The secular evolution of discrete quasi-Keplerian systems. II. Application to a multi-mass axisymmetric disc around a supermassive black hole

TL;DR

This paper models the long-term evolution of a multi-mass, axisymmetric disc around a supermassive black hole using a kinetic equation approach, revealing how stellar populations evolve and how relativistic effects influence diffusion.

Contribution

It applies the inhomogeneous multi-mass Landau equation with Gauss' method to describe secular evolution of a quasi-Keplerian disc, including relativistic precession effects.

Findings

Lighter stars gain eccentricity and move closer to the black hole.

Relativistic precession causes the Schwarzschild barrier, quenching diffusion near the black hole.

The Langevin stochastic framework provides consistent results for stellar diffusion.

Abstract

The drift and diffusion coefficients of the inhomogeneous multi-mass degenerate Landau equation are computed to describe the self-induced resonant relaxation of a discrete self-gravitating quasi-Keplerian razor-thin axisymmetric disc orbiting a massive black hole while relying on Gauss' method. For a disc-like configuration in our Galactic centre, secular diffusion induces an adiabatic distortion of orbits. When considering a disc composed of multiple masses similarly distributed, the population of lighter stars will gain eccentricity, driving it closer to the central black hole provided the distribution function increases with angular momentum. The quenching of the diffusion of a test star in the vicinity of the black hole due to the divergence of the relativistic precessions (the "Schwarzschild barrier") is correctly recovered by the kinetic equation. The dual stochastic Langevin formulation yields consistent results and provides a versatile framework in which to incorporate other stochastic processes.