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

Abstract

We study the stability of a family of spherical equilibrium models of self-gravitating systems, the so-called $\gamma -$models with Osipkov-Merritt velocity anisotropy, by means of $N-$body simulations. In particular, we analyze the effect of self-consistent $N-$body chaos on the onset of radial-orbit instability (ROI). We find that degree of chaoticity of the system associated to its largest Lyapunov exponent ${\Lambda }_{\max }$ 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 ${\lambda }_{\mathrm{m}}$ of the individual particles in the single-particle phase space, we find that more anisotropic systems have a larger fraction of orbits with larger ${\lambda }_{\mathrm{m}}$.

9 pages, 7 figures. Matching the version accepted for publication in MNRAS

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• Introducing a new multi-particle collision method for the evolution of dense stellar systems. Crash-test N-body simulations
• Partial suppression of chaos in relativistic three-body problems
• Chaos in violent relaxation dynamics. Disentangling micro- and macro-chaos in numerical experiments of dissipationless collapse
• Noise, friction and the radial-orbit instability in anisotropic stellar systems: stochastic N-body simulations