Elliptic stars in a chaotic night

We study homeomorphisms of the two-torus, homotopic to the identity, whose rotation set has non-empty interior. For such maps, we give a purely topological characterisation of elliptic islands in a chaotic sea in terms of local rotation subsets. We further show that the chaotic regime defined in this way cannot contain any Lyapunov stable points. In order to demonstrate our results, we introduce a parameter family inspired by an example of Misiurewicz and Ziemian.Comment: 15 pages, 7 Figures; Revised versions with some minor corrections

Stellar intensity interferometry over kilometer baselines: Laboratory simulation of observations with the Cherenkov Telescope Array

A long-held astronomical vision is to realize diffraction-limited optical aperture synthesis over kilometer baselines. This will enable imaging of stellar surfaces and their environments, show their evolution over time, and reveal interactions of stellar winds and gas flows in binary star systems. An opportunity is now opening up with the large telescope arrays primarily erected for measuring Cherenkov light in air induced by gamma rays. With suitable software, such telescopes could be electronically connected and used also for intensity interferometry. With no optical connection between the telescopes, the error budget is set by the electronic time resolution of a few nanoseconds. Corresponding light-travel distances are on the order of one meter, making the method practically insensitive to atmospheric turbulence or optical imperfections, permitting both very long baselines and observing at short optical wavelengths. Theoretical modeling has shown how stellar surface images can be retrieved from such observations and here we report on experimental simulations. In an optical laboratory, artificial stars (single and double, round and elliptic) are observed by an array of telescopes. Using high-speed photon-counting solid-state detectors and real-time electronics, intensity fluctuations are cross correlated between up to a hundred baselines between pairs of telescopes, producing maps of the second-order spatial coherence across the interferometric Fourier-transform plane. These experiments serve to verify the concepts and to optimize the instrumentation and observing procedures for future observations with (in particular) CTA, the Cherenkov Telescope Array, aiming at order-of-magnitude improvements of the angular resolution in optical astronomy.Comment: 18 pages, 11 figures; Presented at SPIE conference on Astronomical Telescopes + Instrumentation in Montreal, Quebec, Canada, June 2014. To appear in SPIE Proc.9146, Optical and Infrared Interferometry IV (J.K.Rajagopal, M.J.Creech-Eakman, F.Malbet, eds.), 201

Long-baseline optical intensity interferometry: Laboratory demonstration of diffraction-limited imaging

A long-held vision has been to realize diffraction-limited optical aperture synthesis over kilometer baselines. This will enable imaging of stellar surfaces and their environments, and reveal interacting gas flows in binary systems. An opportunity is now opening up with the large telescope arrays primarily erected for measuring Cherenkov light in air induced by gamma rays. With suitable software, such telescopes could be electronically connected and also used for intensity interferometry. Second-order spatial coherence of light is obtained by cross correlating intensity fluctuations measured in different pairs of telescopes. With no optical links between them, the error budget is set by the electronic time resolution of a few nanoseconds. Corresponding light-travel distances are approximately one meter, making the method practically immune to atmospheric turbulence or optical imperfections, permitting both very long baselines and observing at short optical wavelengths. Previous theoretical modeling has shown that full images should be possible to retrieve from observations with such telescope arrays. This project aims at verifying diffraction-limited imaging experimentally with groups of detached and independent optical telescopes. In a large optics laboratory, artificial stars were observed by an array of small telescopes. Using high-speed photon-counting solid-state detectors, intensity fluctuations were cross-correlated over up to 180 baselines between pairs of telescopes, producing coherence maps across the interferometric Fourier-transform plane. These measurements were used to extract parameters about the simulated stars, and to reconstruct their two-dimensional images. As far as we are aware, these are the first diffraction-limited images obtained from an optical array only linked by electronic software, with no optical connections between the telescopes.Comment: 13 pages, 9 figures, Astronomy & Astrophysics, in press. arXiv admin note: substantial text overlap with arXiv:1407.599

Nonautonomous saddle-node bifurcations: random and deterministic forcing

We study the effect of external forcing on the saddle-node bifurcation pattern of interval maps. By replacing fixed points of unperturbed maps by invariant graphs, we obtain direct analogues to the classical result both for random forcing by measure-preserving dynamical systems and for deterministic forcing by homeomorphisms of compact metric spaces. Additional assumptions like ergodicity or minimality of the forcing process then yield further information about the dynamics. The main difference to the unforced situation is that at the critical bifurcation parameter, two alternatives exist. In addition to the possibility of a unique neutral invariant graph, corresponding to a neutral fixed point, a pair of so-called pinched invariant graphs may occur. In quasiperiodically forced systems, these are often referred to as 'strange non-chaotic attractors'. The results on deterministic forcing can be considered as an extension of the work of Novo, Nunez, Obaya and Sanz on nonautonomous convex scalar differential equations. As a by-product, we also give a generalisation of a result by Sturman and Stark on the structure of minimal sets in forced systems.Comment: 17 pages, 5 figure

