A Phenomenological Hydrodynamic Limit in Galactic Dynamics: Cross-Scale Consistency and a Parameter-Free Ansatz in the SPARC Catalog.

The radial acceleration relation (RAR) in late-type galaxies exhibits a phenomenologically tight correlation between observed kinematics and the underlying baryonic mass distribution. Traditionally,this behavior is modeled via non-baryonic dark matter halos, an approach that introduces significant parameter degeneracy to accommodate the observed diversity of rotation curve profiles. In thispaper, we present an exhaustive kinematic audit of the RAR utilizing a purely phenomenological fluiddynamic limit. By modeling the galactic outskirts as an environment dominated by an effective vacuumviscosity, we introduce a hydrodynamic ansatz, which becomes operative below a critical, cross-scaleacceleration threshold a0 = (1.200 ± 0.002) × 10−10 ms−2. Applying this universal phase-transitionfunction to 175 galaxies in the Spitzer Photometry & Accurate Rotation Curves (SPARC) catalog,we successfully reproduce the full rotation curves using strictly the total baryonic mass distributionand a rigidly fixed stellar mass-to-light ratio (Υd = 0.5M⊙/L⊙). When applied directly to the raw,unbinned observational data, the global mean absolute error converges to ∼ 15.7%, a scatter that isdominated by the ∼ 7% instrumental noise floor compounded by additional distance and geometric uncertainties inherent to the SPARC sample. However, when the data is bin-averaged to eliminate localinstrumental variance and extract the underlying Radial Acceleration Relation (RAR), the parameterfree hydrodynamic limit predicts the exact macroscopic kinematic behavior with a residual error ofonly 2.65%. To rigorously evaluate predictive economy, we employ the Bayesian Information Criterion(BIC), demonstrating that this rigid, k = 0 fluid ansatz is statistically superior to standard ΛCDMmodels (NFW profiles) that rely on algorithmic overfitting. The mathematical consistency of a0 acrossmultiple astrophysical scales strongly suggests that kinematic effects currently attributed to dark haloscan be accurately and deterministically mimicked by an inherent spatial viscosity in the backgroundfluid.