# Theoretical implications of the galactic radial acceleration relation of McGaugh, Lelli, and Schombert

## Abstract

Velocities in stable circular orbits about galaxies, a measure of centripetal gravitation, exceed the expected Kepler/Newton velocity as orbital radius increases. Standard Λ cold dark matter (ΛCDM) attributes this anomaly to galactic dark matter. McGaugh et al. have recently shown for 153 disc galaxies that observed radial acceleration is an apparently universal function of classical acceleration computed for observed galactic baryonic mass density. This is consistent with the empirical modified Newtonian dynamics (MOND) model, not requiring dark matter. It is shown here that suitably constrained ΛCDM and conformal gravity (CG) also produce such a universal correlation function. ΛCDM requires a very specific dark matter distribution, while the implied CG non-classical acceleration must be independent of galactic mass. All three constrained radial acceleration functions agree with the empirical baryonic v4 Tully-Fisher relation. Accurate rotation data in the nominally flat velocity range could distinguish between MOND, ΛCDM, and CG.