On the Non-Universality of the Radial Acceleration Relation Across Galaxy Populations

Description / Abstract Title: On the Non-Universality of the Radial Acceleration Relation Across Galaxy Populations Abstract: The Radial Acceleration Relation (RAR) connects the observed gravitational acceleration ($g_{\text{obs}}$) to the baryonic acceleration ($g_{\text{bar}}$) and represents a central empirical relation in galaxy dynamics, widely interpreted as a universal empirical law. This study presents a systematic empirical falsification analysis of the RAR by testing its stability across independent datasets, dynamical regimes, and nuisance parameters. We utilize the SPARC dataset, containing 3,391 radial data points from 175 galaxies , and the independent LITTLE THINGS dwarf galaxy sample, comprising 877 radial measurements from 26 galaxies. While the RAR is tightly recovered within the SPARC sample with a Pearson correlation of $r = 0.928879$ and a residual scatter of $\tau = 0.209425$ , the relation collapses in the dwarf galaxy regime, yielding a near-zero correlation of $r = -0.040959$ when applying the SPARC-derived framework to the LITTLE THINGS dataset. Residual analysis reveals that systematic deviations correlate strongly with the local gas fraction ($r \approx 0.62$) and kinematic properties rather than structural parameters. Furthermore, structural parameters previously thought to be independent drivers are demonstrated to be highly degenerate with the local gas fraction, indicating that they primarily act as a proxy for gas-dominated regimes rather than encoding new dynamical information. The robustness of this breakdown is confirmed through parameter variations, including mass-to-light ratios and pressure-support proxies, as well as bootstrap resampling, which demonstrates that the gas fraction correlation remains robust within a 95% confidence interval excluding zero. Additionally, allowing for galaxy-dependent offsets reduces residual variance by approximately 61% (from 0.043846 to 0.017106), demonstrating that a single normalization fails to describe all systems. These findings indicate that the RAR is not a fundamental, universal law of nature but rather an emergent relation that validly manifests only under specific, rotation-dominated dynamical conditions.