Contribution of relaxed and unrelaxed haloes to the total mass function. Left panel: distribution of redshift zero dark matter haloes in the X_off, P and λ plane. Cuts in X_off, P and λ are applied to divide relaxed (blue) and disturbed (orange) structures. The contours contain 1%, 5%, 10%, 30%, and 50% of the data. Right panel: Halo mass functions vs. mass (σ) at redshift 0, as defined in Sect. 2 and using Eqs. (15) and (16). This mass function is built with different subsets of haloes from HMD at z = 0 (see Sect. 3): the red line indicates the model from Comparat et al. (2017), the shaded areas represent the relaxed (blue), unrelaxed (orange), and the full sample (green) of haloes. The areas cover 1σ uncertainties. Lower panel: residuals fraction of each component compared to the red model in the upper panel.