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Black holes and galactic density cusps - I. Radial orbit cusps and bulges
Ist Teil von
Monthly notices of the Royal Astronomical Society, 2011-05, Vol.413 (3), p.1633-1642
Ort / Verlag
Oxford, UK: Blackwell Publishing Ltd
Erscheinungsjahr
2011
Quelle
Wiley Online Library Journals Frontfile Complete
Beschreibungen/Notizen
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.