Bayesian analysis of interiors of HD 219134b, Kepler-10b, Kepler-93b, CoRoT-7b, 55 Cnc e, and HD 97658b using stellar abundance proxies

Using a generalized Bayesian inference method, we aim to explore the possible interior structures of six selected exoplanets for which planetary mass and radius measurements are available in addition to stellar host abundances: HD~219134b, Kepler-10b, Kepler-93b, CoRoT-7b, 55~Cnc~e, and HD~97658b. We aim to investigate the importance of stellar abundance proxies for the planetary bulk composition (namely Fe/Si and Mg/Si) on prediction of planetary interiors. We performed a full probabilistic Bayesian inference analysis to formally account for observational and model uncertainties while obtaining confidence regions of structural and compositional parameters of core, mantle, ice layer, ocean, and atmosphere. We determined how sensitive our parameter predictions depend on (1) different estimates of bulk abundance constraints and (2) different correlations of bulk abundances between planet and host star. [...] Although the possible ranges of interior structures are large, structural parameters and their correlations are constrained by the sparse data. The probability for the tested exoplanets to be Earth-like is generally very low. Furthermore, we conclude that different estimates of planet bulk abundance constraints mainly affect mantle composition and core size.Comment: Astronomy & Astrophysics, 597, A38 (15 pages, 9 figures

Development of a carbon fibre composite active mirror: Design and testing

Carbon fibre composite technology for lightweight mirrors is gaining increasing interest in the space- and ground-based astronomical communities for its low weight, ease of manufacturing, excellent thermal qualities and robustness. We present here first results of a project to design and produce a 27 cm diameter deformable carbon fibre composite mirror. The aim was to produce a high surface form accuracy as well as low surface roughness. As part of this programme, a passive mirror was developed to investigate stability and coating issues. Results from the manufacturing and polishing process are reported here. We also present results of a mechanical and thermal finite element analysis, as well as early experimental findings of the deformable mirror. Possible applications and future work are discussed.Comment: Accepted by Optical Engineering. Figures 1-7 on http://www.star.ucl.ac.uk/~sk/OEpaper_files

A generalized bayesian inference method for constraining the interiors of super Earths and sub-Neptunes

We aim to present a generalized Bayesian inference method for constraining interiors of super Earths and sub-Neptunes. Our methodology succeeds in quantifying the degeneracy and correlation of structural parameters for high dimensional parameter spaces. Specifically, we identify what constraints can be placed on composition and thickness of core, mantle, ice, ocean, and atmospheric layers given observations of mass, radius, and bulk refractory abundance constraints (Fe, Mg, Si) from observations of the host star's photospheric composition. We employed a full probabilistic Bayesian inference analysis that formally accounts for observational and model uncertainties. Using a Markov chain Monte Carlo technique, we computed joint and marginal posterior probability distributions for all structural parameters of interest. We included state-of-the-art structural models based on self-consistent thermodynamics of core, mantle, high-pressure ice, and liquid water. Furthermore, we tested and compared two different atmospheric models that are tailored for modeling thick and thin atmospheres, respectively. First, we validate our method against Neptune. Second, we apply it to synthetic exoplanets of fixed mass and determine the effect on interior structure and composition when (1) radius, (2) atmospheric model, (3) data uncertainties, (4) semi-major axes, (5) atmospheric composition (i.e., a priori assumption of enriched envelopes versus pure H/He envelopes), and (6) prior distributions are varied. Our main conclusions are: [...]Comment: Astronomy & Astrophysics, 597, A37, 17 pages, 11 figure

Accumulation horizons and period-adding in optically injected semiconductor lasers

We study the hierarchical structuring of islands of stable periodic oscillations inside chaotic regions in phase diagrams of single-mode semiconductor lasers with optical injection. Phase diagrams display remarkable {\it accumulation horizons}: boundaries formed by the accumulation of infinite cascades of self-similar islands of periodic solutions of ever-increasing period. Each cascade follows a specific period-adding route. The riddling of chaotic laser phases by such networks of periodic solutions may compromise applications operating with chaotic signals such as e.g. secure communications.Comment: 4 pages, 4 figures, laser phase diagrams, to appear in Phys. Rev. E, vol. 7

The focus of light - linear polarization breaks the rotational symmetry of the focal spot

