Journal Article

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

M. Le Delliou, R. N. Henriksen and J. D. MacMillan

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 413, issue 3, pages 1633-1642
Published in print May 2011 | ISSN: 0035-8711
Published online May 2011 | e-ISSN: 1365-2966 | DOI:
Black holes and galactic density cusps – I. Radial orbit cusps and bulges

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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.

Keywords: gravitation; galaxies: bulges; galaxies: formation; galaxies: haloes; cosmology: theory; dark matter

Journal Article.  7660 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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