A conjugate gradient algorithm for the astrometric core solution of Gaia

The ESA space astrometry mission Gaia, planned to be launched in 2013, has been designed to make angular measurements on a global scale with micro-arcsecond accuracy. A key component of the data processing for Gaia is the astrometric core solution, which must implement an efficient and accurate numerical algorithm to solve the resulting, extremely large least-squares problem. The Astrometric Global Iterative Solution (AGIS) is a framework that allows to implement a range of different iterative solution schemes suitable for a scanning astrometric satellite. In order to find a computationally efficient and numerically accurate iteration scheme for the astrometric solution, compatible with the AGIS framework, we study an adaptation of the classical conjugate gradient (CG) algorithm, and compare it to the so-called simple iteration (SI) scheme that was previously known to converge for this problem, although very slowly. The different schemes are implemented within a software test bed for AGIS known as AGISLab, which allows to define, simulate and study scaled astrometric core solutions. After successful testing in AGISLab, the CG scheme has been implemented also in AGIS. The two algorithms CG and SI eventually converge to identical solutions, to within the numerical noise (of the order of 0.00001 micro-arcsec). These solutions are independent of the starting values (initial star catalogue), and we conclude that they are equivalent to a rigorous least-squares estimation of the astrometric parameters. The CG scheme converges up to a factor four faster than SI in the tested cases, and in particular spatially correlated truncation errors are much more efficiently damped out with the CG scheme.Comment: 24 pages, 16 figures. Accepted for publication in Astronomy & Astrophysic

Use of Docker for deployment and testing of astronomy software

We describe preliminary investigations of using Docker for the deployment and testing of astronomy software. Docker is a relatively new containerisation technology that is developing rapidly and being adopted across a range of domains. It is based upon virtualization at operating system level, which presents many advantages in comparison to the more traditional hardware virtualization that underpins most cloud computing infrastructure today. A particular strength of Docker is its simple format for describing and managing software containers, which has benefits for software developers, system administrators and end users. We report on our experiences from two projects -- a simple activity to demonstrate how Docker works, and a more elaborate set of services that demonstrates more of its capabilities and what they can achieve within an astronomical context -- and include an account of how we solved problems through interaction with Docker's very active open source development community, which is currently the key to the most effective use of this rapidly-changing technology.Comment: 29 pages, 9 figures, accepted for publication in Astronomy and Computing, ref ASCOM19

High-resolution tungsten spectroscopy relevant to the diagnostic of high-temperature tokamak plasmas

The x-ray transitions in Cu- and Ni-like tungsten ions in the 5.19–5.26 A wavelength range that are relevant ˚ as a high-temperature tokamak diagnostic, in particular for JET in the ITER-like wall configuration, have been studied. Tungsten spectra were measured at the upgraded Shanghai- Electron Beam Ion Trap operated with electron-beam energies from 3.16 to 4.55 keV. High-resolution measurements were performed by means of a flat Si 111 crystal spectrometer equipped by a CCD camera. The experimental wavelengths were determined with an accuracy of 0.3–0.4 mA. The wavelength of the ground-state transition in Cu-like tungsten from the ˚ 3p53d104s4d [(3/2,(1/2,5/2)2]1/2 level was measured. All measured wavelengths were compared with those measured from JET ITER-like wall plasmas and with other experiments and various theoretical predictions including COWAN, RELAC, multiconfigurational Dirac-Fock (MCDF), and FAC calculations. To obtain a higher accuracy from theoretical predictions, the MCDF calculations were extended by taking into account correlation effects (configuration-interaction approach). It was found that such an extension brings the calculations closer to the experimental values in comparison with other calculations.National Magnetic Confinement Fusion Program of China 2015GB117000National Natural Science Foundation of China 11374061EURATOM 63305

The astrometric core solution for the Gaia mission. Overview of models, algorithms and software implementation

