A Velocity Coupled Radial Acceleration Ansatz for Disk-Galaxy Rotation Curves: Fits to SPARC, Bayesian Inference, and Parameter Identifiability

Abstract

Observed rotation curves of disk galaxies remain a sharp empirical probe of the relationship between baryons and dynamics. We study a minimal, explicitly \emph{phenomenological} alternative to standard halo parameterizations: an additional inward \emph{radial} acceleration proportional to the local \emph{tangential} speed, $a_{\vca}(r)=\gamma(r)\,v(r)$, with a saturating coupling $\gamma(r)=\vinf/(r+\rzero)$. Combining this ansatz with the circular-motion condition yields a quadratic equation for $v(r)$ with a closed-form physical branch.We fit this ``velocity-coupled acceleration'' (\vca) model to $N_\mathrm{gal}=171$ rotation curves from the SPARC sample using the published baryonic decompositions (gas, disk, bulge), and we compare to two commonly used two-parameter halo models (NFW and Burkert) using an identical optimization pipeline and error model.For a fiducial systematic error floor $\sigma_0=5~\mathrm{km\,s^{-1}}$, the \vca model is typically competitive with an NFW halo and performs comparably (though not uniformly better) than a Burkert halo in information-criterion comparisons.We further perform MCMC inference for \vca parameters, quantify posterior predictive coverage, and show that parameter posteriors exhibit a strong $\vinf$--$\rzero$ degeneracy for many galaxies; only $47/171$ galaxies yield well-identified posteriors under simple width-based criteria. We also perform a simple radial holdout cross-validation (outer 30\% of radii) and find predictive RMSE comparable to NFW and Burkert under this protocol.Finally..