Radial Acceleration Relation from Ultra-light Scalar Dark matter
  We show that ultra-light scalar dark matter (fuzzy dark matter) in galaxies
has a quantum mechanical typical acceleration scale about
$10^{-10}\,\mbox{ms}^{-2}$, which leads to the baryonic Tully-Fisher relation.
Baryonic matter at central parts of galaxies acts as a boundary condition for
dark matter wave equation and influences stellar rotation velocities in halos.
Without any modification of gravity or mechanics this model also explains the
radial acceleration relation and MOND-like behavior of gravitational
acceleration found in galaxies having flat rotation curves. This analysis can
be extended to the Faber-Jackson relation.
