Black holes and galactic density cusps III from black hole to bulge

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.