Velocity and position of the BH in our test setup as a function of time. All simulations are for collisionless DM. The solid lines are from the setup with a box length of l = 829.5 μpc. In contrast, the dashed lines correspond to a setup with a smaller box size of l = 663.6 μpc. The high-resolution results correspond to N_DM = 5 × 10⁶ DM particles, and the low-resolution ones to N_DM = 10⁶. We note that in the smaller box setup, the low resolution implies a higher mass resolution than in the large box setup.