Distances and parallax bias in Gaia DR2

We derive Bayesian distances for all stars in the radial velocity sample of Gaia DR2, and use the statistical method of Schonrich, Binney & Asplund to validate the distances and test the Gaia parallaxes. In contrast to other methods, which rely on special sources, our method directly tests the distances to all stars in our sample. We find clear evidence for a near-linear trend of distance bias f with distance s, proving a parallax offset delta(p). On average, we find delta(p)= -0.054mas (parallaxes in Gaia DR2 need to be increased) when accounting for the parallax uncertainty underestimate in the Gaia set (compared to delta(p)= -0.048mas on the raw parallax errors), with negligible formal error and a systematic uncertainty of about 0.006mas. The value is in concordance with results from asteroseismic measurements, but differs from the much lower bias found on quasar samples. We further use our method to compile a comprehensive set of quality cuts in colour, apparent magnitude, and astrometric parameters. Lastly, we find that for this sample dp appears to strongly depend on sigma(p) (when including the additional 0.043mas) with a statistical confidence far in excess of 10 sigma and a proportionality factor close to 1, though the dependence varies somewhat with sigma(p). Correcting for the sigma(p) dependence also resolves otherwise unexplained correlations of the offset with the number of observation periods n(vis) and ecliptic latitude. Every study using Gaia DR2 parallaxes/distances should investigate the sensitivity of its results on the parallax biases described here and for fainter samples in the DR2 astrometry paper.