Fractal Effects of the Stellar Medium in the Vicinity of the Sun According to Gaia DR2 Data

In this paper, we study the fractal properties of the stellar medium in the solar vicinity based on the Gaia DR2 data for 200 000 stars of all spectral types at distances from 1 to 100 pc from the Sun. We consider the main stages of the development of ideas about the fractal structure in the stellar medium of galaxies. Analysis of the spatial distribution of stars is performed using by the ‘‘mass–radius’’ method. Numerical calculations show that the mean conditional local stellar density in spheres with the increasing radius \(r\) with the center in the \(i\)-th star is approximated by power laws, which confirms the de Vaucouleurs–Mandelbrot conclusions for fractal structures in gravitating media and indicates the presence of fractal structures in the stellar medium in the solar neighborhood with the fractal dimension \(D\simeq 2.41\). The characteristics of the fractal properties of the medium, determined from a sample of 200 000 stars, are discussed and compared with an earlier result obtained for 13 000 F and G dwarfs in the solar neighborhood according to the Geneva–Copenhagen survey.