Fractal properties of stellar systems and random forces

Abstract

The nearest neighbor distance distribution law is generalized to fractal stellar media. The asymptotics of the distribution law for the magnitude of a large random force has been derived for them. An expression for the effective mean interparticle distance in such a medium has been found. The derived asymptotics for a power-law change in conditional density is shown to coincide closely with the results obtained within the framework of a general approach. We conclude that the large random forces in a fractal stellar medium are entirely attributable to the nearest neighbors (clumps) located in a sphere with an effective radius determined from a generalized Holtsmark distribution.