Illustration of the change of orientation of velocity ellipsoid in cylindrical coordinates for halo stars, selected to have [Fe/H] < −1.2 and selected from a narrow range of cylindrical coordinates. The number of stars is about 1600 for bins with smaller R (left) and 800 for bins on the right. The top row shows bins above the plane and the bottom row their symmetric counterparts below the plane (the Sun’s position is in the middle of the figure). The dashed lines mark the direction towards the Galactic center. The change in the velocity ellipsoid tilt in cylindrical coordinates is evident; however, the velocity ellipsoid in spherical coordinates is invariant throughout the probed volume, as illustrated by these four spatial bins.