The Bullet Cluster (1E 0657−56) Tested with the Water Theory Modeling Protocol, Mechanism Assignment, and Results from Observed Inputs

This paper tests the Bullet Cluster (1E 0657−56) with the (gravitational) Water Theory:(1) A general modeling protocol (seven steps) is established. Whenever theWater Theory is applied to any object, the first step is always to decompose it into com-putable geometric components according to the true density distribution. The crucial branchis the judgment of closed / open: a closed shape (sphere, ellipsoid, near-circular) surroundsthe centre, so that matter can flow in every direction, hence fΩ ≡ 1 and the enhancementcan only come from the radial κA; an open shape (cone, disc, column) confines the fluxinto a finite solid angle, so fΩ < 1 and κA = 2, the radial factor is identically 1, and Y isindependent of R.(2) All inputs are taken from observation. Gas axis ratio η = 0.889±0.072 (APEX-SZ elliptical β model, near-circular); bullet gas half-opening angle ϕ ≳ 45◦ (Markevitch2002, original text); gas radial scaling β = 0.803 ± 0.013 together with the core radiusrc = 278.0 ± 6.8 kpc (Brownstein & Moffat 2007, from one and the same Chandra fit —the two must be used as a matched pair), with rc ∼ 274 kpc independently corroborated byTucker 1998 (ROSAT), agreeing to 1.4%.(3) The assessment uses a matched aperture from a single analysis. Withinr < 6′ = 1.59 Mpc, Boyarsky et al. (2007) give simultaneously the lensing mass 1.46×1015 M⊙and the gas mass 2.97 × 1014 M⊙; prediction and observation are therefore compared insidethe same radius.Result: predicted gravitational mass 1.085 × 1015 M⊙ versus observed 1.460 × 1015 M⊙,a deviation of −25.7%. Over the same interval Newton gives −78.3%.