Journal Article

Notes on the stability threshold for radially anisotropic polytropes

E. V. Polyachenko, V. L. Polyachenko and I. G. Shukhman

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 416, issue 3, pages 1836-1843
Published in print September 2011 | ISSN: 0035-8711
Published online September 2011 | e-ISSN: 1365-2966 | DOI:
Notes on the stability threshold for radially anisotropic polytropes

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We discuss some contradictions found in the literature concerning the problem of stability of collisionless spherical stellar systems, which are the simplest anisotropic generalization of the well-known polytrope models. Their distribution function F(E, L) is a product of power-law functions of the energy E and angular momentum L, i.e. FLs (−E)q. On the one hand, calculation of the growth rates in the framework of linear stability theory and N-body simulations shows that these systems become stable when the parameter s characterizing the velocity anisotropy of the stellar distribution is lower than some finite threshold value, s < scrit. On the other hand, Palmer & Papaloizou showed that the instability remains up to the isotropic limit s= 0.

Using our method of determining the eigenmodes for stellar systems, we show that the growth rates in weakly radially anisotropic systems are indeed positive, but decrease exponentially as the parameter s approaches zero, i.e. γ∝ exp(−s*/s). In fact, for systems with a finite lifetime this means stability.

Keywords: Galaxy: centre; galaxies: kinematics and dynamics

Journal Article.  4626 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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