Galactic rotation curves versus ultralight dark matter: Implications of the soliton-host halo relation

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 ∼ (10 −22 ÷ 10 −21 ) 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.

Baryon-driven growth of solitonic cores in fuzzy dark matter halos

“…The density profile of the dark matter core with baryons is well described by a ground state solution of the SP equation taking into account the additional gravitational potential sourced by the baryon density. Similar solitonic solutions with an additional gravitating component have been investigated in the context of supermassive black holes [28,34] and galactic disks [33]. Our simulations confirm and extend these results by providing evidence that modified ground state solutions are approached dynamically in the presence of baryonic feedback (Appendix B).…”

“…Ground state solutions of the SP equation are uniquely determined by their total mass or, alternatively, their central density ρ c . Dark-matter-only simulations show a relation between the masses of FDM halos and their solitonic cores which follows from an equilibrium of their virial temperatures [8,9,11,28].…”

“…In our simulations, cores become more massive and more compact if baryons are included. Rotation curve measurements in galaxies with significant central amounts of baryons are therefore likely to disfavor FDM masses around 10 −22 eV more strongly than already found in [28,29]. It may be fruitful to revisit these constraints using the prescription above.…”

“…Less stringent constraints can be inferred from the high-z galaxy luminosity function [22][23][24][25][26]. Galaxies with measured rotation curves yield even lower masses than inferred from dwarf spheroidals [27] or at least exclude the typical value m ∼ 10 −22 eV [28,29]. In general, the scaling properties of solitons seem to disagree with observational data [30,31].…”

Gravitational microlensing by dark matter in extended structures

“…where λ is the ratio of the gravitational potential energy per scalar constituent to its mass m φ [53]. For the nonrelativistic treatment to be self-consistent, 0 < λ 1.…”