Radial Acceleration Relation from Ultra-light Scalar Dark matter

Understand

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.