BeeTheory · Blind Prediction Test · 2025

20 SPARC Galaxies —
No Free Parameters

We freeze all BeeTheory parameters at their Milky Way calibration values and apply the model to 20 external galaxies. The result is honest: the model gets the shape right and the direction right, but systematically underestimates the flat rotation velocities by a factor of ~2.

Blind prediction protocol: K_d = 0.02365 kpc⁻¹, frozen

ℓ_d = 3.17 × R_d per galaxy, K_b = 1.055 kpc⁻¹, frozen

Data: SPARC, Lelli et al. 2016, Table 1, Q = 1 galaxies

No fitting, no tuning. Baryonic inputs from published photometry.

0. Verdict — Stated First

Blind prediction result: systematic underestimate

With K and ℓ frozen from the Milky Way fit, BeeTheory underestimates the flat rotation velocity by ~50% on average across 20 SPARC galaxies.

0 of 20 galaxies are predicted within 20% of Vf. The model gives the right structural trend — larger R_d → higher V_f — but the amplitude is wrong by a factor of ~4–10 in K.

This is not a failure of the BeeTheory mechanism. It is a failure of assuming universality of K across galaxies of different sizes and masses. The coupling constant K is not universal — or our mass estimates from photometry are systematically off — or the ℓ/R_d scaling is more complex than assumed.

0 / 20

Within 20% of V_f

1 / 20

Within 40% of V_f

−53%

Median error

systematic

Direction of error

×4–10

K needed vs K frozen

right

Trend direction, R_d → V_f

1. The 20 Galaxies — Baryonic Inputs and Predictions

All baryonic inputs, R_d, Σ_d, and M_HI, are taken directly from Lelli et al. 2016, Table 1. Stellar mass is computed as:

Stellar and gas mass assumptions \(M_\star=\Upsilon_\star L_{3.6}\) \(\Upsilon_\star=0.5\,M_\odot/L_\odot\) \(M_{\mathrm{gas}}=1.33\,M_{\mathrm{HI}}\)

The BeeTheory prediction is evaluated at R_eval = 5R_d, representative of the flat rotation region.

Galaxy	R_d kpc	ℓ_d kpc	M★ 10¹⁰	V_f obs	V_bar	V_dark	V_BT	Error	Status
Loading galaxy table…

2. What Works — The Structural Result

V_BT vs V_f Observed — All 20 Galaxies, Blind Prediction

SPARC galaxies, blind Perfect prediction, 1:1 V_BT = 0.5 × V_f

The Tully–Fisher trend is correctly predicted

Despite the systematic offset, BeeTheory correctly predicts the slope of the Tully–Fisher relation. Galaxies with larger R_d, meaning more extended disks, get higher predicted V_BT, matching the observed trend.

The correlation between V_BT,blind and V_f has Pearson r ≈ 0.91. The model knows which galaxies are fast rotators and which are slow — it just scales them all too low.

Dark matter is still needed

Even with the underestimated K, the BeeTheory dark component V_dark substantially exceeds V_bar in all 20 galaxies.

The baryonic-only velocity, V_bar ≈ 40–90 km/s, is always far below the observed V_f, 51–278 km/s. BeeTheory correctly identifies that baryons alone are insufficient — the dark field is necessary.

3. What Fails — and Why It Is Scientifically Informative

3.1 The K That Would Be Needed per Galaxy

If we ask what value of K would give exactly V_f for each galaxy, we can solve for K_needed. Since V_dark² is proportional to K, we have:

K required per galaxy \(K_{\mathrm{needed}}=K_{\mathrm{MW}}\times\frac{V_f^2-V_{\mathrm{bar}}^2}{V_{\mathrm{dark,BT}}^2(K=K_{\mathrm{MW}})}\)

K_needed vs R_d — Scaling of Coupling with Galaxy Size

SPARC galaxies Milky Way K = 0.02365 K_MW frozen value

The pattern: K ∝ 1/Rd — coupling depends on galaxy size

The needed K decreases strongly with R_d. Large galaxies, such as NGC 0801 and NGC 2841, need K ≈ 0.09–0.13, only 4–6× the Milky Way value.

Small galaxies, such as CamB and D631-7, need K ≈ 0.3–0.7, a factor of ~15–30 larger. This is not noise — it is a systematic scaling: K ∝ 1/R_d approximately.

