On the dynamical state of galaxy clusters: insights from cosmological
  simulations II
  Using a suite of cosmology simulations of a sample of $> 120$ galaxy clusters
with $\log(M_{DM, vir}) \le 14.5$. We compare clusters that form in purely dark
matter run and their counterparts in hydro runs and investigate 4 independent
parameters, that are normally used to classify dynamical state. We find that
the virial ratio $\eta$ in hydro-dynamical runs is $\sim 10$ per cent lower
than in the DM run, and there is no clear separation between the relaxed and
unrelaxed clusters for any parameter. Further, using the velocity dispersion
deviation parameter $\zeta$, which is defined as the ratio between cluster
velocity dispersion $\sigma$ and the theoretical prediction $\sigma_t = \sqrt{G
M_{total}/R}$, we find that there is a linear correlation between the virial
ratio $\eta$ and this $\zeta$ parameter. We propose to use this $\zeta$
parameter, which can be easily derived from observed galaxy clusters, as a
substitute of the $\eta$ parameter to quantify the cluster dynamical state.
