Integrating the geodesic equations in the Schwarzschild and Kerr space-times using Beltrami's "geometrical" method

We revisit a little known theorem due to Beltrami, through which the integration of the geodesic equations of a curved manifold is accomplished by a method which, even if inspired by the Hamilton-Jacobi method, is purely geometric. The application of this theorem to the Schwarzschild and Kerr metrics leads straightforwardly to the general solution of their geodesic equations. This way of dealing with the problem is, in our opinion, very much in keeping with the geometric spirit of general relativity. In fact, thanks to this theorem we can integrate the geodesic equations by a geometrical method and then verify that the classical conservation laws follow from these equations.Comment: 12 pages; corrected typos, journal-ref adde

Snapshot coronagraphy with an interferometer in space

Diluted arrays of many optical apertures will be able to provide h igh-resolution snapshot images if the beams are combined according to the densified-pupil scheme. We show that the same principle can also provide coronagraphic images, for detecting faint sources near a bright unresolved one. Recent refinements of coronagraphic techniques, i.e. the use of a phase mask, active apodization and dark-speckle analysis, are also applicable for enhanced contrast. Implemented in the form of a proposed 50-500m Exo-Earth Discoverer array in space, the principle can serve to detect Earth-like exo-planets in the infra-red. It can also provide images of faint nebulosity near stars, active galactic nuclei and quasars. Calculations indicate that exo-planets are detectable amidst the zodiacal and exo-zodiacal emission faster than with a Bracewell array of equivalent area, a consequence of the spatial selectivity in the image.Comment: 23 pages, 10 figures, to appear in Icaru

Theory and laboratory tests of the multi-stage phase mask coronagraph

A large number of coronagraphs have been proposed to overcome the ratio that exists between the star and its planet. The planet finder of the Extremely Large Telescope, which is called EPICS, will certainly need a more efficient coronagraph than the ones that have been developed so far. We propose to use a combination of chromatic Four Quadrant Phase Mask coronagraph to achromatize the dephasing of the device while maintaining a high rejection performance. After describing this multi-stage FQPM coronagraph, we show preliminary results of a study on its capabilities in the framework of the EPICS instrument, the planet finder of the European Extremely Large Telescope. Eventually, we present laboratory tests of a rough prototype of a multi-stage four-quadrant phase mask. On one hand, we deduce from our laboratory data that a detection at the 10^-10 level is feasible in monochromatic light. On the other hand, we show the detection of a laboratory companion fainter than 10^-8 with a spectral bandwidth larger than 20%.Comment: 9 pages, 9 figures, To appear in SPIE proceeding- conference 7015 held in Marseille in June 200

Morphology of the very inclined debris disk around HD 32297

Direct imaging of circumstellar disks at high angular resolution is mandatory to provide morphological information that bring constraints on their properties, in particular the spatial distribution of dust. New techniques combining observing strategy and data processing now allow very high contrast imaging with 8-m class ground-based telescopes (10^-4 to 10^-5 at ~1") and complement space telescopes while improving angular resolution at near infrared wavelengths. We carried out a program at the VLT with NACO to image known debris disks with higher angular resolution in the near IR than ever before in order to study morphological properties and ultimately to detect signpost of planets. The observing method makes use of advanced techniques: Adaptive Optics, Coronagraphy and Differential Imaging, a combination designed to directly image exoplanets with the upcoming generation of "planet finders" like GPI (Gemini Planet Imager) and SPHERE (Spectro-Polarimetric High contrast Exoplanet REsearch). Applied to extended objects like circumstellar disks, the method is still successful but produces significant biases in terms of photometry and morphology. We developed a new model-matching procedure to correct for these biases and hence to bring constraints on the morphology of debris disks. From our program, we present new images of the disk around the star HD 32297 obtained in the H (1.6mic) and Ks (2.2mic) bands with an unprecedented angular resolution (~65 mas). The images show an inclined thin disk detected at separations larger than 0.5-0.6". The modeling stage confirms a very high inclination (i=88{\deg}) and the presence of an inner cavity inside r_0~110AU. We also found that the spine (line of maximum intensity along the midplane) of the disk is curved and we attributed this feature to a large anisotropic scattering factor (g~0.5, valid for an non-edge on disk). Abridged ...Comment: 12 pages, 10 figures, accepted for publication in Astronomy and Astrophysic

Synchronization Properties of Network Motifs

We address the problem of understanding the variable abundance of 3-node and 4-node subgraphs (motifs) in complex networks from a dynamical point of view. As a criterion in the determination of the functional significance of a n-node subgraph, we propose an analytic method to measure the stability of the synchronous state (SSS) the subgraph displays. We show that, for undirected graphs, the SSS is correlated with the relative abundance, while in directed graphs the correlation exists only for some specific motifs.Comment: 7 pages, 3 figure