Geometric Components by Group
Which mass components each galaxy group requires — and the velocity we aim to reproduce
Component presence is read directly from the SPARC rotation-curve file: a component exists for a galaxy when its velocity contribution (Vgas, Vdisk, Vbul) is non-zero. Counts and the figure use real SPARC data (Lelli, McGaugh & Schombert 2016) — nothing reconstructed.
The three geometric building blocks
SPARC resolves every disk galaxy into at most three baryonic components, each with its own geometry:
stellar disk exponential surface density Σd e−R/Rd, mass-to-light Υ = 0.5
gas disk Mgas = 1.33 MHI, more extended: Rd,gas = 2.5 Rd,star
bulge central spheroid, compact (small radius), present only in some galaxies
Components required, group by group
Two components: stellar disk + gas disk. Verified: all 61 have Vdisk > 0 and Vgas > 0, none has a bulge. This is the validated baseline (median 17% error).
Three components: stellar disk + gas disk + bulge. Verified: all 32 have a non-zero bulge contribution. The Milky Way (Gaia DR3) extends this to four components (thin + thick disk + gas + bulge). This is where the wave coupling λ is in question.
Two components: stellar disk + gas disk, no bulge — geometrically like A, but gas-dominated (often Mgas > Mstar). Lowest surface density: the regime where the coherence length ℓfloor matters most.
| Group | N | Stellar disk | Gas disk | Bulge |
|---|---|---|---|---|
| A — bulgeless disks | 61 | ✓ | ✓ | — |
| B — bulged disks | 32 | ✓ | ✓ | ✓ |
| C — gas-rich dwarfs | 81 | ✓ | ✓ | — |
| edge — NGC3769 | 1 | ✓ | ✓ | — |
Two further groups lie outside SPARC and need a different geometry: Group D (dwarf spheroidals) is a single dispersion-supported spheroid with no disk and no rotation — modelled through the Jeans equations, not a rotation curve; Group E (clusters) is a virialized spheroid at Mpc scale.
What we want to reproduce
For every rotating galaxy, the target is the flat rotation velocity Vflat — the asymptotic plateau of the rotation curve. The plot shows the real observed relation between galaxy size (disk scale length Rdisk) and this velocity, coloured by group. BeeTheory must reproduce each point from that galaxy’s own components alone.
The three groups occupy overlapping but distinct regions: gas-rich dwarfs (blue) cluster at small size and low velocity, bulgeless disks (green) span the middle, bulged disks (red) reach the largest sizes and highest velocities. The task of the campaign is to predict each galaxy’s Vflat from its visible components — stellar disk, gas disk, and where present a bulge — using one wave mechanism.
BeeTheory.com — Geometric components by group · Data: Lelli, McGaugh & Schombert 2016 · Initial generation: 21 May 2026 with Claude.ai · © Technoplane S.A.S. 2026