A. G. Butkevich

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 1. Reference frame and optical properties of ICRF sources

Context. As part of the data processing for Gaia Data Release 1 (Gaia DR1) a special astrometric solution was computed, the so-called auxiliary quasar solution. This gives positions for selected extragalactic objects, including radio sources in the second realisation of the International Celestial Reference Frame (ICRF2) that have optical counterparts bright enough to be observed with Gaia. A subset of these positions was used to align the positional reference frame of Gaia DR1 with the ICRF2. Although the auxiliary quasar solution was important for internal validation and calibration purposes, the resulting positions are in general not published in Gaia DR1. Aims. We describe the properties of the Gaia auxiliary quasar solution for a subset of sources matched to ICRF2, and compare their optical and radio positions at the sub-mas level. Methods. Descriptive statistics are used to characterise the optical data for the ICRF sources and the optical-radio differences. The most discrepant cases are examined using online resources to find possible alternative explanations than a physical optical-radio offset of the quasars. Results. In the auxiliary quasar solution 2191 sources have good optical positions matched to ICRF2 sources with high probability. Their formal standard errors are better than 0.76 milliarcsec (mas) for 50% of the sources and better than 3.35 mas for 90%. Optical magnitudes are obtained in Gaia’s unfiltered photometric G band. The Gaia results for these sources are given as a separate table in Gaia DR1. The comparison with the radio positions of the defining sources shows no systematic differences larger than a few tenths of a mas. The fraction of questionable solutions, not readily accounted for by the statistics, is less than 6%. Normalised differences have extended tails requiring case-by-case investigations for around 100 sources, but we have not seen any difference indisputably linked to an optical-radio offset in the sources. Conclusions. With less than a quarter of the data expected from the nominal mission it has been possible to obtain positions at the sub-mas level for most of the ICRF sources having an optical counterpart brighter than 20.5 mag.

Gaia astrometry for stars with too few observations. A Bayesian approach

Context. The astrometric solution for Gaia aims to determine at least five parameters for each star, representing its position, parallax, and proper motion, together with appropriate estimates of their uncertainties and correlations. This requires at least five distinct observations per star. In the early data reductions the number of observations may be insu cient for a five-parameter solution, and even after the full mission many stars will remain under-observed, including faint stars at the detection limit and transient objects. In such cases it is reasonable to determine only the two position parameters. The formal uncertainties of such a two-parameter solution would however grossly underestimate the actual errors in position, due to the neglected parallax and proper motion. Aims. We aim to develop a recipe to calculate sensible formal uncertainties that can be used in all cases of under-observed stars. Methods. Prior information about the typical ranges of stellar parallaxes and proper motions is incorporated in the astrometric solution by means of Bayes’ rule. Numerical simulations based on the Gaia Universe Model Snapshot (GUMS) are used to investigate how the prior influences the actual errors and formal uncertainties when di erent amounts of Gaia observations are available. We develop a criterion for the optimum choice of priors, apply it to a wide range of cases, and derive a global approximation of the optimum prior as a function of magnitude and galactic coordinates. Results. The feasibility of the Bayesian approach is demonstrated through global astrometric solutions of simulated Gaia observations. With an appropriate prior it is possible to derive sensible positions with realistic error estimates for any number of available observations. Even though this recipe works also for well-observed stars it should not be used where a good five-parameter astrometric solution can be obtained without a prior. Parallaxes and proper motions from a solution using priors are always biased and should not be used.

Determining PPN gamma with Gaia's astrometric core solution

The ESA space astrometry mission Gala, due for launch in early 2012, will in addition to its huge output of fundamental astrometric and astrophysical data also provide stringent tests of general relativity. In this paper we present an updated analysis of Gaias capacity to measure the PPN parameter gamma as part of its core astrometric solution. The analysis is based on small-scale astrometric solutions taking into account the simultaneous determination of stellar astrometric parameters and the satellite attitude. In particular, the statistical correlation between PPN gamma and the stellar parallaxes is considered. Extrapolating the results to a full-scale solution using some 100 million stars, we find that PPN gamma could be obtained to about 10(-6), which is significantly better than todays best estimate from the Cassini mission of 2 x 10(-5). (Less)

Rigorous treatment of barycentric stellar motion Perspective and light-time effects in astrometric and radial velocity data

