Astronomy and Astrophysics – Astrophysics – Galaxy Astrophysics
Scientific paper
2009-11-12
Astronomy and Astrophysics
Astrophysics
Galaxy Astrophysics
6 pp, 2 figs, accepted in A&A
Scientific paper
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.
Delliou Morgan Le
Henriksen Richard N.
MacMillan Joseph D.
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