The viability of ultralight bosonic dark matter in dwarf galaxies

The dark matter distribution in dwarf galaxies holds a wealth of information on the fundamental properties and interactions of the dark matter particle. In this paper, we study whether ultralight bosonic dark matter is consistent with the gravitational potential extracted from stellar kinematics. We use velocity dispersion measurements to constrain models for halo mass and particle mass. The posterior likelihood is multimodal. Particle masses of order $m\sim 10^{-22} {\rm{eV}}$ require halos of mass in excess of $\sim 10^{10} M_\odot$, while particle mass of order $m \gtrsim 10^{-20}{\rm{eV}}$ are favored by halos of mass $\sim [10^{8} - 10^{9}] M_\odot$, with a similar behavior to cold dark matter. Regardless of particle mass, the lower halo masses are allowed if stellar dynamics are influenced by the presence of a central black hole of mass at most $\sim 10^{-2}$ the host halo mass. We find no preference for models that contain a black hole over models that do not contain a black hole. Our main conclusion is that either the fuzzy dark matter particle mass must be $m \gtrsim 10^{-20}$ eV, or the Milky Way dwarfs must be unusually heavy given the expected hierarchical assembly of the Milky Way, or the Milky Way dwarfs must contain a central black hole. We find no evidence for either of the last two possibilities and consider them unlikely.