2,301 research outputs found
Formation and evolution of planetary systems: the impact of high angular resolution optical techniques
The direct images of giant extrasolar planets recently obtained around
several main sequence stars represent a major step in the study of planetary
systems. These high-dynamic range images are among the most striking results
obtained by the current generation of high angular resolution instruments,
which will be superseded by a new generation of instruments in the coming
years. It is therefore an appropriate time to review the contributions of high
angular resolution visible/infrared techniques to the rapidly growing field of
extrasolar planetary science. During the last 20 years, the advent of the
Hubble Space Telescope, of adaptive optics on 4- to 10-m class ground-based
telescopes, and of long-baseline infrared stellar interferometry has opened a
new viewpoint on the formation and evolution of planetary systems. By spatially
resolving the optically thick circumstellar discs of gas and dust where planets
are forming, these instruments have considerably improved our models of early
circumstellar environments and have thereby provided new constraints on planet
formation theories. High angular resolution techniques are also directly
tracing the mechanisms governing the early evolution of planetary embryos and
the dispersal of optically thick material around young stars. Finally, mature
planetary systems are being studied with an unprecedented accuracy thanks to
single-pupil imaging and interferometry, precisely locating dust populations
and putting into light a whole new family of long-period giant extrasolar
planets.Comment: 71 pages, published in Astronomy and Astrophysics Review, online at
http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/s00159-009-0028-
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
Global rates of convergence for nonconvex optimization on manifolds
We consider the minimization of a cost function on a manifold using
Riemannian gradient descent and Riemannian trust regions (RTR). We focus on
satisfying necessary optimality conditions within a tolerance .
Specifically, we show that, under Lipschitz-type assumptions on the pullbacks
of to the tangent spaces of , both of these algorithms produce points
with Riemannian gradient smaller than in
iterations. Furthermore, RTR returns a point where also the Riemannian
Hessian's least eigenvalue is larger than in
iterations. There are no assumptions on initialization.
The rates match their (sharp) unconstrained counterparts as a function of the
accuracy (up to constants) and hence are sharp in that sense.
These are the first deterministic results for global rates of convergence to
approximate first- and second-order Karush-Kuhn-Tucker points on manifolds.
They apply in particular for optimization constrained to compact submanifolds
of , under simpler assumptions.Comment: 33 pages, IMA Journal of Numerical Analysis, 201
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&
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