Hunting for ultralight dark matter with galactic kinematics

Bosonic ultra-light dark matter (ULDM) would form cored density distributions (``solitons") at the centre of galactic halos. Numerical simulations found empirical scaling relations between the mass of the halo and the mass of the soliton. We show that the simulations imply specific kinetic energy equilibration, and predict that the peak circular velocity, measured at the outskirts of the galaxy, should repeat itself in the central region, providing a rare opportunity to look for or constrain the particle nature of dark matter with minimal gravity alone. Contrasting this prediction to rotation curves of low surface-brightness galaxies, we show that ULDM with m<10^-21eV, which has been invoked as a solution of small-scale puzzles of LCDM, is in tension with the data. We discuss the potential of dynamical modelling of the Milky Way and other systems to probe ULDM up to m ~ 10^-19eV in the near future.