# Brownian motion of supermassive black holes in galaxy cores

## TL;DR

This paper models the Brownian motion of supermassive black holes in galaxy cores using a semi-analytic Langevin equation approach, validated against simulations, revealing typical displacements of a few parsecs.

## Contribution

It introduces a semi-analytic Langevin-based model for SMBH dynamics in galactic cores, incorporating dynamical friction and stochastic effects, validated with N-body simulations.

## Key findings

- SMBHs exhibit Brownian-like motion with displacements of a few parsecs.
- Model aligns well with N-body simulations for intermediate-mass black holes.
- Results are consistent with parameters of galaxy M87.

## Abstract

We investigate the dynamics of supermassive black holes (SMBHs) in galactic cores by means of a semi-analytic model based on the Langevin equation, including dynamical friction and stochastic noise accounting for the gravitational interactions with stars. The model is validated against direct $N$-body simulations of intermediate-mass black holes in stellar clusters where a realistic number of particles is accessible. For the galactic case, we find that the SMBH experiences a Brownian-like motion with a typical displacement from the geometric center of the Galaxy of a few parsecs, for system parameters compatible with M87. \keywords{stellar dynamics, black hole physics, methods: n-body simulations, methods: statistical.