Galaxy-Independent Radial Structure of Dark-Matter Halos

Abstract

A galaxy-independent radial scaling of the SPARC rotation-curve data reveals a common structure of dark-matter halos across galaxies. Using all 2693 rotation-curve measurements from the 153 SPARC galaxies, we analyze the data within a unified radial framework rather than fitting parametric halo models to individual systems. An empirical relation between the observed centripetal acceleration $g_{obs}$ and the baryonic acceleration $g_{bar}$. The residual scatter of this relation is consistent with the observational uncertainties, indicating no detectable intrinsic galaxy-dependent bias. Motivated by the baryonic acceleration, a scaled radial coordinate $r_{sc}$ is introduced through $r = r_0 r_{sc}$, where $r_0$ is defined by $g_{bar} =2\times 10^{-12} m/s^2$. This transformation removes galaxy-to-galaxy scaling and allows all SPARC measurements to be analyzed within a single radial domain. In this representation empirical radial distributions are obtained for acceleration, dark-matter mass, density, and circular velocity. The combined data indicate the onset of dark-matter effects at $r_{sc} \approx 0.1$, dark-matter dominance for $r_{sc} \gtrsim 0.2$, a linear growth of dark-matter mass with radius $m_{DM}/M_{bar}$ = $(6.9 \pm 0.2)r_{sc} - (0.23 \pm 0.03)$, and a density profile $ρ\propto r_{sc}^{-2}$, and a nearly constant unified rotation velocity for $r_{sc} > 0.2$. The results suggest that the empirical acceleration relation reflects a common radial dark-matter structure shared by the SPARC galaxies.