Stabilization of generalized polytropes

Stabilization of classical generalized polytropic models is studied. We discuss some contradictions found in the literature: on the one hand, calculations of the growth rates in the framework of linear stability theory and N-body simulations show that these systems are stable if the velocity anisotropy parameter of the stellar distribution is lower than some finite positive value. On the other hand, instability is shown to persist up to the isotropic limit (zero anisotropy parameter). We demonstrate that stabilization of generalized polytropic models cannot be adequately described by approximate equations derived for nearly radial orbits. (© 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)