The Reference Curves Tested on the Milky Way
Curves frozen on SPARC, applied blind to our own galaxy — in the normalized space
The two saturating reference curves — calibrated only on SPARC galaxies, never on the Milky Way — were applied blind to the Gaia rotation data, each in its own normalized space. Normalized by its bulge, the Milky Way follows the bulge reference curve to 10%; normalized by its ring, it follows the ring curve to 20%. No parameter was tuned on the Milky Way.
1. The key step: normalize first
The reference curves live in normalized coordinates — V/V_ref against R/R_ref. To test them on the Milky Way, the Milky Way’s own data must be brought into that same space. Its reference quantities, built exactly as for SPARC galaxies, are:
| Reference | radius | velocity |
|---|---|---|
| Ring (disk+gas) | 5.1 kpc | 217 km/s |
| Bulge | 1.8 kpc | 155 km/s |
Each Gaia point is then divided by these — radius by R_ref, velocity by V_ref — and compared to the frozen curve. The two curves are not added: each is a complete description of the same rotation curve seen from one reference, so each is tested on its own.
The two reference curves, fixed beforehand on the SPARC sample, are:
Both pass through (1, 1) by construction and flatten in the limit — the ring toward 1.60·V_ring, the bulge toward 1.51·V_bulge.
2. The blind comparison
In the bulge frame the agreement is close across the whole range, including the gentle decline at large radius. In the ring frame the inner points follow the curve well, then fall below it outward: the Milky Way’s curve declines at its edge — the last Gaia point drops to 0.79·V_ring — while the median SPARC galaxy keeps rising slowly toward 1.6. The Milky Way is a slightly declining case.
A shape calibrated on a large external sample, with no Milky Way tuning, predicts our galaxy’s rotation to 10–20% once the data are placed in the correct normalized space. This is a genuine out-of-sample test: the reference curves carry real, transferable information about how rotation curves rise above their visible reference and flatten. The residual at large radius is itself informative — it measures how much the Milky Way declines relative to the typical galaxy, rather than being a failure of the curve.
Gaia data from Ou et al. 2024 (real). The Milky Way is not in SPARC; its reference quantities were built from its known baryonic components (thin + thick disk, gas, bulge) using the same recipe as for SPARC galaxies. The reference curves’ coefficients were fixed on the SPARC sample beforehand and not adjusted here. The earlier attempt that added the two curves in quadrature was a method error: the curves describe the same total rotation from two references and must each be tested alone, not summed.
BeeTheory.com — Reference curves tested on the Milky Way · Data: Gaia / Ou et al. 2024; SPARC / Lelli et al. 2016 · Initial generation: 21 May 2026 with Claude.ai · © Technoplane S.A.S. 2026