Gravitational Encounters and the Evolution of Galactic Nuclei. III. Anomalous Relaxation

TL;DR

This study extends models of stellar orbital evolution near supermassive black holes by incorporating anomalous relaxation effects, revealing impacts on core formation and star capture rates in galactic nuclei.

Contribution

It introduces generalized diffusion coefficients for anomalous relaxation and demonstrates their effects on steady-state structures and capture rates in galactic nuclei.

Findings

Anomalous relaxation results in less prominent cores.

Capture rates decrease by up to an order of magnitude with anomalous relaxation.

Steady-state solutions show longer diffusion times for eccentric orbits.

Abstract

This paper is the third in a series presenting the results of direct numerical integrations of the Fokker-Planck equation for stars orbiting a supermassive black hole (SBH) at the center of a galaxy. The algorithm of Paper II included diffusion coefficients that described the effects of random ("classical") and correlated ("resonant") relaxation. In this paper, the diffusion coefficients of Paper II have been generalized to account for the effects of "anomalous relaxation," the qualitatively different way in which eccentric orbits evolve in the regime of rapid relativistic precession. Two functional forms for the anomalous diffusion coefficients are investigated, based on power-law or exponential modifications of the resonant diffusion coefficients. The parameters defining the modified coefficients are first constrained by comparing the results of Fokker-Planck integrations with previously-published N-body integrations. Steady-state solutions are then obtained via the Fokker-Planck equation for models with properties similar to those of the Milky Way nucleus. Inclusion of anomalous relaxation leads to the formation of less prominent cores than in the case of resonant relaxation alone, due to the lengthening of diffusion timescales for eccentric orbits. Steady-state capture rates of stars by the SBH are found to always be less, by as much as an order of magnitude, than capture rates in the presence of resonant relaxation alone.