Fractal Properties of the Stellar Medium in the Solar Neighborhood Based on GAIA DR2 Data

The study of fractal structures in the stellar medium of the Galaxy is one of the important problems of stellar dynamics, since it makes it possible to construct a kinetic theory of the stellar medium, which is more consistent with observational data, and to refine the basic equations of stellar dynamics for fractal stellar media. In connection of this it is studied the fractal properties of $$\sim 200\,000$$ stars of all spectral types in solar neighborhood at distance of 1 to 100 parsecs from the Sun based on GAIA DR2 data. The main stages in the development of ideas about fractal structures in the stellar medium of galaxies are considered. The analysis of spatial distribution of stars is carried out by the ‘‘mass–radius’’ method. Numerical calculations for selected $$\sim 200\,000$$ stars show that mean conditional local star density in spheres with increasing radius ‘‘ $$r$$ ’’ with center in the $$i$$ th star is approximated by power laws, that indicates on the presence of fractal structures in stellar medium in solar neighborhood with fractal (Hausdorff) dimension $$D\approx 2.41$$ . The data obtained for $$\sim 200\,000$$ stars are discussed and compared with previous result, received for $$\sim 13\,000$$ stars of F, G-type dwarfs in solar neighborhood based on the data of Geneva–Copenhagen Survey.