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.