Rotation Curves of the SPARC Sample

All galaxies, three normalizations, coloured by group

BeeTheory.com · Real data · 21 May 2026

Source & method

Every curve is a real measured rotation curve from the SPARC database (Lelli, McGaugh & Schombert 2016), drawn point by point — 3391 measurements across 175 galaxies. Normalization is only a change of axes applied to the real data; no point is reconstructed. Colours: Group A — bulgeless disks, Group B — bulged disks, Group C — gas-rich dwarfs/irregulars.

1. Raw curves

Radius in kpc, velocity in km/s — the curves as observed. The vertical spread is enormous: dwarfs plateau near 30 km/s, massive bulged disks near 300.

SPARC normalization 1
Raw rotation curves, 175 galaxies. Bulged disks (red) reach the highest velocities, gas-rich dwarfs (blue) the lowest.

2. Velocity normalized — V / V_flat

Each curve divided by its own flat velocity. All curves head toward 1: every galaxy reaches a plateau. The differences are in how they get there.

SPARC normalization 2
Velocity-normalized curves, 134 galaxies with a measured V_flat. All converge toward V/V_flat = 1.

3. Fully normalized — V / V_flat vs R / R_disk

Both axes scaled to each galaxy’s own units. All 134 galaxies collapse onto a common shape — a rise over a few disk scale lengths, then a flat plateau.

SPARC normalization 3
Fully normalized curves. The shape is shared across groups; bulged disks (red) rise fast, gas-rich dwarfs (blue) rise slowly and some never reach the plateau.
What these plots show

Across four decades of mass, rotation curves share one common shape — they rise, then stay flat, instead of falling as the visible matter alone would require. Bulged disks rise steeply, gas-rich dwarfs rise gently. Reproducing this shared shape from the visible components alone is the task BeeTheory must meet.

BeeTheory.com — SPARC rotation curves · Data: Lelli, McGaugh & Schombert 2016 · Initial generation: 21 May 2026 with Claude.ai · © Technoplane S.A.S. 2026