Mathematics – Functional Analysis
Scientific paper
Jun 2010
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010aipc.1241..912h&link_type=abstract
INVISIBLE UNIVERSE: Proceedings of the Conference. AIP Conference Proceedings, Volume 1241, pp. 912-917 (2010).
Mathematics
Functional Analysis
Black Holes, Galaxy, Dark Matter, Functional Analysis, Galactic Nuclei, Circumnuclear Matter, And Bulges, Origin, Formation, Evolution, Age, And Star Formation, Dark Matter, Functional Analysis
Scientific paper
Currently central black holes in collisionless self-gravitating systems such as the bulges of galaxies are abundant. One of the most definite cases lies in the center of the milky way [3]. Simulations (e.g.[12]) have studied surrounding cusp profiles as produced by binary black hole mergers. However there seems to be no unified picture that places a black hole in a surrounding bulge and distant halo in a self-consistent state. Moreover the time and nature of the growth of the black hole, together with the reason for the correlation between its mass and that of the distant galactic bulge, remain unidentified and unexplained. In this paper we study the problem analytically. We seek distribution functions that have a `memory' of previous dynamical evolution. We justify these by fits to numerical simulations. One simple choice of distribution function is able to give a `zero flux' [1] outer boundary region, followed by a 1/r inner shell that gives way to an 1/r2 cusp surrounding the black hole. The black hole e-folding time is a few million years. It is likely to apply during the rapid growth phase of the dark matter halo since it is very anisotropic.
Henriksen Richard N.
Ledelliou M.
MacMillan Joseph D.
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