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 10−10ms−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.