial lightning. If the current is intense enough, a powerful circular impulse magnetic field is generated around the instantaneous virtual electric conductor. Such magnetic field is capable of magnetizing dust grains containing ferromagnetic components present in its vicinity to their saturation levels. As a result, dust grains attract one another, forming the aggregates. This magnetically driven attraction suggests an important process possibly operational at an early stage of the planetary accretion. Based on both a classical model for electric conductor, and the theory of Lienard–Wiechert electromagnetic potentials, our calculations show that the magnetic impulse due to a discharge channel of a few cm in diameter transferring a charge of about 10⁴ electrons reaches as high as 10 T. At these magnetic fields, the ferromagnetic dust grains, and possibly the already-formed larger aggregates as well, are easily magnetized to the saturation levels, producing compact clusters exhibiting permanent magnetic moments.     

Two-Parametric Families of Orbits and Multiseparability of Planar Potentials

Combining the results of the inverse problem of dynamics with the theory of multiseparability of planar potentials, we find biparametric families of orbits, whose existence guarantees the multiseparability of the potential. We also study the allowed regions of the plane, where these orbits are traced.     

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.     

Chemical Enrichment of the Intra-Cluster Medium

We investigate the metal enrichment of the intra-cluster medium by using a method that combines N-Body simulations and a semi-analytic model (SAM) of galaxy formation. The cluster of galaxies is simulated in a flat, low density universe, with a numerical resolution that allows the detection of substructures in the dark matter background of the cluster. The phenomenological approach used to model the physical processes involved in the galaxy formation and metal production is applied to the substructures found in the dark matter halos detected at different redshifts. Details of the chemical implementation in the SAM and first results related to the mean properties of the baryonic matter components are presented. This revised version was published online in August 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.