Galactic rotation curves vs. ultralight dark matter

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Bosonic ultra-light dark matter (ULDM) would form cored density distributions at the centres of galaxies. These cores admit analytic description as the lowest energy bound state solution ("soliton") of the Schrödinger-Poisson equations. Numerical simulations of ULDM galactic halos found empirical scaling relations between the mass of the large-scale host halo and the mass of the central soliton. 
We connect the simulation results of different groups to basic properties of the soliton. Importantly, simulations imply that the specific kinetic energy in the soliton and in the host halo should be approximately equal. This relation predicts that the peak circular velocity, measured for the host halo in the outskirts of the galaxy, should repeat itself in the central region. Contrasting this prediction to the measured rotation curves of low surface-brightness galaxies, we show that ULDM in the mass range m ~ 10⁻²²-10⁻²¹ eV, which has been invoked as a possible solution of small-scale puzzles of ΛCDM, is in tension with the data. We discuss the potential of detailed dynamical modelling of the Milky Way and other well-resolved galaxies to probe ULDM up to m ~ 10⁻¹⁹ eV.