The Gaia satellite will observe about one billion stars and other point-like sources. The astrometric core solution will determine the astrometric parameters (position, parallax, and proper motion) for a subset of these sources, using a global solution approach which must also include a large number of parameters for the satellite attitude and optical instrument. The accurate and efficient implementation of this solution is an extremely demanding task, but crucial for the outcome of the mission. We provide a comprehensive overview of the mathematical and physical models applicable to this solution, as well as its numerical and algorithmic framework. The astrometric core solution is a simultaneous least-squares estimation of about half a billion parameters, including the astrometric parameters for some 100 million well-behaved so-called primary sources. The global nature of the solution requires an iterative approach, which can be broken down into a small number of distinct processing blocks (source, attitude, calibration and global updating) and auxiliary processes (including the frame rotator and selection of primary sources). We describe each of these processes in some detail, formulate the underlying models, from which the observation equations are derived, and outline the adopted numerical solution methods with due consideration of robustness and the structure of the resulting system of equations. Appendices provide brief introductions to some important mathematical tools (quaternions and B-splines for the attitude representation, and a modified Cholesky algorithm for positive semidefinite problems) and discuss some complications expected in the real mission data.Comment: 48 pages, 19 figures. Accepted for publication in Astronomy & Astrophysic

Added-value interfaces to asteroid photometric and spectroscopic data in the Gaia database

Abstract We present two added-value interfaces (AVIs) for analyzing photometric and spectroscopic data observed by the Gaia satellite. The Gaia Added-Value Interface for Temporal Analysis (GAVITEA) is used to calculate an estimate for the spin state and shape of an asteroid from its photometric data, and the Gaia Added-Value Interface for Spectral Classification (GAVISC) provides tools to define the taxonomic type and surface absorption coefficient based on spectroscopic asteroid data. Computations are mainly carried out using well-known methods of asteroid data analysis but the AVIs also offer the possibility to test novel methods that are specifically developed for analyzing temporally sparse photometric data, typical for Gaia.Peer reviewe

Preparing Red-Green-Blue (RGB) Images from CCD Data

We present a new, and we believe arguably correct, algorithm for producing Red-Green-Blue (RBG) composites from 3-band astronomical images. Our method ensures that an object with a specified astronomical color (e.g. g-r and r-i) has a unique color in the RGB image, as opposed to the burnt-out white stars to which we are accustomed. A natural consequence of this is that we can use the same colors to code color-magnitude diagrams, providing a natural `index' to our images. We also introduce the use of an asinh stretch, which allows us to show faint objects while simultaneously preserving the structure of brighter objects in the field, such as the spiral arms of large galaxies. We believe that, in addition to their aesthetic value, our images convey far more information than do the traditional ones, and provide examples from Sloan Digital Sky Survey (SDSS) imaging, the Hubble Deep Field (HDF), and Chandra to support our claims. More examples are available at http://www.astro.princeton.edu/~rhl/PrettyPicture

Relativistic quantum backflow

In this paper we discuss relativistic quantum backflow. The general theory of relativistic
 backflow is written down and it is shown that the backflow can be written as a function of
 a simple parameter epsilon which is defined in terms of fundamental constants and the 
 backflow period. Backflow eigenfunctions are determined numerically for a range of values 
 of epsilon and an explicit expression for the relativistic backflow eigenvalue in terms of the 
 non-relativistic backflow constant is presented. Then backflow eigenvectors are fitted with 
 some standard functions which lead to substantially higher backflow than has been found 
 previously with fitting procedures, for some values of epsilon. In analysing the non-relativistic 
 limit of the theory we show that this problem is one of those rare cases where the relativistic 
 theory is intrinsically more simple than the non-relativistic theory

Gold nanoparticles electrodeposited on glassy carbon using cyclic voltammetry: Application to Hg(II) trace analysis

The electrochemical determination of Hg(II) at trace level using gold nanoparticles–modified glassy carbon (AuNPs–GC) electrodes is described. Starting from HAuCl4 in NaNO3, gold nanoparticles (AuNPs) were deposited onto Glassy Carbon (GC) electrodes using Cyclic Voltammetry (CV). Different deposits were obtained by varying the global charge consumed during the whole electroreduction step, depending on the number of cyclic potential scans (N). AuNPs were characterized as a function of the charge using both CV in H2SO4 and Field Emission Gun Scanning Electron Microscopy (FEG-SEM). The AuNPs–GC electrodes were then applied to determine low Hg(II) concentrations using Square Wave Anodic Stripping Voltammetry (SWASV). The AuNPs–GC electrodes provided significantly improved performances in Hg(II) determination compared to unmodified GC and bare Au electrodes. It was shown that the physico-chemical properties of the deposits are correlated to the performances of the AuNPs–GC electrode with respect to Hg(II) assay. The best results were obtained for four electrodeposition cyclic scans, where small-sized particles (36 ± 13 nm) with high density (73 particles μm-²) were obtained. Under these conditions, a linearity range from 0.64 to 4.00 nM and a limit of detection of 0.42 nM were obtained