Quantum Scales of Galaxies from Self-interacting Ultralight Dark Matter

We derive the characteristic scales for physical quantities of dwarf galaxies, such as mass, size, acceleration, and angular momentum, within the self-interacting ultralight dark matter (ULDM) model. Due to the small mass of ULDM, even minor self-interactions can drastically alter these scales in the Thomas-Fermi limit. We suggest that these characteristic scales are connected to mysteries of observed galaxies. Oscillation of ULDM field can explain the current cosmological density of dark matter. Many cosmological constraints suggest that the energy scale $\tilde{m}$ for self-interacting ULDM is typically of the order $10~eV$, whereas the mass $m$ for the non-interacting case is around $10^{-21}~eV$. Self-interacting ULDM provides the better explanation for cosmological observations than the non-interacting case.