Catalogue of wide binary, trinary and quaternary candidates from the Gaia data release 2 (region $\mid b\mid >25\mathrm{deg}$)

The occurrence of multiple stars, dominantly binaries, is studied using the $\mathit{\text{Gaia}}$-ESA DR2 catalogue. We apply the optimized statistical method that we previously developed for the analysis of 2D patterns. The field of stars is divided into a mosaic of small pieces, which represent a statistical set for analysis. Specifically, data input is represented by a grid of circles (events) with radius $0.02\mathrm{deg}$ covering the sky in the field of galactic latitude $\mid b\mid >25\mathrm{deg}$. The criteria for selecting candidates for multiple stars are based on two parameters: angular separation and collinearity of proper motion. Radial separation, due to limited accuracy, is used only as a weaker supplementary constraint. Due attention is paid to the accurate calculation of the background, which is a necessary input for evaluating the quality of the candidates. Our selection algorithm generates the catalogue of candidates: $900,842$ binaries, $5,282$ trinaries and $30$ quaternaries.