Gravitational Encounters and the Evolution of Galactic Nuclei. I. Method

TL;DR

This paper introduces a novel numerical algorithm for modeling the evolution of stellar distributions around a black hole, incorporating complex encounter effects and gravitational wave emission to improve understanding of galactic nuclei dynamics.

Contribution

The paper presents a new method based on the Fokker-Planck equation that includes both random and resonant relaxation effects, as well as gravitational wave energy loss, for evolving stellar systems near black holes.

Findings

Successfully computes time-dependent and steady-state stellar distributions.

Quantifies star loss rates into the black hole.

Demonstrates the algorithm's capability with illustrative examples.

Abstract

An algorithm is described for evolving the phase-space density of stars or compact objects around a massive black hole at the center of a galaxy. The technique is based on numerical integration of the Fokker-Planck equation in energy-angular momentum space, f(E,L,t), and includes, for the first time, diffusion coefficients that describe the effects of both random and correlated encounters (resonant relaxation), as well as energy loss due to emission of gravitational waves. Destruction or loss of stars into the black hole are treated by means of a detailed boundary-layer analysis. Performance of the algorithm is illustrated by calculating two-dimensional, time-dependent and steady-state distribution functions and their corresponding loss rates.