Fractal properties of stellar systems and random forces

TL;DR

This paper extends the understanding of gravitational forces in fractal stellar systems by deriving a distribution for large random forces, emphasizing the role of nearest neighbors in such media.

Contribution

It generalizes the nearest neighbor distribution to fractal stellar systems and derives an asymptotic distribution for large random forces.

Findings

Large random forces are primarily due to nearest neighbors in fractal media.

Derived asymptotic distribution aligns with general approach results for power-law densities.

Effective interparticle spacing is formulated for fractal stellar systems.

Abstract

The nearest neighbor distribution (Chandrasekhar 1943) is generalized to fractal stellar systems.For such systems an asymptotic distribution of the magnitude of large random forces and a formula for the effective mean interparticle spacing are derived. It is shown that in the case of a power-law distribution of conditional density the derived asymptotic fully agrees with the results obtained in terms of a general approach. It is concluded that large random forces in a fractal stellar medium are due entirely to the nearest neighbors (clumps) located inside the sphere of the effective radius determined from the generalized Holtsmark distribution.