Constrained Low-Dimensional Structure in Normalized SPARC Rotation Curves

This work analyzes normalized galaxy rotation curves from the SPARC sample to determine whether their population-level diversity is effectively low-dimensional in a common radial representation. Rather than fitting individual galaxies, the study treats rotation curves as elements of a shared function space and evaluates their collective structure. Principal component analysis (PCA) shows that three dominant modes account for approximately 99% of the variance across multiple radial grid resolutions when the galaxy sample is held fixed. This result indicates that rotation-curve diversity is highly structured and can be described by a small number of dominant modes. We interpret this as a population-level empirical constraint: successful models of galaxy dynamics should reproduce not only individual rotation curves and mean scaling relations, but also the observed low-dimensional organization of the full ensemble. The inferred dimensionality is representation-dependent and should be understood as an effective property of the adopted normalization and interpolation scheme rather than a direct measurement of the underlying dynamical parameter space.