The Kuzmin-Kutuzov two integral axisymmetric galaxy model revisited

Astronomy and Astrophysics – Astrophysics

Scientific paper

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Scientific paper

We present, for the first time, a completely analytic, axisymmetric self-consistent two integral model for a stellar system with a Stackel potential, which is expressible in terms of elementary functions. The calculation of the corresponding distribution function is given in a form that is of practical use. We also discuss the remarkable result that the most prolate Kuzmin- KutuzoV model has a singular, yet positive distribution function. However, a continuous sequence of models with increasing prolateness bounded by the singular model, cannot be constructed. No prolate axisymmetric two integral elliptical galaxy can exist beyond E2, simply because there is no positive distribution function that is able to make them. We therefore speculate that the requirement of a positive distribution function may help to explain why ellipticals, in so far as they are prolate, are not very flat.

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