On the threshold anisotropy for unstable spherical stellar systems

The radial orbit instability generally arises in anisotropic collisionless stellar systems with the dominance of radial motions over transverse ones. Using the simplest anisotropic generalization of polytrope models for spherical clusters as an example, we show that the instability growth rates become exponentially small as the isotropic limit is approached. Given the finite lifetime of real astronomical objects, these systems should be assumed to become stable at some finite radial anisotropy.