Quantum Scales of Galaxies from Ultralight Dark Matter

We propose that the ultralight dark matter (ULDM) model, in which dark matter particles have a tiny mass of $m=O(10^{-22})eV$, has characteristic scales for physical quantities of observed galaxies such as mass, size, acceleration, mass flux, and angular momentum from quantum mechanics. The typical angular momentum per dark matter particle is $\hbar$ and the typical physical quantities are functions of specific angular momentum $\hbar/m$ and average background density of the particles. If we use the Compton wavelength instead for the length scale, we can obtain bounds for these physical quantities. For example, there is an upper bound for acceleration of ULDM dominated objects, $a_c={c^3 m}/{\hbar}$. We suggest that the physical scales of galaxies depend on the time of their formation and that these characteristic scales are related to some mysteries of observed galaxies. Future observations from the James Webb Space Telescope and NANOGrav can provide evidences for the presence and evolution of these scales.