Black holes and galactic density cusps

From black hole to bulge

¹ Instituto de Física Teórica UAM/CSIC, Facultad de Ciencias, C-XI, Universidad Autónoma de Madrid Cantoblanco, 28049 Madrid, Spain
e-mail: Morgan.LeDelliou@uam.es
² Queen’s University, Kingston, Ontario, Canada
e-mail: henriksn@astro.queensu.ca
³ Faculty of Science, University of Ontario Institute of Technology, Oshawa, L1H 7K4 Ontario, Canada
e-mail: joseph.macmillan@gmail.com

Received: 11 November 2009
Accepted: 26 October 2010

Abstract

Aims. In this paper we continue our study of density cusps that may contain central black holes.

Methods. Our previous thus attempts to use distribution functions with a memory of self-similar relaxation apply mainly 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 ρ ∝ 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.