Numerical model of the binary star density as a function of distance to Earth and contrast (left) and angular separation (right). The grey scales and the histograms are linear and relative to the maximum bin. We select stars in the magnitude range 18 ≤ I(AB) ≤ 24.5. Both plots exhibit bimodal distributions with low-mass main stars located at shorter distances. More massive stars are not located in our direct neighbourhood, as suggested by the distribution of angular separation with distance. Companions of very low mass stars (down to the brown dwarf limit) are rare with the applied selection cuts.