Baryonic Coupling in Galaxy Rotation Curves

This repository contains the data, fitting pipeline, and full results table for the manuscript: "A Rational Taper Model for Galaxy Rotation Curves" (Schneider, 2026; Under Consideration).

Key Finding

The Rational Taper model ( $V_{model} = V_{bary} + \omega R / (1 + R/R_t)$ ) saturates at an asymptotic velocity $V_{sat} = \omega \cdot R_t$. Across the 127 Tapered-model-preferred galaxies (of 171 quality-controlled SPARC galaxies; BIC selects the Tapered form in 74.3% of cases), $V_{sat}$ scales with total baryonic mass as a power law with slope $0.221 \pm 0.026$ — consistent with the canonical Baryonic Tully-Fisher Relation ($R^2 = 0.364$, $p = 6.2 \times 10^{-14}$). This consistency is mediated by the dynamic transition: the taper radius $R_t$ — the scale at which the kinematic correction saturates — is significantly correlated with the photometric disk scale length $R_d$, linking local baryonic structure to global kinematic scaling.

Overview

This project explores a phenomenological extension to the empirical velocity correction model proposed by Flynn & Cannaliato (2025). By upgrading from point-mass approximations to full baryonic mass decompositions using the SPARC database, we test two kinematic models:

1. Linear Model (Flynn & Cannaliato 2025): $$V_{model}(R) = V_{bary}(R) + \omega R$$

2. Rational Taper Model (Schneider 2026): $$V_{model}(R) = V_{bary}(R) + \frac{\omega R}{1 + R / R_t}$$

The Tapered model introduces a transition radius $R_t$ where the linear correction saturates to $V_{sat} = \omega \cdot R_t$. Across 171 quality-controlled SPARC galaxies, BIC selects the Tapered model in 74.3% of cases, and the saturation scale correlates with the baryonic disk scale: median $R_t \approx 2.4 R_d$.

The kinematic correction is applied additively (rather than in quadrature), consistent with the FC25 baseline and preserving the physical interpretation of a non-mass kinematic correction. A catalog-wide empirical comparison (results/tables/additive_vs_quadrature_catalog.csv) shows that quadrature yields marginally lower RMSE in 66.1% of cases (113 of 171 galaxies), but the median RMSE difference is only 0.32 km/s. The additive form is retained for physical and methodological reasons detailed in Section 4.4 of the manuscript. A mass-to-light ratio sensitivity analysis (Section 3.5; data in results/tables/upsilon_sensitivity.csv) confirms that while individual parameters $\omega$ and $R_t$ respond to $\Upsilon_\mathrm{disk}$ variation, their product $V_\mathrm{sat} = \omega R_t$ is substantially more stable (variation $\lesssim 28%$ across $\Upsilon \in [0.3, 0.8]$).

Gemini Gem

An LLM has been configured to engage with this research on Google Gemini. This chatbot is capable of answering many questions about the analysis performed in this work, though as is always the case, responses should be verified via the data directly, available in this repository.

Reproducing the Manuscript Figures

Reviewers and readers can reproduce the exact figures and statistical analyses found in the manuscript using the provided Jupyter Notebooks:

Notebooks

#	Notebook	Description
01	M33 Calibration	Pipeline validation against Corbelli 2014 data
02	Linear vs Quadrature	Mechanism test: kinematic boost vs. force addition
03	Tapered Models	Rational taper and tanh taper on M33
04	SPARC Batch	118-galaxy batch fit with $k \cdot R_d$ parameterization
05	Phase II Analysis	Population split, density coupling, $\Upsilon$ sensitivity
06	Model Gallery	Head-to-head Linear vs. Tapered across galaxy types
07	Full Catalog Analysis	Phase III: BIC selection, $R_t$–$R_d$ scaling, $\Sigma_0$ regime test on all 175 SPARC galaxies
08	Full Gallery	Rotation-curve gallery for all 171 quality-controlled galaxies (29 pages, sorted by $\Delta$ BIC)
09	Publication Figures	Generates the four manuscript-ready figures: M33 calibration, $V_{\rm sat}$ – $M_{\rm bary}$ scaling, data truncation artifact, and $\Delta$ BIC distribution
10	Surface Brightness vs. $\omega$	Pearson/Spearman correlation of $\omega$ against central surface brightness $\Sigma_0$; establishes that model preference is $\Sigma_0$-independent while coupling amplitude is weakly modulated by baryonic surface density

Quick Start

The pipeline is written in Python and uses SQLite for data management. All raw data files and the compiled database are included in the repository — no separate download or ingestion step is required to reproduce the manuscript figures.

# Clone the repository
git clone https://github.com/JustinSchneider/baryonic-omega-analysis.git
cd baryonic-omega-analysis

# Install dependencies
pip install -r requirements.txt

# Open Jupyter and run the notebooks in order
jupyter lab

The notebooks are self-contained: Notebook 01 initializes the database and ingests M33 data on first run, and Notebook 07 reads SPARC data directly from the included .mrt files. For developers who want to reinitialize or re-ingest from scratch:

# (Optional) Manually reinitialize and reingest
python src/database.py --init
python src/ingest.py --m33
python src/ingest.py --mrt data/raw/MassModels_Lelli2016c.mrt --metadata data/raw/SPARC_Lelli2016c.mrt

# (Optional) Run the comparative fit on a single galaxy
python src/fit.py --galaxy NGC3198 --plot

Repository Structure

• src/ — Core Python modules (database, physics, ingestion, fitting pipeline)
• notebooks/ — Analysis and visualization notebooks mapped to manuscript figures
• data/ — Raw SPARC data (LMS16) and the compiled SQLite database
• results/figures/ — Publication-quality plots generated by the notebooks
• results/tables/ — Full fit parameters and summary statistics (CSV)
• docs/ — Internal documentation and mathematical methodology

Data Sources

• SPARC Database (Lelli, McGaugh, & Schombert 2016): 175 disk galaxies with Spitzer photometry and rotation curves. http://astroweb.cwru.edu/SPARC/
• M33 Calibration (Corbelli et al. 2014): Surface density profiles from Table 1, converted to velocity components via Casertano (1983) thin-disk method.

Citation

(Citation details will be updated upon publication. For preprint inquiries, please reference the GitHub URL).

License

This project is licensed under the MIT License - see the LICENSE file for details.