Distribution of β_m parameter as a function of structural halo properties. Top left panel: distribution of β_m dipole contribution (m = 1) as a function of the centre-of-mass offset. Top right panel: distribution of β_m quadrupole contribution (m = 2) as a function of the 2D ellipticity of DM. Bottom left panel: distribution of β_m quadrupole contribution (m = 2) as a function of the 3D ellipticity of DM. Bottom right panel: high azimuthal symmetries’ β_m contribution (summing contributions from m = 3, 4, 5, 6, 7, 8, 9) as a function of the mass fraction of sub-structures. The mean profiles of β are shown by solid lines, and the error bars are the mean errors computed by bootstrap re-sampling. The β values for the DM distribution with apertures R <  0.5 × R₂₀₀, R <  1 × R₂₀₀ and R <  2 × R₂₀₀, are, respectively, plotted in light, medium, and dark blue. The β values for 2D hot-gas distribution with R <  R₂₀₀ are plotted in red. In each panel, the number of objects used to compute the average in each x-axis bin (shown in grey dotted lines) is written above the figures in grey.