ESSC v6.3: Radial Structure of the Radial Acceleration Relation and the Disk–Halo Transition in Disk Galaxies

This work investigates the radial structure of the Radial Acceleration Relation (RAR) residuals in disk galaxies using the SPARC database. While the global RAR provides a tight empirical relation between the observed gravitational acceleration (gₒbs) and the baryonic acceleration (gbar), the radial structure of deviations from this relation has not been extensively examined. In this study we analyze the logarithmic RAR residual ΔRAR = ln (gₒbs) − ln (gRAR) as a function of the normalized radius R/Rd. By stacking residual profiles from the SPARC galaxy sample we identify a systematic radial structure in the residual field. The radial gradient of the stacked residual profile reveals a characteristic transition radius Rₜrans / Rd ≈ 1. 6. A bootstrap analysis of the galaxy sample confirms that this transition scale is statistically robust. We further evaluate the halo fraction at the transition radius and find a median value fₕalo ≈ 0. 5, suggesting that the transition occurs near the radius where the gravitational contributions of baryonic and halo components become comparable. These results indicate that disk galaxies may exhibit a two–regime dynamical structure consisting of a baryon-dominated inner region and a halo-dominated outer region when expressed in units of the disk scale length. Within the ESSC framework this transition scale may be interpreted as a structural boundary associated with scale-dependent coupling between baryonic and halo components.