Black Holes and Galactic Density Cusps : From Black Hole to Bulge

TL;DR

This paper models the density structure of galactic bulges with central black holes, revealing a transition from a 1/r density profile to a steeper cusp, and shows black hole growth dynamics in this context.

Contribution

It introduces a simple distribution function describing galactic bulge density profiles with black holes, including a transition from a 1/r to a steeper cusp, and analyzes black hole growth from first principles.

Findings

Density cusp transitions from 1/r to steeper profiles.

Black holes grow exponentially with a few million-year e-folding time.

Distribution functions describe bulge structure with a central black hole.

Abstract

Aims. In this paper we continue our study of density cusps that may contain central black holes. Methods. We recall our attempts to use distribution functions with a memory of self-similar relaxation, but mostly they apply only in restricted regions of the global system. We are forced to consider related distribution functions that are steady but not self-similar. Results. One remarkably simple distribution function that has a filled loss cone describes a bulge that transits from a near black hole domain to an outer 'zero flux' regime where$\rho\propto r^{-7/4}$. The transition passes from an initial inverse square profile through a region having a 1/r density profile. The structure is likely to be developed at an early stage in the growth of a galaxy. A central black hole is shown to grow exponentially in this background with an e-folding time of a few million years. Conclusions. We derive our results from first principles, using only the angular momentum integral in spherical symmetry. The initial relaxation probably requires bar instabilities and clump-clump interactions.