Context. High-precision astrometric and radial-velocity observations require accurate modelling of stellar motions in order to extrapolate measurements over long time intervals, and to detect deviations from uniform motion caused, for example, by unseen companions. Aims. We aim to explore the simplest possible kinematic model of stellar motions, namely that of uniform rectilinear motion relative to the solar system barycentre, in terms of observable quantities including error propagation. Methods. The apparent path equation for uniform rectilinear motion is solved analytically in a classical (special-relativistic) framework, leading to rigorous expressions that relate the (apparent) astrometric parameters and radial velocity to the (true) kinematic parameters of the star in the barycentric reference system. Results. We present rigorous and explicit formulae for the transformation of stellar positions, parallaxes, proper motions, and radial velocities from one epoch to another, assuming uniform rectilinear motion and taking light-time effects into account. The Jacobian matrix of the transformation is also given, allowing accurate and reversible propagation of errors over arbitrary time intervals. The light-time effects are generally very small, but exceed 0.1 mas or 0.1 m s(-1) over 100 yr for at least 33 stars in the Hipparcos catalogue. For high-velocity stars within a few tens of pc from the Sun, light-time effects are generally more important than the effects of the curvature of their orbits in the Galactic potential. (Less)

Impact of basic angle variations on the parallax zero point for a scanning astrometric satellite

Context. Determination of absolute parallaxes by means of a scanning astrometric satellite such as Hipparcos or Gaia relies on the short-term stability of the so-called basic angle between the two viewing directions. Uncalibrated variations of the basic angle may produce systematic errors in the computed parallaxes. Aims. We examine the coupling between a global parallax shift and specific variations of the basic angle, namely those related to the satellite attitude with respect to the Sun. Methods. The changes in observables produced by small perturbations of the basic angle, attitude, and parallaxes were calculated analytically. We then looked for a combination of perturbations that had no net effect on the observables. Results. In the approximation of infinitely small fields of view, it is shown that certain perturbations of the basic angle are observationally indistinguishable from a global shift of the parallaxes. If these kinds of perturbations exist, they cannot be calibrated from the astrometric observations but will produce a global parallax bias. Numerical simulations of the astrometric solution, using both direct and iterative methods, confirm this theoretical result. For a given amplitude of the basic angle perturbation, the parallax bias is smaller for a larger basic angle and a larger solar aspect angle. In both these respects Gaia has a more favourable geometry than Hipparcos. In the case of Gaia, internal metrology is used to monitor basic angle variations. Additionally, Gaia has the advantage of detecting numerous quasars, which can be used to verify the parallax zero point.

TESTING LOCAL LORENTZ INVARIANCE WITH HIGH-ACCURACY ASTROMETRIC OBSERVATIONS

This paper summarizes the analysis of the consequences of the violation of the Local Lorentz Invariance (LLI) on astrometric observations. We demonstrate that from the point of view of the LLI astrometric observations represent an experiment of Michelson-Morley type. The future high-accuracy astrometric projects (e.g., Gaia) will be used to test the LLI.

Determination of the barycentric velocity of an astrometric satellite using its own observational data

The problem of determination of the orbital velocity of an astrometric satellite from its own observational data is studied. It is well known that data processing of microarcsecond- level astrometric observations imposes very stringent requirements on the accuracy of the orbital velocity of the satellite (a velocity correction of 1.45 mm/s implies an aberrational correction of 1 µas). Because of a number of degeneracies the orbital velocity cannot be fully restored from observations provided by the satellite. Seven constraints that must be applied on a velocity pa- rameterization are discussed and formulated mathematically. It is shown what part of velocity can be recovered from astrometric data by a combined fit of both velocity parameters and astro- metric parameters of the sources. Numerical simulations show that, with the seven constraints applied, the velocity and astrometric parameters can be reliably estimated from observational data. It is also argued that the idea to improve the velocity of an astrometric satellite from its own observational data is only useful if the a priori information on the orbital velocity justifies the applicability of the velocity constraints. The proposed model takes into account only transla- tional motion of the satellite and ignores any satellite-specific parameters. Therefore, the results of this study are equally applicable to both scanning missions similar to Gaia, and pointing ones like SIM, provided that enough sources were observed sufficiently uniformly.