Optical aperture synthesis with electronically connected telescopes

Highest resolution imaging in astronomy is achieved by interferometry, connecting telescopes over increasingly longer distances, and at successively shorter wavelengths. Here, we present the first diffraction-limited images in visual light, produced by an array of independent optical telescopes, connected electronically only, with no optical links between them. With an array of small telescopes, second-order optical coherence of the sources is measured through intensity interferometry over 180 baselines between pairs of telescopes, and two-dimensional images reconstructed. The technique aims at diffraction-limited optical aperture synthesis over kilometre-long baselines to reach resolutions showing details on stellar surfaces and perhaps even the silhouettes of transiting exoplanets. Intensity interferometry circumvents problems of atmospheric turbulence that constrain ordinary interferometry. Since the electronic signal can be copied, many baselines can be built up between dispersed telescopes, and over long distances. Using arrays of air Cherenkov telescopes, this should enable the optical equivalent of interferometric arrays currently operating at radio wavelengths.Comment: 9 pages, 2 figures; published under open access in Nature Communications, http://www.nature.com/ncomms

A near-infrared interferometric survey of debris disc stars. II. CHARA/FLUOR observations of six early-type dwarfs

High-precision interferometric observations of six early-type main sequence stars known to harbour cold debris discs have been obtained in the near-infrared K band with the FLUOR instrument at the CHARA Array. The measured squared visibilities are compared to the expected visibility of the stellar photospheres based on theoretical photospheric models taking into account rotational distortion, searching for potential visibility reduction at short baselines due to circumstellar emission. Our observations bring to light the presence of resolved circumstellar emission around one of the six target stars (zeta Aql) at the 5 sigma level. The morphology of the emission source cannot be directly constrained because of the sparse spatial frequency sampling of our interferometric data. Using complementary adaptive optics observations and radial velocity measurements, we find that the presence of a low-mass companion is a likely origin for the excess emission. The potential companion has a K-band contrast of four magnitudes, a most probable mass of about 0.6 Msun, and is expected to orbit between about 5.5 AU and 8 AU from its host star assuming a purely circular orbit. Nevertheless, by adjusting a physical debris disc model to the observed Spectral Energy Distribution of the zeta Aql system, we also show that the presence of hot dust within 10 AU from zeta Aql, producing a total thermal emission equal to 1.69 +- 0.31% of the photospheric flux in the K band, is another viable explanation for the observed near-infrared excess. Our re-interpretation of archival near- to far-infrared photometric measurements shows however that cold dust is not present around zeta Aql at the sensitivity limit of the IRS and MIPS instruments onboard Spitzer, and urges us to remove zeta Aql from the category of bona fide debris disc stars.Comment: 14 pages, accepted for publication in A&

Testing a hypothesis of the \nu Octantis planetary system

We investigate the orbital stability of a putative Jovian planet in a compact binary \nu Octantis reported by Ramm et al. We re-analyzed published radial velocity data in terms of self-consistent Newtonian model and we found stable best-fit solutions that obey observational constraints. They correspond to retrograde orbits, in accord with an earlier hypothesis of Eberle & Cuntz, with apsidal lines anti-aligned with the apses of the binary. The best-fit solutions are confined to tiny stable regions of the phase space. These regions have a structure of the Arnold web formed by overlapping low-order mean motion resonances and their sub-resonances. The presence of a real planet is still questionable, because its formation would be hindered by strong dynamical perturbations. Our numerical study makes use of a new computational Message Passing Interface (MPI) framework MECHANIC developed to run massive numerical experiments on CPU clusters.Comment: 12 pages, 12 figures, accepted to Monthly Notices of the RA

Dynamics of Barred Galaxies

Some 30% of disc galaxies have a pronounced central bar feature in the disc plane and many more have weaker features of a similar kind. Kinematic data indicate that the bar constitutes a major non-axisymmetric component of the mass distribution and that the bar pattern tumbles rapidly about the axis normal to the disc plane. The observed motions are consistent with material within the bar streaming along highly elongated orbits aligned with the rotating major axis. A barred galaxy may also contain a spheroidal bulge at its centre, spirals in the outer disc and, less commonly, other features such as a ring or lens. Mild asymmetries in both the light and kinematics are quite common. We review the main problems presented by these complicated dynamical systems and summarize the effort so far made towards their solution, emphasizing results which appear secure. (Truncated)Comment: This old review appeared in 1993. Plain tex with macro file. 82 pages 18 figures. A pdf version with figures at full resolution (3.24MB) is available at http://www.physics.rutgers.edu/~sellwood/bar_review.pd