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

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

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

Astrometric radial velocities. I. Non-spectroscopic methods for measuring stellar radial velocity

High-accuracy astrometry permits the determination of not only stellar tangential motion, but also the component along the line-of-sight. Such non-spectroscopic (i.e. astrometric) radial velocities are independent of stellar atmospheric dynamics, spectral complexity and variability, as well as of gravitational redshift. Three methods are analysed: (1) changing annual parallax, (2) changing proper motion and (3) changing angular extent of a moving group of stars. All three have significant potential in planned astrometric projects. Current accuracies are still inadequate for the first method, while the second is marginally feasible and is here applied to 16 stars. The third method reaches high accuracy (<1 km/s) already with present data, although for some clusters an accuracy limit is set by uncertainties in the cluster expansion rate.Comment: 13 pages, 2 figures. Accepted for publication in Astronomy & Astrophysics (main journal

The Gaia inertial reference frame and the tilting of the Milky Way disk

While the precise relationship between the Milky Way disk and the symmetry planes of the dark matter halo remains somewhat uncertain, a time-varying disk orientation with respect to an inertial reference frame seems probable. Hierarchical structure formation models predict that the dark matter halo is triaxial and tumbles with a characteristic rate of ~2 rad/Hubble time (~30 muas/yr). These models also predict a time-dependent accretion of gas, such that the angular momentum vector of the disk should be misaligned with that of the halo. These effects, as well as tidal effects of the LMC, will result in the rotation of the angular momentum vector of the disk population with respect to the quasar reference frame. We assess the accuracy with which the positions and proper motions from Gaia can be referred to a kinematically non-rotating system, and show that the spin vector of the transformation from any rigid self-consistent catalog frame to the quasi-inertial system defined by quasars should be defined to better than 1 muas/yr. Determination of this inertial frame by Gaia will reveal any signature of the disk orientation varying with time, improve models of the potential and dynamics of the Milky Way, test theories of gravity, and provide new insights into the orbital evolution of the Sagittarius dwarf galaxy and the Magellanic Clouds.Comment: 16 pages; accepted for publication in Ap

Error characterization of the Gaia astrometric solution I. Mathematical basis of the covariance expansion model

Context. Accurate characterization of the astrometric errors in the forthcoming Gaia Catalogue will be essential for making optimal use of the data. This includes the correlations among the estimated astrometric parameters of the stars as well as their standard uncertainties, i.e., the complete (variance-)covariance matrix of the relevant astrometric parameters. Aims. Because a direct computation of the covariance matrix is infeasible due to the large number of parameters, approximate methods must be used. The aim of this paper is to provide a mathematical basis for estimating the variance-covariance of any pair of astrometric parameters, and more generally the covariance matrix for multidimensional functions of the astrometric parameters. The validation of this model by means of numerical simulations will be considered in a forthcoming paper. Methods. Based on simplifying assumptions (in particular that calibration errors can be neglected), we derive and analyse a series expansion of the covariance matrix of the least-squares solution. A recursive relation for successive terms is derived and interpreted in terms of the propagation of errors from the stars to the attitude and back. We argue that the expansion should converge rapidly to useful precision. The recursion is vastly simplified by using a kinematographic (step-wise) approximation of the attitude model. Results. Low-order approximations of arbitrary elements from the covariance matrix can be computed efficiently in terms of a limited amount of pre-computed data representing compressed observations and the structural relationships among them. It is proposed that the user interface to the Gaia Catalogue should provide the tools necessary for such computations