It should therefore be regarded as an intrinsic physical property rather than a result of different data sets.

Mass Dependence
---------------

As we suggest above, mass dependence can explain the discrepancy between the spins of [haloes]{} and sub[haloes]{}. To validate this, we further explore the mass dependence of (sub-)halo spin. [Figure \[piclm1\]]{} and [Figure \[piclm2\]]{} show the two dimensional histogram of spin against (sub-)halo mass. They present a straightforward picture of how the spin distribution changes with mass. We use four simulations to expand the mass range. Contours for each simulation at the same redshift are normalized and stacked together into one subplot. We then divide the sample into 40 bins by $log$(sub-)halo mass, fit the distribution by [Equation \[eqn:bettfit\]]{} and [Equation \[eqn:bullockfit\]]{} (if the sample volume in that bin is large enough). $\lambda_0$($\lambda_0'$) in each mass bin is calculated and marked on the plots with a cross, and a linear fit to $\lambda_0$($\lambda_0'$) against mass is indicated by the red solid line. From the subplots corresponding to redshift 0 (top left and top right), we can see that, for sub[haloes]{}, $\lambda_0$($\lambda_0'$) clearly increases with increasing subhalo mass. In contrast, the spin distribution of [haloes]{} is almost independent of mass. 