Dynamical friction for circular orbits in self-interacting ultralight dark matter and Fornax globular clusters

Abstract: We investigate the impact of repulsive self-interaction in ultralight dark matter (ULDM) on dynamical friction in circular orbits in ULDM halos and its implications for the Fornax dwarf spheroidal (dSph) galaxy's globular clusters. Using the Gross-Pitaevskii-Poisson equations, we derive the dynamical friction force considering soliton density profiles for both non-interacting and strongly self-interacting ULDM. Our results show that self-interactions reduce the dynamical friction effect further than both the non-interacting ULDM and standard cold dark matter models. Furthermore, we derive the low Mach number approximation to simplify the analysis in the subsonic motion, where the tangential component of dynamical friction dominates. Applying these findings to the Fornax dSph, we calculate the infall timescales of globular clusters, demonstrating that strong self-interaction can address the timing problem more effectively. We constrain the parameter space for ULDM particle mass and self-coupling constant, which are consistent with other constraints from astronomical and cosmological observations.