Escapes and Recurrence in a Simple Hamiltonian System

Many physical systems can be modeled as scattering problems. For example, the motions of stars escaping from a galaxy can be described using a potential with two or more escape routes. Each escape route is crossed by an unstable Lyapunov orbit. The region between the two Lyapunov orbits is where the particle interacts with the system. We study a simple dynamical system with escapes using a suitably selected surface of section. The surface of section is partitioned in different escape regions which are defined by the intersections of the asymptotic manifolds of the Lyapunov orbits with the surface of section. The asymptotic curves of the other unstable periodic orbits form spirals around various escape regions. These manifolds, together with the manifolds of the Lyapunov orbits, govern the transport between different parts of the phase space. We study in detail the form of the asymptotic manifolds of a central unstable periodic orbit, the form of the escape regions and the infinite spirals of the asymptotic manifolds around the escape regions. We compute the escape rate for different values of the energy. In particular, we give the percentage of orbits that escape after a finite number of iterations. In a system with escapes one cannot define a Poincaré recurrence time, because the available phase space is infinite. However, for certain domains inside the lobes of the asymptotic manifolds there is a finite minimum recurrence time. We find the minimum recurrence time as a function of the energy.This revised version was published online in October 2005 with corrections to the Cover Date.     

Search for short cosmic gamma-ray bursts using data from the APEX and LILAS experiments onboard the Phobos-2 interplanetary spacecraft

A statistical analysis of the spectral and temporal parameters for 546 triggering events on the APEX gamma-ray detector onboard the Phobos-2 spacecraft has revealed a group of 28 events that are probably short cosmic gamma-ray bursts (GRBs). The distribution of the full group of 74 events of the APEX experiment in duration parameter is bimodal in shape, which is in good agreement with the bimodal shape of the BATSE GRB distribution. A search for the detected group of short events using data from the LILAS X-ray and soft gamma-ray detector onboard the same spacecraft has yielded no positive result. A comparison of the APEX and LILAS data has led us to conclude that the short GRBs have a significantly reduced soft gamma-ray flux at energies <100 keV relative to the power law dN/dE=CE^?α with the average index α=2.62.     

Radiative Transfer in Inhomogeneous Atmospheres. III

The approach proposed in the previous parts of this series of papers is used to solve the radiative transfer problem in scattering and absorbing multicomponent atmospheres. Linear recurrence relations are obtained for both the reflectance and transmittance of these kinds of atmospheres, as well as for the emerging intensities when the atmosphere contains energy sources. Spectral line formation in a one-dimensional inhomogeneous atmosphere is examined as an illustration of the possibility of generalizing our approach to the matrix case. It is shown that, in this case as well, the question reduces to solving an initial value problem for linear differential equations. Some numerical calculations are presented.     

On the existence of prevalent westward shifts in the solar atmosphere

A statistical analysis of the deviations of the sideral angular rotation velocities () of single sunspot groups from the averaged rotation curve , shows that positive deviations tend to be greater than negative ones: we can therefore deduce the existence of prevalent westward shifts in the solar atmosphere. This effect is only partially due to the sunspot group proper motions at the beginning of their evolution, and it could indicate the prevalence of westward currents in the solar photosphere.     

Joint NANCAY RADIOHELIOGRAPH AND LASCO OBSERVATIONS OF CORONAL MASS EJECTIONS – II. The 9 July 1996 Event

The development of a coronal mass ejection on 9 July 1996 has been analyzed by comparing the observations of the LASCO/SOHO coronagraphs with those of the Nancay radioheliograph. The spatial and temporal evolution of the associated radioburst is complex and involves a long-duration continuum. The analysis of the time sequence of the radio continuum reveals the existence of distinct phases associated with distinct reconnection processes and magnetic restructuring of the corona. Electrons are accelerated in association with these reconnection processes. An excellent spatial association is found between the position and extension of the radio source and the CME seen by LASCO. Furthermore, it is shown that the topology and evolution of the source of the radio continuum involve successive interactions between two systems of loops. These successive interactions lead to magnetic reconnection, then to a large scale coronal restructuring. Thus electrons of coronal origin may have access to the interplanetary medium in a large range of heliographic latitudes as revealed by the Ulysses observations.     

The Varying Multipolar Structure of the Sun's Magnetic Field and the Evolution of the Solar Magnetosphere Through the Solar Cycle

The Sun's magnetic field extends far from the photosphere, into the corona, defining a magnetically dominated region before being drawn out radially by the solar wind flow. This region, where the internal sources of the solar field dominate the plasma structures and the energetic particle movement, can be properly considered the solar magnetosphere. The magnetic field in this region can be approximately described by models that extrapolate photospheric magnetic field observations under some simplifying assumptions. In this paper we use a potential field model which describes the solar field up to a source surface at 3.25 R_s, where the field is constrained to become radial. We present the variation of the magnitude and inclination of the various multipolar components throughout the solar magnetic cycle that characterise the changes in the structure of the solar magnetosphere over a period of 22 years. We also present some 3-D images of the coronal magnetic structure to show the global evolution of the solar magnetosphere throughout the solar cycle and discuss the importance of taking this structure into account in order to relate interplanetary and solar features.     

Coronal line-width variations

Line-width measurements of the coronal ion Siviii confirm earlier observations which show an increase in the non-thermal velocity above the solar limb. The present data, taken at the equatorial limb, show an increase from 24 km s^-1 at the limb to 28 km s^-1 some 25000 km above the limb. The electron density as measured from the Siviii line pair shows a decrease from 3.5 × 10⁸ cm^-3 to 1.8 × 10⁸ cm^-3 over the same distance. These data imply that the non-thermal velocity is inversely proportional to the quadratic root of the electron density, in excellent agreement with that predicted for undamped radially propagating Alfvén waves.