Mass discrepancy-acceleration relation: A universal maximum dark matter acceleration and implications for the ultralight scalar dark matter model

Recent analysis of the rotation curves of a large sample of galaxies with very diverse stellar properties reveals a relation between the radial acceleration purely due to the baryonic matter and the one inferred directly from the observed rotation curves. Assuming the dark matter (DM) exists, this acceleration relation is tantamount to an acceleration relation between DM and baryons. This leads us to a universal maximum acceleration for all halos. Using the latter in DM profiles that predict inner cores implies that the central surface density μDM=ρsrs must be a universal constant, as suggested by previous studies of selected galaxies, revealing a strong correlation between the density ρs and scale rs parameters in each profile. We then explore the consequences of the constancy of μDM in the context of the ultralight scalar field dark matter model (SFDM). We find that for this model μDM=648M⊙ pc−2 and that the so-called WaveDM soliton profile should be a universal feature of the DM halos. Comparing with the data from the Milky Way and Andromeda satellites, we find that they are all consistent with a boson mass of the scalar field particle of the order of 10−21 eV/c2, which puts the SFDM model in agreement with recent cosmological constraints.