Mariateresa Crosta

Gaia Data Release 1 - Astrometry: one billion positions, two million proper motions and parallaxes

Gaia Data Release 1 (Gaia DR1) contains astrometric results for more than 1 billion stars brighter than magnitude 20.7 based on observations collected by the Gaia satellite during the first 14 months of its operational phase. We give a brief overview of the astrometric content of the data release and of the model assumptions, data processing, and validation of the results. For stars in common with the Hipparcos and Tycho-2 catalogues, complete astrometric single-star solutions are obtained by incorporating positional information from the earlier catalogues. For other stars only their positions are obtained by neglecting their proper motions and parallaxes. The results are validated by an analysis of the residuals, through special validation runs, and by comparison with external data. Results. For about two million of the brighter stars (down to magnitude ~11.5) we obtain positions, parallaxes, and proper motions to Hipparcos-type precision or better. For these stars, systematic errors depending e.g. on position and colour are at a level of 0.3 milliarcsecond (mas). For the remaining stars we obtain positions at epoch J2015.0 accurate to ~10 mas. Positions and proper motions are given in a reference frame that is aligned with the International Celestial Reference Frame (ICRF) to better than 0.1 mas at epoch J2015.0, and non-rotating with respect to ICRF to within 0.03 mas/yr. The Hipparcos reference frame is found to rotate with respect to the Gaia DR1 frame at a rate of 0.24 mas/yr. Based on less than a quarter of the nominal mission length and on very provisional and incomplete calibrations, the quality and completeness of the astrometric data in Gaia DR1 are far from what is expected for the final mission products. The results nevertheless represent a huge improvement in the available fundamental stellar data and practical definition of the optical reference frame.

Gaia Data Release 2 - The astrometric solution

Context. Gaia Data Release 2 (Gaia DR2) contains results for 1693 million sources in the magnitude range 3 to 21 based on observations collected by the European Space Agency Gaia satellite during the first 22 months of its operational phase. Aims. We describe the input data, models, and processing used for the astrometric content of Gaia DR2, and the validation of these resultsperformed within the astrometry task. Methods. Some 320 billion centroid positions from the pre-processed astrometric CCD observations were used to estimate the five astrometric parameters (positions, parallaxes, and proper motions) for 1332 million sources, and approximate positions at the reference epoch J2015.5 for an additional 361 million mostly faint sources. These data were calculated in two steps. First, the satellite attitude and the astrometric calibration parameters of the CCDs were obtained in an astrometric global iterative solution for 16 million selected sources, using about 1% of the input data. This primary solution was tied to the extragalactic International Celestial Reference System (ICRS) by means of quasars. The resulting attitude and calibration were then used to calculate the astrometric parameters of all the sources. Special validation solutions were used to characterise the random and systematic errors in parallax and proper motion. Results. For the sources with five-parameter astrometric solutions, the median uncertainty in parallax and position at the reference epoch J2015.5 is about 0.04 mas for bright (G < 14 mag) sources, 0.1 mas at G = 17 mag, and 0.7 masat G = 20 mag. In the proper motion components the corresponding uncertainties are 0.05, 0.2, and 1.2 mas yr−1, respectively.The optical reference frame defined by Gaia DR2 is aligned with ICRS and is non-rotating with respect to the quasars to within 0.15 mas yr−1. From the quasars and validation solutions we estimate that systematics in the parallaxes depending on position, magnitude, and colour are generally below 0.1 mas, but the parallaxes are on the whole too small by about 0.03 mas. Significant spatial correlations of up to 0.04 mas in parallax and 0.07 mas yr−1 in proper motion are seen on small (< 1 deg) and intermediate (20 deg) angular scales. Important statistics and information for the users of the Gaia DR2 astrometry are given in the appendices.

A General Relativistic Model of Light Propagation in the Gravitational Field of the Solar System: The Static Case

Modern astrometry is based on angular measurements at the microarcsecond level. At this accuracy, a fully general relativistic treatment of the data reduction is required. This paper concludes a series of articles dedicated to the problem of relativistic light propagation, presenting the final, microarcsecond version of a relativistic astrometric model that enables us to trace back a light path to its source through the nonstationary gravitational field of the moving bodies in the solar system. The previous model is used as test bed for numerical comparisons with the present one. We also test different versions of the computer code implementing the model at different levels of complexity to start exploring the best trade-off between numerical efficiency and the microarcsecond accuracy that needs to be reached.

Tracing light propagation to the intrinsic accuracy of spacetime geometry

Advancement in astronomical observations requires codification of light propagation and of the processes of its physical measurement at a high level of accuracy. This could unveil a new window of several subtle relativistic effects suffered by light while propagating. Indeed, light modeling and its subsequent detection should be conceived in a fully relativistic context, in order to interpret the outcome of the observing process in accordance with the geometrical environment affecting light propagation itself and the precepts of measurement. This paper deals with the complexity of such a topic by showing how the geometrical framework of RAMOD, a relativistic model initially developed for astrometric observations in the visible, constitutes an appropriate environment for back-tracing photons. Through gauging the energy content of a given gravitationally bound system, the geometrical aspects that match the required accuracy of present and future observational capabilities are evidenced. Then, by comparing different formulations of the null geodesic, their domain of validity within the given geometrical scheme is refined. Finally, by proving its ability in retrieving recent literature cases, RAMOD is promoted as a measurement-based general relativistic method for any present and future advancement in the light-tracing problem.

