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

TL;DR

This study investigates how chaos in N-body simulations influences the stability of spherical gamma-models with velocity anisotropy, finding that overall chaos levels do not directly correlate with radial-orbit instability onset.

Contribution

It reveals that the degree of chaos measured by the largest Lyapunov exponent is not linked to stability, but more anisotropic systems have more orbits with higher Lyapunov exponents.

Findings

Chaos level (Lambda_max) does not predict stability.

More anisotropic models have more orbits with higher Lyapunov exponents.

Radial-orbit instability is not directly related to overall chaos.

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 $\Lambda_{\rm max}$ 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 $\lambda_{\rm m}$ of the individual particles in the single-particle phase space, we find that more anisotropic systems have a larger fraction of orbits with larger $\lambda_{\rm m}$.