A Framework for Generalising the Newton Method and Other Iterative Methods from Euclidean Space to Manifolds

The Newton iteration is a popular method for minimising a cost function on Euclidean space. Various generalisations to cost functions defined on manifolds appear in the literature. In each case, the convergence rate of the generalised Newton iteration needed establishing from first principles. The present paper presents a framework for generalising iterative methods from Euclidean space to manifolds that ensures local convergence rates are preserved. It applies to any (memoryless) iterative method computing a coordinate independent property of a function (such as a zero or a local minimum). All possible Newton methods on manifolds are believed to come under this framework. Changes of coordinates, and not any Riemannian structure, are shown to play a natural role in lifting the Newton method to a manifold. The framework also gives new insight into the design of Newton methods in general.Comment: 36 page

Nulling interferometry: impact of exozodiacal clouds on the performance of future life-finding space missions

Earth-sized planets around nearby stars are being detected for the first time by ground-based radial velocity and space-based transit surveys. This milestone is opening the path towards the definition of missions able to directly detect the light from these planets, with the identification of bio-signatures as one of the main objectives. In that respect, both ESA and NASA have identified nulling interferometry as one of the most promising techniques. The ability to study distant planets will however depend on exozodiacal dust clouds surrounding the target stars. In this paper, we assess the impact of exozodiacal dust clouds on the performance of an infrared nulling interferometer in the Emma X-array configuration. For the nominal mission architecture with 2-m aperture telescopes, we found that point-symmetric exozodiacal dust discs about 100 times denser than the solar zodiacal cloud can be tolerated in order to survey at least 150 targets during the mission lifetime. Considering modeled resonant structures created by an Earth-like planet orbiting at 1 AU around a Sun-like star, we show that the tolerable dust density for planet detection goes down to about 15 times the solar zodiacal density for face-on systems and decreases with the disc inclination. The upper limits on the tolerable exozodiacal dust density derived in this study must be considered as rather pessimistic, but still give a realistic estimation of the typical sensitivity that we will need to reach on exozodiacal discs in order to prepare the scientific programme of future Earth-like planet characterisation missions.Comment: 17 pages, accepted for publication in A&

The long period eccentric orbit of the particle accelerator HD167971 revealed by long baseline interferometry

Using optical long baseline interferometry, we resolved for the first time the two wide components of HD167971, a candidate hierarchical triple system known to efficiently accelerate particles. Our multi-epoch VLTI observations provide direct evidence for a gravitational link between the O8 supergiant and the close eclipsing O + O binary. The separation varies from 8 to 15 mas over the three-year baseline of our observations, suggesting that the components evolve on a wide and very eccentric orbit (most probably e>0.5). These results provide evidence that the wide orbit revealed by our study is not coplanar with the orbit of the inner eclipsing binary. From our measurements of the near-infrared luminosity ratio, we constrain the spectral classification of the components in the close binary to be O6-O7, and confirm that these stars are likely main-sequence objects. Our results are discussed in the context of the bright non-thermal radio emission already reported for this system, and we provide arguments in favour of a maximum radio emission coincident with periastron passage. HD167971 turns out to be an efficient O-type particle accelerator that constitutes a valuable target for future high angular resolution radio imaging using VLBI facilities.Comment: 8 pages, including 4 figures, accepted by Monthly Notices of the Royal Astronomical Societ

Prospects for near-infrared characterisation of hot Jupiters with VSI

In this paper, we study the feasibility of obtaining near-infrared spectra of bright extrasolar planets with the 2nd generation VLTI Spectro-Imager instrument (VSI), which has the required angular resolution to resolve nearby hot Extrasolar Giant Planets (EGPs) from their host stars. Taking into account fundamental noises, we simulate closure phase measurements of several extrasolar systems using four 8-m telescopes at the VLT and a low spectral resolution (R = 100). Synthetic planetary spectra from T. Barman are used as an input. Standard chi2-fitting methods are then used to reconstruct planetary spectra from the simulated data. These simulations show that low-resolution spectra in the H and K bands can be retrieved with a good fidelity for half a dozen targets in a reasonable observing time (about 10 hours, spread over a few nights). Such observations would strongly constrain the planetary temperature and albedo, the energy redistribution mechanisms, as well as the chemical composition of their atmospheres. Systematic errors, not included in our simulations, could be a serious limitation to these performance estimations. The use of integrated optics is however expected to provide the required instrumental stability (around 10^-4 on the closure phase) to enable the first thorough characterisation of extrasolar planetary emission spectra in the near-infrared.Comment: 10 pages, 8 figures, Proc. SPIE conference 7013 "Optical and Infrared Interferometry" (Marseille 2008

Vortex Image Processing (VIP) package for high-contrast direct imaging

VIP is a Python instrument-agnostic toolbox featuring a flexible framework for reproducible and robust data reduction. VIP currently supports three high-contrast imaging observational techniques: angular, reference-star and multi-spectral differential imaging. The code can be downloaded from our git repository on Github: http://github.com/vortex-exoplanet/VI