Gaia relativistic astrometric models I. Proper stellar direction and aberration

The high accuracy achievable by modern space astrometry requires the use of General Relativity to model the stellar light propagation through the gravitational field encountered from a source to a given observer inside the Solar System. The general relativisticdefinition of an astrometric measurement needs an appropriate use of the concept of reference frame, which should then be linked to the conventions of the IAU resolutions. On the other hand, a definition of the astrometric observables in the context of General Relativity is also essential for finding the stellar coordinates and proper motion uniquely, this being the main physical task of the inverse raytracing problem. The aim of this work is to set the level of reciprocal consistency of two relativistic models, GREM and RAMOD (Gaia, ESA mission), in order to guarantee a physically correct definition of the light’s local direction to a star and deduce the star coordinates and proper motions at the level of accuracy required by these models consistently with the IAU’s adopted reference systems.

The ray tracing analytical solution within the RAMOD framework. The case of a Gaia-like observer

This paper presents the analytical solution of the inverse ray tracing problem for photons emitted by a star and collected by an observer located in the gravitational field of the Solar System. This solution has been conceived to suit the accuracy achievable by the ESA Gaia satellite (launched on December 19, 2013) consistently with the measurement protocol in General relativity adopted within the RAMOD framework. Aim of this study is to provide a general relativistic tool for the science exploitation of such a revolutionary mission, whose main goal is to trace back star directions from within our local curved space-time, therefore providing a three-dimensional map of our Galaxy. The results are useful for a thorough comparison and cross-checking validation of what already exists in the field of Relativistic Astrometry. Moreover, the analytical solutions presented here can be extended to model other measurements that require the same order of accuracy expected for Gaia.

Relativistic Models for a GAIA-Like Astrometry Mission

Abstract : A non-perturbative general relativistic approach to global astrometry was developed by de Felice et al. (1998) to handle satellite astrometry data in a genuine relativistic framework. In this contribution, the framework above has been further exploited to account for stellar motions and parallax. Because of the relevance that accurate knowledge (to 10(exp -5) or better) of the relativistic parameter gamma has to fundamental physics, a Parametrized Post-Newtonian (PPN) model also has been implemented, which allows the direct estimation of gamma along with the astrometric parameters. These models have been tested on end-to-end simulations of the mission GAIA. The results show that, within the limitations of the simulation and the assumptions of the adopted model, measurements accurate to 100 microarcseconds of large arcs among stars repeated over a few years can be modelled to establish a dense reference frame with a precision of a few tens of microarcseconds. Moreover, the experiments indicate that gamma can be estimated to better than 10(exp -6).

The Erez–Rosen metric and the role of the quadrupole on light propagation

The gravitational field of a static body with the quadrupole moment is described by an exact solution found by Erez and Rosen. Here, we investigate the role of the quadrupole in the motion, deflection and lensing of a light ray in the above metric. The standard lensing observables such as image positions and magnification have been explicitly obtained in the weak-field and small-quadrupole limit. In this limit, the spacetime metric appears as the natural generalization to quadrupole corrections of the metric form adopted also in current astrometric models. Hence, the corresponding analytical solution of the inverse ray tracing problem and the consistency with other approaches are also discussed.

Gravitation Astrometric Measurement Experiment (GAME)

GAME is a recent concept for a small/medium class mission aimed at Fundamental Physics tests in the Solar system, by means of an optimised instrument in the visible, based on smart combination of coronagraphy and Fizeau interferometry. The targeted precision on the γ and β parameters of the Parametrised Post-Newtonian formulation of General Relativity are respectively in the 10-7-10-8 and 10-5-10-6 range, improving by one or two orders of magnitude with respect to the expectations on current or near future experiments. Such precision is suitable to detect possible deviations from the unity value, associated to generalised Einstein models for gravitation, with potentially huge impacts on the cosmological distribution of dark matter and dark energy from a Solar system scale experiment. The measurement principle is based on the differential astrometric signature on the stellar positions, i.e. based on the spatial component of the effect rather than the temporal component as in the most recent experiments using radio link delay timing variation (Cassini). The instrument concept is based on multiple field, multiple aperture Fizeau interferometry, observing simultaneously regions close to the Solar limb (requiring the adoption of coronagraphic techniques), and others in opposition to the Sun. The diluted optics approach is selected for achieving an efficient rejection of the scattered solar radiation, while retaining an acceptable angular resolution on the science targets. The multiple field observation is aimed at cost-effective control of systematic effects through simultaneous calibration. We describe the science motivation, the proposed mission profile, the instrument concept and the expected performance.

Relativistic satellite astrometry: the stellar radial velocity

We present a general-relativistic analysis that allows the stellar radial velocities to be determined from a suitable implementation of the spectroscopic data with the astrometric ones shortly to be provided by new generations of astrometric satellites at μarcsec levels of accuracy at least. This analysis leads to an enhancement of the c −1 Doppler-shift formula presently planned for the Gaia mission to an all-inclusive, general-relativistic formula at the c −3 level, consistently with the expected accuracy. From this formula, which is shown to provide relevant corrections already at the c −2 level to a previously proposed one, we are then able to derive the explicit expression for the stellar radial velocity in terms of the spectroscopic and astrometric data, thereby accounting for all the necessary relativistic corrections up to and including the c −3 level.