Baryonic Deficits in SPARC Rotation Curves: Density- and Acceleration-Conditioned Trends in the Full Late-Type Sample

We present a fully reproducible empirical analysis of baryonic contributions to galaxyrotation curves using the complete late-type SPARC sample. Using a fixed parsingpipeline applied to publicly available mass-model files, we compute baryonic velocityfractions 𝑅(𝑟) = 𝑉bar(𝑟)/𝑉obs(𝑟) and a bounded deficit statistic Δ(𝑟) = ma x(1 − 𝑅, 0)across 165 galaxies (3345 radial measurements).We recover the established radial acceleration relation (𝑅𝐴𝑅), confirming that baryonicacceleration strongly constrains galaxy dynamics. We then investigate residual structureat fixed baryonic acceleration by introducing a simple effective surface-density proxyΣeff, defined as the median disk surface brightness.We find that Σeff systematically organizes residual variation in baryonic velocityfractions: at fixed acceleration, lower surface-density systems exhibit larger deficits,while higher surface-density systems approach baryonic dominance. This orderingpersists across the full sample and remains robust under bootstrap resampling andalternative surface-brightness summaries.We quantify the reduction in residual scatter when including Σeff alongside acceleration,demonstrating that acceleration alone does not fully capture the structure of galaxyrotation curves. These results establish effective surface density as an additionalempirical parameter governing galaxy dynamics. The analysis is model-independentand provides a reproducible benchmark for theoretical frameworks. The analysis notebook and derived statistics are available at: https://doi.org/10.5281/zenodo.18904974