Notes on the stability threshold for radially anisotropic polytrope

Details Notes on the stability threshold for radially anisotropic polytrope Notes on the stability threshold for radially anisotropic polytrope

2011-04-05

arxiv.org/abs/1104.0741v1

Astronomy and Astrophysics

Astrophysics

Solar and Stellar Astrophysics

17 pages, 6 figures, 1 table

Scientific paper

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-low functions of the energy $E$ and the angular momentum $L$, i.e. $F\propto L^{-s}(-E)^q$. On the one hand, calculation of the growth rates in the framework of linear stability theory and N-body simulations show 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

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