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 (Vflat); (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 χ2ν = 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.
Versions
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BibTeX
@misc{guhdar2026singleparameter,
title = {{Single-Parameter Exponential Model Outperforms Standard Dark Matter and Modified Newtonian Frameworks in Predicting Galactic Rotation Curves}},
author = {Mohammed Guhdar},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27876},
eprint = {2610.27876},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27876},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Single-Parameter Exponential Model Outperforms Standard Dark Matter and Modified Newtonian Frameworks in Predicting Galactic Rotation Curves
AU - Mohammed Guhdar
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.27876
UR - https://arxiv.org/abs/2610.27876
AB - 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_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 χ^2_ν = 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.
ER -