Quantifying the Velocity Anisotropy Profile of Galaxy Clusters Using the Uchuu Cosmological Simulation

Abstract

Galaxy clusters are powerful laboratories for studying both cosmic structure formation and galaxy evolution. We present a comprehensive analysis of the velocity anisotropy profile, β ( r ), in galaxy clusters using the Uchuu-UniverseMachine mock galaxy catalog, which combines the large-volume Uchuu N -body simulation with the UniverseMachine galaxy formation model. Focusing on clusters with $\mathrm{log}{M}_{200}\geqslant 13.9\,[{h}^{-1}{M}_{\odot }]$ up to redshift z = 1.5, we investigate the behavior of β ( r ) as a function of clustercentric radius, mass, and redshift. We find that β ( r ) exhibits a universal shape: it rises from isotropic values near the cluster core, peaks at ∼1.7 R _200 , declines around 3.4 R _200 due to orbital mixing, and increases again in the outskirts, due to the dominance of first-infalling galaxies. Our results show that more massive clusters have higher radial anisotropy and larger peak β values. Moreover, β ( r ) evolves with redshift, with high-redshift clusters displaying more radially dominated orbits and enhanced infall motions. We further derive redshift-dependent power-law scaling relations between M _200 and key physical radii—hydrostatic ( R _hs ), infall ( ${R}_{\inf }$ ), and turnaround ( R _ta ). These findings offer a robust theoretical framework for interpreting the dynamical properties of observed galaxy clusters and provide key insights into the evolution of their dynamical state over cosmic time.

Keywords

• Galaxy clusters
• Dynamical evolution
• N-body simulations
• Galaxies