Structure Dependent Scaling Galaxy Dynamics

We analyze galaxy rotation curve data from the SPARC database to investigate whether deviations from the baryonic Tully–Fisher relation (BTFR) are related to internal structural properties. We introduce a dimensionless parameter, K = |∇ρ|/ρ, which quantifies density gradients, and examine its relation to residuals from the BTFR. We find a weak but measurable correlation (r ≈ 0.1), indicating that galaxy dynamics may include subdominant structure-dependent contributions beyond standard one-dimensional scaling. We propose a phenomenological interpretation in which density gradients drive flows that redistribute matter, forming a self-regulating system. Within this framework, galaxies can be viewed as operating between diffuse and structured regimes, with spiral morphology emerging as a manifestation of phase-modulated dynamics. These results suggest that galaxy dynamics are primarily governed by BTFR scaling, with an additional geometric layer linked to internal structure.