Damping of dynamical friction force in self-interacting ultralight dark matter and Fornax timing problem

Abstract The dynamics of globular clusters (GCs) in the Fornax dwarf galaxy pose a challenge for the standard cold dark matter and can be used to test other models of dark matter (DM). We study this dynamics in the context of an ultralight bosonic DM model, accounting for the damping term in a generalized Gross–Pitaevskii equation. Employing analytic formulas for the dynamical friction force, the infall time and evolution of GCs are compared in the cases with and without the damping term. It is argued that the damping term plays an important role in the Fornax timing problem in ultralight DM (ULDM) models. We found that the ULDM model with repulsive self-interaction can solve the Fornax timing problem in the absence of or with very small self-interaction, even if the initial position of the GC is not far from the center of the galaxy. Still, the problem is resolved for strongly interacting repulsive ULDM, even for the most pressing case of GC GC3, if its starting position exceeds 1.5 kpc.