The Radial Profile of RAR Residuals in SPARC Galaxies: Systematic Overprediction Inside r/r_d < 0.8

The radial acceleration relation (RAR) of disk galaxies has been reported to show no significant correlation between residuals and galactocentric radius (Lelli et al. 2017). However, previous analyses examined residuals against absolute radius R rather than radius normalized by the disk scale length r_d. Here we stack RAR residuals from 163 SPARC galaxies (3,271 data points) as a function of r/r_d. Using per-galaxy averaging to account for within-galaxy correlations, we find that the RAR systematically overpredicts observed accelerations in the inner disk: the per-galaxy mean residual at r/r_d < 0.8 is -0.10 ± 0.03 dex (98 galaxies, p = 4.5 × 10⁻⁴), with 63% of galaxies showing the effect. The signal is partially independent of the baryonic acceleration g_bar (partial correlation r = 0.24 after controlling for g_bar). However, the signal is sensitive to the assumed mass-to-light ratio: it vanishes at Υ_disk < 0.35 and strengthens at Υ_disk > 0.5. The peak deviation at r/r_d ~ 0.3–0.5 overlaps with the radial address where NFW dark matter cusps produce theoretical hooks in the RAR (Navarro et al. 2017; Li et al. 2022), providing the first empirical measurement of this predicted inner-disk structure. The RAR scatter also increases from ~0.12 dex at r/r_d > 5 to ~0.30 dex at r/r_d < 0.2. These results quantify the radial structure of RAR residuals as a function of the baryonic disk coordinate r/r_d for the first time.