Single-Parameter Exponential Model Outperforms Standard Dark Matter and Modified Newtonian Frameworks in Predicting Galactic Rotation Curves

Abstract

The functional forms of galactic rotation curves provide a fundamental test for models of gravity and dark matter. In this work, we conduct a rigorous statistical comparison of five distinct models against the complete sample of 175 galaxies from the SPARC database. The models under consideration are: (1) a one-parameter empirical law, physically constrained by each galaxy's measured flat disc rotation velocity ($V_{\text{flat}}$); (2) a classical two-parameter Freeman disk; (3) a three-parameter Navarro-Frenk-White (NFW) dark matter halo plus baryons model; (4) a one-parameter Modified Newtonian Dynamics (MOND) model; and (5) a two-parameter Bosma/Dark Matter Disk model. We employ a Bayesian framework with Markov Chain Monte Carlo (MCMC) for parameter estimation, and use the Akaike Information Criterion (AICc) to assess the goodness-of-fit and statistical parsimony of the best-fit models. Our results reveal a decisive preference for the constrained one-parameter empirical model. It is selected as the best descriptor for a clear majority of the sample (60.6\%) and, critically, also achieves the best median goodness-of-fit, with a reduced chi-squared of ${\chi }_{\nu }^2=0.41$. In contrast, the standard NFW framework is preferred in only 12.6\% of cases, while the MOND and Freeman disk models are selected as optimal for just 10.3\% and 9.1\%, respectively. The Bosma model, despite linking dynamics to the gas distribution, is preferred in only 7.4\% of cases. The pronounced statistical and descriptive success of this simple, physically-anchored law over more complex, established theories suggests that its functional form represents a fundamental and highly efficient organizing principle in the dynamics of disk galaxies.

arXiv comment18 pages, 2 figures

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