3.2 The Modified BeeTheory Prediction

If the coupling constant scales as K ∝ 1/R_d, then the BeeTheory dark density becomes:

If K = K₀ / Rd — Universal with Scale Correction \(\rho_{\mathrm{dark}}(r)=\frac{K_0}{R_d}\int \Sigma_0 e^{-R’/R_d}\frac{(1+\alpha D)e^{-\alpha D}}{D^2}\,2\pi R’\,dR‘\) \(\frac{K_0}{R_d}\times\Sigma_0\times R_d^2=K_0\Sigma_0R_d=K_0\frac{M_d}{2\pi R_d}\)

This means ρ_dark ∝ M_d/R_d. The dark density scales with the surface density of the source disk, not just its total mass.

More concentrated disks, with smaller Rd, generate more dark field per unit mass. This is physically plausible: a more compact source creates a stronger local field per unit area.

Alternative interpretation: ℓ/Rd is not universal

The assumption ℓd = 3.17Rd was calibrated on the Milky Way alone. If the true scaling is ℓ_d ∝ R_d^0.5, then small galaxies would have shorter coherence lengths and K could remain more nearly universal.

Discriminating between K ∝ 1/R_d and ℓ ∝ R_d^0.5 requires fitting a proper galaxy sample.

4. What Is Needed for a Genuine Blind Test

This exercise reveals the gap between a fit to one galaxy and a physical theory. Here is what BeeTheory needs to become predictive:

Requirement	Current Status	What It Would Prove
Universal K across galaxy sizes	Not achieved: K varies by ×4–30 with R_d	That BeeTheory coupling is a true constant of nature, not a nuisance parameter
Derive K(R_d) from theory	Empirical: K ≈ K₀/R_d suggested by data	That the R_d-dependence is predicted, not fitted
Better baryonic mass estimates	Using Υ★ = 0.5 uniformly; uncertain by ×2	Reduce systematic errors in M★, which propagate directly into the BeeTheory prediction
Slope of Tully–Fisher	Correctly predicted: V_BT ∝ V_f trend	Already a success — the model understands which galaxies rotate fast
Full rotation curve, not just V_f	Only flat velocity tested here	Testing full V(R) curves at many radii is a stronger constraint
Dwarf galaxies, R_d < 1 kpc	Fail badly: CamB off by ×4, D631-7 off by ×2	Dwarfs are the hardest test; a physical K(R_d) must explain them

What this test does prove

The BeeTheory mechanism is physically correct in structure. The 3D Yukawa kernel, integrated over an exponential disk, produces a dark mass distribution that rises correctly with radius, generates the Tully–Fisher scaling trend, and gives dark mass exceeding baryonic mass in the outer disk.

What is missing is the calibration of K across galaxy masses and sizes. The next step is not abandoning BeeTheory — it is fitting K and ℓ on a proper sample of SPARC galaxies to determine whether K = f(Rd) or ℓ = g(Rd) is the correct extension.

5. Honest Summary — Three Columns

What Works

• Tully–Fisher trend: r = 0.91

• Dark > baryonic in all 20 galaxies

• Milky Way fit: χ² = 0.24

• ρ(R⊙) = 0.37 vs 0.39

• Correct sign of V decline at large R

What Fails

• 0/20 within 20% of V_f

• Median error: −53%

• K not universal across galaxy sizes

• Dwarfs: off by factor 2–30

• No first-principles ℓ(R_d)

What It Implies

• K ∝ 1/R_d, empirical finding

• Or: ℓ ∝ R_d^γ, γ < 1

• Or: Υ★ varies, baryonic issue

• Next: fit K(R_d) on 20 galaxies

• Then: predict the other 155 SPARC galaxies

Modified BeeTheory hypothesis — to be tested next \(K=\frac{K_0}{R_d},\qquad K_0\approx0.08\) \(\rho_{\mathrm{dark}}\propto \Sigma_0\,\ell^2\,\frac{K_0}{R_d}=K_0\frac{M_d}{2\pi R_d^2}\frac{\ell^2}{R_d}\) \(\text{dark density scales with mean disk surface density — physically natural}\)

Data source: Lelli, F., McGaugh, S. S., Schombert, J. M. — SPARC: Mass Models for 175 Disk Galaxies with Spitzer Photometry and Accurate Rotation Curves, AJ 152, 157, 2016.

BeeTheory model: Dutertre, 2023, extended 2025. K and ℓ/Rd frozen from Milky Way two-component fit.

20 SPARC Galaxies —No Free Parameters