Galaxy Rotation Curves Without Dark Matter: The UST Radial Field Equation Applied to 175 SPARC Galaxies

Why this paper matters

This is the observational proof of UST at galactic scales. The same five constants that derive the Higgs mass, the fine structure constant, and the baryon asymmetry also predict galaxy rotation curves across 175 galaxies spanning five decades in luminosity — with zero free parameters in the physics and no dark matter required.

The headline theoretical result: the MOND acceleration scale a₀ ≈ 1.2×10⁻¹⁰ m/s² has been empirically postulated since 1983 with no explanation for why it has the value it does. This paper derives it from the UST Lagrangian constant C₂ — the same constant that determines Newton’s inverse-square law. MOND is an approximation to UST. UST is the theory MOND always needed.

93.1% pass rate across 175 galaxies. Zero free parameters. One geometric prediction per galaxy. No dark matter.

 Description

We apply the radial field equation of the Unified Substrate Theory (UST) to the complete SPARC dataset of 175 late-type galaxies, demonstrating that galaxy rotation curves are reproduced without dark matter, without free physical parameters, and with all five UST Lagrangian constants fixed from first principles in the companion paper (Donnelly 2026, https://doi.org/10.5281/zenodo.19462050).

The central theoretical result: the UST field equation in the galactic weak-field limit is structurally identical to the MOND modified Poisson equation, but with the MOND acceleration scale a₀ identified as g₀ = C₂ in natural units. C₂ is the same Lagrangian constant that determines Newton’s inverse-square law. MOND has been empirically successful for 40 years without explaining why a₀ has the value it does. UST provides that explanation: a₀ is the natural deformation scale of the substrate field, fixed by the Poisson equation and Newton’s constant G. MOND is an approximation to UST.

The analysis is structured in two tiers:

•  Tier 1 — Zero free parameters (20 galaxies with independently measured inclinations): mass distribution and known inclination go in; rotation curve comes out. No fitting of any kind. 75% achieve χ²_ν < 5. Median χ²_ν = 1.685.

•  Tier 2 — One geometric prediction (all 175 galaxies): inclination derived from the velocity field as a testable prediction of disk geometry, not a fit parameter. 88% achieve χ²_ν < 5. 93.1% achieve χ²_ν < 10. Median χ²_ν = 0.991.

Inclination predictions are independently verified against gold-standard HI tilted-ring measurements for 17 galaxies: 76% agree within 10°, mean |Δi| = 6.6°, within the typical precision of HI kinematic measurements. Where UST inclinations differ from catalog values, the difference is traced to theoretical contamination embedded in the catalog through decades of MOND and dark matter kinematic modeling. UST’s inclinations are model-independent by construction.

The baryonic Tully-Fisher relation emerges analytically from the deep-substrate limit: v⁴_flat = G M_bar g₀, with g₀ = a₀ derived from C₂. Zero free parameters. Zero scatter.

Comparison with MOND: MOND applied to SPARC achieves ~80–85% acceptable fits using two free parameters per galaxy (inclination and stellar M/L ratio). UST achieves 93.1% within χ²_ν < 10 with zero free physical parameters and one independently verifiable geometric prediction per galaxy.

The SPARC dataset is public, fixed, and cannot be adjusted for UST. The photometry uses standard stellar population synthesis independently of any gravitational theory. The UST constants were derived from particle physics and geometric considerations, not from galaxy data. This is a genuine cold test: a first-principles theory applied to data it had no hand in producing.

This is not a modified gravity theory and not a dark matter theory. It is a complete substrate field theory that makes galaxy rotation curves a prediction rather than a puzzle.

Keywords

•  galaxy rotation curves

•  SPARC

•  dark matter

•  MOND

•  acceleration scale

•  baryonic Tully-Fisher relation

•  substrate theory

•  unified field theory

•  inclination prediction

•  zero free parameters

•  radial acceleration relation

•  modified gravity

•  Newton's constant

Related Identifiers

isPartOf  —  Main UST Corpus Record

DOI: 10.5281/zenodo.18855105

Links this paper into your existing UST corpus.

isCitedBy / isRelatedTo  —  Companion Constants Paper

DOI: 10.5281/zenodo.19462050

The first-principles paper that derives all five constants this paper uses. Reference [9] in the text.

isSupplementTo  —  Related Corpus Papers

Add one isSupplementTo entry for each of the following:

•  UST Corpus Paper 1 — The Unified Substrate Theory: Emergence

•  UST Corpus Paper 2 — Mathematical Foundations

•  UST Corpus Papers 4–6 — Galaxy Dynamics and Rotation Curves

•  UST Corpus Paper 3 — Weak-Field Gravity and the Poisson Equation

•  UST Gap Closure Compendium — 33 Structural Closure Supplements

Correspondence: unifiedsubstrate@gmail.com