Ulrich Bastian

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

Context. 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. Aims. We aim to provide a comprehensive overview of the mathematical and physical models applicable to this solution, as well as its numerical and algorithmic framework. Methods. 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. Results. A complete software system called AGIS (Astrometric Global Iterative Solution) is being built according to the methods described in the paper. Based on simulated data for 2 million primary sources we present some initial results, demonstrating the basic mathematical and numerical validity of the approach and, by a reasonable extrapolation, its practical feasibility in terms of data management and computations for the real mission. (Less)

The Hipparcos proper motion of the Magellanic Clouds

Abstract The proper motion of the Large (LMC) and Small (SMC) Magellanic Cloud using data acquired with the Hipparcos satellite is presented. Hipparcos measured 36 stars in the LMC and 11 stars in the SMC. A correctly weighted mean of the data yields the presently available most accurate values, μαcos(δ) = 1.94±0.29 mas/yr, μδ = −0.14±0.36 mas/yr for the LMC. For the SMC, μαcos(δ) = 1.23±0.84 mas/yr, μδ = −1.21±0.75 mas/yr is obtained, whereby care is taken to exclude likely tidal motions induced by the LMC. Both galaxies are moving approximately parallel to each other on the sky, with the Magellanic Stream trailing behind. The Hipparcos proper motions are in agreement with previous measurements using PPM catalogue data by Kroupa et al. (1994) [MNRAS, 266, 412] and by Jones et al. (1994) [AJ, 107, 1333] using background galaxies in a far-outlying field of the LMC. For the LMC the Hipparcos data suggest a weak rotation signal in a clockwise direction on the sky. Comparison of the Hipparcos proper motion with the proper motion of the field used by Jones et al. (1994) [AJ, 107, 1333], which is about 7.3 kpc distant from the center of the LMC, also suggeests clockwise rotation. Combining the three independent measurments of the proper motion of the LMC and the two independent measurements of the proper motion of the SMC improves the estimate of the proper motion of the LMC and SMC. The corresponding galactocentric space motion vectors are computed. Within the uncertainties, the LMC and SMC are found to be on parallel trajectories. Recent theoretical work concerning the origin of the Magellanic System is briefly reviewed, but a unique model of the Magellanic Stream, for the origin of the Magellanic Clouds, and for the mass distribution in the Galaxy cannot yet be decided upon. Future astrometric space missions are necessary to significantly improve our present knowledge of the space motion of the two most conspicous galactic neighbours of the Milky Way.

Gaia: organisation and challenges for the data processing

Gaia is an ambitious space astrometry mission of ESA with a main objective to map the sky in astrometry and photometry down to a magnitude 20 by the end of the next decade. While the mission is built and operated by ESA and an industrial consortium, the data processing is entrusted to a consortium formed by the scientific community, which was formed in 2006 and formally selected by ESA one year later. The satellite will downlink around 100 TB of raw telemetry data over a mission duration of 5 years from which a very complex iterative processing will lead to the final science output: astrometry with a final accuracy of a few tens of microarcseconds, epoch photometry in wide and narrow bands, radial velocity and spectra for the stars brighter than 17 mag. We discuss the general principles and main difficulties of this very large data processing and present the organization of the European Consortium responsible for its design and implementation.

GAIA: global astrometric interferometer for astrophysics

We describe a concept for an interferometric space mission dedicated to global (wide-angle) astrometry. The GAIA satellite contains two small (baseline APEQ 3 m) optical interferometers of the Fizeau type, mechanically set at a large and fixed angle to each other. Each interferometer has a field of view of about one degree. Continuous rotation of the whole satellite provides angular connections between the stars passing through the two fields of view. Positions, absolute parallaxes and annual proper motions can be determined with accuracies on the 20 micro-arcsec level. The observing programme may consist of all objects to a limiting magnitude around V = 15-16, including 50 million stars. The GAIA concept, which has been proposed for a Cornerstone Mission within the European Space Agencys long-term science programme, is based on the same general principles as the very successful ESA Hipparcos mission, but takes advantage of the much higher resolution and efficiency permitted by interferometry and modern detector techniques.

