Radial Acceleration Relation from Ultra-light Scalar Dark matter.

We show that ultra-light scalar dark matter (fuzzy dark matter) has a quantum mechanical universal acceleration scale about $10^{-10}ms^{-2}$, which naturally leads to the baryonic Tully-Fisher relation dynamically established. Baryon matter at central parts of galaxies acts as a boundary condition for dark matter wave equation and influences stellar rotation velocities in halos. This model also explains the radial acceleration relation and MOND-like behavior of gravitational acceleration found in various type of galaxies without any modification of gravity or mechanics. This analysis can be extended to the Faber-Jackson relation.