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

Periodic orbits in the logarithmic potential

Analytic methods to investigate periodic orbits in galactic potentials. To evaluate the quality of the approximation of periodic orbits in the logarithmic potential constructed using perturbation theory based on Hamiltonian normal forms. The solutions of the equations of motion corresponding to periodic orbits are obtained as series expansions computed by inverting the normalizing canonical transformation. To improve the convergence of the series a resummation based on a continued fraction may be performed. This method is analogous to that looking for approximate rational solutions (Prendergast method). It is shown that with a normal form truncated at the lowest order incorporating the relevant resonance it is possible to construct quite accurate solutions both for normal modes and periodic orbits in general position.Comment: 10 pages, 9 figures, accepted for publication on Astronomy and Astrophysic

Stability of axial orbits in galactic potentials

We investigate the dynamics in a galactic potential with two reflection symmetries. The phase-space structure of the real system is approximated with a resonant detuned normal form constructed with the method based on the Lie transform. Attention is focused on the stability properties of the axial periodic orbits that play an important role in galactic models. Using energy and ellipticity as parameters, we find analytical expressions of bifurcations and compare them with numerical results available in the literature.Comment: 20 pages, accepted for publication on Celestial Mechanics and Dynamical Astronom

BIGRE: a low cross-talk integral field unit tailored for extrasolar planets imaging spectroscopy

Integral field spectroscopy (IFS) represents a powerful technique for the detection and characterization of extrasolar planets through high contrast imaging, since it allows to obtain simultaneously a large number of monochromatic images. These can be used to calibrate and then to reduce the impact of speckles, once their chromatic dependence is taken into account. The main concern in designing integral field spectrographs for high contrast imaging is the impact of the diffraction effects and the non-common path aberrations together with an efficient use of the detector pixels. We focus our attention on integral field spectrographs based on lenslet-arrays, discussing the main features of these designs: the conditions of appropriate spatial and spectral sampling of the resulting spectrograph's slit functions and their related cross-talk terms when the system works at the diffraction limit. We present a new scheme for the integral field unit (IFU) based on a dual-lenslet device (BIGRE), that solves some of the problems related to the classical TIGER design when used for such applications. We show that BIGRE provides much lower cross-talk signals than TIGER, allowing a more efficient use of the detector pixels and a considerable saving of the overall cost of a lenslet-based integral field spectrograph.Comment: 17 pages, 18 figures, accepted for publication in Ap

Quantitative predictions with detuned normal forms

The phase-space structure of two families of galactic potentials is approximated with a resonant detuned normal form. The normal form series is obtained by a Lie transform of the series expansion around the minimum of the original Hamiltonian. Attention is focused on the quantitative predictive ability of the normal form. We find analytical expressions for bifurcations of periodic orbits and compare them with other analytical approaches and with numerical results. The predictions are quite reliable even outside the convergence radius of the perturbation and we analyze this result using resummation techniques of asymptotic series.Comment: Accepted for publication on Celestial Mechanics and Dynamical Astronom

SPICES: Spectro-Polarimetric Imaging and Characterization of Exoplanetary Systems

SPICES (Spectro-Polarimetric Imaging and Characterization of Exoplanetary Systems) is a five-year M-class mission proposed to ESA Cosmic Vision. Its purpose is to image and characterize long-period extrasolar planets and circumstellar disks in the visible (450 - 900 nm) at a spectral resolution of about 40 using both spectroscopy and polarimetry. By 2020/22, present and near-term instruments will have found several tens of planets that SPICES will be able to observe and study in detail. Equipped with a 1.5 m telescope, SPICES can preferentially access exoplanets located at several AUs (0.5-10 AU) from nearby stars ($<$25 pc) with masses ranging from a few Jupiter masses to Super Earths ($\sim$2 Earth radii, $\sim$10 M$_{\oplus}$) as well as circumstellar disks as faint as a few times the zodiacal light in the Solar System

VizieR Online Data Catalog: SPHERE and NaCo images of HD 19467B (Maire+, 2020)

The SPHERE and NaCo high-contrast images processed with angular differential imaging are provided. The SPHERE and NaCo/Lp images were processed with TLOCI-ADI (see Galicher et al., 2018A&A...615A..92G) and are normalized to the stellar peak (contrast with respect to the star). The NaCo/Mp image was processed with PCA (see Cheetham et al., 2019A&A...622A..80C). (2 data files)