Are the orbital poles of binary stars in the solar neighbourhood anisotropically distributed?

We test whether or not the orbital poles of the systems in the solar neighbourhood are isotropically distributed on the celestial sphere. The problem is plagued by the ambiguity on the position of the ascending node. Of the 95 systems closer than 18 pc from the Sun with an orbit in the 6th Catalogue of Orbits of Visual Binaries, the pole ambiguity could be resolved for 51 systems using radial velocity collected in the literature and CORAVEL database or acquired with the HERMES-Mercator spectrograph. For several systems, we can correct the erroneous nodes in the 6th Catalogue of Orbits and obtain new combined spectroscopic-astrometric orbits for seven systems [WDS 01083+5455Aa,Ab; 01418+4237AB; 02278+0426AB (SB2); 09006+4147AB (SB2); 16413+3136AB; 17121+4540AB; 18070+3034AB]. We used of spherical statistics to test for possible anisotropy. After ordering the binary systems by increasing distance from the Sun, we computed the false-alarm probability for subsamples of increasing sizes, from N = 1 up to the full sample of 51 systems. Rayleigh-Watson and Beran tests deliver a false-alarm probability of 0.5% for the 20 systems closer than 8.1 pc. To evaluate the robustness of this conclusion, we used a jackknife approach, for which we repeated this procedure after removing one system at a time from the full sample. The false-alarm probability was then found to vary between 1.5% and 0.1%, depending on which system is removed. The reality of the deviation from isotropy can thus not be assessed with certainty at this stage, because only so few systems are available, despite our efforts to increase the sample. However, when considering the full sample of 51 systems, the concentration of poles toward the Galactic position l = 46.0{\deg}, b = 37{\deg}, as observed in the 8.1 pc sphere, totally vanishes (the Rayleigh-Watson false-alarm probability then rises to 18%).