Brownian dynamics around the core of self-gravitating systems

TL;DR

This paper models the distribution of particles in self-gravitating systems using a stochastic approach, deriving a non-Maxwellian distribution that aligns with the King model near the core and is validated through simulations.

Contribution

It introduces a stochastic model based on the Fokker-Planck equation to describe the core distribution of self-gravitating systems, connecting it to the King model.

Findings

Number density matches the King model around the core.

Model applies to systems with heavier particles.

Validation through numerical simulations confirms the model's accuracy.

Abstract

We derive the non-Maxwellian distribution of self-gravitating $N$-body systems around the core by a model based on the random process with the additive and the multiplicative noise. The number density can be obtained through the steady state solution of the Fokker-Planck equation corresponding to the random process. We exhibit that the number density becomes equal to that of the King model around the core by adjusting the friction coefficient and the intensity of the multiplicative noise. We also show that our model can be applied in the system which has a heavier particle. Moreover, we confirm the validity of our model by comparing with our numerical simulation.