The detection and treatment of distance errors in kinematic analyses of stars

We present a new method for detecting and correcting systematic errors in the distances to stars when both proper motions and line-of-sight velocities are available. The method, which is applicable for samples of 200 or more stars that have a significant extension on the sky, exploits correlations between the measured U, V and W velocity components that are introduced by distance errors. We deliver a formalism to describe and interpret the specific imprints of distance errors including spurious velocity correlations and shifts of mean motion in a sample. We take into account correlations introduced by measurement errors, Galactic rotation and changes in the orientation of the velocity ellipsoid with position in the Galaxy. Tests on pseudodata show that the method is more robust and sensitive than traditional approaches to this problem. We investigate approaches to characterising the probability distribution of distance errors, in addition to the mean distance error, which is the main theme of the paper. Stars with the most overestimated distances bias our estimate of the overall distance scale, leading to the corrected distances being slightly too small. We give a formula that can be used to correct for this effect. We apply the method to samples of stars from the SEGUE survey, exploring optimal gravity cuts, sample contamination, and correcting the used distance relations.