The Pseudo Evolution of Galaxy-Cluster Masses and Its Connection to Mass Density Profile

Abstract: A mass of dark matter halo is commonly defined as the spherical over-density (SO) mass with respect to a reference density, whereas the time evolution of an SO mass can be affected by the redshift evolution of the reference density as well as the physical mass accretion around halos. In this study, we directly measure the amount of pseudo evolution of the SO masses of cluster-sized halos by the changes in the reference density from a time series of $N$-body simulations for the first time. We find that the $52\pm19\%$ difference in the virial SO masses between $z=0$ and $1$ can be accounted for by the pseudo evolution of clusters with a virial mass of $10^{14}\, h^{-1}M_{\odot}$ at $z=0$. The amount of pseudo evolution is found to be correlated with the age and density environment of a galaxy cluster. The stacked mass density profiles of cluster-sized halos with a greater amount of pseudo evolution in the SO mass shows the higher concentration ${\it and}$ greater linear bias parameter that is a counter-example of the known secondary halo bias due to concentration on the scale of clusters. We discuss how more concentrated clusters can show larger clustering amplitudes than their less concentrated counterparts and argue that the presence of rich filamentary structures plays a critical role in determining the linear halo bias of galaxy clusters.