Journal Article

Two-component galaxy models: the effect of density profile at large radii on the phase-space consistency

Luca Ciotti and Lucia Morganti

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 393, issue 1, pages 179-191
Published in print February 2009 | ISSN: 0035-8711
Published online January 2009 | e-ISSN: 1365-2966 | DOI:
Two-component galaxy models: the effect of density profile at large radii on the phase-space consistency

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It is well known that the density and anisotropy profile in the inner regions of a stellar system with positive phase-space distribution function (DF) are not fully independent. Here, we study the interplay between density profile and orbital anisotropy at large radii in physically admissible (consistent) stellar systems. The analysis is carried out by using two-component (n - γ, γ1) spherical self-consistent galaxy models, in which one density distribution follows a generalized γ profile with external logarithmic slope n, and the other a standard γ1 profile (with external slope 4). The two density components have different ‘core’ radii, the orbital anisotropy is controlled with the Osipkov–Merritt recipe, and for simplicity we assume that the mass of the γ1 component dominates the total potential everywhere. The necessary and sufficient conditions for phase-space consistency are determined analytically, also in the presence of a dominant massive central black hole, and the analytical phase-space DF of (n - γ,1) models, and of n - γ models with a central black hole, is derived for γ= 0, 1, 2. It is found that the density slope in the external regions of a stellar system can play an important role in determining the amount of admissible anisotropy: in particular, for fixed density slopes in the central regions, systems with a steeper external density profile can support more radial anisotropy than externally flatter models. This is quantified by an inequality formally identical to the ‘cusp slope-central anisotropy’ theorem by An & Evans, relating at all radii (and not just at the centre) the density logarithmic slope and the anisotropy indicator in all Osipkov–Merritt systems.

Keywords: black holes; stellar dynamics; galaxies: elliptical and lenticular, cD; dark matter

Journal Article.  10992 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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