Dynamical Friction and Black Holes in Ultralight Dark Matter Solitons

We numerically simulate the motion of a black hole as it plunges radially through an ultralight dark matter soliton. We investigate the timescale in which dynamical friction reduces the kinetic energy of the black hole to a minimum, and consider the sensitivity of this timescale to changes in the ULDM particle mass, the total soliton mass, and the mass of the black hole. We contrast our numerical results with a semi-analytic treatment of dynamical friction, and find that the latter is poorly suited to this scenario. In particular, we find that the back-reaction of the soliton to the presence of the black hole is significant, resulting in oscillations in the coefficient of dynamical friction which cannot be described in the simple semi-analytical framework. Furthermore, we observe a late-time reheating effect, in which a significant amount of kinetic energy is transferred back to the black hole after an initial damping phase. This complicates the discussion of ULDM dynamical friction on the scales relevant to the final parsec problem.