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&

Gaia astrometry for stars with too few observations - a Bayesian approach

Gaia's astrometric solution aims to determine at least five parameters for each star, 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 insufficient 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. Their formal uncertainties would however grossly underestimate the actual errors, due to the neglected parallax and proper motion. We aim to develop a recipe to calculate sensible formal uncertainties that can be used in all cases of under-observed stars. 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 different 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. 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.Comment: Revised version, accepted 21st of August 2015 for publication in A&

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

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. 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. The changes in observables produced by small perturbations of the basic angle, attitude, and parallaxes are calculated analytically. We then look for a combination of perturbations that has no net effect on the observables. 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 such 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.Comment: 8 pages, 2 figures; Accepted for publication in Astronomy & Astrophysic

Electrode level Monte Carlo model of radiation damage effects on astronomical CCDs

Current optical space telescopes rely upon silicon Charge Coupled Devices (CCDs) to detect and image the incoming photons. The performance of a CCD detector depends on its ability to transfer electrons through the silicon efficiently, so that the signal from every pixel may be read out through a single amplifier. This process of electron transfer is highly susceptible to the effects of solar proton damage (or non-ionizing radiation damage). This is because charged particles passing through the CCD displace silicon atoms, introducing energy levels into the semi-conductor bandgap which act as localized electron traps. The reduction in Charge Transfer Efficiency (CTE) leads to signal loss and image smearing. The European Space Agency's astrometric Gaia mission will make extensive use of CCDs to create the most complete and accurate stereoscopic map to date of the Milky Way. In the context of the Gaia mission CTE is referred to with the complementary quantity Charge Transfer Inefficiency (CTI = 1-CTE). CTI is an extremely important issue that threatens Gaia's performances. We present here a detailed Monte Carlo model which has been developed to simulate the operation of a damaged CCD at the pixel electrode level. This model implements a new approach to both the charge density distribution within a pixel and the charge capture and release probabilities, which allows the reproduction of CTI effects on a variety of measurements for a large signal level range in particular for signals of the order of a few electrons. A running version of the model as well as a brief documentation and a few examples are readily available at http://www.strw.leidenuniv.nl/~prodhomme/cemga.php as part of the CEMGA java package (CTI Effects Models for Gaia).Comment: Accepted by MNRAS on 13 February 2011. 15 pages, 7 figures and 5 table

Photometric colors of late-type giants: theory versus observations

To assess the current status in the theoretical modeling of the spectral properties of late-type giants, we provide a comparison of synthetic photometric colors of late-type giants (calculated with PHOENIX, MARCS and ATLAS model atmospheres) with observations, at [M/H]=0.0 and -2.0. Overall, there is a good agreement between observed and synthetic colors, and synthetic colors and published Teff-color relations, both at [M/H]=0.0 and -2.0. Deviations from the observed trends in Teff-color planes are generally within \pm 150K (or less) in the effective temperature range Teff=3500-4800K. Synthetic colors calculated with different stellar atmosphere models typically agree to ~100K, within a large range of effective temperatures and gravities. Some discrepancies are seen in the Teff-(B-V) plane below Teff~3800K at [M/H]=0.0, due to difficulties in reproducing the 'turn-off' to the bluer colors which is seen in the observed data at Teff~3600K. Note that at [M/H]=-2.0 effective temperatures given by the scale of Alonso et al. (1999) are generally lower than those resulting from other Teff-color relations based both on observed and synthetic colors.Comment: 2 pages, 1 figure. Proceedings of the IAU Symposium 232 "The Scientific Requirements for Extremely Large Telescopes", eds. P. Whitelock, B. Leibundgut, and M. Dennefel

The impact of CCD radiation damage on Gaia astrometry: I. Image location estimation in the presence of radiation damage

The Gaia mission has been designed to perform absolute astrometric measurements with unprecedented accuracy; the end-of-mission parallax standard error is required to be 30 micro-arcseconds for a G2V type star of magnitude 15. These requirements set a stringent constraint on the accuracy of the estimation of the location of the stellar image on the CCD for each observation: e.g., 0.3 milli-arseconds (mas) or 0.005 pixels for the same V=15 G2V star. However the Gaia CCDs will suffer from charge transfer inefficiency (CTI) caused by radiation damage that will degrade the stellar image quality and may degrade the astrometric performance of Gaia if not properly addressed. For the first time at this level of detail, the potential impact of radiation damage on the performance of Gaia is investigated. In this first paper we focus on the evaluation of the CTI impact on the image location accuracy. We show that CTI decreases the stellar image signal-to-noise ratio and irreversibly degrades the image location estimation precision. As a consequence the location estimation standard errors increase by up to 6% for a radiation damage level equivalent to the end-of-mission. In addition the CTI-induced image distortion introduces a systematic bias in the image location estimation (up to 0.05 pixels or 3 mas in the Gaia operating conditions). We present a novel approach to CTI mitigation that enables, without correction of the raw data, the unbiased estimation of the image location and flux from damaged observations. Its implementation reduces the maximum measured location bias for the faintest magnitude to 0.005 pixels (~4e-4 pixels at magnitude 15). In a second paper we will investigate how the CTI effects affect the final astrometric accuracy of Gaia by propagating residual errors through the astrometric solution.Comment: 23 figures, 6 tables, accepted for publication in the Monthly Notices of the Royal Astronomical Society the 4th of October 201

