Journal Article

Consistency criteria for generalized Cuddeford systems

Luca Ciotti and Lucia Morganti

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 401, issue 2, pages 1091-1098
Published in print January 2010 | ISSN: 0035-8711
Published online January 2010 | e-ISSN: 1365-2966 | DOI: http://dx.doi.org/10.1111/j.1365-2966.2009.15697.x
Consistency criteria for generalized Cuddeford systems

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General criteria to check the positivity of the distribution function (phase-space consistency) of stellar systems of assigned density and anisotropy profile are useful starting points in Jeans-based modelling. Here, we substantially extend previous results, and present the inversion formula and the analytical necessary and sufficient conditions for phase-space consistency of the family of multicomponent Cuddeford spherical systems: the distribution function of each density component of these systems is defined as the sum of an arbitrary number of Cuddeford distribution functions with arbitrary values of the anisotropy radius, but identical angular momentum exponent. The radial trend of anisotropy that can be realized by these models is therefore very general. As a surprising byproduct of our study, we found that the ‘central cusp–anisotropy theorem’ (a necessary condition for consistency relating the values of the central density slope and of the anisotropy parameter) holds not only at the centre but also at all radii in consistent multicomponent generalized Cuddeford systems. This last result suggests that the so-called mass–anisotropy degeneracy could be less severe than what is sometimes feared.

Keywords: stellar dynamics; celestial mechanics; galaxies: kinematics and dynamics

Journal Article.  5915 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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