Dynamical Evolution of Brightest Cluster Galaxies and Their Host Clusters: Insights from IllustrisTNG

We explore the redshift evolution of dynamical scaling relations between massive clusters and their brightest cluster galaxies (BCGs) at $z < 2$ based on the IllustrisTNG-300 simulation. We select 270 massive clusters with $M_{200} > 10^{14}$ M$_{\odot}$ at $z = 0$ and trace their progenitors based on merger trees. From 67 redshift snapshots covering $z < 2$, we use the subhalo velocity dispersion to compute the cluster velocity dispersion ($\sigma_{cl}$). We also calculate the stellar velocity dispersion of the BCGs ($\sigma_{BCG}$). Both $\sigma_{cl}$ and $\sigma_{BCG}$ increase as universe ages. The BCG velocity dispersion grows more slowly than the cluster velocity dispersion. At $z > 1$, $\sigma_{BCG}$ is comparable with $\sigma_{cl}$ offering an interesting observational test. We also derive the $(\sigma_{BCG}/ \sigma_{cl}) - \sigma_{cl}$ scaling relation; the slope of the relation steepens at high redshift. The simulated redshift evolution of $\sigma_{cl}$ and $\sigma_{BCG}$ generally agrees with an observed cluster sample for $z < 0.3$ but with large scatter. Future large spectroscopic surveys will test the implications of the simulations for the mass evolution of both clusters and their BCGs.Comment: 15 pages, 13 figures, 1 table, submitted to the Ap