The Velocity Deficit — what the missing mass really looks like
Not the rotation speed, but the gap between observed and visible — normalized across the sample
When we plot not the rotation velocity but the deficit — the part of the velocity that visible matter cannot account for, normalized by each galaxy’s own plateau — the 135 SPARC galaxies follow a common shape. The deficit rises from near zero at the centre to ≈ 0.85–0.90 of the plateau at the outskirts, for every group. The way it rises depends on where the visible mass sits; the destination is shared.
1. The right quantity: the difference, not the total
A galaxy’s stars and gas already produce a certain rotation — the “natural” speed the visible matter can sustain. The real puzzle is not that speed, but the gap between it and what is observed. We isolate that gap at every radius:
Vbaryon is built from the measured component velocities (gas, stellar disk, bulge) in SPARC. Vdiff is exactly what any missing-mass theory — dark matter, or the BeeTheory wave field — has to supply. To compare galaxies of very different sizes, we divide by each galaxy’s flat velocity Vflat.
2. The deficit follows a common shape
3. Reading the curves
| Group | Deficit at centre | Deficit at plateau (R/R_disk > 3) |
|---|---|---|
| A — bulgeless disks | ≈ 0 (rises slowly) | 0.85 |
| B — bulged disks | ≈ 0.55 (rises fast) | 0.85 |
| C — gas-rich dwarfs | ≈ 0 (rises slowly) | 0.89 |
Two facts stand out. First, the endpoint is essentially the same for all three groups — at large radius the deficit is about 85–90% of the plateau, regardless of galaxy type. Second, the onset differs by geometry: bulged disks (red) show a deficit already near the centre, because their visible mass is concentrated there; bulgeless disks and dwarfs (green, blue) start with almost no deficit and build it up gradually.
The missing mass is not arbitrary from galaxy to galaxy. The deficit has a regular, shared form — it grows outward and saturates near a common fraction of the plateau. Its rise is governed by where the visible matter sits, exactly as a wave field tied to that matter would predict: concentrated mass (a bulge) produces an early deficit, diffuse mass (gas, low-surface-brightness disks) a gradual one. This regularity is what a single mechanism must reproduce — and it is the velocity-space precursor to the radial acceleration relation, the sharper test that expresses the same gap in terms of acceleration.
Every point is real SPARC data (Lelli, McGaugh & Schombert 2016); Vbaryon uses the standard stellar mass-to-light Υ = 0.5. The medians summarize the data, they are not a model fit. No BeeTheory parameter enters this plot — it shows the problem the theory must solve, measured directly, before any model is applied.
BeeTheory.com — The normalized velocity deficit · Data: Lelli, McGaugh & Schombert 2016 · Initial generation: 21 May 2026 with Claude.ai · © Technoplane S.A.S. 2026