Co-evolution of the Brightest Cluster Galaxies and their Host Clusters in IllustrisTNG

Abstract: We use the IllustrisTNG simulations to explore the dynamic scaling relation between massive clusters and their central galaxies (BCGs). The Illustris TNG300-1 simulation we use includes 280 massive clusters with $M_{200} > 10^{14}$ M${\odot}$ enabling a robust statistical analysis. We derive the line-of-sight velocity dispersion of the stellar particles of the BCGs ($\sigma{, BCG}$), analogous to the observed BCG stellar velocity dispersion. We also compute the subhalo velocity dispersion to measure the cluster velocity dispersion ($\sigma_{cl}$). Both $\sigma_{, BCG}$ and $\sigma_{cl}$ are proportional to the cluster halo mass, but the slopes differ slightly. Thus like the observed relation, $\sigma_{, BCG} / \sigma_{cl}$ declines as a function of $\sigma_{cl}$, but the scatter is large. We explore the redshift evolution of $\sigma_{, BCG} - \sigma_{cl}$ scaling relation for $z \lesssim 1$ in a way that can be compared directly with observations. The scaling relation has a similar slope at high redshift, but the scatter increases because of the large scatter in $\sigma_{*, BCG}$. The simulations imply that high redshift BCGs are dynamically more complex than their low redshift counterparts.