Illustration of the steps followed to locate the saddle point v_φ,OLR for the band at 40 deg. First column: scatter plot of the velocities in bins in radius as indicated in the top right part of the panels. The red cross in these panels shows our determination of the saddle point. Second column: velocity distribution computed with the kernel adaptive method after a rotation of coordinates by an angle θ = 15 deg. Third column: distribution of inside the region limited by black vertical lines shown in the second column. The red vertical line and red error bar show the position of the minimum corresponding to the velocity of the saddle point and its error e_bst. The black vertical line indicates the Hercules peak. Fourth column: distribution in inside the green rectangle shown in the second column. The green vertical line and green error bar shows the position of the maximum which corresponds to the velocity of the saddle point and its error e_bst.