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 unprecedented number of sources (more than 1.3 billion, mostly stars). This new wealth of data will enable the undertaking of statistical analysis of many astrophysical problems that were previously infeasible for lack of reliable astrometry, and in particular because of the lack of parallaxes. However, the use of this wealth of astrometric data comes with a specific challenge: how can the astrophysical parameters of interest be properly inferred from these data? Aims. The main focus of this paper, but not the only focus, 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 we also show that negative parallaxes, or parallaxes with relatively large 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 data, and more precise data. Nevertheless, to fully use 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 find the correct approach.