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arXiv:1507.02963 by D. Michalik et al: 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. more

arXiv:1507.02105 by C.A.L. Bailer-Jones: Astrometric surveys such as Gaia and LSST will measure parallaxes for hundreds of millions of stars. Yet they will not measure a single distance. Rather, a distance must be estimated from a parallax. In this didactic article, I show that doing this is not trivial once the fractional parallax error is larger than about 20%, which will be the case for about 80% of stars in the Gaia catalogue. Estimating distances is an inference problem in which the use of prior assumptions is unavoidable. I investigate the properties and performance of various priors and examine their implications. A supposed uninformative uniform prior in distance is shown to give very poor distance estimates (large bias and variance). Any prior with a sharp cut-off at some distance has similar problems. The choice of prior depends on the information one has available - and is willing to use - concerning, for example, the survey and the Galaxy. I demonstrate that a simple prior which decreases asymptotically to zero at infinite distance has good performance, accommodates non-positive parallaxes, and does not require a bias correction. more

arXiv:1505.07019 by R. J. Jackson et al: The Gaia-ESO Survey (GES) is a large public spectroscopic survey at the European Southern Observatory Very Large Telescope. A key aim is to provide precise radial velocities (RVs) and projected equatorial velocities (v sin i) for representative samples of Galactic stars, that will complement information obtained by the Gaia astrometry satellite. We present an analysis to empirically quantify the size and distribution of uncertainties in RV and v sin i using spectra from repeated exposures of the same stars. We show that the uncertainties vary as simple scaling functions of signal-to-noise ratio (S/N) and v sin i, that the uncertainties become larger with increasing photospheric temperature, but that the dependence on stellar gravity, metallicity and age is weak. The underlying uncertainty distributions have extended tails that are better represented by Student's t-distributions than by normal distributions. Parametrised results are provided, that enable estimates of the RV precision for almost all GES measurements, and estimates of the v sin i precision for stars in young clusters, as a function of S/N, v sin i and stellar temperature. The precision of individual high S/N GES RV measurements is 0.22-0.26 km/s, dependent on instrumental configuration. more