Generalization of the Fokker-Planck equation for stellar orbit diffusion in multi-mass star systems

TL;DR

This paper extends the Fokker-Planck equation to multi-mass stellar systems, providing a more accurate model for star cluster dynamics with continuous mass distributions.

Contribution

It generalizes the diffusion coefficients and derives a new Fokker-Planck equation for systems with multiple stellar masses, aligning with common globular cluster models.

Findings

Derived a new expression for the Fokker-Planck equation in multi-mass systems.

Validated a King-like distribution function for such systems.

Enhanced the theoretical framework for modeling stellar orbit diffusion.

Abstract

We improve the standard theory of collisional stellar systems by considering the presence of a continuous mass distribution. The calculus of the diffusion coefficients is generalized and a new expression of the Fokker-Planck equation is found for multi-mass systems. A King-like distribution function, which validates the basic assumptions of most multi-mass models for Globular Clusters existing in literature, is obtained.