Abstract
Bosonic ultra-light dark matter (ULDM) would form cored density distributions at the center of galaxies. These cores, seen in numerical simulations, admit analytic description as the lowest energy bound state solution ("soliton") of the Schroedinger-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 discuss how the simulation results of different groups can be understood in terms of the basic properties of the soliton. Importantly, simulations imply that the energy per unit mass in the soliton and in the virialised host halo should be approximately equal. This relation lends itself to observational tests, because it predicts that the peak circular velocity, measured for the host halo in the outskirts of the galaxy, should approximately repeat itself in the central region. Contrasting this prediction to the measured rotation curves of well-resolved near-by galaxies, we show that ULDM in the mass range $m\sim (10^{-22}\div 10^{-21})$ eV, which has been invoked as a possible solution to the small-scale puzzles of $\Lambda$CDM, is in tension with the data. We suggest that a dedicated analysis of the Milky Way inner gravitational potential could probe ULDM up to $m\lesssim 10^{-19}$ eV.
Highlights
Two forms of matter could provide the cosmological equation of state, required for dark matter (DM): nonrelativistic massive particles (e.g., WIMPs), or the classical background of an ultralight bosonic field oscillating around a minimum of its potential
Contrasting this prediction with the measured rotation curves of well-resolved nearby galaxies, we show that ultralight dark matter (ULDM) in the mass range m ∼ ð10−22 ÷ 10−21Þ eV, which has been invoked as a possible solution to the small-scale puzzles of ΛCDM, is in tension with the data
We suggest that a dedicated analysis of the Milky Way inner gravitational potential could probe ULDM up to m ≲ 10−19 eV
Summary
Two forms of matter could provide the cosmological equation of state, required for dark matter (DM): nonrelativistic massive particles (e.g., WIMPs), or the classical background of an ultralight bosonic field oscillating around a minimum of its potential (e.g., axions or axionlike particles). Axionlike particles with exponentially suppressed masses arise in the context of string theory [12,14,15,16]. ULDM with mass m ∼ ð10−22 ÷ 10−21Þ eV is motivated due to several puzzles, facing the standard WIMP paradigm on galactic scales (see, e.g., [12,17] for recent reviews). This range of m is in some tension with the matter power spectrum, inferred from Ly-α forest analyses [18,19,20,21,22], which yields a bound m ≳ 10−21 eV. Since the strongest Ly-α bound constraints come from the smallest and most nonlinear scales, where systematic effects are challenging, we believe it prudent to seek additional methods to constrain the model for m ≳ 10−22 eV
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