Black Holes and Galactic Density Cusps Spherically Symmetric Anisotropic Cusps

TL;DR

This paper investigates the structure of density cusps containing black holes, proposing self-similar models to explain the co-evolution of black holes and galactic bulges, supported by simulations and theoretical analysis.

Contribution

It introduces self-similar steady-state models for black hole cusps that incorporate collisionless matter dynamics and explains the black hole-bulge mass correlation.

Findings

Self-similar models match simulation data for density and velocity dispersion.

Black hole growth can be explained by co-eval self-similar evolution.

Distribution functions retain a memory of self-similarity, aiding understanding of collisionless systems.

Abstract

Aims: In this paper we study density cusps that may contain central black holes. The actual co-eval self-similar growth would not distinguish between the central object and the surroundings. Methods: To study the environment of a growing black hole we seek descriptions of steady `cusps' that may contain a black hole and that retain at least a memory of self-similarity. We refer to the environment in brief as the `bulge' and on smaller scales, the `halo'. Results: We find simple descriptions of the simulations of collisionless matter by comparing predicted densities, velocity dispersions and distribution functions with the simulations. In some cases central point masses may be included by iteration. We emphasize that the co-eval self-similar growth allows an explanation of the black hole bulge mass correlation between approximately similar collisionless systems. Conclusions: We have derived our results from first principles assuming adiabatic self-similarity and either self-similar virialisation or normal steady virialisation. We conclude that distribution functions that retain a memory of self-similar evolution provide an understanding of collisionless systems. The implied energy relaxation of the collisionless matter is due to the time dependence. Phase mixing relaxation may be enhanced by clump-clump interactions.