Discreteness effects, N-body chaos and the onset of radial-orbit instability

We study the stability of a family of spherical equilibrium models of self-gravitating systems, the so-called γ models with Osipkov–Merritt velocity anisotropy, by means of N-body simulations. In particular, we analyse the effect of self-consistent N-body chaos on the onset of radial-orbit instability. We find that degree of chaoticity of the system associated with its largest Lyapunov exponent Λmax has no appreciable relation with the stability of the model for fixed density profile and different values of radial velocity anisotropy. However, by studying the distribution of the Lyapunov exponents λm of the individual particles in the single-particle phase space, we find that more anisotropic systems have a larger fraction of orbits with larger λm.