Quasi integral of motion for axisymmetric potentials

We present an estimate of the third integral of motion for axisymmetric three-dimensional potentials. This estimate is based on a Staeckel approximation and is explicitly written as a function of the potential. We tested this scheme for the Besancon Galactic model and two other disc-halo models and find that orbits of disc stars have an accurately conserved third quasi integral. The accuracy ranges from of 0.1% to 1% for heights varying from z = 0~kpc to z= 6 kpc and Galactocentric radii R from 5 to 15kpc. We also tested the usefulness of this quasi integral in analytic distribution functions of disc stellar populations: we show that the distribution function remains approximately stationary and that it allows to recover the potential and forces by applying Jeans equations to its moments.Comment: 9 pages, 9 figures, accepted for publication in Astron. and Astrophy

The distribution of nearby stars in phase space mapped by Hipparcos III. Clustering and streaming among A-F type stars

This paper presents the detailed results obtained in the search of density- velocity inhomogeneities in a volume limited and absolute magnitude limited sample of A-F type dwarfs within 125 parsecs of the Sun. A 3-D wavelet analysis is used to extract inhomogeneities, both in the density and velocity distributions. Having established a real picture of the phase space without assumption we come back to previously known observational facts regarding clusters and associations, superclusters. In the 3-D position space, well known open clusters (Hyades, Coma Berenices and Ursa Major), associations (parts of the Scorpio-Centaurus association) as well as the Hyades evaporation track are retrieved. Three new probably loose clusters are identified (Bootes, Pegasus 1 and 2). The sample is relatively well mixed in the position space since less than 7 per cent of the stars belong to structures with coherent kinematics, most likely gravitationally bound. In the velocity space, the majority of large scale velocity structures ($\sigma$ ~ 6.3 $km s-1$) are Eggen's superclusters (Pleiades SCl, Hyades SCl and Sirius SCl) with the whole Centaurus association. A new supercluster-like structure is found with a mean velocity between the Sun and Sirius SCl velocities. These structures are all characterized by a large age range which reflects the overall sample age distribution. Moreover, a few old streams of ~ 2 Gyr are also extracted at this scale with high U components. We show that all these large velocity dispersion structures represent 46% of the sample. Smaller scales (\sigma ~ 3.8 and 2.4 $km s-1$) reveal that superclusters are always substructured by 2 or more streams which generally exhibit a coherent age distribution. Percentages of stars in these streams are 38% and 18% respectively.Comment: 25 pages, Latex, 29 figures, 4 tables to be published in A&A Supplements Serie

Economie politique de la gouvernance de l’Union européenne.

Le rapport s’inscrit dans le débat approfondissement / élargissement de l’Union. Il souligne la dimension politique de la construction économique européenne en abordant les thèmes du nombre et de la taille des nations, de l’intégration économique, de l’extension des ‘bonnes pratiques’ de ‘gouvernance’ économique. Il passe en revue les principaux instruments de politique économique dont les États se sont en tout ou partie dessaisis – le policy mix monnaie -budget, les instruments d’action destinés à orienter l’offre globale et le tissu industriel-. Il évoque pour terminer la question du découpage des compétences entre États, Régions et Autorités supranationales. Les responsabilités politiques encourues devant les coûts d’ajustement entraînés par la dynamique économique posent le problème de la légitimité comme de l’efficacité des autorités européennes. Ces questions passent par une réflexion sur l’approfondissement du modèle européen. Nécessitent – elles une pause dans l’agrandissement de l’UE ou l’invention d’une autre solution ?Gouvernance; construction économique européenne; bilan économique; économie pure; mobilité du travail; mobilité des capitaux; intégration; efficacité; légitimité politique;

On high proper motion white dwarfs from photographic surveys

The interpretation of high proper motion white dwarfs detected by Oppenheimer et al (2001) was the start of a lively controversy. While the discoverers identify a large fraction of their findings as dark halo members, others interpret the same sample as essentially made of disc and/or thick disc stars. We use the comprehensive description of Galactic stellar populations provided by the "Besancon" model to produce a realistic simulation of Oppenheimer et al. data, including all observational selections and calibration biases. The conclusion is unambiguous: Thick disc white dwarfs resulting from ordinary hypotheses on the local density and kinematics are sufficient to explain the observed objects, there is no need for halo white dwarfs. This conclusion is robust to reasonable changes in model ingredients. The main cause of the misinterpretation seems to be that the velocity distribution of a proper motion selected star sample is severely biased in favour of high velocities. This has been neglected in previous analyses. Obviously this does not prove that no such objects like halo white dwarfs can exist, but Oppenheimer et al. observations drive their possible contribution in the dark matter halo down to an extremely low fraction.Comment: 4 pages, 1 figure, A&A Letters, accepte

Approximate integrals of motion

We determine approximate numerical integrals of motion of 2D symmetric Hamiltonian systems. We detail for a few gravitational potentials the conditions under which quasi-integrals are obtained as polynomial series. We show that each of these potentials has a wide range of regular orbits that are accurately modelled with a unique approximate integral of motion.Comment: 11 pages, 11 figures, accepted for publication in Astronomy and Astrophysic

On the kinematic deconvolution of the local neighbourhood luminosity function

A method for inverting the statistical star counts equation, including proper motions, is presented; in order to break the degeneracy in that equation it uses the supplementary constraints required by dynamical consistency. The inversion gives access to both the kinematics and the luminosity function of each population in three r\'egimes: the singular ellipsoid, the constant ratio Schwarzschild ellipsoid plane parallel models and the epicyclic model. This more realistic model is taylored to account for local neighbourhood density and velocity distribution. The first model is fully investigated both analytically and via means of a non-parametric inversion technique, while the second model is shown to be formally its equivalent. The effect of noise and incompleteness in apparent magnitude is investigated. The third model is investigated via a 5D+2D non-parametric inversion technique where positivity of the underlying luminosity function is explicitely accounted for. It is argued that its future application to data such as the Tycho catalogue (and in the upcoming satellite GAIA) could lead -- provided the vertical potential, and/or the asymmetric drift or w_0 are known -- to a non-parametric determination of the local neighbourhood luminosity function without any reference to stellar evolution tracks. It should also yield the proportion of stars for each kinematic component and a kinematic diagnostic to split the thin disk from the thick disk or the halo.Comment: 18 pages, LateX (or Latex, etc), mnras, accepted for publicatio