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A New Empirical Fit to Galaxy Rotation Curves

David C. Flynn, Jim Cannaliato

Abstract

We present a new empirical model for galaxy rotation curves that introduces a velocity correction term ω, derived from observed stellar motion and anchored to Keplerian baselines. Unlike parametric halo models or modified gravity theories, this approach does not alter Newtonian dynamics or invoke dark matter distributions. Instead, it identifies a repeatable kinematic offset that aligns with observed rotation profiles across a wide range of galaxies. Using SPARC data [1], we demonstrate that this model consistently achieves high fidelity fits, often outperforming MOND and CDM halo models in RMSE and R-squared metrics without parametric tuning. The method is reproducible, minimally dependent on mass modeling, and offers a streamlined alternative for characterizing galactic dynamics. While the velocity correction ω lacks a definitive physical interpretation, its empirical success invites further exploration. We position this model as a local kinematic tool rather than a cosmological framework, and we welcome dialogue on its implications for galactic structure and gravitational theory. Appendix B presents RMSE and R2 comparisons showing that this method consistently outperforms MOND and CDM halo models across a representative galaxy sample.

A New Empirical Fit to Galaxy Rotation Curves

Abstract

We present a new empirical model for galaxy rotation curves that introduces a velocity correction term ω, derived from observed stellar motion and anchored to Keplerian baselines. Unlike parametric halo models or modified gravity theories, this approach does not alter Newtonian dynamics or invoke dark matter distributions. Instead, it identifies a repeatable kinematic offset that aligns with observed rotation profiles across a wide range of galaxies. Using SPARC data [1], we demonstrate that this model consistently achieves high fidelity fits, often outperforming MOND and CDM halo models in RMSE and R-squared metrics without parametric tuning. The method is reproducible, minimally dependent on mass modeling, and offers a streamlined alternative for characterizing galactic dynamics. While the velocity correction ω lacks a definitive physical interpretation, its empirical success invites further exploration. We position this model as a local kinematic tool rather than a cosmological framework, and we welcome dialogue on its implications for galactic structure and gravitational theory. Appendix B presents RMSE and R2 comparisons showing that this method consistently outperforms MOND and CDM halo models across a representative galaxy sample.
Paper Structure (9 sections, 12 equations, 9 figures, 9 tables)

This paper contains 9 sections, 12 equations, 9 figures, 9 tables.

Table of Contents

  1. Acknowledgments
  2. Funding
  3. Data Availability
  4. Ethics and Conflict of Interest
  5. Author Contributions
  6. Use of AI (Microsoft Copilot)
  7. Appendix B.1: Method for Bitmap-Based Calculation of RMSE and R2

Figures (9)

  • Figure 1: Conceptual framework illustrating the relationship between key variables and model outcomes.
  • Figure 2: M33 Classic Velocity Curve
  • Figure 4: Comparative visualization of model performance across input scenarios, highlighting predictive accuracy and R-squared values. The figure presents 20 representative selections from our dataset, all sourced from the SPARC archive.
  • Figure 5: Model output for galaxy DDO161, generated using adjusted Keplerian dynamics via Equation 2. The graph overlays our computed trajectory with SPARC-derived data curves from multiple reconstruction methods, providing contextual comparison across empirical and theoretical profiles.
  • Figure 6: Model output for galaxy ESO079-G014, generated using adjusted Keplerian dynamics via Equation 2. The graph overlays our computed trajectory with SPARC-derived data curves from multiple reconstruction methods, providing contextual comparison across empirical and theoretical profiles.
  • ...and 4 more figures