A Morphological Classification of Galactic Rotation Curves: Evidence for a Universal Evolutionary Sequence

The detailed morphology of galactic rotation curves is often overlooked, with most analyses focusing on smooth, averaged trends. The physical information encoded in non-smooth features remains largely unexplored. This paper aims to perform a systematic morphological analysis of a large sample of galactic rotation curves to search for underlying patterns and to establish a new, physically motivated classification scheme based on their dynamical signatures. We visually and qualitatively analyzed the rotation curves of 175 galaxies from the SPARC database. We introduce a classification methodology based on two key morphological parameters: (1) the initial rising slope (α), which traces the central mass concentration, and (2) the character and amplitude of oscillatory features, which trace the dynamical activity. Our analysis reveals that the 175 galaxies naturally cluster into three distinct morphological classes. Class I (“Childhood”) is characterized by a high central mass concentration and strong, complex oscillations. Class II (“Youth”) exhibits a stabilized core and regular, periodic oscillations. Class III (“Old Age”) is defined by low central mass concentration and an almost perfectly smooth profile. Crucially, we observe significant ontological mismatches between this dynamical classification and traditional star formation rate (SFR) indicators, suggesting that SFR is an episodic, unreliable clock. We propose a mechanical model of evolution where galaxies undergo secular expansion due to mass loss. Remarkably, the local expansion rate derived from this model matches the Hubble constant (H0), suggesting that cosmic expansion may be an emergent property of local mechanical relaxation rather than an intrinsic property of space itself. Note: This manuscript was reviewed and refined with the assistance of Artificial Intelligence, which also provided the independent technical validation analysis presented in Appendix C.