A compact model for the planar rhomboidal 4-body problem

We obtain a compact model for the global study of the planar rhomboidal 4-body problem in a level of constant negative energy. This model is a variation of the non compact model obtained through a McGehee blow up transformation. but compactness permits to obtain results which are not clear in the other case.     

Observations of the OH Radical in Comet C/1995 O1 (Hale-Bopp) with the Nançay Radio Telescope

We present OH 18-cm observations of comet Hale-Bopp (C/1995 O1) at the Nançay radio telescope. On nucleus and offset position observations allowed us to obtain both OH production rates and quenching radii. The maximum OH production rate was reached around perihelion, at about10³¹ s^-1.     

Stability of interplay motions

A family of rectilinear periodic solutions of the three-body problem, in which the central body collides alternately with each of the two other bodies, is investigated numerically for all values of the three masses. It is found that for every mass combination there exists just one solution of this kind. The linear stability of the orbits with respect to arbitrary three-dimensional perturbations is also investigated. Domains of stability and instability are displayed in a triangular mass diagram. Their boundaries form one-parameter families of critical orbits, which are tabulated. Limiting cases where one or two masses vanish are studied in detail. The domains of stability cover nearly one half of the total area in the mass diagram: this reinforces the conclusion that real triple stars might have motions of a kind entirely different from the usual hierarchical arrangement.     

Solar abundance of praseodymium

16 lines of Pr ii possibly present in the solar photospheric spectrum have been studied. When including hyperfine structure in synthetic calculations, investigations of 9 lines result in an abundance A _Pr = 0.71 ± 0.08 in the log A _H = 12.00 scale.     

Helical structures around quiescent solar prominences computed from observable magnetic fields

We analyse the magnetic support of solar prominences in two-dimensional linear force-free fields. A line current is added to model a helical configuration, well suited to trap dense plasma in its bottom part. The prominence is modeled as a vertical mass-loaded current sheet in equilibrium between gravity and magnetic forces.We use a finite difference numerical technique which incorporates both vertical photospheric and horizontal prominence magnetic field measurements. The solution of this mixed boundary problem generally presents singularities at both the bottom and top of the model prominence. The removal of the singularities is achieved by superposition of solutions. Together with the line current equilibrium, these three conditions determine the amplitude of the magnetic field in the prominence, the flux below the prominence and the current intensity, for a given height of the line current. A numerical check of accuracy in the removal of singularities, is done by using known analytical solutions in the potential limit.We have investigated both bipolar and quadrupolar photospheric regions. In this mixed boundary problem the polarity of the field component orthogonal to the prominence is mainly fixed by the imposed height of the line current. For bipolar regions above (respectively below) a critical height the configuration is inverse (respectively normal). For quadrupolar regions the polarity is reversed if we refer the prominence polarity to the closest photospheric polarities. We introduce the polarity of the component parallel to the prominence axis with reference to a sheared arcade. Increasing the shear with fixed boundary conditions can increase or decrease the mass supported depending on the configuration.     

Observed interstellar magnetized supershells and stellar-wind theories

Early theories of stellar winds from an association of OB stars predicted the formation of a common superbubble enclosed by athin, dense supershell, through the combined effort of the winds from the stars at the center. These early theories were adequate for explaining the primary observational features (defined as: shell age, outer radius, shell speed, shell mass, shell energy), but they were not adequate to explain the secondary features (defined as: shell thickness, shell magnetic field, shell gas density). A recently published theory for a stellar-wind-bubble and supershell, predicting a range ofthick supershells, can now be compared with the secondary observational features.Using the observed parameters from all large (> 100 pc) interstellar magnetized supershells near the sun (< 1 kpc away), I assemble for comparison with stellar-wind theories: (a) the primary observational features of these shells — I find: large shell age, large outer radius, low shell speed, large shell mass, large shell energy; and (b) some of their secondary observational features — I find: thick shell, low shell magnetic field strengh, low shell gas density.     

On the Centre Manifold of Collinear Points in the Planar Three-Body Problem

We study the existence of invariant tori in a neighbourhood of the collinear equilibrium points of the planar three-body problem. To this end some properties of the normal form of the Hamiltonian reduced to the 4D central manifold are proved. Using this normal form, we show that the nondegeneracy conditions of KAM theorem are satisfied for all positive masses, including the 2:1 resonance case. The evaluation of the conditions is done numerically.