Illustration of the selection of physical pairs and the contamination by optical pairs. Top panels: proper motion difference (Δμ) vs. separation (ρ) for source pairs in sample A (a) and B1 (b) before making the cut ρ > 2.2 arcsec indicated by the dashed vertical line. The three solid lines correspond to ρΔμ = 0.5, 1, and 2 arcsec mas yr⁻¹. The points are colour-coded by the median parallax difference between the components. In panel b the separation of the faint source is measured from the position of the bright source displaced by + 0.1° in declination. Bottom panels: normalised parallax difference vs. ρΔμ for the samples in the top panels, but now after the selection ρ > 2.2 arcsec. The three vertical lines correspond to the values of ρΔμ indicated in the top panels. The thin green curves show the 16th, 50th, and 84th percentiles of the distribution in normalised parallax difference.