The Three Hundred: Cluster Dynamical States and Relaxation Time Scale
  Using the galaxy clusters from The Three Hundred Project, we define a new
parameter: $\lambda_{DS}$ to describe the dynamical state of clusters, which
assumes a double-Gaussian distribution in logarithm scale for our mass-complete
cluster sample at $z=0$ from the dark-matter-only (DMO) run. Therefore, the
threshold for distinguishing relaxed and unrelaxed clusters is naturally
determined by the crossing point of the double-Gaussian fitting which has a
value of $\lambda_{DS} = 3.424$. By applying $\lambda_{DS}$ with the same
parameters from the DMO run to the hydro-dynamically simulated clusters
(Gadget-X run and GIZMO-SIMBA run), we investigate the effect of baryons on the
cluster dynamical state. We find a weak baryon-model dependence for the
$\lambda_{DS}$ parameter. Finally, we study the evolution of $\lambda_{DS}$
along with clusters mass accretion history. We notice an upper limit of halo
mass change $\frac{\Delta M_{200}}{M_{200}} \sim 0.12$ that don't alter the
cluster dynamical state, i.e. from relaxed to unrelaxed. We define relaxation
period (from the most relaxed state to disturb and relaxed again) which
reflects how long the dynamical state of a cluster restores its relaxation
state, and propose a correlation between this relaxation period and the
strength of halo mass change $\frac{\Delta M_{200}}{M_{200}}$. With the
proposed fitting to such correlation, we verify the relaxation period can be
estimated from $\frac{\Delta M_{200}}{M_{200}}$ (including multi mass change
peaks) with considerably small error.
