Galactic Gravitational Field Measurements Part 3: Galaxy Clusters

This paper extends to Part 3 of the Galactic Gravitational field Measurements, to the scale of galaxy clusters, demonstrating how energy dynamics within the auxiliary modulation coordinate explain cluster-scale gravitational phenomena without invoking dark matter.We analyze the Intracluster Medium (ICM) as a primary carrier of energy flow, showing that it accounts for 80-90 percent of the baryonic energy contribution to space-time curvature in clusters. Our mathematical model reveals how energy propagates through cluster volumes via a “bubble-within-bubble” architecture, with individual galactic energy structures nested within the larger ICM energy field.Using entropy-resolved resonance profile principles, we calculate energy density distributions, space-time curvature, and gravitational lensing effects across cluster scales. We provide a detailed case study of the Bullet Cluster, demonstrating how our framework explains the observed separation between X-ray emitting gas and gravitational lensing centers through differential energy flow dynamics in the auxiliary modulation coordinate.The framework accurately predicts cluster-scale phenomena including weak and strong gravitational lensing, X-ray emissions, and velocity dispersions of member galaxies. Our findings reveal that galaxy clusters represent cosmic-scale energy processing networks, with supermassive black holes providing localized energy injection that sustains global cluster dynamics through the auxiliary modulation coordinate dimension.