A Common Galaxy-Independent Radial Structure of Dark Matter
A galaxy-independent scaled radial coordinate is introduced, extending from the galactic center to the radius where the baryonic acceleration equals $10^{-12}\ m/s^2$. Using this coordinate, the SPARC galaxies are found to share a common radial structure, resulting in common radial distributions of the enclosed dark-matter mass, the dark-matter density, and the unified velocity. These quantities constitute mathematically equivalent representations of the common radial structure. Consequently, the radial acceleration relation, the approximately flat outer rotation curves, and the BTFR follow directly from the fitted radial dependence of the enclosed dark-matter mass. The enclosed dark-matter mass itself increases linearly with the scaled radius, reaching about seven times the enclosed baryonic mass within the observed SPARC range. The common radial structure reported here is determined from the SPARC sample, because it provides sufficiently accurate rotation curves to determine the radial dark-matter distribution empirically. However, there is presently no observational evidence that the derived common radial structure is unique to the SPARC sample. The common radial structure identified here provides new empirical information about the organization of dark matter in galaxies. Beyond serving as an observational constraint on halo models, it may also help guide the development of a deeper physical understanding of the processes responsible for this organization.