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

Authors

  • M. Le Delliou,

    Corresponding author
    1. Instituto de Física Teórica UAM/CSIC, Facultad de Ciencias, C-XI, Universidad Autónoma de Madrid Cantoblanco, 28049 Madrid, Spain
      E-mail: Morgan.LeDelliou@uam.es (MLeD); henriksn@astro.queensu.ca (RNH); joseph.macmillan@gmail.com (JDM)
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  • R. N. Henriksen,

    Corresponding author
    1. Queen’s University, Kingston, ON K7L 3N6, Canada
      E-mail: Morgan.LeDelliou@uam.es (MLeD); henriksn@astro.queensu.ca (RNH); joseph.macmillan@gmail.com (JDM)
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  • J. D. MacMillan

    Corresponding author
    1. Faculty of Science, University of Ontario Institute of Technology, Oshawa, ON L1H 7K4, Canada
      E-mail: Morgan.LeDelliou@uam.es (MLeD); henriksn@astro.queensu.ca (RNH); joseph.macmillan@gmail.com (JDM)
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E-mail: Morgan.LeDelliou@uam.es (MLeD); henriksn@astro.queensu.ca (RNH); joseph.macmillan@gmail.com (JDM)

ABSTRACT

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.

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