We experimentally demonstrate for the first time that a linearly polarized beam is focussed to an asymmetric spot when using a high-numerical aperture focussing system. This asymmetry was predicted by Richards and Wolf [Proc.R.Soc.London A, 253, 358 (1959)] and can only be measured when a polarization insensitive sensor is placed in the focal region. We used a specially modified photodiode in a knife edge type set up to obtain highly resolved images of the total electric energy density distribution at the focus. The results are in good agreement with the predictions of a vectorial focussing theory.Comment: to be published in "Journal of Modern Optics

Electron impact double ionization of helium from classical trajectory calculations

With a recently proposed quasiclassical ansatz [Geyer and Rost, J. Phys. B 35 (2002) 1479] it is possible to perform classical trajectory ionization calculations on many electron targets. The autoionization of the target is prevented by a M\o{}ller type backward--forward propagation scheme and allows to consider all interactions between all particles without additional stabilization. The application of the quasiclassical ansatz for helium targets is explained and total and partially differential cross sections for electron impact double ionization are calculated. In the high energy regime the classical description fails to describe the dominant TS1 process, which leads to big deviations, whereas for low energies the total cross section is reproduced well. Differential cross sections calculated at 250 eV await their experimental confirmation.Comment: LaTeX, 22 pages, 10 figures, submitted to J. Phys.

On the AdS Higher Spin / O(N) Vector Model Correspondence: degeneracy of the holographic image

We explore the conjectured duality between the critical O(N) vector model and minimal bosonic massless higher spin (HS) theory in AdS. In the boundary free theory, the conformal partial wave expansion (CPWE) of the four-point function of the scalar singlet bilinear is reorganized to make it explicitly crossing-symmetric and closed in the singlet sector, dual to the bulk HS gauge fields. We are able to analytically establish the factorized form of the fusion coefficients as well as the two-point function coefficient of the HS currents. We insist in directly computing the free correlators from bulk graphs with the unconventional branch. The three-point function of the scalar bilinear turns out to be an "extremal" one at d=3. The four-leg bulk exchange graph can be precisely related to the CPWs of the boundary dual scalar and its shadow. The flow in the IR by Legendre transforming at leading 1/N, following the pattern of double-trace deformations, and the assumption of degeneracy of the hologram lead to the CPWE of the scalar four-point function at IR. Here we confirm some previous results, obtained from more involved computations of skeleton graphs, as well as extend some of them from d=3 to generic dimension 2<d<4.Comment: 22 pages, 5 figure

Double ionization of helium by electron-impact: complete pictures of the four-body breakup dynamics

The dynamics of He double ionization by 2 keV electron impact is studied experimentally for a momentum transfer of 0.6 a.u. at excess energies of 10 and 40 eV. Complete sets of fivefold differential cross sections are presented for all electron emission angles in coplanar geometry. Contributions beyond the first Born approximation are identified comparing experimental data with first order convergent close-coupling calculations which are in considerably better agreement with the present experiment than with the earlier measurement of Kheifets et al. [J. Phys. B 32, 5047 (1999)]

Impact of the measured parameters of exoplanets on the inferred internal structure

Exoplanet characterization is one of the main foci of current exoplanetary science. For super-Earths and sub-Neptunes, we mostly rely on mass and radius measurements, which allow to derive the body's mean density and give a rough estimate of the planet's bulk composition. However, the determination of planetary interiors is a very challenging task. In addition to the uncertainty in the observed fundamental parameters, theoretical models are limited due to the degeneracy in determining the planetary composition. We aim to study several aspects that affect internal characterization of super-Earths and sub-Neptunes: observational uncertainties, location on the M-R diagram, impact of additional constraints as bulk abundances or irradiation, and model assumptions. We use a full probabilistic Bayesian inference analysis that accounts for observational and model uncertainties. We employ a Nested Sampling scheme to efficiently produce the posterior probability distributions for all the planetary structural parameter of interest. We include a structural model based on self-consistent thermodynamics of core, mantle, high-pressure ice, liquid water, and H-He envelope. Regarding the effect of mass and radius uncertainties on the determination of the internal structure, we find three different regimes: below the Earth-like composition line and above the pure-water composition line smaller observational uncertainties lead to better determination of the core and atmosphere mass respectively, and between them structure characterization only weakly depends on the observational uncertainties. We show that small variations in the temperature or entropy profiles lead to radius variations that are comparable to the observational uncertainty, suggesting that uncertainties linked to model assumptions can become more relevant to determine the internal structure than observational uncertainties.Comment: 12 pages, 12 figure