2020ApJ...904..161B

Whereas cold dark matter (CDM) simulations predict central dark matter cusps with densities that diverge as ρ(r) ∼ 1/r, observations often indicate constant-density cores with finite central densities ρ₀ and a flat density distribution within a core radius r₀. This paper investigates whether this core-cusp problem can be solved by fuzzy dark matter (FDM), a hypothetical particle with a mass of the order of m ≃ 10^–22 eV and a corresponding de Broglie wavelength on astrophysical scales. We show that galaxies with CDM halo virial masses M_vir <= 10¹¹M_☉ follow two core-scaling relations. In addition to the well-known universal core column density Σ₀ ≡ ρ₀ x r₀ = 75 M_☉ pc^–2, core radii increase with virial masses as r₀ ∼ M_vir^γ^ with γ of order unity. Using the simulations by Schive et al. we demonstrate that FDM can explain the r₀-M_vir scaling relation if the virial masses of the observed galaxy sample scale with the formation redshift z as M_vir ∼ (1 + z)^–0.4. The observed constant Σ₀ is however in complete disagreement with FDM cores which are characterized by a steep dependence Σ₀ ∼ r₀^–3, independent of z. More high-resolution simulations are now required to confirm the simulations of Schive et al. and explore the transition region between the soliton core and the surrounding halo. If these results hold, FDM can be ruled out as the origin of observed dark matter cores and other physical processes are required to account for their formation.