DARK SECTOR PHYSICS

VFT · Guhdar · Univ. of Zakho

MODEL 01☽

Baryonic Only (Keplerian)

Stars + gas alone. V∝r⁻¹/² beyond disk. No dark sector.

Keplerian failure: V falls off like outer planets. Ruled out by all 165 SPARC galaxies. Missing ~90% of gravitational mass. Zero pressure, zero dark sector.

V_bar = √(V_gas² + 0.5·V_disk² + 0.7·V_bul²) [SPARC fixed-baryon protocol]

M_bar scale5800

MODEL 02◆

Cold Dark Matter (NFW)

Collisionless, P=0. ∇P=0 → ρ∝r⁻¹→∞ cusp. R²=0.924.

Cusp singularity: No pressure → ρ∝r⁻¹→∞ at r=0. Inner slope γ→−1. The grid plunges into a spike. Every observed dwarf has a flat core instead — the 25-year cusp-core crisis.

ρ_NFW = ρ_s/[(r/r_s)(1+r/r_s)²] | γ = −1−2x/(1+x) → −1

V_peak — NFW peak vel.110 km/s

r_s NFW scale radius (kpc)4.5 kpc

MODEL 03◉

Vacuum Fluid Theory (VFT)

P=σ²ρ. Hydrostatic ∇P=−ρ∇Φ. GR unchanged. R²=0.961.

FLAT BOWL, not a spike: Φ_VFT∝arctan(x)/x → 1 as x→0 (finite!). Flat floor IS the flat core. Pressure halts collapse at r<r_s. γ→0 (flat) vs NFW γ→−1.

V∞ sets halo structure: σ_therm=V∞/(2√π). Hotter fluid → larger r_s, lower ρ₀ (diffuse core); colder → compact, dense, steeper ∇P. NOTE: cluster mergers (Bullet / Abell 520) are set by COLLISION VELOCITY vs a Landau v_c in the superfluid extension — not by halo temperature (validated separately in SPH).

ρ₀=V∞²/(4πGr_s²) | σ_therm=V∞/2√π | σ_SIS=V∞/√2 | λ_J=r_s ✓

V∞ — fluid temp. (km/s)110 km/s

r_s — Jeans length (kpc)4.5 kpc

ASTROPHYSICAL PRESETS (halo structure)

⚙ VISUAL SETTINGS

Grid Opacity80%

Halo Opacity70%

Animation Speed1.0×

Hydrostatic Flow (∇P vs −ρ∇Φ)

Pressure Waves (σ_therm)

Jeans Ring (λ_J = r_s)

AGN Jets

Flat Core Floor Disc

MOND curve in graphs

LIVE SENSOR PROBE

Probe Radius r 15.0 kpc

VFT — HYDROSTATIC EQUILIBRIUM

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ρ̃(r) = ρ/ρ₀

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P(r) pressure

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V_vac(r) km/s

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V_total(r) km/s

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σ_therm km/s

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σ_SIS km/s

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ρ₀ M☉/kpc³

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γ(r) log slope

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MODEL COMPARISON · 165 SPARC galaxies · fixed-baryon protocol (Guhdar)

Vacuum Fluid (VFT)R²=0.961 · 0.092 dex RAR

NFW (CDM)R²=0.924 · 0.128 dex RAR

MOND (free a₀)R²=0.791 · — RAR

MOND (fixed a₀)R²=0.457 · 0.202 dex RAR

All models: identical baryonic inputs, same optimiser. AICc favors VFT in 99/165 galaxies. Zero-param VFT matches MOND-fixed on the RAR (0.193 vs 0.202 dex).

ρ(r) DENSITY — NFW CUSP DIVERGES / VFT CORE γ→0 [log scale] (each model's own params)

V(r) ROTATION CURVE — each model uses its own (V∞, r_s) · fair comparison

Φ(r) POTENTIAL — VFT flat bowl arctan(x)/x vs NFW funnel (own params)

V·F·T

DARK SECTOR PHYSICS