Runaway and walkaway stars from the ONC with Gaia DR2

Theory predicts that we should find fast, ejected (runaway) stars of all masses around dense, young star-forming regions. $N$-body simulations show that the number and distribution of these ejected stars could be used to constrain the initial spatial and kinematic substructure of the regions. We search for runaway and slower walkaway stars within 100 pc of the Orion Nebula Cluster (ONC) using $Gaia$ DR2 astrometry and photometry. We compare our findings to predictions for the number and velocity distributions of runaway stars from simulations that we run for 4 Myr with initial conditions tailored to the ONC. In $Gaia$ DR2, we find 31 runaway and 54 walkaway candidates based on proper motion, but not all of these are viable candidates in three dimensions. About 40 per cent are missing radial velocities, but we can trace back 9 3D-runaways and 24 3D-walkaways to the ONC, all of which are low/intermediate-mass (<8 M$_{\odot}$). Our simulations show that the number of runaways within 100 pc decreases the older a region is (as they quickly travel beyond this boundary), whereas the number of walkaways increases up to 3 Myr. We find fewer walkaways in $Gaia$ DR2 than the maximum suggested from our simulations, which may be due to observational incompleteness. However, the number of $Gaia$ DR2 runaways agrees with the number from our simulations during an age of $\sim$1.3-2.4 Myr, allowing us to confirm existing age estimates for the ONC (and potentially other star-forming regions) using runaway stars.Comment: 19 pages, 7 figures, accepted for publication in MNRA

Benfords law in the Gaia universe

Benfords law states that for scale- and base-invariant data sets covering a wide dynamic range, the distribution of the first significant digit is biased towards low values. This has been shown to be true for wildly different datasets, including financial, geographical, and atomic data. In astronomy, earlier work showed that Benfords law also holds for distances estimated as the inverse of parallaxes from the ESA Hipparcos mission. We investigate whether Benfords law still holds for the 1.3 billion parallaxes contained in the second data release of Gaia (Gaia DR2). In contrast to previous work, we also include negative parallaxes. We examine whether distance estimates computed using a Bayesian approach instead of parallax inversion still follow Benfords law. Lastly, we investigate the use of Benfords law as a validation tool for the zero-point of the Gaia parallaxes

Scale-free dynamical models for galaxies: flattened densities in spherical potentials

This paper presents two families of phase-space distribution functions (DFs) that generate scale-free spheroidal mass densities in scale-free spherical potentials. The `case I' DFs are anisotropic generalizations of the flattened f(E,L_z) model, which they include as a special case. The `case II' DFs generate flattened constant-anisotropy models, in which the constant ratio of rms tangential to radial motion is characterized by Binney's parameter beta. The models can describe the outer parts of galaxies and the density cusp structure near a central black hole, but also provide general insight into the dynamical properties of flattened systems. The dependence of the intrinsic and projected properties on the model parameters and the inclination is described. The observed ratio of the rms projected line-of-sight velocities on the projected major and minor axes of elliptical galaxies is best fit by the case II models with beta > 0. These models also predict non-Gaussian velocity profile shapes consistent with existing observations. The distribution functions are used to model the galaxies NGC 2434 (E1) and NGC 3706 (E4), for which stellar kinematical measurements out to two effective radii indicate the presence of dark halos (Carollo et al.). The velocity profile shapes of both galaxies can be well fit by radially anisotropic case II models with a spherical logarithmic potential. This contrasts with the f(E,L_z) models studied previously, which require flattened dark halos to fit the data.Comment: LaTeX file, uses standard macros mn.sty, epsf.sty. 17 pages including 7 figure

A refurbished convergent point method for finding moving groups in the Hipparcos Catalogue

The Hipparcos data allow a major step forward in the research of `moving groups' in the Solar neighbourhood, as the common motion of group members causes converging proper motions. Previous knowledge on these coherent structures in velocity space has always been limited by the availability, reliability, and accuracy of ground-based proper motion measurements. A refurbishment of Jones' convergent point method is presented which takes full advantage of the quality of the Hipparcos data. The original implementation of this method determines the maximum likelihood convergent point on a grid on the sky and simultaneously selects group members from a given set of stars with positions and proper motions. The refurbished procedure takes into account the full covariance matrix of the Hipparcos measurements instead of standard errors only, allows for internal motions of the stars, and replaces the grid-based approach by a direct minimization. The method is tested on Monte Carlo simulations of moving groups, and applied to the Hyades. Despite the limited amount of data used by the convergent point method, the results for stars in and around the cluster- centre region agree very well with those of the recent comprehensive study by Perryman et al. (1998).Comment: 14 pages, 7 Postscript figures, LaTeX using mn.sty and psfig.sty; accepted for publication in MNRA

Gaia Data Release 2: using Gaia parallaxes

Context. The second Gaia.data release (Gaia DR2 ) provides precise five-parameter astrometric data (positions, proper motions and parallaxes) for an unprecendented amount of sources (more than 1.3 billion, mostly stars). This new wealth of data will enable the undertaking of statistical analyses of many astrophysical problems that were previously unfeasible for lack of reliable astrometry, and in particular because of the lack of parallaxes. But the use of this wealth of astrometric data comes with a specific challenge: how does one properly infer from these data the astrophysical parameters of interest? Aims. The main - but not only - focus of this paper is the issue of the estimation of distances from parallaxes, possibly combined with other information. We start with a critical review of the methods traditionally used to obtain distances from parallaxes and their shortcomings. Then we provide guidelines on how to use parallaxes more efficiently to estimate distances by using Bayesian methods. In particular also we show that negative parallaxes, or parallaxes with relatively larger uncertainties still contain valuable information. Finally, we provide examples that show more generally how to use astrometric data for parameter estimation, including the combination of proper motions and parallaxes and the handling of covariances in the uncertainties. Methods. The paper contains examples based on simulated Gaia data to illustrate the problems and the solutions proposed. Furthermore, the developments and methods proposed in the paper are linked to a set of tutorials included in the Gaia archive documentation that provide practical examples and a good starting point for the application of the recommendations to actual problems. In all cases the source code for the analysis methods is provided. Results. Our main recommendation is to always treat the derivation of (astro-) physical parameters from astrometric data, in particular when parallaxes are involved, as an inference problem which should preferably be handled with a full Bayesian approach. Conclusions. Gaia will provide fundamental data for many fields of astronomy. Further data releases will provide more and more precise data. Nevertheless, for full use of the potential it will always be necessary to pay careful attention to the statistical treatment of parallaxes and proper motions. The purpose of this paper is to help astronomers finding the correct approach

ESA’s Gaia mission: a billion stars with a billion pixels

Astrometry is the astronomical discipline of measuring the positions, and changes therein, of celestial bodies. Accurate astrometry from the ground is limited by the blurring effects induced by the Earth’s atmosphere. Since decades, Europe has been at the forefront of making astrometric measurements from space. The European Space Agency (ESA) launched the first satellite dedicated to astrometry, named Hipparcos, in 1989, culminating in the release of the Hipparcos Catalogue containing astrometric data for 117 955 stars in 1997. Since mid 2014, Hipparcos’ successor, Gaia, has been collecting astrometric data, with a 100 times improved precision, for 10 000 times as many stars