  In this paper, we use two hydrodynamic simulations to study the barycentre
offsets $r_{{\rm off}}$ between the entire halo and the gas or dark matter
subhalo with largest overdensity. We restrict our analysis to those halos with
large rescaled offsets, i.e. $r_{{\rm off}}/r_{200}\gtrsim 0.05$. The halos
which are less massive and at higher redshifts are more likely to have larger
$r_{{\rm off}}/r_{200}$. The 3D velocity dispersion of the subhalos with
largest overdensity is found to have a similar mass and redshift dependence as
$r_{{\rm off}}/r_{200}$. We also find that the gas subhalos with maximum
overdensity and larger gas velocity dispersion $\sigma_{v}^{\rm
ICM,sub}/\sigma_{200}$ tend to have smaller barycentre offsets $r_{{\rm
off}}/r_{200}$. Similar result is found for the highest overdensity dark matter
subhalos but with less significance. This anti-correlation is more significant
for the snapshot $z=0$ than $z=0.2$ and $0.5$. The underlying physical
mechanism for this anti-correlation remains to be explored.
