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

Abstract

The dynamics of globular clusters in the Fornax dwarf galaxy poses a challenge for the standard cold dark matter and can be used to test other models of dark matter. We study this dynamics in the context of ultralight bosonic dark matter 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 globular clusters are compared in the cases with and without the damping term. It is argued that the damping term plays an important role for the Fornax timing problem in ultralight dark matter (ULDM) models. In particular, the infall time of globular cluster GC3 can attain the required value, provided that ULDM is non-interacting or has a very small repulsive self-interaction. In the strongly-interacting ULDM, there is no solution for the required infall time for GC3 if its starting position is $r_0\lesssim 1.5$ kpc.