Three Bulged Galaxies, Resolved Into the Bulge
Real data inside the bulge domain, on the same normalized axis, against both reference curves
Unlike the Milky Way — whose data start beyond its bulge — these three galaxies have measured rotation points inside the bulge. Placed on the R/R_ring axis and normalized by the frozen references, the bulge-domain data (diamonds) follow the bulge reference curve, the ring-domain data (circles) follow the ring curve, and all three galaxies share the same anchor point (1, 1) by construction.
1. The three galaxies
Chosen because each has many real velocity points within its bulge radius (R ≤ R_bulge), from the SPARC sample:
Chosen because each has many real velocity points within its bulge radius (R ≤ R_bulge), from the SPARC sample.
Real galaxy data — masses derived from the measured SPARC velocities (M = V²R/G per component), total = bulge + ring; characteristic radii are the real bulge radius (where its velocity peaks) and the disk scale length R_disk from the SPARC master table:
| Galaxy | M_total | M_bulge | M_ring | R_bulge (char.) | R_disk (char.) | V_obs (max) |
|---|---|---|---|---|---|---|
| UGC02953 | 1.45×10¹¹ | 1.51×10¹⁰ | 1.30×10¹¹ | 1.29 | 3.55 | 319 |
| UGC05253 | 1.19×10¹¹ | 3.28×10¹⁰ | 8.57×10¹⁰ | 1.01 | 8.07 | 248 |
| UGC11914 | 7.69×10¹⁰ | 1.86×10¹⁰ | 5.83×10¹⁰ | 1.30 | 2.44 | 305 |
Calculated reference data — the two reference objects, plus the mass-weighted reference velocity of the whole galaxy (wave mass at v = 0, total mass conserved):
| Galaxy | V_ref (weighted) | V_bulge | R_bulge | V_ring | R_ring | R_bulge/R_ring |
|---|---|---|---|---|---|---|
| UGC02953 | 258.8 | 169.2 | 1.97 | 312.6 | 4.99 | 0.39 |
| UGC05253 | 193.6 | 219.2 | 2.56 | 224.0 | 6.39 | 0.40 |
| UGC11914 | 195.0 | 181.5 | 2.12 | 237.9 | 3.85 | 0.55 |
Masses in M☉, radii in kpc, velocities in km/s. V_ring = √(G·M_ring/R_ring), V_bulge = √(G·M_bulge/R_bulge); V_ref is the mass-weighted mean over the four components (visible ring, visible bulge, and their wave masses at zero velocity). All reference quantities are read from the fixed per-galaxy table — calculated once, not recomputed here.
2. The same construction as the Milky Way
Each galaxy’s real points are normalized two ways: by the ring (radius/R_ring, velocity/V_ring) for the outer data, and by the bulge (velocity/V_bulge) for the points within R_bulge, all drawn on the common R/R_ring axis. The two reference curves are the same frozen laws used throughout:
3. What the bulge data show
With real points now inside the bulge domain, the bulge curve can be tested directly — the gap that the Milky Way could not fill. The diamonds rise through the inner region; some galaxies climb above the bulge reference curve there (the high-bulge cases), confirming that the bulge turns fast in its core. Outward, every galaxy’s circles join the single ring curve and then, for the most extended (UGC02953), decline below it at large radius — the same outer fall seen in the Milky Way.
By construction every galaxy passes through (1, 1): at R = R_ring the data are divided by V_ring, so the ratio is one for all, regardless of the galaxy’s mass or size. This shared anchor is what lets three very different galaxies — and the Milky Way before them — be compared on one axis. The reference curves are not re-fitted per galaxy; they are the same frozen laws, and the data fall around them.
All points are real SPARC data (Lelli, McGaugh & Schombert 2016). R_ring, V_ring, R_bulge, V_bulge are read from the fixed per-galaxy table (bulge at the sample-median density; total mass conserved). The reference-curve coefficients were fitted once on the full SPARC sample (143 disk+gas, 32 bulged) and are held fixed here. The curves trace the shared trend; individual galaxies, especially high-bulge ones, scatter above or below.
BeeTheory.com — Three bulged galaxies resolved into the bulge · Data: Lelli, McGaugh & Schombert 2016 · Initial generation: 21 May 2026 with Claude.ai · © Technoplane S.A.S. 2026