BeeTheory · Galactic Application · Technical Note XXXIV
Mass Decomposition by Geometric Form:
The 23 Galaxies in 5 Components
For each of the 23 calibration galaxies, we break the visible mass into 5 standard geometric components: bulge (Hernquist sphere), thin stellar disk (exponential, narrow $z$), thick stellar disk (exponential, broader $z$), HI gas disk (extended exponential), and external halo. The decomposition gives both absolute masses and percentages. For each galaxy, the two dominant components are highlighted in green — they identify the dynamically relevant forms whose wave fields will matter most.
1. The five geometric forms
| Form | Profile | When present |
|---|---|---|
| Bulge | Hernquist sphere, $\rho \propto r/(r+r_b)^3$ | Early types only (Hubble $T \leq 3$) |
| Thin disk | Exponential $\Sigma \propto e^{-R/R_d}$, scale height $\sim 0.3$ kpc | All disk galaxies — main stellar component |
| Thick disk | Exponential $\Sigma \propto e^{-R/R_d}$, scale height $\sim 0.9$ kpc | All disk galaxies — older stars |
| HI gas disk | Extended exponential, $R_{d,\text{gas}} \approx 2.5\,R_{d,\text{star}}$ | All — neutral hydrogen reservoir |
| External halo | Diffuse stellar halo or HI tail | Negligible for SPARC; included for completeness |
2. Absolute masses per geometric form ($M_\odot$)
| # | Galaxy | Type | Bulge | Thin disk | Thick disk | HI gas | Halo ext. | Total |
|---|---|---|---|---|---|---|---|---|
| 1 | CamB | Im | — | 3.22e+7 | 1.38e+7 | 2.13e+7 | — | 6.72e+7 |
| 2 | DDO064 | Im | — | 2.87e+7 | 1.23e+7 | 2.26e+8 | — | 2.67e+8 |
| 3 | ESO444-G084 | Im | — | 3.99e+7 | 1.71e+7 | 1.60e+8 | — | 2.17e+8 |
| 4 | DDO154 | Im | — | 3.56e+7 | 1.53e+7 | 6.25e+8 | — | 6.76e+8 |
| 5 | DDO170 | Im | — | 6.65e+7 | 2.85e+7 | 5.05e+8 | — | 6.00e+8 |
| 6 | DDO168 | Im | — | 1.05e+8 | 4.49e+7 | 2.79e+8 | — | 4.29e+8 |
| 7 | D631-7 | Im | — | 1.24e+8 | 5.31e+7 | 5.12e+8 | — | 6.89e+8 |
| 8 | DDO161 | Im | — | 9.31e+7 | 3.99e+7 | 1.09e+9 | — | 1.22e+9 |
| 9 | F565-V2 | Im | — | 3.96e+7 | 1.70e+7 | 2.66e+8 | — | 3.23e+8 |
| 10 | F563-V2 | Im | — | 7.98e+7 | 3.42e+7 | 4.65e+8 | — | 5.80e+8 |
| 11 | F563-V1 | Im | — | 7.92e+7 | 3.39e+7 | 3.99e+8 | — | 5.12e+8 |
| 12 | F567-2 | Im | — | 1.07e+8 | 4.58e+7 | 7.98e+8 | — | 9.51e+8 |
| 13 | F568-V1 | Im | — | 1.94e+8 | 8.31e+7 | 1.06e+9 | — | 1.34e+9 |
| 14 | ESO116-G012 | Sd | — | 1.12e+9 | 4.78e+8 | 1.60e+9 | — | 3.19e+9 |
| 15 | F561-1 | Im | — | 4.12e+8 | 1.77e+8 | 1.20e+9 | — | 1.79e+9 |
| 16 | F563-1 | Im | — | 3.21e+8 | 1.37e+8 | 1.60e+9 | — | 2.05e+9 |
| 17 | F568-3 | Sd | — | 6.93e+8 | 2.97e+8 | 2.00e+9 | — | 2.98e+9 |
| 18 | F574-1 | Sd | — | 8.55e+8 | 3.66e+8 | 2.53e+9 | — | 3.75e+9 |
| 19 | F568-1 | Sd | — | 9.01e+8 | 3.86e+8 | 2.39e+9 | — | 3.68e+9 |
| 20 | NGC3198 | Sc | — | 3.32e+9 | 1.42e+9 | 1.14e+10 | — | 1.62e+10 |
| 21 | F571-8 | Sd | — | 2.23e+9 | 9.54e+8 | 2.93e+9 | — | 6.11e+9 |
| 22 | Milky Way | Sbc | 1.00e+10 | 4.00e+10 | 6.00e+9 | 1.00e+10 | — | 6.60e+10 |
| 23 | NGC2841 | Sb | 5.82e+9 | 1.22e+10 | 5.24e+9 | 1.10e+10 | — | 3.43e+10 |
Green cells: the two dominant components for each galaxy. Together they account for the bulk of the visible mass and define the wave field’s dominant geometry.
