Structural Pattern of the Outer Rotation-Curve Slope Distribution in the SPARC Galaxy Sample

This record presents an empirical re-analysis of the outer rotation-curve slopes in the SPARC galaxy sample. The analysis measures the logarithmic outer slope s = d log10(V_obs) / d log10(R) using ordinary least squares regression in log–log space. The study applies strict selection criteria (Q ≤ 2, R > 2.5 R_disk, N_outer ≥ 8), resulting in an accepted sample of 79 galaxies. The slope distribution shows a central tendency very close to zero (median −0.000632), indicating that the characteristic outer dynamical state of disk galaxies is approximately flat, while still exhibiting significant dispersion. A strong negative correlation is found between the outer slope and the asymptotic rotation velocity (Pearson r = −0.626; Spearman ρ = −0.661), demonstrating that the outer slope is a scale-dependent dynamical parameter. Sensitivity tests using alternative outer-region definitions confirm that the ensemble average slope approaches zero as increasingly large galactocentric radii are considered. This work extends the empirical analysis presented in the previous record:DOI: 10.5281/zenodo.18904301 The results provide a quantitative characterization of the statistical structure of the outer rotation-curve slope distribution in the SPARC dataset.