The CL fits against what the fits never saw

All 175 SPARC galaxies. On one axis, a parameter from your CL fit of the rotation curve. On the other, a quantity SPARC measured independently: 3.6 μm light, bulge light, HI mass, sizes, surface brightness, Hubble type. A correlation here is information the fit did not put in. Two control views show what circular comparisons look like.

Horizontal axis Vertical axis Colour by

CL parameters from uniform single-L fit (with errors) final model, inner Lagrangian

Statistics

Galaxies shown–

Spearman ρ–

Partial ρ, V_flat held fixed–

Log–log slope (95% CI)–

Scatter about the fit–

Median ratio y / x–

The partial correlation removes what both quantities share with V_flat, since nearly everything in a galaxy scales with its size. A strong ρ that drops toward 0 here is mostly that shared size. Click a point to open the galaxy.

Galaxy

SPARC rotation curve with errors, the single-L CL fit (amber) and the baryonic curve from SPARC's gas, disk and bulge components with Υ_disk = 0.5 and Υ_bulge = 0.7 (grey).

Fit category against independent morphology

Share of each final fit category per bin. The categories were set from the rotation curves alone, so any trend with Hubble type or surface brightness was not built into them. Numbers: galaxies per bin.

What is independent of what

From the rotation curve: the CL parameters M, R and v_L = √1.5·(√(2GM/R) − H_zR), the fit category, and SPARC's V_flat.
From photometry and HI maps: L_[3.6], L_bulge, M_HI, R_eff, R_d, R_HI, Σ_eff, Hubble type. Stellar masses use Υ_disk = 0.5 and Υ_bulge = 0.7 M☉/L☉ at 3.6 μm; gas is 1.33 M_HI.
Distance enters both sides (luminosities ∝ D², radii ∝ D, while the fitted M ∝ D and R ∝ D), which adds a small shared trend.

About the fits used

Uniform single-L: the same two-parameter fit for every galaxy, H_z = 2.2×10⁻¹⁸ s⁻¹, with 1σ errors and the M–R correlation from the fit covariance (scaled by √χ²ν when χ²ν > 1). It reproduces the pipeline's χ²ν.
Unconstrained: in 25 galaxies, mostly massive bulge or descent systems, the single-L radius runs to its lower bound and only M/R is measured. They are hidden by default.
Final model, inner Lagrangian: the (M, R) of the first Lagrangian in each galaxy's adopted model (two-L, descent, windows). It has no error bars here and is missing for 23 galaxies.