Skip to content

SPARC.md

Latest commit

 

History

History
80 lines (63 loc) · 5.07 KB

SPARC.md

File metadata and controls

80 lines (63 loc) · 5.07 KB
Raw

Blind SPARC rotation-curve benchmark — QLF vs Newton / MOND

A blind, parameter-free test of QLF's dark-matter sector (the radial-acceleration law of DarkMatter.md §7.5) against the real SPARC rotation-curve database (Lelli, McGaugh & Schombert 2016, 175 disk galaxies). Issue #77; pipeline in sparc/sparc_blind_pipeline.py.

The protocol (blind)

The predictor reads baryonic inputs only — Vgas, Vdisk, Vbul, radius R — and never the observed velocity Vobs. Predictions V_pred(r) are written and SHA-256 sealed before Vobs is revealed and scored. No per-galaxy tuning of any kind (per-galaxy tuning is disqualifying, #77).

The QLF model — zero parameters fit to the rotation curves

  • Acceleration scale a₀ = c H₀ / 2π — derived (the de Sitter horizon / loop phase, QLF_DarkMatter mond_acceleration); H₀ is declared, not fitted.
  • Mass-to-light Υ_disk = 0.5, Υ_bul = 0.7 — the canonical global 3.6 µm stellar-population values (the same ones MOND/RAR use); not fit to the curves.
  • Radial-acceleration relation (the closure-balance, Lean radialAccel_self_consistent): g_obs = ½(g_bar + √(g_bar² + 4 g_bar a₀)), the positive root of g² = g_bar·(g + a₀).

So the prediction has no free parameter fit to the rotation curves — a₀ is derived, Υ is from stellar populations.

Result — curated sample (147 galaxies, 2696 points; Q ≤ 2, Inc ≥ 30°, e_Vobs < 0.1·Vobs)

Residual = log₁₀ g_obs − log₁₀ g_pred (dex). scatter is RMS about the model's own mean; mean is the systematic offset. Machine-readable sparc/receipt.json.

model free params mean (dex) scatter (dex)
Newton (g_bar, no dark matter) 0 +0.431 0.281
NFW halo, fit per galaxy 294 −0.005 0.059
QLF form, a₀ fitted to SPARC 1 −0.009 0.133
QLF, a₀ = cH₀/2π DERIVED (H₀ = 73) 0 −0.000 0.133
  • Newton fails: a +0.431 dex offset is a factor 2.7× of "missing gravity" — the dark-matter signal itself.
  • QLF, parameter-free, hits the observational floor: 0.133 dex scatter (= McGaugh+2016's measured RAR scatter ~0.13 dex), with a zero mean offset, and identical to the same form with a₀ fitted — the derived a₀ = cH₀/2π is essentially exact. Insensitive to H₀ (0.13–0.14 dex for H₀ = 67–73).
  • vs NFW — the parameter economy. NFW fits tighter (0.059 dex), but only by giving 2 free halo parameters to every galaxy (294 total): it absorbs the per-galaxy scatter. The RAR's observed tightness (0.13 dex, mostly observational error) shows there is no room for that halo-to-halo diversity — so NFW's lower scatter is over-fitting noise, not better prediction. QLF matches the data with 0 free parameters; NFW needs 294.

So QLF predicts the SPARC rotation curves blind, parameter-free, at the observational floor — as well as best-fit MOND, far better than Newton, and with 294× fewer parameters than NFW for the same data — the galactic Radial Acceleration Relation reproduced with a₀ derived, not fit.

Honest scope

  • The interpolation form is substrate-motivated (the closure-balance conjunction; DarkMatter.md §7.5) and the two limits are forced (Newton; geometric-mean/Tully–Fisher), but the exact ν-function is not yet proven the unique one — other interpolations fit at this level. The scatter cannot distinguish them; the parameter-free a₀ is the real win.
  • The 1/2π prefactor is confirmed: fit a₀ in QLF's own closure-balance form (not McGaugh's exponential, which gives g† = 1.20×10⁻¹⁰) and the data prefers a₀ = 1.127×10⁻¹⁰ = cH₀/2π at H₀ = 72.9 — the local Hubble constant. So the old "~13%" was a wrong-form comparison; the prefactor is right to < 1% at the local H₀, and the only residual is the Hubble tension itself (the galaxy data picks the local H₀ = 73, not the CMB 67). (DarkMatter.md §5.)
  • Curation, NFW, and the receipt are now done: the standard SPARC RAR cuts (Q ≤ 2, Inc ≥ 30°) from Table 1, an explicit per-galaxy NFW fit, and a SHA-256 verification receipt (sparc/receipt.json).

Reproduce

cd sparc
# data (public; Lelli, McGaugh & Schombert 2016), GitHub mirror:
curl -sSL https://raw.githubusercontent.com/jobovy/sparc-rotation-curves/main/data/MassModels_Lelli2016c.mrt -o MassModels_Lelli2016c.mrt
python3 sparc_blind_pipeline.py

References

  • F. Lelli, S. McGaugh & J. Schombert, SPARC: Mass Models for 175 Disk Galaxies, AJ 152 (2016) 157.
  • S. McGaugh, F. Lelli & J. Schombert, Radial Acceleration Relation, PRL 117 (2016) 201101.
  • DarkMatter.md §7.5 (the closure-balance RAR), lean/QLF_DarkMatter.lean.