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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>log</mml:mi> <mml:msub> <mml:mi>M</mml:mi> <mml:mn>200</mml:mn> </mml:msub> <mml:mo>≥</mml:mo> <mml:mn>13.9</mml:mn> <mml:mspace width="1em"/> <mml:mo stretchy="false">[</mml:mo> <mml:msup> <mml:mi>h</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> <mml:msub> <mml:mi>M</mml:mi> <mml:mo>⊙</mml:mo> </mml:msub> <mml:mo stretchy="false">]</mml:mo> </mml:math> 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 ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>R</mml:mi> <mml:mi>inf</mml:mi> </mml:msub> </mml:math> ), 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.