The acceleration relation in galaxies and scale invariant dynamics: another challenge for dark matter

A relation between the centripetal acceleration g_obs in galaxies and the gravity due to the baryon distribution g_bar has been found by McGaugh (2016) and Lelli et al.(2017). It also summarizes properties such as the Tully-Fisher and Faber-Jackson relations. Below about g_bar= 10E-10 m s^(-2), the observed relation deviates from the 1:1 line, g_obs being much larger than g_bar. The acceleration relation is followed by late and early type galaxies, and also by the dwarf spheroidals where the deviations from the 1:1 line are the largest ones. These deviations are currently attributed to dark matter. We show that the scale invariant theory, with the assumption of the scale invariance of the empty space, correctly predicts the observed deviations in the acceleration relation. The large deviations (up to a factor 400) and the flattening of the acceleration relation observed for the dwarf spheroidal galaxies are also well described. The presence of dark matter is no longer necessary in the scale invariant context, which also accounts why dark matter usually appears to dominate in galactic regions with low baryonic gravities.