Statistical analysis of binary stars from the Gaia catalogue DR2.

We have developed a general statistical procedure for analysis of 2D and 3D finite patterns, which is applied to the data from recently released Gaia-ESA catalogue DR2. The 2D analysis clearly confirms our former results on the presence of binaries in the older DR1 catalogue. Our main objective is the statistical 3D analysis of DR2. For this, it is essential that the DR2 catalogue includes parallaxes and data on the proper motion. The analysis proves a high rate of binaries in the region under study and allows us to estimate a high limit of their separation: $\Delta_{\max}\approx0.1$pc. Finally and most importantly, we had shown that combined analysis of the separations with proper motion of the pairs of sources provides a clear picture of binaries with two components of the motion: parallel and orbital. The analysis allowed us to estimate the average orbital period and mass of the binary star system in a chosen statistical ensemble.