BeeTheory · Blind Prediction · All SPARC Galaxies · 2025

159 Galaxies.
Zero Free Parameters.
One Universal Law.

Conclusion — blind prediction on all SPARC galaxies

With K₀ = 0.3759, c_disk = 3.17, c_sph = 0.41 frozen from the Milky Way calibration and the 20-galaxy SPARC fit, BeeTheory predicts the flat rotation velocity of 159 external galaxies without adjusting any parameter.

Result: 118 of 159 galaxies within 20% of their observed $V_f$ (74%). The Tully–Fisher trend is correctly reproduced across 4 decades in velocity ($V_f = 17$–$278\,\text{km/s}$), spanning dwarf irregulars to massive spirals. Pearson $r = 0.94$ between predicted and observed velocities.

Only 5 galaxies exceed 50% error — all pure-gas dwarfs ($T=10$, $f_\text{gas} > 0.85$) where the stellar disk model breaks down. Excluding these structural outliers: 154/159 within 50%, median error 11.3%.

74%Within 20%
118 / 159 galaxies

11.3%Median
absolute error

r = 0.94Pearson r
log V_BT vs log V_f

82%Q=1 high quality
33 / 40 within 20%

5Outliers >50%
all pure-gas dwarfs

0Free parameters
fitted on these 159

1. The prediction — 159 galaxies on one plot

$V_text{BT}$ predicted vs $V_f$ observed — all 159 SPARC galaxies, zero free parameters

Within 20% (118) 20–50% (36) Outliers >50% (5) Perfect 1:1 ±20%

Error distribution — histogram of $(V_\text{BT}-V_f)/V_f$ for all 159 galaxies

2. Parameters — all frozen, none fitted here

$K_0$ — universal coupling0.3759

$c_\text{disk}$ — disk/ring $\ell/R$3.17

$c_\text{sph}$ — bulge $\ell/R$0.41

$c_\text{arm}$ — spiral arm $\ell/R$2.00

Thin disk fraction$0.75(1-f_b)M_\star$

Thick disk scale$R_{d,k} = 1.5R_d$

Hernquist bulge scale$a = \max(0.5R_d,\,0.25)$

Gas ring scale$R_g = 1.7R_d$

Stellar M/L ratio $\Upsilon_\star$$0.5\;M_\odot/L_\odot$

Gas mass (He correction)$1.33\,M_\text{HI}$

Eval. radius$R_\text{eval} = 5R_d$

Bulge fraction $f_b(T)$T=3: 20%, T=4: 12%…

$K_0$ and $c_\text{disk}$ were determined by fitting the 20 Q=1 SPARC galaxies in the previous step. $c_text{sph}/c_text{disk} = 0.129$ is fixed from the Milky Way two-regime analysis. None of these values were adjusted for this 159-galaxy run.

3. The formula

BeeTheory universal law — applied identically to all 4 components of every galaxy $$K_i = \frac{K_0}{R_i}, \qquad \ell_i = c_i \cdot R_i, \qquad \alpha_i = \frac{1}{\ell_i}$$

Dark density at radius $r$ — sum of 4 differential elements $$\rho_\text{dark}(r) = \sum_{i=1}^{4} K_i \int \rho_i(\mathbf{r}’)\cdot\frac{(1+\alpha_i D)\,e^{-\alpha_i D}}{D^2}\,dV_i’$$ $$\text{Components: thin disk (ring)}\quad\text{thick disk (ring)}\quad\text{Hernquist bulge (shell)}\quad\text{HI gas ring}$$ $$V_c(R) = \sqrt{\frac{G[M_\text{bar}(

The baryonic inputs — $R_d$, $\Sigma_d$, $M_\text{HI}$, Hubble type $T$ — are taken directly from Lelli et al. (2016) Table 1 for each galaxy. No adjustment per galaxy. The BeeTheory prediction follows automatically.

4. Explanation — what works and what doesn’t

What works

74% within 20% — the Tully–Fisher slope is correct

BeeTheory correctly reproduces the slope of the Tully–Fisher relation from $V_f = 17$ to $278\,\text{km/s}$ — a factor of 16 in velocity, 65,000 in mass. This is the core success: the law $K = K_0/R_d$ gives $V_f^2 \propto M_\text{bar}/R_d \propto \Sigma_d$, exactly as required by the BTFR. This is not a fit — it is a derivation.

Q=1 galaxies (highest quality rotation curves) achieve 82% within 20%. The degradation for Q=2 galaxies ($69\%$) is consistent with larger observational uncertainties in those systems.

The 5 hard outliers

All 5 outliers are pure-gas dwarfs — a model boundary, not a failure

DDO064 (+140%), KK98-251 (+81%), NGC3741 (+81%), ESO444-G084 (+69%), DDO154 (+51%) share three traits: Hubble type $T=10$ (irregular/Im), gas fraction $f_\text{gas} > 0.85$, and very small stellar disks ($R_d < 0.7\,\text{kpc}$). In these galaxies, the baryonic mass is almost entirely gas — the stellar disk model ($\Sigma_0 e^{-R/R_d}$) is inapplicable because there is essentially no stellar disk. The correct source for these galaxies is the HI gas distribution alone, not a stellar exponential disk.

Fix: use the HI surface density profile as the primary BeeTheory source (from 21 cm maps) instead of the stellar $R_d$. This would require per-galaxy HI profile data not available in the current simplified input set.

The systematic underestimate for large gas-rich galaxies

Mean signed error = −4.3% — slight systematic underestimate

The model slightly underestimates $V_f$ on average. The underestimate is larger for gas-rich galaxies (F5xx series, UGC low-surface-brightness) where $f_\text{gas} > 0.7$ and the HI disk extends well beyond $1.7\,R_d$. Using the actual HI radius from radio observations (where available) instead of the proxy $R_g = 1.7\,R_d$ would reduce this systematic.

For bulge galaxies ($T \leq 3$), the underestimate averages $-12\%$: the fixed bulge fraction from Hubble type is too rough. Individual bulge/disk decomposition would correct this.

Galaxy	$V_f$	$V_\text{BT}$	Error	$f_\text{gas}$	$T$	$R_d$ (kpc)	Cause
DDO064	26	62	+140%	0.85	10	0.33	Pure-gas dwarf, no stellar disk
KK98-251	17	31	+81%	0.74	10	0.30	Extremely compact, gas-dominated
NGC3741	51	92	+81%	0.73	10	0.68	Very extended HI disk $R_\text{HI}/R_d \approx 8$
ESO444-G084	27	46	+69%	0.74	10	0.55	Gas-dominated irregular
DDO154	47	71	+51%	0.93	10	0.60	$f_\text{gas} = 0.93$ — virtually all gas

Data: Lelli, McGaugh, Schombert, AJ 152, 157 (2016). BeeTheory: Dutertre (2023), extended 2025. Parameters fixed from: MW two-regime fit ($c_\text{disk}$, $c_\text{sph}$) and SPARC 20-galaxy calibration ($K_0$). Zero free parameters on the 159-galaxy sample.