The mass discrepancy-acceleration relation: a universal maximum dark
  matter acceleration and implications for the ultra-light scalar field dark
  matter model
  Recent analysis of the rotation curves of a large sample of galaxies with
very diverse stellar properties reveal 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 $\mu_{DM} = \rho_s r_s$ must be a universal constant, as
suggested by previous studies in selected galaxies, revealing a strong
correlation between the density $\rho_s$ and scale $r_s$ parameters in each
profile. We then explore the consequences of the constancy of $\mu_{DM}$ in the
context of the ultra-light scalar field dark matter model (SFDM). We find that
for this model $\mu_{DM} = 648 \, M_\odot {\rm pc}^{-2}$, and that the
so-called WaveDM soliton profile should be an universal feature of the DM
halos. Comparing with data from the Milky Way and Andromeda satellites, we find
that they are consistent with a boson mass of the scalar field particle of the
order of $10^{-21} \, {\rm eV}/c^2$, which puts the SFDM model in agreement
with recent cosmological constraints.
