Black holes and galactic density cusps - I. Radial orbit cusps and bulges

• Published in: Monthly notices of the Royal Astronomical Society 2011-05, Vol.413 (3), p.1633-1642
• Main Authors: Le Delliou, M., Henriksen, R. N., MacMillan, J. D.
• Format: Article
• Language: English
• Subjects: Astronomy; Astrophysics; Black holes; cosmology: theory; dark matter; Earth, ocean, space; Exact sciences and technology; galaxies: bulges; galaxies: formation; galaxies: haloes; gravitation; Orbits; Stars & galaxies
• ISSN: 0035-8711; 1365-2966
• DOI: 10.1111/j.1365-2966.2011.18236.x

In this paper, we study the distribution functions that arise naturally during self-similar radial infall of collisionless matter. Such matter may be thought of either as stars or as dark matter particles. If a rigorous steady state is assumed, then the system is infinite and is described by a universal distribution function given the self-similar index. The steady logarithmic potential case is exceptional and yields the familiar Gaussian for an infinite system with an inverse-square density profile. We show subsequently that for time-dependent radial self-similar infall, the logarithmic case is accurately described by the Fridman-Polyachenko distribution function. The system in this case is finite but growing. We are able to embed a central mass in the universal steady distribution only by iteration, except in the case of massless particles. The iteration yields logarithmic corrections to the massless particle case and requires a 'renormalization' of the central mass. A central spherical mass may be accurately embedded in the Fridman-Polyachenko growing distribution, however. Some speculation is given concerning the importance of radial collisionless infall in actual galaxy formation.