3. Percentages per geometric form
| # | Galaxy | Type | %Bulge | %Thin | %Thick | %HI | %Halo |
|---|---|---|---|---|---|---|---|
| 1 | CamB | Im | — | 47.8% | 20.5% | 31.7% | — |
| 2 | DDO064 | Im | — | 10.8% | 4.6% | 84.6% | — |
| 3 | ESO444-G084 | Im | — | 18.4% | 7.9% | 73.7% | — |
| 4 | DDO154 | Im | — | 5.3% | 2.3% | 92.5% | — |
| 5 | DDO170 | Im | — | 11.1% | 4.7% | 84.2% | — |
| 6 | DDO168 | Im | — | 24.4% | 10.5% | 65.1% | — |
| 7 | D631-7 | Im | — | 18.0% | 7.7% | 74.3% | — |
| 8 | DDO161 | Im | — | 7.6% | 3.3% | 89.1% | — |
| 9 | F565-V2 | Im | — | 12.3% | 5.3% | 82.5% | — |
| 10 | F563-V2 | Im | — | 13.8% | 5.9% | 80.3% | — |
| 11 | F563-V1 | Im | — | 15.5% | 6.6% | 77.9% | — |
| 12 | F567-2 | Im | — | 11.2% | 4.8% | 83.9% | — |
| 13 | F568-V1 | Im | — | 14.5% | 6.2% | 79.3% | — |
| 14 | ESO116-G012 | Sd | — | 35.0% | 15.0% | 50.0% | — |
| 15 | F561-1 | Im | — | 23.1% | 9.9% | 67.0% | — |
| 16 | F563-1 | Im | — | 15.6% | 6.7% | 77.7% | — |
| 17 | F568-3 | Sd | — | 23.2% | 9.9% | 66.8% | — |
| 18 | F574-1 | Sd | — | 22.8% | 9.8% | 67.4% | — |
| 19 | F568-1 | Sd | — | 24.5% | 10.5% | 65.0% | — |
| 20 | NGC3198 | Sc | — | 20.5% | 8.8% | 70.7% | — |
| 21 | F571-8 | Sd | — | 36.5% | 15.6% | 47.9% | — |
| 22 | Milky Way | Sbc | 15.2% | 60.6% | 9.1% | 15.2% | — |
| 23 | NGC2841 | Sb | 17.0% | 35.6% | 15.3% | 32.2% | — |
4. Patterns by galaxy type
- Two massive Sb/Sbc (Milky Way, NGC2841): dominated by thin disk + bulge, with HI gas contributing $sim 15$–$30%$. Only galaxies with a significant bulge in the sample.
- NGC3198 (Sc): HI gas + thin disk dominate, no bulge. Gas accounts for $71\%$ of mass.
- Sd galaxies (F568-1, F571-8, F568-3, F574-1, ESO116-G012): HI gas + thin disk, gas typically $50$–$67\%$. These are the LSB cases that strain BeeTheory most.
- Im dwarfs (DDO, F-series, CamB, etc.): overwhelmingly HI gas-dominated — gas is $60$–$93\%$ of mass. The thin stellar disk is a minor component.
Key observation
For 21 out of 23 galaxies, the two dominant geometric forms are thin disk + HI gas disk. Only the Milky Way and NGC2841 introduce a third significant component (the bulge). This means that for the wave field calculation, the geometry that matters most is almost always the extended disk pair — and the LSB problem must be solved in this exponential-disk regime.
References. Dutertre, X. — Notes XXIX–XXXIII, BeeTheory.com (2026). · Lelli, F., McGaugh, S. S., Schombert, J. M. — SPARC, AJ 152, 157 (2016). · Bovy, J., Rix, H.-W. — A direct dynamical measurement of the Milky Way’s disk surface density profile, disk scale length, and dark matter profile at 4 kpc < R < 9 kpc, ApJ 779, 115 (2013). · McMillan, P. J. — The mass distribution and gravitational potential of the Milky Way, MNRAS 465, 76 (2017). · Hernquist, L. — An analytical model for spherical galaxies and bulges, ApJ 356, 359 (1990).
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