Gaia Data Release 2: The celestial reference frame (Gaia-CRF2)

Context. The second release of Gaia data (Gaia DR2) contains the astrometric parameters for more than half a million quasars. This set defines a kinematically non-rotating reference frame in the optical domain. A subset of these quasars have accurate VLBI positions that allow the axes of the reference frame to be aligned with the International Celestial Reference System (ICRF) radio frame. Aims: We describe the astrometric and photometric properties of the quasars that were selected to represent the celestial reference frame of Gaia DR2 (Gaia-CRF2), and to compare the optical and radio positions for sources with accurate VLBI positions. Methods: Descriptive statistics are used to characterise the overall properties of the quasar sample. Residual rotation and orientation errors and large-scale systematics are quantified by means of expansions in vector spherical harmonics. Positional differences are calculated relative to a prototype version of the forthcoming ICRF3. Results: Gaia-CRF2 consists of the positions of a sample of 556 869 sources in Gaia DR2, obtained from a positional cross-match with the ICRF3-prototype and AllWISE AGN catalogues. The sample constitutes a clean, dense, and homogeneous set of extragalactic point sources in the magnitude range G ≃ 16 to 21 mag with accurately known optical positions. The median positional uncertainty is 0.12 mas for G < 18 mag and 0.5 mas at G = mag. Large-scale systematics are estimated to be in the range 20 to 30 μas. The accuracy claims are supported by the parallaxes and proper motions of the quasars in Gaia DR2. The optical positions for a subset of 2820 sources in common with the ICRF3-prototype show very good overall agreement with the radio positions, but several tens of sources have significantly discrepant positions. Conclusions: Based on less than 40% of the data expected from the nominal Gaia mission, Gaia-CRF2 is the first realisation of a non-rotating global optical reference frame that meets the ICRS prescriptions, meaning that it is built only on extragalactic sources. Its accuracy matches the current radio frame of the ICRF, but the density of sources in all parts of the sky is much higher, except along the Galactic equator.

Optical design for DIVA

DIVA (deutsches interferometer fuer vielkanalphotometrie und astrometrie) is a project of a small satellite, aiming to measure positions, proper motions, parallaxes and spectra of several million stars. DIVA will carry two Fizea interferometers with a baseline of 100 mm using a novel telescope design. It consists of a Gregory configuration with high secondary magnification and a four-component field lens system at the intermediate focus. We present the optical layout which allows diffraction-limited imaging over a 0.5 degree of view in the wavelength range 400-1000 nm. Critical aspects of the design are discussed. The present status of the project is briefly outlined.

PPM: A Tool for Astronomers

The new catalogue of Positions and Proper Motions ( “PPM” ) was compiled to replace the AGK3 and SAO catalogues as an astrometric reference on the northern celestial hemisphere. It provides more than 180 000 reference stars, is on the system of FK5 (J2000.0) and has a higher accuracy than the two older catalogues.

Completion of the Sternberg Astronomical Institute Astrographic Catalogue Project

The first astronomical photographic survey, the Carte du Ciel was initiated in 1887 by a group of French astronomers. The observational campaign was started in 1891, while the last of more than 22,000 total plates were photographed in 1950; most of observations (more than 90%) were performed prior to 1920. Detailed description of the Carte du Ciel development can be found elsewhere (Kolchinsky 1989, Eichhorn 1974, Debarbat et al. 1987).

OVERVIEW OF THE TYCHO CATALOGUE

The final Tycho Catalogue (ESA 1997b) has been derived from 37 months of observations with the star mapper of the astrometric satellite Hipparcos. The Hipparcos Catalogue (ESA 1997a) with about 120,000 stars is the result of the main Hipparcos mission and has, e.g., been described by Kovalevsky et al. (1995). Both catalogues will be published in 1997.

Diva - A Small Satellite for Global Astrometry and Photometry

DIVA (Double Interferometer for Visual Astrometry) is a Fizeau interferometer on a small satellite. It will perform astrometric and photometric observations of at least 4 million stars. A launch in 2002 and a minimum mission length of 24 months are aimed at. A detailed description of the experiment can be obtained from the DIVA homepage at http://www.aip.de:8080/dso/diva. An overview is given by Roser et al. , 1997. The limiting magnitude of DIVA is about V = 15 for spectral types earlier than M0, but drops to about V = 17.5 for stars later than M5. Table 1 gives a short overview on DIVA’s performance. DIVA will carry out a skysurvey complete to V = 12.5. For the first time this survey will comprise precise photometry in at least 8 bands in the wavelength range from 400 to 1000 nm. DIVA will improve parallaxes by a factor of 3 compared to Hipparcos; proper motions by at least a factor of 2 and, in combination with the Hipparcos observations, by a factor of 10 for Hipparcos stars. At least 30 times asmany stars as Hipparcos will be observed, and doing this DIVA will fill the gap in observations between Hipparcos and GAIA. DIVA’s combined astrometric and photometric measurements of high precision will have important impacts on astronomy and astrophysics in the next decade.