Space-borne global astrometric surveys: the hunt for extra-solar planets

The proposed global astrometry mission {\it GAIA}, recently recommended within the context of ESA's Horizon 2000 Plus long-term scientific program, appears capable of surveying the solar neighborhood within $\sim$ 200 pc for the astrometric signatures of planets around stars down to the magnitude limit of $V$=17 mag, which includes late M dwarfs at 100 pc. Realistic end-to-end simulations of the GAIA global astrometric measurements have yielded first quantitative estimates of the sensitivity to planetary perturbations and of the ability to measure their orbital parameters. Single Jupiter-mass planets around normal solar-type stars appear detectable up to 150 pc ($V\le$12 mag) with probabilities $\ge$ 50 per cent for orbital periods between $\sim$2.5 and $\sim$8 years, and their orbital parameters measured with better than 30 per cent accuracy to about 100 pc. Jupiter-like objects (same mass and period as our giant planet) are found with similar probabilities up to 100 pc.These first experiments indicate that the {\it GAIA} results would constitute an important addition to those which will come from the other ongoing and planned planet-search programs. These data combined would provide a formidable testing ground on which to confront theories of planetary formation and evolution.Comment: 13 pages, 10 figures, uses mn.sty, accepted by MNRA

Fourteen New Companions from the Keck & Lick Radial Velocity Survey Including Five Brown Dwarf Candidates

We present radial velocities for 14 stars on the California & Carnegie Planet Search target list that reveal new companions. One star, HD 167665, was fit with a definitive Keplerian orbit leading to a minimum mass for the companion of 50.3 Mjup at a separation from its host of ~5.5 AU. Incomplete or limited phase coverage for the remaining 13 stars prevents us from assigning to them unique orbital parameters. Instead, we fit their radial velocities with Keplerian orbits across a grid of fixed values for Msini and period, P, and use the resulting reduced chi-square surface to place constraints on Msini, P, and semimajor axis, a. This technique allowed us to restrict Msini below the brown dwarf -- stellar mass boundary for an additional 4 companions (HD 150554, HD 8765, HD 72780, HD 74014). If the combined 5 companions are confirmed as brown dwarfs, these results would comprise the first major catch of such objects from our survey beyond ~3 AU.Comment: 29 pages, 14 figures, accepted to Ap

GAIA: Composition, Formation and Evolution of the Galaxy

The GAIA astrometric mission has recently been approved as one of the next two `cornerstones' of ESA's science programme, with a launch date target of not later than mid-2012. GAIA will provide positional and radial velocity measurements with the accuracies needed to produce a stereoscopic and kinematic census of about one billion stars throughout our Galaxy (and into the Local Group), amounting to about 1 per cent of the Galactic stellar population. GAIA's main scientific goal is to clarify the origin and history of our Galaxy, from a quantitative census of the stellar populations. It will advance questions such as when the stars in our Galaxy formed, when and how it was assembled, and its distribution of dark matter. The survey aims for completeness to V=20 mag, with accuracies of about 10 microarcsec at 15 mag. Combined with astrophysical information for each star, provided by on-board multi-colour photometry and (limited) spectroscopy, these data will have the precision necessary to quantify the early formation, and subsequent dynamical, chemical and star formation evolution of our Galaxy. Additional products include detection and orbital classification of tens of thousands of extra-Solar planetary systems, and a comprehensive survey of some 10^5-10^6 minor bodies in our Solar System, through galaxies in the nearby Universe, to some 500,000 distant quasars. It will provide a number of stringent new tests of general relativity and cosmology. The complete satellite system was evaluated as part of a detailed technology study, including a detailed payload design, corresponding accuracy assesments, and results from a prototype data reduction development.Comment: Accepted by A&A: 25 pages, 8 figure

The spectroscopic orbit of Capella revisited

Context. Capella is among the few binary stars with two evolved giant components. The hotter component is a chromospherically active star within the Hertzsprung gap, while the cooler star is possibly helium-core burning. Aims. The known inclination of the orbital plane from astrometry in combination with precise radial velocities will allow very accurate masses to be determined for the individual Capella stars. This will constrain their evolutionary stage and possibly the role of the active star's magnetic field on the dynamical evolution of the binary system. Methods. We obtained a total of 438 high-resolution \'echelle spectra during the years 2007-2010 and used the measured velocities to recompute the orbital elements. Our double-lined orbital solution yields average residuals of 64 m/s for the cool component and 297 m/s for the more rapidly rotating hotter component. Results. The semi-amplitude of the cool component is smaller by 0.045 km/s than the orbit determination of Torres et al. from data taken during 1996-1999 but more precise by a factor of 5.5, while for the hotter component it is larger by 0.580 km/s and more precise by a factor of 3.6. This corresponds to masses of 2.573\pm0.009 M_sun and 2.488\pm0.008 M_sun for the cool and hot component, respectively. Their relative errors of 0.34% and 0.30% are about half of the values given in Torres et al. for a combined literature- data solution but with absolute values different by 4% and 2% for the two components, respectively. The mass ratio of the system is therefore q = M_A/M_B = 0.9673 \pm 0.0020. Conclusions. Our orbit is the most precise and also likely to be the most accurate ever obtained for Capella