spin distribution of [<span style="font-variant:small-caps;">subfind</span>]{} sub[haloes]{} against their relative distance from the host halo center. $r$ is the distance of sub[haloes]{} from the center of their host halo. $R_{vir}$ is the virial radius of host halo. The crosses indicate the peak of every radial bin and the red line is a linear fitting to these marks. Contours with different colors represent different level of number density ( calculated as $dN/dlog\lambda(or \lambda')/dlog(r/R_{vir})/10000$ ) as indicated in the color bars to the right.[]{data-label="pic2"}](2dHisto_LR_Subfind_Peebles "fig:"){width="1\linewidth"}\
![The average Peebles (upper) and Bullock (lower) spin distribution of [<span style="font-variant:small-caps;">subfind</span>]{} sub[haloes]{} against their relative distance from the host halo center. $r$ is the distance of sub[haloes]{} from the center of their host halo. $R_{vir}$ is the virial radius of host halo. The crosses indicate the peak of every radial bin and the red line is a linear fitting to these marks. Contours with different colors represent different level of number density ( calculated as $dN/dlog\lambda(or \lambda')/dlog(r/R_{vir})/10000$ ) as indicated in the color bars to the right.[]{data-label="pic2"}](2dHisto_LR_Subfind_Bullock "fig:"){width="1\linewidth"}

Redshift Dependence
-------------------

So far all our analysis was conducted on the $z=0$ snapshot. However, the spin distribution is known to change with redshift [@hetznecker_2006]. Hence, we investigated the 