Black Holes and Galactic Density Cusps I Radial Orbit Cusps and Bulges

Aims. In this paper we study density cusps made from radial orbits 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 an existing black hole we seek distribution functions 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 ’ or sometimes the ‘halo’. This depends on whether the black hole is a true singularity dominating its halo or rather a core mass concentration that dominates a larger bulge. The hierarchy might extend to include galactic bulge and halo. Results. We find simple descriptions of simulated collisionless matter in the process of examining the presence of central masses. The Fridmann & Polyachenko distribution function describes co-eval growth of a bulge and black hole that might explain the observed mass correlation. Conclusions. We derive our results from first principles assuming either self-similar virialisation or normal steady virialisation. The implied energy relaxation of the collisionless matter is due to the time dependence. Phase mixing relaxation may be enhanced by clump-clump interactions. Key words. theory-dark matter-galaxies:haloes-galaxies:nuclei-black hole physics-gravitation. 1