Searching for faint companions with VLTI/PIONIER. I. Method and first results

Context. A new four-telescope interferometric instrument called PIONIER has recently been installed at VLTI. It provides improved imaging capabilities together with high precision. Aims. We search for low-mass companions around a few bright stars using different strategies, and determine the dynamic range currently reachable with PIONIER. Methods. Our method is based on the closure phase, which is the most robust interferometric quantity when searching for faint companions. We computed the chi^2 goodness of fit for a series of binary star models at different positions and with various flux ratios. The resulting chi^2 cube was used to identify the best-fit binary model and evaluate its significance, or to determine upper limits on the companion flux in case of non detections. Results. No companion is found around Fomalhaut, tau Cet and Regulus. The median upper limits at 3 sigma on the companion flux ratio are respectively of 2.3e-3 (in 4 h), 3.5e-3 (in 3 h) and 5.4e-3 (in 1.5 h) on the search region extending from 5 to 100 mas. Our observations confirm that the previously detected near-infrared excess emissions around Fomalhaut and tau Cet are not related to a low-mass companion, and instead come from an extended source such as an exozodiacal disk. In the case of del Aqr, in 30 min of observation, we obtain the first direct detection of a previously known companion, at an angular distance of about 40 mas and with a flux ratio of 2.05e-2 \pm 0.16e-2. Due to the limited u,v plane coverage, its position can, however, not be unambiguously determined. Conclusions. After only a few months of operation, PIONIER has already achieved one of the best dynamic ranges world-wide for multi-aperture interferometers. A dynamic range up to about 1:500 is demonstrated, but significant improvements are still required to reach the ultimate goal of directly detecting hot giant extrasolar planets.Comment: 11 pages, 6 figures, accepted for publication in A&

Improving Interferometric Null Depth Measurements using Statistical Distributions: Theory and First Results with the Palomar Fiber Nuller

A new "self-calibrated" statistical analysis method has been developed for the reduction of nulling interferometry data. The idea is to use the statistical distributions of the fluctuating null depth and beam intensities to retrieve the astrophysical null depth (or equivalently the object's visibility) in the presence of fast atmospheric fluctuations. The approach yields an accuracy much better (about an order of magnitude) than is presently possible with standard data reduction methods, because the astrophysical null depth accuracy is no longer limited by the magnitude of the instrumental phase and intensity errors but by uncertainties on their probability distributions. This approach was tested on the sky with the two-aperture fiber nulling instrument mounted on the Palomar Hale telescope. Using our new data analysis approach alone-and no observations of calibrators-we find that error bars on the astrophysical null depth as low as a few 10-4 can be obtained in the near-infrared, which means that null depths lower than 10-3 can be reliably measured. This statistical analysis is not specific to our instrument and may be applicable to other interferometers

Nulling interferometry: performance comparison between Antarctica and other ground-based sites

Detecting the presence of circumstellar dust around nearby solar-type main sequence stars is an important pre-requisite for the design of future life-finding space missions such as ESA's Darwin or NASA's Terrestrial Planet Finder (TPF). The high Antarctic plateau may provide appropriate conditions to perform such a survey from the ground. We investigate the performance of a nulling interferometer optimised for the detection of exozodiacal discs at Dome C, on the high Antarctic plateau, and compare it to the expected performance of similar instruments at temperate sites. Based on the currently available measurements of the turbulence characteristics at Dome C, we adapt the GENIEsim software (Absil et al. 2006, A&A 448) to simulate the performance of a nulling interferometer on the high Antarctic plateau. To feed a realistic instrumental configuration into the simulator, we propose a conceptual design for ALADDIN, the Antarctic L-band Astrophysics Discovery Demonstrator for Interferometric Nulling. We assume that this instrument can be placed above the 30-m high boundary layer, where most of the atmospheric turbulence originates. We show that an optimised nulling interferometer operating on a pair of 1-m class telescopes located 30 m above the ground could achieve a better sensitivity than a similar instrument working with two 8-m class telescopes at a temperate site such as Cerro Paranal. The detection of circumstellar discs about 20 times as dense as our local zodiacal cloud seems within reach for typical Darwin/TPF targets in a integration time of a few hours. Moreover, the exceptional turbulence conditions significantly relax the requirements on real-time control loops, which has favourable consequences on the feasibility of the nulling instrument.Comment: 10 pages, accepted for publication in A&

Low-rank plus sparse decomposition for exoplanet detection in direct-imaging ADI sequences. The LLSG algorithm

Context. Data processing constitutes a critical component of high-contrast exoplanet imaging. Its role is almost as important as the choice of a coronagraph or a wavefront control system, and it is intertwined with the chosen observing strategy. Among the data processing techniques for angular differential imaging (ADI), the most recent is the family of principal component analysis (PCA) based algorithms. It is a widely used statistical tool developed during the first half of the past century. PCA serves, in this case, as a subspace projection technique for constructing a reference point spread function (PSF) that can be subtracted from the science data for boosting the detectability of potential companions present in the data. Unfortunately, when building this reference PSF from the science data itself, PCA comes with certain limitations such as the sensitivity of the lower dimensional orthogonal subspace to non-Gaussian noise. Aims. Inspired by recent advances in machine learning algorithms such as robust PCA, we aim to propose a localized subspace projection technique that surpasses current PCA-based post-processing algorithms in terms of the detectability of companions at near real-time speed, a quality that will be useful for future direct imaging surveys. Methods. We used randomized low-rank approximation methods recently proposed in the machine learning literature, coupled with entry-wise thresholding to decompose an ADI image sequence locally into low-rank, sparse, and Gaussian noise components (LLSG). This local three-term decomposition separates the starlight and the associated speckle noise from the planetary signal, which mostly remains in the sparse term. We tested the performance of our new algorithm on a long ADI sequence obtained on β Pictoris with VLT/NACO. Results. Compared to a standard PCA approach, LLSG decomposition reaches a higher signal-to-noise ratio and has an overall better performance in the receiver operating characteristic space. This three-term decomposition brings a detectability boost compared to the full-frame standard PCA approach, especially in the small inner working angle region where complex speckle noise prevents PCA from discerning true companions from noise