Fractal Distribution of Stars in the Solar Neighborhood and Random Forces

In this paper, we study the distribution law of the random force modulus in the nearest neighbor approximation (generalized Holtsmark distribution) and the asymptotic behavior of the Holtsmark distribution for large random forces for a fractal stellar medium in the solar neighborhood. The role of collisional processes and random forces in the dynamics of stellar systems is considered. This study is based on the investigation of the spatial distribution of 200 000 stars of all spectral classes at distances from 1 to 100 pc from the Sun according to Gaia DR2 data, the results of which indicate the presence of fractal structures in the solar neighborhood with a fractal dimension of \(D\simeq 2.41\). The asymptotic distribution of random force derived for a fractal stellar medium demonstrates the important role of strong fields, with the magnitude of the random force decreasing somewhat more slowly compared to its distribution for a homogeneous medium.