The Sakin–Mutaharrik Cosmic Fluid Framework (Phase 3): Cosmological Fluid Lensing and Resolution of the Bullet Cluster (1E 0657-56) Offset Anomaly Without Dark Matter

Series: The Sakin–Mutaharrik Cosmic Fluid Framework — Phase 3 (Final Part of the Trilogy)Principal Investigator / Author: Jafar Husain (Independent Researcher, India)Phase 3 DOI: 10.5281/zenodo.23729793Phase 1 DOI (SPARC 175 Galaxies): 10.5281/zenodo.23724656Phase 2 DOI (Planck CMB & Hubble Tension): 10.5281/zenodo.23727415 Abstract & Executive Summary:The merging galaxy cluster 1E 0657-56 (the "Bullet Cluster" at z = 0.296) is widely regarded as the premier empirical benchmark for testing collisionless Dark Matter against hydrodynamic and modified-gravity alternatives. During the supersonic cluster collision (~4500–4800 km/s), the X-ray-emitting intracluster medium (ICM) plasma (~83% of baryonic mass) is decelerated by electromagnetic and hydrodynamic ram pressure, whereas the gravitational lensing convergence (κ) peaks remain spatially aligned with the collisionless galaxies (~17% of baryonic mass). Furthermore, recent JWST lensing reconstructions confirm that standard Modified Newtonian Dynamics (MOND) underpredicts the lensing amplitude in the Bullet Cluster core by a factor of 4 to 5. In this third and final paper of The Sakin–Mutaharrik Cosmic Fluid Framework trilogy—inspired by the continuum cosmological descriptions in Nahj al-Balagha (Sermons 1 and 91)—we prove that both the amplitude and spatial offset anomalies of the Bullet Cluster are naturally resolved by inviscid superfluid vacuum hydrodynamics without invoking Dark Matter particles. Operating strictly on the universally locked Phase-1 fluid constants derived from 175 SPARC galaxies (a_mawj = 3150 (km/s)²/kpc, g_kabs = 6800 (km/s)²/kpc, M_sakin = 12000 (km/s)²·kpc, and η_makhd = 0.14) with zero free per-galaxy tuning, we formulate the Relativistic Refractive Fluid Metric for the cosmic vortex (Lujjat Tayyar). Key Quantitative Milestones Achieved in Phase 3: Cluster Radial Lensing Profile Validation: Reproduces the observed NFW cluster light-bending acceleration profile (M_200 = 1.50 × 10¹⁵ M☉) across r ∈ [20, 1000] kpc at R² = 99.68% using the measured virial baryonic mass (2.69 × 10¹⁴ M☉). Emergent Hydrodynamic Spatial Offsets: A 150 Myr time-stepping ram-pressure collision integrator naturally decelerates the collisional X-ray plasma while allowing the inviscid superfluid vortices (Lujjat Tayyar) to pass through unhindered, yielding emergent gas-to-lensing spatial offsets of 210 kpc (Main Cluster) and 185 kpc (Bullet Sub-cluster). 1D Collision-Axis Lensing Convergence κ(x) Match: Using 3D-to-2D numerical Abel line-of-sight integration, the model matches the 18 observational HST/Magellan weak and strong lensing convergence data points (Bradač et al. 2006; Clowe et al. 2006) across the collision axis at R² = 98.68%, accurately predicting both the Main Cluster peak (κ = 0.36 vs. observed 0.362 ± 0.024) and the Bullet Sub-cluster peak (κ = 0.29 vs. observed 0.288 ± 0.024) with 0% Dark Matter. Uploaded Assets in This Record: Complete Research Paper III Manuscript (PDF) Python Numerical Simulation & Abel Integration Script (mission3_step1_lensing.py) High-Resolution Validation Figure (Mission3_Real_Bullet_Cluster_Validated.png)