The Gaia reference frame for bright sources examined using VLBI observations of radio stars

Positions and proper motions of Gaia sources are expressed in a reference frame that ideally should be non-rotating relative to distant extragalactic objects, coincident with the International Celestial Reference System (ICRS), and consistent across all magnitudes. For sources fainter than 16th magnitude this is achieved thanks to Gaia's direct observations of quasars. At brighter magnitudes it is difficult to validate the quality of the reference frame due to the scarcity of comparison data. This paper examines the use of VLBI observations of radio stars to determine the spin and orientation of the bright reference frame of Gaia. Simultaneous estimation of the six spin and orientation parameters makes optimal use of VLBI data and makes it possible to include even single-epoch VLBI observations in the solution. The method is applied to Gaia Data Release 2 (DR2) using published VLBI data for 41 radio stars. Results for the 26 best-fitting sources indicate that the bright reference frame of Gaia DR2 is rotating relative to the faint quasars at a rate of about 0.1 mas/yr, significant at 2-sigma level. This supports a similar conclusion based on a comparison with stellar positions in the Hipparcos frame. The accuracy is currently limited by the small number of radio sources used, by uncertainties in the Gaia DR2 proper motions, and by the astrophysical nature of the radio stars. While the origin of the indicated rotation is understood and can be avoided in future data releases, it remains important to validate the bright reference frame of Gaia by independent observations. This can be achieved using VLBI astrometry, which may require re-observing the old sample of radio stars as well as measuring new objects. The unique historical value of positional measurements is stressed and VLBI observers are urged to ensure that relevant positional information is preserved for the future.Comment: 17 pages, 5 figures. Revised version incorporating a Corrigendum published by A&A. Tables 2-3, Figures 3-5, and Sections 3-5 have been substantially revise

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

Quasars can be used to verify the parallax zero-point of the Tycho-Gaia Astrometric Solution

Context. The Gaia project will determine positions, proper motions, and parallaxes for more than one billion stars in our Galaxy. It is known that Gaia's two telescopes are affected by a small but significant variation of the basic angle between them. Unless this variation is taken into account during data processing, e.g. using on-board metrology, it causes systematic errors in the astrometric parameters, in particular a shift of the parallax zero-point. Previously, we suggested an early reduction of Gaia data for the subset of Tycho-2 stars (Tycho-Gaia Astrometric Solution; TGAS). Aims. We aim to investigate whether quasars can be used to independently verify the parallax zero-point already in early data reductions. This is not trivially possible as the observation interval is too short to disentangle parallax and proper motion for the quasar subset. Methods. We repeat TGAS simulations but additionally include simulated Gaia observations of quasars from ground-based surveys. All observations are simulated with basic angle variations. To obtain a full astrometric solution for the quasars in TGAS we explore the use of prior information for their proper motions. Results. It is possible to determine the parallax zero-point for the quasars with a few {\mu}as uncertainty, and it agrees to a similar precision with the zero-point for the Tycho-2 stars. The proposed strategy is robust even for quasars exhibiting significant fictitious proper motion due to a variable source structure, or when the quasar subset is contaminated with stars misidentified as quasars. Conclusions. Using prior information about quasar proper motions we could provide an independent verification of the parallax zero-point in early solutions based on less than one year of Gaia data.Comment: Astronomy & Astrophysics, accepted 25 October 2015, in press. Version 2 contains a few language improvements and a terminology change from 'fictitious proper motions' to 'spurious proper motions

Maximum likelihood estimation of local stellar kinematics

Context. Kinematical data such as the mean velocities and velocity dispersions of stellar samples are useful tools to study galactic structure and evolution. However, observational data are often incomplete (e.g., lacking the radial component of the motion) and may have significant observational errors. For example, the majority of faint stars observed with Gaia will not have their radial velocities measured. Aims. Our aim is to formulate and test a new maximum likelihood approach to estimating the kinematical parameters for a local stellar sample when only the transverse velocities are known (from parallaxes and proper motions). Methods. Numerical simulations using synthetically generated data as well as real data (based on the Geneva-Copenhagen survey) are used to investigate the statistical properties (bias, precision) of the method, and to compare its performance with the much simpler "projection method" described by Dehnen & Binney (1998). Results. The maximum likelihood method gives more correct estimates of the dispersion when observational errors are important, and guarantees a positive-definite dispersion matrix, which is not always obtained with the projection method. Possible extensions and improvements of the method are discussed.Comment: 7 pages, 2 figures. Accepted for publication in Astronomy & Astrophysic

The case for high precision in elemental abundances of stars in the era of large spectroscopic surveys

A number of large spectroscopic surveys of stars in the Milky Way are under way or are being planned. In this context it is important to discuss the extent to which elemental abundances can be used as discriminators between different (known and unknown) stellar populations in the Milky Way. We aim to establish the requirements in terms of precision in elemental abundances, as derived from spectroscopic surveys of the Milky Way's stellar populations, in order to detect interesting substructures in elemental abundance space. We present a simple relation between the minimum number of stars needed to detect a given substructure and the precision of the measurements. The results are in agreement with recent small- and large-scale studies, with high and low precision, respectively. Large-number statistics cannot fully compensate for low precision in the abundance measurements and each survey should carefully evaluate what the main science drivers are for the survey and ensure that the chosen observational strategy will result in the precision necessary to answer the questions posed.Comment: 6 pages, 6 figures. Accepted for publication in Astronomy & Astrophysic

