Spin-Mediated Acceleration as a Phenomenological Fitting Function for Galaxy Rotation

Overview

This project applies a simple phenomenological fitting function to galaxy rotation curves. The model adds an angular-momentum-dependent acceleration term to the baryonic contribution and tests whether this improves fits to 175 SPARC disk galaxies.

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Model

The total circular velocity is modelled as:

$$ v_\text{model}^2(r) = v_\text{vis}^2(r) + r \cdot a_\text{extra}(r) $$

where the extra acceleration term is:

$$ a_\text{extra}(r) = k \cdot \frac{J_\text{vis}}{(r + r_0)^2} $$

• $k$ — coupling constant [kg⁻¹ m⁻¹ s²], fitted per galaxy or globally
• $J_\text{vis}$ — visible-matter angular momentum computed from baryonic components only ($v_\text{gas}$, $v_\text{disk}$, $v_\text{bulge}$), evaluated at the half-mass radius — not from the observed curve
• $r_0 = 2 \times r_\text{half}$ per galaxy (robustness-scan optimum; previously fixed at 0.5 kpc)

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Updated Results (Version 2)

Per-galaxy fit — primary result:

Metric	Value
Galaxies	175 SPARC
Mean error	18.52% ± 14.96%
Median error	15.76%
Best fit	UGC 00731 (1.86%)
Worst fit	UGC 02455 (107.91%)

Global model comparison:

	Model A (universal $k$)	Model B (power-law)
Parameters	1	2
$k_0$	$1.49 \times 10^{-36}$	$9.42 \times 10^{7}$
$\beta$	0	−0.652
Mean error	32.60%	34.52%
Median error	29.62%	23.34%
ΔAIC	—	−141,371 (B preferred)

Two-population structure: ~11% of galaxies (20/175) converge to $k \approx 0$ — the baryonic mass model already reproduces those curves without coupling. The global power-law cannot fit both populations simultaneously.

Morphological correlations (weak):

• $\log_{10} k$ vs $\log_{10} J_\text{vis}$: $r = -0.405$, $R^2 \approx 0.16$
• $\log_{10} k$ vs disk scale length $h$: $r = -0.249$
• $\log_{10} k$ vs B/T: not significant

Cluster test: Mean error 72.5% on 6 galaxy clusters — model correctly fails for pressure-supported systems.

Lense-Thirring comparison: Fitted $k$ values ($10^{-36}$ to $10^{-32}$) exceed bare LT predictions ($10^{-46}$ to $10^{-48}$) by 10–14 orders of magnitude. No rigorous derivation of this gap exists. The LT functional form motivates the $J/r^2$ scaling but cannot be used to claim a physical mechanism.

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How to Use

Clone and install:

uv sync

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Citation

If you use this code or model in your research:

@software{spinning-space-2026,
  title={Spin-Mediated Acceleration as a Phenomenological Fitting Function for Galaxy Rotation},
  author={Kherki, M.},
  year={2026},
  version={2.0},
  url={https://github.com/Alpha-Centauri-00/a_extra}
}

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License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Zenodo DOI

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Data Resource

Rotmod_LTG SPARC

Questions or Issues?

• Open an issue on GitHub

• Discussions welcome!