Distances and separations of the WB sample. Top left: the histogram of ${\chi }_{\mathrm{D}}^2$ values (black full line). The blue line shows the cumulative distribution of ${\chi }_{\mathrm{D}}^2$, the dashed black and blue lines show the χ² distribution and its cumulative for 2 degrees of freedom. Top right: the difference $D_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}}-{\overline{D}}_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}}$ as a function of ${\overline{D}}_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}}$. The difference is zero within the errors. Bottom left: crosses show r̄ (the WB separations estimated using Gaia distances and Eq. (15)) as a function of the mean WB distance ${\overline{D}}_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}}$. The blue and red points show r, the best fitting WB separations. The largest r̄ are observed at the largest distances. They overestimate r by an order of magnitude or more. Bottom right: the ratio $\overline{s}/{\overline{s}}_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}}$ as a function of D_mean. The blue and red points show $s/{\overline{s}}_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}}$. The WB separation on the sky ${\overline{s}}_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}}$ (estimated by scaling the angular separation θ with the mean WB distance), increasingly overestimates s (obtained by scaling θ with the minimal Gaia distance), as the distance to the WB increases. The best fitting distances deliver $s/{\overline{s}}_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}}\approx 1$.