The dangers of deprojection of proper motions

TL;DR

This paper critically assesses the deprojection method for stellar proper motions, revealing biases when velocity dispersion varies with galactic radius, and proposes a correction scheme to improve accuracy.

Contribution

It identifies limitations of the deprojection method under certain galactic conditions and introduces a bias compensation scheme to enhance its reliability.

Findings

Deprojection method can produce biased results with decreasing velocity dispersion.

Simple models demonstrate the conditions leading to spurious results.

A bias correction scheme is proposed to improve deprojection accuracy.

Abstract

We re-examine the method of deprojection of proper motions, which has been used for finding the velocity ellipsoid of stars in the nearby Galaxy. This method is only legitimate if the lines of sight to the individual stars are uncorrelated with the stars' velocities. Very simple models are used to show that spurious results similar to ones recently reported are obtained when velocity dispersion decreases with galactocentric radius in the expected way. A scheme that compensates for this bias is proposed.