A New Empirical Fit to Galaxy Rotation Curves

TL;DR

This paper introduces an empirical velocity correction model for galaxy rotation curves that fits observed data well without relying on dark matter or modified gravity, offering a new streamlined approach to galactic dynamics.

Contribution

The paper presents a novel empirical velocity correction {} that improves rotation curve fits without altering Newtonian physics or invoking dark matter, outperforming existing models.

Findings

Achieves high-fidelity fits to galaxy rotation data

Outperforms MOND and CDM halo models in RMSE and R-squared metrics

Model is reproducible and minimally dependent on mass modeling

Abstract

We present a new empirical model for galaxy rotation curves that introduces a velocity correction term {\omega}, 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 {\omega} 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.