Structured Residuals in the Radial Acceleration Relation a Multi Variable Analysis of the SPARC Dataset

Abstract

Barry Kieran Radcliffe

The Radial Acceleration Relation (RAR) provides one of the strongest empirical descriptions of galaxy dynamics, linking observed gravitational acceleration to that predicted from baryonic matter. While the relation captures the dominant structure of galaxy rotation curves, small residual deviations remain and are often treated as random scatter. In this study, we investigate whether these deviations contain predictable structure. Using the full SPARC (Spitzer Photometry and Accurate Rotation Curves) dataset comprising 175 galaxies and 3,391 radial measurements, we examine residuals relative to a standard RAR reference model. Predictor variables include local quantities such as baryonic acceleration, normalized radius, and rotation-curve slope, together with global galaxy properties including baryonic mass, gas fraction, surface brightness, flat rotation velocity, and morphology. We find that the signed residual is only weakly predictable, indicating limited deterministic predictability of individual deviations. In contrast, the magnitude and statistical structure of the residuals exhibit clear and reproducible dependence on both local and global galaxy properties. Residual magnitude varies systematically across acceleration regimes and predictive performance improves progressively as additional variables are incorporated. Variables associated with global galaxy state, including flat rotation velocity and morphology, provide independent predictive information beyond local acceleration alone. These results demonstrate that deviations from the RAR are not adequately described as featureless random scatter. Instead, they follow a structured, multi-variable pattern that can be partially predicted from observable galaxy properties. The findings suggest that galaxy dynamics are characterized not only by a leading-order acceleration relation but also by a constrained and informative structure of deviations that warrants further investigation.

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