Local differential merger rate density of BH–NS systems as a function of the tilt angle. Different colors represent different values of the natal-kick velocity dispersion σ. For reference, we show the two different LVK BH–NS merger rates (LVK low in cyan and LVK high in pink) weighted by the distribution of the misalignment of the primary spin in GW200115. Different panels represent different values of the common-envelope efficiency parameter α. Top: α = 1; center: α = 3; bottom: α = 5.