The secular evolution of discrete quasi-Keplerian systems

II. Application to a multi-mass axisymmetric disc around a supermassive black hole

¹ Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540, USA
e-mail: fouvry@ias.edu
² Institut d’Astrophysique de Paris and UPMC, CNRS (UMR 7095), 98bis boulevard Arago, 75014 Paris, France
³ Korea Institute for Advanced Study (KIAS), 85 Hoegiro, 02455 Seoul Dongdaemun-gu, Republic of Korea
⁴ Laboratoire de Physique Théorique (IRSAMC), CNRS and UPS, Univ. de Toulouse, 31062 Toulouse, France

Received: 2 May 2017
Accepted: 13 September 2017

Abstract

A discrete self-gravitating quasi-Keplerian razor-thin axisymmetric stellar disc orbiting a massive black hole sees its orbital structure diffuse on secular timescales as a result of a self-induced resonant relaxation. In the absence of collective effects, such a process is described by the recently derived inhomogeneous multi-mass degenerate Landau equation. Relying on Gauss’ method, we computed the associated drift and diffusion coefficients to characterise the properties of the resonant relaxation of razor-thin discs. For a disc-like configuration in our Galactic centre, we showed how this secular diffusion induces an adiabatic distortion of orbits and estimate the typical timescale of resonant relaxation. When considering a disc composed of multiple masses similarly distributed, we have illustrated how 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 kinetic equation recovers as well the quenching of the resonant diffusion of a test star in the vicinity of the black hole (the “Schwarzschild barrier”) as a result of the divergence of the relativistic precessions. The dual stochastic Langevin formulation yields consistent results and offers a versatile framework in which to incorporate other stochastic processes.