# Dressed diffusion and friction coefficients in inhomogeneous multicomponent self-gravitating systems

## TL;DR

This paper derives comprehensive expressions for diffusion and friction coefficients in inhomogeneous, multicomponent self-gravitating systems, linking kinetic equations and providing tools for modeling their secular evolution.

## Contribution

It introduces a self-consistent formalism for diffusion and friction in multicomponent systems, connecting Fokker-Planck, Balescu-Lenard, and Landau equations, with practical Langevin equations.

## Key findings

- Derived general expressions for diffusion and friction coefficients.
- Demonstrated the equivalence of Fokker-Planck, Balescu-Lenard, and Landau equations.
- Provided Langevin equations as practical tools for simulations.

## Abstract

General self-consistent expressions for the coefficients of diffusion and dynamical friction in a stable, bound, multicomponent self-gravitating and inhomogeneous system are derived. They account for the detailed dynamics of the colliding particles and their self-consistent dressing by collective gravitational interactions. The associated Fokker-Planck equation is shown to be fully consistent with the corresponding inhomogeneous Balescu-Lenard equation and, in the weak self-gravitating limit, to the inhomogeneous Landau equation. Hence it provides an alternative derivation to both and demonstrates their equivalence. The corresponding stochastic Langevin equations are presented: they can be a practical alternative to numerically solving the inhomogeneous Fokker-Planck and Balescu-Lenard equations. The present formalism allows for a self-consistent description of the secular evolution of different populations covering a spectrum of masses, with a proper accounting of the induced secular mass segregation, which should be of interest to various astrophysical contexts, from galactic centers to protostellar discs.