# Radial Acceleration Relation from Ultra-light Scalar Dark matter

## TL;DR

This paper demonstrates that ultra-light scalar dark matter naturally produces a quantum acceleration scale that explains galaxy rotation curves, the baryonic Tully-Fisher relation, and MOND-like behavior without modifying gravity.

## Contribution

It introduces a model where fuzzy dark matter's quantum properties account for galactic dynamics and observed acceleration relations without new physics.

## Key findings

- Dark matter quantum acceleration scale ~10^{-10} m/s^2
- Explains baryonic Tully-Fisher relation
- Accounts for MOND-like galactic acceleration behavior

## Abstract

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.