[#14] Dark Matter Dissolved — Effective Mass Integral & SPARC Validation
Part III/The True Face of Gravity/Ch. 2 §2.1–2.2
✦ Post #14 · Part III Ch. 2 §2.1–2.2
Part III — Gravity: Not a Pull — a Flow
Dark Matter Dissolved — Effective Mass Integral & SPARC Validation
ρ_s(r) ∝ 1/r² integrated → M_eff ∝ r → rotation curves flatten. No dark matter. SPARC 10 galaxies: GC-HR 9:1 over NFW.
Author Kim Donghak (HeeRim)
Section Part III · Ch. 2 · §2.1–2.2
Type Theorem + Quantitative Validation
Series progress — 14 / 26 posts
§ 2.1 — Introduction
Why Do Stars at Galaxy Edges Rotate So Fast?
The galaxy rotation curve problem is the greatest mystery of 20th-century astronomy. Stars at galactic edges orbit far too fast for the visible mass to explain under Newtonian gravity. The mainstream solution: Dark Matter — invisible mass with unknown properties. After 70 years, every direct detection experiment has failed.
GC-HR asks differently: "What if the missing mass is not invisible matter, but the Space Fluid displaced by visible matter, acting as additional gravitational source?"
§ 2.1 — Derivation
Displaced Space Fluid Integrated: M_eff(r) ∝ r
Effective mass integral — 4 steps
Step 1 — Density redistribution when galaxy center forms
ρ_s(r) = ρ_s0 + k / r²
When mass concentrates at the galactic center (Bernoulli sink, #12), displaced Space Fluid disperses over spherical shells. Shell surface area ∝ r², so the density increment scales as Δρ_s = k/r².
Step 2 — Effective mass = spherical volume integral
When M_eff ∝ r, the r cancels in v² = GM/r. Rotation velocity is constant regardless of distance. Galaxy rotation curve flattening — derived without dark matter.
§ 2.1 — Theorem
Theorem 4 — Effective Mass & Dark Matter Dissolved
Galaxy rotation curve flattening — no dark matter ✓
The density increment of displaced Space Fluid (k/r²), integrated over a sphere, yields effective mass linear in r. Rotation velocity automatically flattens. The "missing mass" is not invisible exotic matter — it is the cumulative tension of Space Fluid displaced by visible matter.
§ 2.2 — Quantitative Validation
SPARC Galaxy Rotation Curve Fitting — GC-HR vs NFW
Theory must face data. We fitted both GC-HR and the standard NFW dark matter halo to 10 representative galaxies from the SPARC database (Lelli, McGaugh & Schombert, 2016) under identical conditions.
SPARC 10-galaxy fitting summary
Metric
GC-HR
NFW (Dark Matter)
Free parameters
2 (v_sf, r_sf)
2 (V200, c)
Mean χ²r
3.40
23.48
AIC wins
9 / 10
1 / 10
BIC wins
9 / 10
1 / 10
Dark matter needed
No
Yes
GC-HR mean χ²r = 3.40 vs NFW mean χ²r = 23.48
With the same number of free parameters (2), GC-HR outperforms NFW by a factor of ~7. Strongest wins: NGC2841 (ΔBIC = +1349), NGC6946 (ΔBIC = +493).
The implication is clear. With equal parameter count, a model without dark matter fits the observed data better than one that requires it. GC-HR wins 9 out of 10 galaxies.
Future work: full SPARC 175-galaxy fitting, and discriminating the density profile (ρ ∝ r⁻² vs NFW ρ ∝ r⁻¹) via Euclid/Roman Space Telescope weak lensing.
§2.1–2.2 Core Insight — Theorem 4 + SPARC
Why dark matter has never been found: Because it does not exist.
Galaxy rotation curve flattening is fully explained by the cumulative tension of Space Fluid displaced by visible matter. ρ_s(r) = ρ_s0 + k/r² → M_eff ∝ r → v_flat = const. SPARC validation: GC-HR defeats NFW 9:1 with equal parameters. After 70 years and billions of dollars, every direct detection experiment (XENON, LUX, PandaX) has returned null. The simplest explanation: what they were looking for was never there.
▶ Next — #15 · Part III §2.3
GC-HR Galaxy Rotation Equation — Complete
Theorem 4 applied to full galaxies. Space Synchronous Rotation — extreme viscosity locks stars and Space Fluid into co-rotation. Plus: the Bullet Cluster reinterpreted without dark matter.