Densities in the action space. Top: original PGS after applying the isochrone filtering method, in the most metal-poor interval (–4.0 ≤ [Fe/H] < –1.7). Same plot as the right panel of Fig. 7. Bottom: same as the top panel, after rotating the (central) coordinates of each pixel by +45 degrees. The limits of the plot in that space correspond to the rotated coordinates of the four corners of the original action space. The grey dashed lines of the bottom panel correspond to different values of L_z/J_tot: [–0.95, –0.8, –0.5, 0, 0.5, 0.8, 0.95].