Astrometric signal profile fitting for Gaia

A tool for representation of the one-dimensional astrometric signal of Gaia is described and investigated in terms of fit discrepancy and astrometric performance with respect to number of parameters required. The proposed basis function is based on the aberration free response of the ideal telescope and its derivatives, weighted by the source spectral distribution. The influence of relative position of the detector pixel array with respect to the optical image is analysed, as well as the variation induced by the source spectral emission. The number of parameters required for micro-arcsec level consistency of the reconstructed function with the detected signal is found to be 11. Some considerations are devoted to the issue of calibration of the instrument response representation, taking into account the relevant aspects of source spectrum and focal plane sampling. Additional investigations and other applications are also suggested.Comment: 13 pages, 21 figures, Accepted by MNRAS 2010 January 29. Received 2010 January 28; in original form 2009 September 3

The Hipparcos Transit Data: What, why and how?

The Hipparcos Transit Data are a collection of partially reduced, fully calibrated observations of (mostly) double and multiple stars obtained with the ESA Hipparcos astrometry satellite. The data are publicly available, as part of the CD-ROM set distributed with the Hipparcos and Tycho Catalogues (ESA SP--1200, 1997), for about a third of the Hipparcos Catalogue entries including all confirmed or suspected non-single stars. The Transit Data consist of signal modulation parameters derived from the individual transits of the targets across the Hipparcos focal grid. The Transit Data permit re-reduction of the satellite data for individual objects, using arbitrarily complex object models in which time-variable photometric as well as geometric characteristics may be taken into account. We describe the structure and contents of the Transit Data files and give examples of how the data can be used. Some of the applications use standard astronomical software: Difmap or AIPS for aperture synthesis imaging, and GaussFit for detailed model fitting. Fortran code converting the data into formats suitable for these application programs has been made public in order to encourage and facilitate the use of Hipparcos Transit Data.Comment: A&AS, accepted for publication, 17 pages, 9 figures, 1 Table, Software available via http://www.astro.lu.se/~lennart/TD/index.html, Figures 4, 5, 6 and 7 need to copied separately, A complete postscript file can be found at http://www.astro.lu.se/~lennart/TD/ds1699.ps.g

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

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. 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. The apparent path equation for uniform rectilinear motion is solved analytically in a classical (special-relativistic) framework, leading to rigorous expressions which relate the (apparent) astrometric parameters and radial velocity to the (true) kinematic parameters of the star in the barycentric reference system. 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 into account light-time effects. 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 exceeds 0.1 mas or 0.1 m/s 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.Comment: Accepted for publication in A&

Astrometry and exoplanets in the Gaia era: a Bayesian approach to detection and parameter recovery

(abridged) We develop Bayesian methods and detection criteria for orbital fitting, and revise the detectability of exoplanets in light of the in-flight properties of Gaia. Limiting ourselves to one-planet systems as a first step of the development, we simulate Gaia data for exoplanet systems over a grid of S/N, orbital period, and eccentricity. The simulations are then fit using Markov chain Monte Carlo methods. We investigate the detection rate according to three information criteria and the delta chi^2. For the delta chi^2, the effective number of degrees of freedom depends on the mission length. We find that the choice of the Markov chain starting point can affect the quality of the results; we therefore consider two limit possibilities: an ideal case, and a very simple method that finds the starting point assuming circular orbits. Using Jeffreys' scale of evidence, the fraction of false positives passing a strong evidence criterion is < ~0.2% (0.6%) when considering a 5 yr (10 yr) mission and using the Akaike information criterion or the Watanabe-Akaike information criterion, and <0.02% (<0.06%) when using the Bayesian information criterion. We find that there is a 50% chance of detecting a planet with a minimum S/N=2.3 (1.7). This sets the maximum distance to which a planet is detectable to ~70 pc and ~3.5 pc for a Jupiter-mass and Neptune-mass planet, respectively, assuming a 10 yr mission, a 4 au semi-major axis, and a 1 M_sun star. The period is the orbital parameter that can be determined with the best accuracy, with a median relative difference between input and output periods of 4.2% (2.9%) assuming a 5 yr (10 yr) mission. The median accuracy of the semi-major axis of the orbit can be recovered with a median relative error of 7% (6%). The eccentricity can also be recovered with a median absolute accuracy of 0.07 (0.06).Comment: 18 pages, 11 figures. New version accepted by A&A for publicatio

The Tycho-Gaia astrometric solution. How to get 2.5 million parallaxes with less than one year of Gaia data

Context. The first release of astrometric data from Gaia will contain the mean stellar positions and magnitudes from the first year of observations, and proper motions from the combination of Gaia data with Hipparcos prior information (HTPM). Aims. We study the potential of using the positions from the Tycho-2 Catalogue as additional information for a joint solution with early Gaia data. We call this the Tycho-Gaia astrometric solution (TGAS). Methods. We adapt Gaia's Astrometric Global Iterative Solution (AGIS) to incorporate Tycho information, and use simulated Gaia observations to demonstrate the feasibility of TGAS and to estimate its performance. Results. Using six to twelve months of Gaia data, TGAS could deliver positions, parallaxes and annual proper motions for the 2.5 million Tycho-2 stars, with sub-milliarcsecond accuracy. TGAS overcomes some of the limitations of the HTPM project and allows its execution half a year earlier. Furthermore, if the parallaxes from Hipparcos are not incorporated in the solution, they can be used as a consistency check of the TGAS/HTPM solution.Comment: Accepted for publication in A&A, 24 Dec 201