Dynamical friction force as a function of the Mach number for our simulations. This plot is analogue to Fig. 2, which gives the analytic description of the dynamical friction force. Different cross-sections are shown, indicated by the Knudsen number. Here, Kn = ∞ corresponds to a collisionless medium and Kn = 0.0 to a gaseous medium. We note that in the simulation the BH initially starts at a high velocity, i.e. at the right side of the plot and slows down throughout the simulation, i.e. moves towards the left side of the plot.