Top: observed tangential velocity v_ℓ as a function of Galactic longitude for populations II to VII. Middle: same as top panel, showing only population II. The dashed line is the expected relation for a non-expanding group of stars with systemic velocity 23 km s⁻¹ (shifted vertically to overlap with the observed data). Bottom: corrected velocity (residuals of the observed velocities minus virtual contraction correction).